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rspa_1910_0077

0950-1207

The absorption spectra of sulphur vapour at different temperatures and pressures and their relation to the molecular complexity of this element.

311

324

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

J. Ivon Graham, B. Sc. (Lond.), A. R. C. Sc. I|Prof. W. N. Harley, F. R. S.

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6.0.4

http://dx.doi.org/10.1098/rspa.1910.0077

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1910_0077

10.1098/rspa.1910.0077

Atomic Physics

Thermodynamics

Atomic Physics

311 The Absorption Spectra of Sulphur Vapour at Different Temperatures and Pressures and their Relation to the Molecular Complexity of this Element . By J. Ivon Graham , B.Sc. ( Bond . ) , A.R.C.Sc . I , Royal College of Science , Dublin . ( Communicated by Prof. W. N. Hartley , F.R.S. Received May 12 , \#151 ; Read June 23 , 1910 . ) [ Plate 5 . ] This piece of work was undertaken at the suggestion of Prof. W. 1ST . Hartley , who pointed out that it would be of interest to photograph the absorption spectra of sulphur vapour at temperatures corresponding to the two molecular masses S8 and Sa , the existence of which has been proved from vapour density determinations . The absorption spectra of the vapour were photographed at temperatures varying from 530 ' C. up to 900 ' C. at atmospheric pressure , and at constant temperatures under pressures reduced down to about 10 mm. of mercury . The results and their deductions may be briefly summarised as follows :\#151 ; The photographs at constant pressure with the above variation of temperature show the presence of two distinct absorption spectra , which undoubtedly correspond to two definite molecular complexes . These two spectra are , from reasons stated later , attributed to the oscillations of the S8 and S2-molecular systems , the former producing , by taking up vibrations of certain frequencies , a series of absorption bands between frequency n(= 1/ \ ) 2000 and n 2600 and having maximum absorption about n 2500 , whilst the relatively lighter S2 system , by taking up vibrations of greater frequencies , produces a series of bands lying between n 2900 and n 3820 , with maximum absorption about n3750 . Moreover , since only two distinct spectra are evident , it is concluded that the equation S8 = 4 S2 represents the sole reaction that occurs in the dissociation of sulphur vapour on heating from its boiling point , 448 ' C. , up to about 900 ' C. The interpretation of the photographs of the absorption spectra of the vapour at different ( constant ) temperatures , but with reduction of pressure , shows that above 580 ' C. the dissociation of the molecule S8 is simple , that is to say , there is direct ( and complete ) dissociation into S2 molecules , but at or below 520 ' C. the dissociation takes place with the formation of molecules intermediate in complexity between the above two aggregates . Mr. J. I. Graham . Absorption Spectra of [ May 12 , The work of previous investigators* has shown that the absorption spectrum of sulphur vapour changes with variation of temperature . Thus at the boiling point of the element , only the red end of the spectrum is transmitted ( a thickness of 500 mm. being examined ) , but if the temperature be raised , groups of dark bands are seen furrowing the violet and blue , the maximum intensity of each band being at the more refrangible side . All these observations were , however , made visually , and no mention is made of the approximate temperature ( except when examined at the boiling point ) . Experimental.\#151 ; The sulphur vapour in the following series of experiments was examined in a vitreous silica tube with two approximately parallel sides , the thickness of the vapour being about 5 mm. , since preliminary experiments had shown that , for varying temperatures , only a small thickness of sulphur vapour could be satisfactorily examined . To produce a tube of this description was at first a source of some difficulty ; however , finally , the following method was employed and found to work satisfactorily:\#151 ; A flat piece of graphite of the required thickness was placed inside a vitreous silica test-tube ( special precautions being taken to free the latter from all basic matter ) , and the opposite sides of this were then blown flat against the graphite , using an oxy-hydrogen blow-pipe flame ; a tube was thus formed having two walls practically parallel . For the source of continuous rays , a spark passing between two metallic uranium electrodes , and condensed on the slit of the spectrograph by a cylindrical lens ( a method devised by Prof. Hartley ) , was used in taking most of the photographs ( see Plate 5 ) , while a series of photographs was also taken with the vapour at varying temperatures , but constant pressure , using an ordinary acetylene flame . This flame gives a continuous spectrum , extending approximately to n3000 , being , however , greatly weakened from about n 2500 . For the plate of fig. 1 , the test-tube , prepared in the manner described above , was fitted with ( a ) a small quartz tube sealed at one end and containing a thermocouple ; ( b)a second small tube to allow the excess of sulphur to escape . Two to three grammes of pure recrystallised sulphur having been introduced into the apparatus , the latter was fixed in a horizontal position between the source of light and the cylindrical quartz lens . The rays from the spark ( or acetylene flame , as the case was ) thus passed through an approximately uniform thickness of sulphur vapour , and were then focussed on the slit of the spectrograph with the aid of the lens . * Salet , ' Compt . Rend . , ' 1871 , vol. 73 , pp. 559 , 742 ; 1872 , vol. 74 , p. 865 . Gernez , ibid. , 1872 , vol. 74 , p. 803 . Lockyer , ' Roy . Soc. Proc. , ' 1873\#151 ; 4 , vol. 22 , pp. 374 6 . 1910 . ] Sulphur Vapour at Different , etc. 313 The apparatus was heated by means of a large rectangular-shaped Mecke burner , the temperature of the sulphur vapour being varied by altering the position of the burner and regulating the height of the flame . The spectrograph , lens , etc. , were protected from the strong heat of the flame by sheets of asbestos , a horizontal piece being placed just above the silica tube to deflect the heat downwards again , so that there might be the least possible difference in the temperature of the vapour in the upper and lower portions of the tube . The temperature was measured by means of a platinum-platinum-rhodium thermocouple , connected to a reflecting galvanometer , the deflection of the latter being noted at the commencement and end of the exposure at each different temperature ; as the apparatus was heated up very slowly and carefully , the temperature remained practically constant during this period , the mean deflection , however , being taken . The spectrograph employed had one Cornu 's quartz prism of 60 ' , and lenses of 15-inch focus . The photographs were taken on 5 x 4 panchromatic ( backed ) plates , supplied by Messrs. Wratten and Wainwright . The apparatus , etc. , being arranged in the manner described , photographs of the absorption spectra of the sulphur vapour were taken at temperatures ranging from 530 ' C. up to 900 ' C. , using the spark spectrum of uranium as the source of continuous rays . Fig. 1 , Plate 5 , is the reproduction of this series ; thus , spectrum 2 of this figure is taken through the vapour at . 530 ' C. , spectrum 3 at 610 ' C. , spectrum 4 at 770 ' C. , spectrum 5 at 840 ' C. , spectrum 6 at 870 ' C. , and spectrum 7 at 900 ' C. On this figure only the portions of the spectra lying between n 2000 ( or 5000 ) and 3500 ( 2860 ) are shown . A similar series was then taken , using the acetylene flame instead of the uranium spark , the temperature being varied from 490 ' up to-900 ' C. The measurements of the spectra were made with a micrometer fitted with a travelling microscope* and capable of reading to 1/ 10,000th of an inch , and also by means of an ivory scale , graduated to 1 / 200th of an inch , , but capable of being read to 1/ 500th of an inch with the aid of a lens . The latter method was found , on the whole , to be the more satisfactory of the two , as , owing to its high power , the microscope did not reveal some of the bands distinctly . Each spectrum was measured once with the micrometer and twice with the scale . These measurements were made in l/ 100ths of an inch , and the corresponding wave-lengths ascertained from an interpolation curve ( previously made for this spectrograph ) on which measurements ( in l/ 100ths of an inch ) of the principal lines of the cadmium , * For more detailed description of this instrument , vide W. N. Hartley , ' Phil. Trans. , Roy . Soc. , ' A , vol. 208 , p. 478 . 314 Mr. J. I. Graham . Absorption Spectra [ May 12 lead , and tin spark spectra were plotted against their known wavelengths ( Angstrom units ) . On each of the plates the spark spectrum of alloys of Cd , Pb , and Sn ( not reproduced ) was taken to check the measurements of the absorption spectra . The bands observed all show a maximum absorption towards the more refrangible edge ; the edges are not well defined , so that it is difficult to tell where the bands really commence and where they end ; they are therefore described by measurements of the positions of maximum absorption in .each case . The width of the bands present in the visible region corresponds to about 25 Angstrom units , that of the bands in the ultra-violet ( about %3750 ) to approximately 15 Angstrom units . The maxima of absorption of the bands are stated in wave-lengths and also in oscillation frequencies \#166 ; ( n ) ; owing to the comparatively small dispersion employed , and the difficulty .of determining exactly where the strongest absorption in the bands occurs , these measurements can only be relied on to within 5 or 10 Angstrom \#166 ; units , according to the position of the bands . Again , in measuring some of the very faint bands , it was not always easy to tell whether certain weakenings of the spectra were due to absorption by the sulphur vapour or .to the general diminution of intensity of the uranium spark spectrum . To \#166 ; decide this point , careful comparison of the absorption spectrum was made with a spark spectrum of uranium of practically the same intensity , and in this way the bands , whose wave-lengths are given later on , were shown to be undoubtedly due to the absorption by the sulphur vapour . Turning to an examination of Plate 5 , fig. 1 , in spectra 2 and 3 it will be noticed that a series of bands occurs in the violet region , becoming apparently stronger in the more refrangible direction , until merged into complete absorption ; thus , in spectra 2 and 3 , there is complete absorption beyond %2440 . In the next spectrum ( 4 ) , at 770 ' C. , there is a marked \#166 ; change ; at this temperature we still have the bands in the violet , with strong absorption beyond n 2425 , but about n 2650 we get the spectrum again transmitted , extending to . n3170 , whilst a second series of bands , starting about n 2850 and lying fairly close together , extends to the end .of the spectrum . As the temperature is raised the absorption in the region w2425 to n2650 becomes weaker , being resolved into a series of bands , the maxima of any two consecutive bands differing , on an average , in oscillation frequency { n ) by about 30 , and finally , at 900 ' C. , the spectrum is transmitted practically continuously over this region . The .series of bands starting about n 2850 remains pronounced , extending further into the ultra-violet as the vapour diminishes in density ( i.e. as the 1910 . ] Sulphur Vapour at Different , etc. temperature is raised ) . In No. 7 ( i. . at 900 ' C. ) it is found that the spectrum is again faintly transmitted far down in the ultra-violet ; that is to say , at this temperature we have practically continuous transmission as far as n 2850 , then a series of bands , stretching as far as n 3330 ( the absorption becoming stronger towards the more refrangible end of the spectrum ) , beyond this there is complete absorption as far as n 4270 , but from this point , however , there is faint continuous transmission to about n 4400 . At relatively low temperatures , therefore ( i.e. 500 ' to 700 ' C. ) , we have strong absorption in the blue and violet , stretching even for a short way into the ultra-violet , the mean position of maximum absorption being about n 2500 . As the temperature is raised this absorption becomes resolved into a series of bands , the maximum absorption of the individual bands being in each case toward the more refrangible edge , and finally , at the highest temperature of the experiment ( 900 ' C. ) , these bands disappear almost entirely . At this temperature , however , the strong absorption in the ultra-violet is still evident , the mean position of maximum absorption being about n 3750 . Other experiments at this temperature , with a relatively smaller thickness of vapour , indicate that this absorption is , in reality , composed of a series of bands ( some of which , indeed , are shown on Plate 5 , fig. 1 , spectra 4 to 7 ) , the maximum absorption of each of these bands being , as in the case of those occurring in the visible region , towards the more refrangible edge ; these bands extend as far as n 3820 , beyond which there is transmission of the continuous spectrum again , for a short distance further into the ultra-violet . Prom these descriptions , it is evident that we must here be dealing with two distinct vibrating systems , which yield absorption spectra of great .similarity , and which may conveniently be referred to as and B , where\#151 ; A is that system existing in greater proportion at lower temperatures ( i.e. 500 ' to 700 ' C. ) , and producing a series of absorption bands between n 2000 and n 2600 , having a mean position of maximum absorption about n 2500 , whilst\#151 ; B is that system which , coming more into evidence at higher temperatures ( about 900 ' C. ) produces by its vibrations a series of absorption bands similar in character to those produced by A , but extending from 2850 to n 3820 , with a mean position of maximum absorption about n 3750 . ( See fig. 4 , Plate 5 . ) At temperatures intermediate between 500 ' and 900 ' C. , we thus have a mixture of the two spectra . With an increase in the number of the oscillating systems A or B , the .bands evident in the two regions of the spectrum mentioned become merged 316 Mr. J. I. Graham . Absorption Spectra of [ May 12 into strong broad absorption bands ; for example , at 770 ' C. , the number of systems A present , being greater than at the higher temperature 840 ' C the bands , evident in the spectrum at the latter temperature , become merged into strong absorption between n 2425 and n 2650 ( i.e. between X4125 and X 3770 ) . From the numerous investigations on the vapour density of sulphur , * the existence of the molecular aggregates S8 and S2 has been proved beyond dispute , the eight-atom complex occurring in greatest proportion about the boiling point of the element , whilst above 900 ' C. ( and up to 1600 ' C. ) the vapour is evidently composed solely of S2 molecules . There can be no doubt , therefore , that the absorption spectrum described as due to the vibrating system B is produced by the intra-molecular motions of the S2 aggregates . The question then becomes , to what molecular complex may we assign the absorption spectrum produced by the system A ? At the lowest temperature at which the vapour was examined in taking the plate for fig. 1 ( i.e. 530 ' C. ) , the value for the vapour density lies between the figures corresponding to S8 and Sg respectively , approximating more nearly to the latter complex ; accepting Biltz 's figures at 534 ' C. , there must , however , be quite an appreciable proportion of S8 molecules , even assuming that no S2 aggregates are present . Now , if the series of absorption bands in the blue and violet be due to the vibrations of the Sg systems , and since the series of bands in the ultra-violet is , without doubt , due to the presence of S2 molecules , it seems perfectly legitimate to assume that the S8 complex would produce absorption of some description in regions less refrangible than the blue , and that this absorption would diminish with rise of temperature . No such absorption , however , or change in absorption , has been observed between n 2090 and 1600 , when the temperature of the vapour was varied from 530 ' C. to 900 ' C. It seems reasonable , therefore , to attribute the two , and only two , distinct absorption spectra observed when sulphur vapour is heated from about 500 ' C. up to 900 ' C. to the presence of the two molecular complexes S8 and S2 . From evidence of the absorption spectra , we must therefore come to the conclusion that , on heating sulphur from its boiling point up to 900 ' C. , there is direct dissociation of S%into \gt ; S2 molecules , without the production of complexes ( such as / Sg or S\#177 ; ) intermediate in size between the above-mentioned aggregates . It will thus be seen that these results verify the conclusions of Biltz , who , * Deville and Troost , ' Compt . Bend./ vol. 56 , p. 891 . Biltz , ' Ber . , ' 1888 , vol. 21 , pp. 2013\#151 ; 2017 . Bleier and Kohn , ' Monatsh . , ' 1899 , vol. 20 , p. 505 . Biltz , *Ber . , ' 1901 , vol. 34 , p. 2490 . Bleier and Kohn , ' Ber./ 1900 , vol. 33 , p. 50 . Bleier and Kohn , ' Monatsh . , ' 1900 , vol. 21 , p. 575 , etc. 1910 . ] Sulphur Vapour at Different Temperatures , etc31 from the course of the curve connecting the vapour density of this element with rise of temperature , felt justified in making the following statement:\#151 ; " Demnach besitzt der Schwefel nur zweierlei Molekeln , namlich Molekeln S8 , und zwar im gelosten Zustande , und ferner Molekeln S2 , die rein im Schwefelgase oberhalb 850 ' , und mit Molekeln S8 gemisclit im Schwefelgase bei niederer Temperatur vorliegen " ( ' Ber . , ' 1901 , vol. 34 , p. 2495 ) . The Absorption Spectra of Sulphur Vapour at Different ( Temperatures , under Reduced Pressures . Having arrived at the conclusions already stated , for the dissociation of the S8 molecule under the action of heat , at constant pressure , it seemed advisable to examine the change produced in the absorption spectrum under reduced pressures , but at constant temperatures , in order to ascertain , if . possible , whether under these conditions there is evidence of the existence of molecules other than the S8 and S2 complexes . This part of the work was especially desirable , since it has been shown by G. Preuner , from examination of the isotherms of dissociation of sulphur vapour at different temperatures , that the presence of molecules intermediate in size between S8 and S2 is highly probable . The deductions of Preuner , * from the isotherm of dissociation at 448 ' C. , point to the occurrence of S8 , S8 , S4 , and S2 molecules , but lately this author , in conjunction with W. Schupp , j* has come to the conclusion that only the complexes S8 , S8 , and S2 are present during the dissociation produced by reduction of pressure , at temperatures between 300 ' C. and 850 ' C. Experimental.\#151 ; For these experiments another silica test-tube was flattened in the manner already described . This tube was fitted with a rubber bung , through which passed ( aa closed tube holding the thermocouple ; ( b ) the exit tube , through which the apparatus was exhausted . Some asbestos fibre was wrapped round the tube containing the thermocouple , in a position just above the point where the test-tube had been flattened , in order to prevent the molten sulphur condensed in the upper portion of the tube from running down the parallel faces , and thus preventing free transmission of the light . The rubber bung was wired into the tube , after introducing the sulphur , and on testing , the apparatus was proved to be gas-tight . The tube was fixed in a vertical position between the uranium spark and the cylindrical focussing lens , the exit tube ( ) being connected to a Topler evacuating pump ; the silica tube passed through two horizontal sheets of * Preuner , ' Zeit . Phys. Chem. , ' 1903 , vol. 44 , p. 733 . t Preuner and Schupp , 'Zeit . Phys. 0116111 . , ' 1909 , vol. 68 , p. 129 . VOL. LXXXIV.\#151 ; A. Z 318 Mr. J. I. Graham . Absorption Spectra of [ May 12 asbestos , in order to keep the upper portion as cool as possible , while the lower , flattened portion remained at a constant temperature . In taking the plate for fig. 2 , a horizontal Mecke burner was used for heating purposes , the temperature of the vapour remaining constant at 580 ' C. In the series reproduced in figs. 2 and 3 the pressure was gradually reduced from atmospheric down to about 10 mm. , photographs being taken at different intermediate pressures . To obtain the photographs in fig. 3 , i.e. with sulphur at 450 ' C. , it was found necessary to place the tube containing the sulphur in a small heating apparatus , composed of two vertical curved copper cells , mounted on a flat piece of copper , and containing an alloy of aluminium and zinc ( melting about 600 ' C. ) , the two cells being sufficiently far apart to allow the passage of light through the silica tube containing the sulphur vapour . This cell was heated from underneath by means of a large Mecke burner , and in this way it was found possible to keep the vapour at a constant temperature , which however , could be varied by regulating the Mecke burner . It was found that different pieces of silica apparatus varied in their capability of transmission of light . Thus the tube used in the case of fig. 1 was found to be very transparent ( see spectrum 1 , fig. 1 ) , whilst that used in the experiments under reduced pressure ( figs. 2 and 3 ) was found to exert rather a considerable general weakening of the spectrum ( compare spectra 1 and 2 on fig. 2 , spectrum 1 being the uranium spark spectrum , spectrum 2 the same after passing through the silica tube , the same period of exposure ( 30 seconds ) being given in each case ) . The fact that the spectra exhibited on the plates of figs. 2 and 3 were much weaker than those on the first plate is attributed to this absorption by the silica apparatus . Fig. 2 shows the effect of reduction of pressure at 580 ' C. , the series of photographs being taken through 4\#163 ; mm. of sulphur vapour , the pressure varying from atmospheric ( 756 mm. ) down to 25 mm. In this figure spectrum 3 shows the absorption at 756 mm. , spectrum 4 that at 691 mm. , spectrum 5 at 616 mm. , and so on , the pressure being gradually reduced to 25 mm. ( spectrum 10 ) . A glance at the reproduction of this plate shows the similarity to fig. 1 . Thus spectrum 3 is altogether cut off about n 2325 , spectrum 4 is cut oft about n 2380 , then there is absorption as far as n 2715 , but from this point we have the spectrum again transmitted to n 3095 , beyond which there is ^ complete absorption . In this spectrum bands are present in the violet region coinciding in position with those previously measured on the plate of fig. 1 . In the next spectrum ( 5 ) the bands in this region are still evident , 1910 . ] Sulphur Vapour at Different Temperatures , etc. 319 whilst bands are to be seen in the ultra-violet , starting about 3040 . As the pressure is reduced the absorption in the violet region becomes less , whilst the series of bands beyond n 3040 becomes more pronounced , extending further into the ultra-violet , until at a pressure of 272 mm. ( spectrum 8 ) there is continuous transmission as far as n 3040 , then the series of bands mentioned above , the spectrum being cut off about n 3420 . As the pressure is still further reduced , more of the spectrum is transmitted , until at 25 mm. there is continuous transmission as far as n 3040 , then a series of bands occurs ( the maximum absorption of each band being , as in the series shown in fig. 1 , towards the more refrangible edge , whilst from the measurements of the spectra the maxima of these bands were found to have the .same wave-lengths as those measured in fig. 1 , in the corresponding region of the spectrum , and previously attributed to the presence of S2 molecules ) . The absorption becomes stronger towards the more refrangible end , until about n 3580 there is complete absorption , stretching to approximately n 4130 , from which point , however , as far as n 4400 there is faint continuous transmission . ( Note.\#151 ; The change in the absorption spectrum on fig. 2 is roughly outlined , in order that the variation of absorption may be more evident , whilst some of the bands are dotted , in order to indicate their positions more clearly . ) A careful comparison of figs. 1 and 2 , with reference to the measurements of the absorption bands , positions of maximum absorption , etc. , makes it evident that here we are dealing with a case of dissociation , similar in every respect to that taking place when sulphur is heated from its boiling point up to 900 ' C. at constant pressure . In other words , the dissociation the sulphur molecides a , t a temperature of 580 ' C. , and produced by reduction of pressure , evidently takes place according to the equation S8 = 4S2 , without the formation of molecules intermediate complexity . Other series of photographs showing the variation in the absorption spectrum of the vapour with reduction of pressure , whilst at constant temperatures , were then taken ; thus photographs were taken showing the effect at temperatures of 450 ' ( fig. 3 ) and 380 ' C. respectively ( the latter plate not being reproduced ) . A comparison of the series in fig. 3 with figs. 1 and 2 shows at first glance that here we must evidently be dealing with a case of dissociation different in the extreme to that already described . There is , under these conditions of temperature and pressure , no evidence of any band or bands in the violet region , the only effect of reduction of z 2 320 Mr. J. I. Graham . Absorption Spectra of [ May 12 pressure being to cause an extension of the spectrum towards the more refrangible end , until pressures below 90 mm. are reached , when it is seen that bands begin to appear in the ultra-violet . Thus , in spectrum 8 we have a series of bands starting about n3340 and extending to n 3530 , where the spectrum has become exceedingly weak , and beyond which there is complete absorption . As the pressure is further reduced , these bands extend for a greater distance into the ultra-violet , until at 11 mm. ( spectrum 10 ) the bands are evident to about n 3820 , beyond which point the continuous spectrum is again faintly transmitted , being finally cut off about n 3870 . The wave-lengths of the maxima of these bands were found to agree with the figures for the bands occurring in fig. 2 , spectra 9 and 10 , and which have been attributed to the intra-molecular motions of the S2 complexes . At the temperature of 380 ' C. , a similar effect was produced on the absorption spectrum by reduction of pressure , bands being present at pressures below 80 mm. , coinciding in position with those measured on fig. 3 in the ultra-violet . A similar set of photographs through the vapour at a temperature between 450 ' and 580 ' was then taken ; this showed a series of absorption spectra when the temperature of the sulphur remained constant at 520 ' C. It was evident from a study of this plate that at the latter temperature the course of dissociation , as interpreted by change in the absorption spectrum , is similar to that taking place at the lower temperatures . Let us suppose , for the moment , that molecular complexes such as S6 and S4 exist ; from what has previously been said concerning the connection between the absorption spectra attributed to the S8 and S2 molecules , one would expect that absorption spectra similar in character to the two types already observed and assigned to these two molecules would be produced by aggregates such as S6 and S4 . That is , for the S6 molecules we might expect a series of absorption bands having strongest absorption somewhere about n 2800 , and for the S4 molecules a series of bands with maximum absorption about n 3200 ( the mean position of maximum absorption for the S8 and S2 aggregates being , as already pointed out , at % 2500 and w3750 respectively ) . Suppose now we have a gaseous mixture composed of the four sets of molecules , S8 , S6 , S4 , S2 , the most probable effect on the absorption spectrum of the vapour would be that bands similar to those measured on figs. 1 and 2 in regions less refrangible than n 3200 would not be seen distinctly , owing to the overlapping of the four different spectra , due to the intra-molecular vibrations of S8 , S6 , S4 , and S2 complexes , but a general weakening of the spectrum might be expected from about n 2300 ( or further towards the ultra1910 . ] Sulphur Vapour at Different Temperatures , etc. 321 violet , depending on the concentration of the S8 molecules in the mixture ) . On referring again to the spectra in fig. 3 , it will be noticed that in this series in no case does the spectrum appear sharply cut off , but there is distinct evidence of a weakening from a certain region to the end of the spectrum ; thus in fig. 3 , spectrum 3 , a gradual weakening is noticeable from about ? t2350 to the end of the spectrum at ? t2570 . Similarly in the other spectra a corresponding weakening is evident , whilst by comparison of fig. 3 with fig. 1 the difference between the sharp cutting off of the spectra on the latter and the shading off of the spectra on the former figure is clearly shown . The obvious conclusion to be deduced from these results is that molecules intermediate in size between the eight-atom complex and that containing two atoms are formed as products of the dissociation of the complexes , when this takes place at temperatures below 520 ' whereas at 580 ' ( ) the equation S8 = 4 $2 evidently expresses the sole reaction that occurs . It will thus be seen that results obtained from a purely spectroscopic source give independent evidence in confirmation of the thermodynamic deductions of G. Preuner , * given in 1903 , in explanation of the course of dissociation of sulphur vapour at 448 ' C. ; the recent conclusions , however , arrived at by this investigator ( in collaboration with W. Schupp)f from the isotherms of dissociation of the vapour at temperatures above 550 ' C.'do not appear to be in agreement with the interpretation given in this paper of the changes produced in the absorption spectrum of sulphur vapour at 580 ' by reduction of pressure . A plate , which has not been reproduced , was taken especially for the red end of the spectrum , employing the acetylene flame . On this plate a fetv weak bands , lying in the blue and indigo , were measured , which were not evident on the plate of fig. 1 . These bands gradually disappeared as the temperature was raised , vanishing altogether above 870 ' C. The following were the wave-lengths of these bands :\#151 ; 4775 , 4705 , 4645 , 4580 , 4530 , 4465 , 4405 , 4350 . In addition , the bands measured on the plate of fig. 1 , in the violet , were also evident on this plate . It has been already pointed out that the bands lying between %2000 ( X , 5000 ) and n 2600 ( X 3846 ) , ( measured on the plates of figs. 1 and 2 ) , may be attributed to the presence of the S8 molecules , whilst those occurring beyond n 2920 in the more refrangible direction are due to S2 molecules . These results may be summarised in the following tables :\#151 ; * Preuner , 'Zeit . Phys. Chem. , ' 1903 , vol. 44 , p. 733 . t Preuner and Schupp , ' Zeit . Phys. Chem. , ' 1909 , vol. 68 , p. 129 . Mr. J. I. Graham . Absorption Spectra of [ May 12 , A. Bands due to Sg Molecules . Position of maximum - \#151 ; absorption . Remarks . A. \#187 ; ( = ! /*\#166 ; ) . 4775 2094 The maxima of these bands appear to be , in every case , towards 4705 2125 the more refrangible edge of the band ( this fact being pre4645 2153 viously noted by Salet* for the visible region ) . 4580 2183 4530 2207 The strongest bands occur about n 2500 . 4465 2239 4405 2270 4350 2299 4290 2331 4245 2356 4195 2384 4150 2410 4100 2439 4050 2469 4005 2497 3985 2509 * ' Compt . Rend./ 1872 , vol. 74 , p. 865 . B. Bands due to S2 Molecules . Position of maximum absorption . Remarks . A. n( = l/ \ ) . 3415 2928 All these bands are in the ultra-violet . 3365 2972 3330 3003 The maxima of absorption of these bands are towards the more 3290 3039 refrangible edge of the band in each case . 3255 3072 3215 3110 The strongest bands ( maximum absorption ) occur about ^3750 . 3170 3155 3130 3195 3095 3231 3060 3268 3025 3306 2990 3344 2960 3378 2930 3413 2900 3448 2860 3496 2835 3527 2805 3565 2770 3610 2745 3643 2715 3683 2690 3717 2665 3752 2640 3788 2620 3817 \#166 ; . 1910 . ] Sulphur Vapour at Different , etc. 323 These tables contain what are believed to be the principal bands due to the molecular complexes S8 and S2 , but there is no intention of implying that they are the only bands due to these two molecules . It is interesting to note that the difference in wave-length between the two extreme bands of each series is approximately the same in both cases . Thus , in Series A , the first and last bands , given above , differ by 790 Angstrom units ; whilst in Series B there is a difference of 795 Angstrom units . The two series of bands , A and B , are shown on Plate 5 , fig. 4 , mapped in oscillation frequencies , the black lines and shading indicating absorption . The position of maximum absorption of each band is towards the more refrangible edge , whilst the individual bands of each series appear to become stronger also in the more refrangible direction . When mapped in this fashion , the similarity between the two series becomes more evident . Apologies must be made for the reproductions , which in several cases do not bring out portions of the spectra , bands , etc. , that were clearly shown on the original plates . Above portions of certain of the spectra , horizontal lines have been drawn to indicate the presence of the continuous spectrum transmitted beyond n 3820 , whilst some of the bands are indicated by dots . An approximate scale of oscillation frequencies has been affixed to each plate . It is hoped to repeat these experiments shortly , employing much greater dispersion , in order that the bands given by the sulphur vapour may be further examined , and more accurate determinations made of their wavelengths and oscillation frequencies . With finer measurements , attempts will be made to see whether these bands conform to any law similar to that given by Deslandres* for the band spectrum of nitrogen . In conclusion , I have to thank Prof. Hartley for his kindness in giving me many fruitful suggestions , and also for the trouble he has taken in the revision of this paper . * -Compt . Rend . , ' 1902 , vol. 13J , pp. 747\#151 ; 750 . 324 The Abso^tion Spectra of Sulphur , etc. DESCRIPTION OF PLATE . Fig. 1.\#151 ; Series taken at constant pressure,742 mm. Thickness of sulphur vapour , 51 mm. Spect . 1.\#151 ; Spark spectrum of uranium through empty silica tube . 2.\#151 ; Same through sulphur vapour at 530 ' C.* 3.\#151 ; 55 55 610 ' 4.\#151 ; 55 55 770 ' 5.\#151 ; 55 55 840 ' 6.\#151 ; 55 55 870 ' 7.\#151 ; 55 55 900 ' Lengths of Exposure.\#151 ; Spectrum 1 , 30 seconds ; spectra 2\#151 ; 7 ( inclusive ) , 1 minute . Fig. 2.\#151 ; Series taken at constant temperature , 580 ' C. Thickness of sulphur vapour , 4^ mm. Spect . 1.\#151 ; Spark spectrum of uranium . 2.\#151 ; Same through empty silica apparatus . 3 . , , sulphur vapour ( 580 ' C. ) , press . 756 mm. 4- )\gt ; 55 55 691 " 5 . , , 55 55 616 " 6.\#151 ; " 55 55 500 " 7.\#151 ; 55 55 386 " 8.\#151 ; 55 55 272 " 9.\#151 ; 55 55 168 " 10* JJ V 11.\#151 ; Spark spectrum of uranium . 55 25 " Lengths of Exposure.\#151 ; Spectra 1 , 2 and 11 , 30 seconds ; spectra 3\#151 ; 10 ( inclusive ) , 1 minute . Fig. 3.\#151 ; Series at constant temperature , 450 ' C. Uranium spark spectrum through sulphur vapour at 450 ' C. ; thickness , 4 mm. Spect . 1.\#151 ; Press . 770 mm. Spect . 6.\#151 ; Press . 229 mm. 2 . " 639 55 7.- " 91 55 3.\#151 ; " 558 55 8 . , , 36 55 4.- " 452 55 9.\#151 ; " 21 55 5 . 350 55 10.- " 11 *5 11.\#151 ; Uranium spark spectrum through empty silica apparatus . Lengths of Exposure.\#151 ; Spectra 1\#151 ; 10 ( inclusive ) , 1 minute ; spectrum 11 , 30 seconds . Fig. 4.\#151 ; Diagram of oscillation frequencies of two series of bands , A and B. * The exposure at this temperature ( 530 ' C. ) was slightly longer than at the others , with the result that rays up to n 2440 are shown , whilst at the next higher temperature the spectrum is not evident beyond n 2425 . Roy . Soc. Proc. A. Vol. PI . 5 . Fig- Oscillation Frequency\#151 ; 1/ \ Temperature of Vapour=58o'c . Oscillation Frequency\#151 ; 1/ \ \lt ; PQ pjg Temperature of Vapour=45o'c . Pressure . 770 mms . 639 . . Oscillation Frequency\#151 ; 1/ \ London Stereoscopic Co. imp .

rspa_1910_0078

0950-1207

A determination of the ratio of mass to weight for a radioactive substance.

325

344

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

L. Southerns, B. A. (Cantab.), B. Sc. (Lond.)|Sir J. J. Thomson, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1910.0078

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1910_0078

10.1098/rspa.1910.0078

Measurement

Tables

Measurement

]\gt ; A Determinaiion of the Ratio of Mass to Weight for a Radioactive Substance . By L SOUTHERNS , . ( Cantab . ) , B.Sc. ( Lond. ) , Whitworth Scholar , Exhibition Scholar , Emmanuel ( Communicated by Sir J. J. Thomson , F.R.S. Received June 30 , \mdash ; Read , 1910 . ) Experiments have been made from time to time by different ervers . with a view of testing the con stancy of the ratio of mass to weight for various substances . Their results have been uniformly negative so far as any deviation from constancy is concerned . Several years an experiment of this nature was undertaken by Prof. Sir J. J. Thomson , who used a pendulum the bob of which was made of . The quantity of radium , however , was small , and it was found to be impossible to obtain a very high degree of accuracy . The considerations which led to the supposition that radium might differ from non-radioactive substances in the above respect were as follows:\mdash ; * " " The simplest electrical system we know , an electrified sphere , has attached to it a mass of ether proportional to its potential , and such if the mass were to move with the velocity of light its kinetic equal the electrostatic potential of the particle . This result be tended to any electrified system , and it can be shown that such a system binds a mass of the ether proportional to its potential energy . Thus a rt of the mass of any system is proportional to the potential energy of the system . " " The question now arises , Does this part of the add anything to the weight of the body ? If the ether were not subject to gravitational attraction it certainly would not , and even if the ether were ponderable we might expect th as the mass is swimming in a sea of ether it would not increase the weight of the body to which it is attached . if it does not , then a body with a large amount of potential energy may have an amount of its mass ) a form which does not increase its weight , and thus the weight of a iven mass of it may be less than that of an equad mass of some substance with a smaller amount of potential energy . Thus the of equal masses of these substances vould be different . " " The radioactive substances are constantly giving out large quantities of heat , presumably at the expense of their potential energy ; thus , when these substances reach their final non-radioactive state their potential energy must * Prof. Sir J. J. Thomson , Presidential Address , British Association , Winnipeg , 1909 . weight for radium would be greater by about 1 part in 13,000 than for its 4 non-radioactive products These considerations also apply to uranium , for " " we have got good reason for that uranium is a parent of radium , so that the great potential energy and large ethereal mass possessed by the radium will be also in the uranium In the present paper some experiments made with uranium oxide are described . The results , however , show that the ratio of mass to weight of this substance does not differ appreciably from that of the non-radioactive substance with which it was compared . The paper is divided into the following sections:\mdash ; 1 . Preliminary experiments with a wire pendulum . 2 . Theory of a new rigid pendulum . 3 . Description of the apparatus . 4 . Method of experiment . 5 . Experimental results . 6 . Conclusion . 1 . with ( a Wire A pendulum based on the principle employed by Bessel in his investigations on the value of for various substances was constructed for Prof. Thomson by the Cambridge Scientific Instrument Company , and observations were made upon it by the writer at Prof. Thomson 's request . Although sufficiently accurate results were not obtained with this apparatus , it may be briefly described , as it was of great service in shaping the subsequent course of the investigation . It consisted of a hollow cylindrical bob of aluminium , which could be suspended by a wire from a by means of a suitable attachment . Either of two wires , of lengths 75 and 150 cm . respectively , could be used . The method of experiment was as follows : bob was filled with red lead and suspended by means of the long wire and the 1910 . ] to Veight for a Radioactive Substance . time of swing deterluined . Then the short wire was substituted for the long one and the time again observed . The red lead was then replaced by uranium oxide , and the times taken as before . The pendulums approximate to simplependulums . Assuming them to be actually simple , and writing , for the times of the long and short pendulums respectively and , l2 , for the lengths when the first substance , for which the acceleration of ravity is , is employed , and the same letters dashed for the corresponding quantities for the second substance , we have . But difference in the lengths of the wires irrespective of the absolute ] , and therefore so that the ratio of the values of is deduced from the times alone . In the actual case , since the pendulums are not simple , it is necessary to know approximately the distance of the centre of ravity from the in each case , as well as the other dimensions of the appal.atus , errors in the packing of the bob , with corresponding displacements of the centre of gravity of the substance , will have but little influence on the accuracy of the nents . After many experiments had been made with this ratus , and considerable experience ained on minor points , it was discarded , mainly because it was found to be impossible to fit ether the different parts of the pendulum always in exactly the same way , so as to give sufficiently consistent results . Thus differences of 1 in 10,000 or 20,000 frequently occurred in the time of swing after all other errors which could be detected had been as far as possible eliminated . In view of this , it appeared desirable to the writer to construct a rigid pendulum with two knife-edges permanently fixed to it , and to employ some kind of lifting apparatus by means of which the from one knife-edge to the other could be made without in any way handling the pendulum , or opening the case in which it was enciosed . Such an apparatus . was constructed in the laboratory workshop to the writer 's designs , and a standard invar pendulum was supplied by the Scientific Instruntent Company for the purpose of checking the clock which was used in the experiments , as the rate of this had been foumd to be somewhat variable . The theory given above is of course inapplicable to the new pendulum , but a method of the results in a simple manner will be given in the next section . The only vback in the use of a rigid pendulum is that The pendulum consists of a rod AA ( fig. 1 ) , having two knife-edges fixed at the places shown in the figure , and a hollow cylindrical bob which can be filled with either of the substances to be experimented on . The bob is not permanently fixed , but can be moved through a small range up and down the rod . By means of suitable arrangements the time of be taken first about one of the knife-edges and then about the other , the position of the bob remaining unaltered . Considering the time of swing about one of the knife-edges , we have , where I is the moment of inertia about the knife-edge , the total weight of the pendulum , and the distance of the centre of gravity from the . We shall assume that gravity does not change during the course of the experiments , but may be different for the different substances used . total weight , however , of the pendulum remains constant through all the experiments , for the weight of the bob is always carefully adjusted by means of a balance after being filled . The balance of course ensures ] of weights and not of masses , the ordinary use of the balance for the determination of masses depending on the supposed invariability of for the substances employed . Since therefore in the case of uranium we know neither mass nor acceleration of gravity , but only weight , it will be convenient to write the expression for the time where is a constant and is the total weight of the pendulum . iations of mass will only affect the moment of inertia in this expression . It is possible to fill the bob so uniformly that the centre of gravity shall always be exactly at the same point , but it will be seen that errors due to this can be rendered unimportant by the method to be explained . We will first , however , assume that the bob is uniformly packed , and that a normal substance is used so that has its ordinary value throughout the pendulum . It is possible to find a point X , say , on the rod about which the time of swing of the pendulum is independent of small changes in the position of the bob . In practice , the knife-edges are fixed one above the point X and one below it . The time of swing of the pendulum about a point of the rod above X will be increased by a slight lowering of the bob . The time of swing about a point below X will be diminished by the lowering of the bob . Let , be the times about the upper and lower points respectively , the bob bein in its fl ff 1910 . ] Mass to Weight for Radioactive Substance . 329 first position , and , the times with the bob lowered . Then and . This is shown on the accompanying small diagram , in which the ordinates represent times from the upper point and abscissae times from the lower point . : . DIAGRAM A. RAlf B. Points corresponding to other positions of the bob will lie on the line 1 , which will be nearly straight if the displacements are very small . This line will be called the characteristic li of the pendulum for the given points of suspension . We will now return to the expression for the time of , and suppose it to apply to one of the observations on the diagram . Suppose the mass of the bob to be increased by the use of another substance , the weight remaining unaltered . Now I will be increased , and therefore will be greater than before . This is true whatever point of suspension be used . If the bob be replaced in exactly the same position as it was when point 1 was taken , and the new packing be exactly uniform , the new point , 3 say , will be higher up the diagram than 1 , and also more to the , both its co-ordinates having been increased in magnitude see small . If the bob be now moved down to the position which it occupied when point 2 was determined , a new point 4 will be obtained on the line approximately parallel to 1 , 2 . Thus the pendulum will have a new characteristic line nearly parallel to the old one . In order , , to find out whether equal weights of different substances possess different masses , it is only necessary to plot a few points on the diagram for different positions of the bob for each substance , and to draw the characteristic lines . If the masses are different , the lines will be separated ; if not , they will coincide . Accidental variations of the height of the centre of gravity of the bob , due to inequalities of packing , merely cause displacements of the points the characteristic lines , and are therefore of no consequence . It is necessary , however , to exercise care in packing , as otherwise later , and it will appear that they also are unimportant . Corrections for changes of temperature of the pendulum and of the density of the air will be required . As the experiment is not intended to give absolute , but only relative , results , it will not be necessary to reduce to zero of temperature and density , and therefore we shall only consider deviations from the mean conditions . Thus the corrections will be small , and an approximate ation of them will suffice . As regards temperature of the pendulum , it will be sufficient to assume that the whole expands uniformly with rise of temperature . Let coefficient 'of linear expansion at , then the time of swing at will be , where Thus for a rise of one degree we reduced the observed result by , where is the time at the standard temperature With to the effect of changes in the density of the air , we need only consider buoyancy and the mass of air carried along with the pendulum . This latter consists of two parts , namely , that which surrounds the pendulum :and moves with it , and that within the hollow bob ( which is not air-tight ) between the particles of the substance therein contained . Some air will pass in and out of the bob as the conditions change . We shall calculate the buoyancy as affecting the whole volume of the bob , as well as the rest of the pendulum , and therefore any air which enters the bob must be considered to add its weight to the bob as well as its mass . We thus have to apply corrections for\mdash ; ( 1 ) A variation in the weight of the moving system , equal to the variation in the weight of the air displaced by the whole pendulum , and acting at the centre of gravity of this displaced air . ( 2 ) A variation in the moment of inertia of the system , equal to that in the air carried along around the pendulum . ( 3 ) A variation in the weight of the bob , equal to the variation in the weight of the enclo air . .(4 ) A variation in the moment of inertia of the bob , equal to the variation in that of the enclosed air . 1910 . ] Mass to for Radioactire Substance . 331 The standard invar pendulum is also subject to corrections ( 1 ) and ( 2 ) . The effect of this is to partially eliminate the corrections , and in view of this it will be allowable to make the assulnption that the mass of air carried with each pendulum is equal to the mass displaced . to corrections ( 3 ) and ( 4 ) , will be assumed that the density of the air inside the bob is equal to that outside . The corrections will be considered in detail in a later section of the paper . 3 . of th The main apparatus is shoWll generally in fig. 1 , and an portion in profile in fig. 2 . The same letters are used for corresponding parts in the two figures . , A represents the rod of the experimental pendulum , is the bob , the cast-iron supporting bracket , which is slotted at and which carries slotted plates , , which can be levelled , and to which are fixed planes , , on which the of the pendulum bear . The upper plate is thrown back 1 cm . , as shown in fig. 2 . The pelldulum is there shown with the upper knife-edge in contact with its planes , and in this position the lower is free . On the other hand , when the lower knife-edge is in position the upper one ings clear of its planes . This change of position is accomplished by means of the apparatus in the ures . Two pairs of brackets , , are attached to a flat rod , this lies exactly behind the pendulum rod in fig. 1 ) , which is moved its own plane by eccentrics , , so that any point in it describes a part of a circle whose radius is 5 mms . This throw is slightly erated in fig. 2 for the sake of clearness . The arms , , have -shaped grooves , in which pins , are seen lying in fig. 2 . These pins are fixed to the pendulum , and by means of them the are , lift the pendulum and carr ) it over from ] position shown in fig. 2 to that in which the lower knife-edge engao e with its The arms then continue their motion htly , so as to release the pins , and allow the pendudum to clear of its supports . The eccentrics actuated by rods , cranks , and connecting rod , as shown at , in fig. 1 . These pass outside the case in which the pendulum is enclosed , so that the change from one knife-edge to the other can be elf'ected without the case . This is an important point in experiments of this nature . A mirror is fixed to the pendulum at , and another one , , which emains stationary during an observation , is attached to an adjustable support Q. This has two motions controlled rods which pass the case at . The bracket carrying this fixed mirror arrangement is at S. A )racket with two screws is shown at , near the bob in . The screws are adjusted so as to very nearly touch the rod whenever the bob is for 332 Mr. L. Southerns . FIG. 1 . FIG. 2 . : 1910 . Mass to Weight for a Substance . , 333 : ' replaced . They are for the purpose of steadying the rod , and are screwed out of the way when the bob is in position . is a rod similar to the pendulum rod . It has a brass projection , which is drilled to receive the bulb of a thermometer W. The reading of this thermometer is taken as indicating with sufficient accuracy the temperature of the pendulum rod . A thermometer is also suspended in the case to indicate the temperature of the air . The standard invariable pendulum , to which all observations are finally referred , is shown to the left of the experimental pendulum , in fig. 1 . The rod is of invar , and the bob of brass . It is provided with mirrors , similar to those of the other pendulum . The pendulums are set up in a niche in the wall of one of the rooms ou the ground floor of the new of the Cavendish Laboratory . The cast-iron brackets are bolted to the wall which forms the back of the niche . Double partitions of wood , packed with sawdust , are fixed above and to the right of the pendulums , and the front is closed with two doors similarly made , an upper and a lower door . The lower one can be opened independently , when it is necessary to remove and replace the bob . A plate glass window is fixed in the upper door opposite the mirrors . This is closed by a shutter , except when observations are being made . There is also a partition between the two pendulums . No culty was anticipated , nor has any been experienced , due to the fact that both pendulums are fixed to the same wall . Their periods are quite different , and even if any slight resonance did occur , it would not favour either of the substances llsed . ( There is , moreover , no necessity taking observations on both pendulums simultaneously . It is sufficient , if a good clock be used , to take them alternately . ) To set the pendulums in motion , tubes with rubber bulbs are used , by means of which puffs of air can be projected against the bobs . In taking observations a flashing apparatus is employed . It consists of a clock capable of giving electrical signals each second , a lever actuated by these and arranged so as to interrupt the primary current of an induction coil , the said coil , and a helium tube , which is connected to the secondary of the coil . For most of this apparatus , the writer is indebted to Dr. F. Horton , who has described it in detail . * The helium tube is set up horizontally on a shelf fixed to the wall of the room opposite the pendulums , at a distance frolll them of metres and about metre above the level of the mirrors . cylindrical concave mirror is placed slightly behind and below the tube , so as to give a fine and sharp line-image each time a flash occurs . This imsge is observed by reflection in the pendulum mirrors by means of telescopes , one * See ' Phil. Trans , vol. 204 . VOL. LXXXIV.\mdash ; A. 2 about 1 metre in front of the mirrors . The telescopes tilt slightly upward towards the mirrors , and the rays from the flashing apparatus to the mirrors pass just above the observer 's head . As the clock which controls the flashes is in another part of . the laboratory , a chronometer is placed near the telescopes for the indication of time . 4 . Method of Experiment . It is necessary , as has been explained in section 2 , to make determinations of the of swing of the experimental pendulum about its two knife-edges for various positions of the bob , one of the substances to be experimented upon being con tained therein , and then to change to the second substance and repeat the series of observations . As , however , only comparative determinations are required , it is not necessary to express the times in seconds . Any other invariable unit of time will do equally well . The unit actually adopted is nearly 1 second , it is , where is the time of a complete swing of the standard pendulum under normal conditions of temperature , air density , and amplitude of oscillation , and is approximately the average value of the time of the standard as determined directly in the experiment in clock seconds . is assumed to be accurately constant during a series of observations . Its absolute value is not required , and has not been determined by reference to transit is , of course , very nearly . Corrections are made for changes from the normal density of the air , but corrections for variation of amplitude and temperature of the pendulum itself ( the rod of which is of invar ) are negligibly small and have not been applied . Now suppose the time of the experimental pendulum , and also that of the standard , to be observed in clock seconds , then if their actual times are and in mean solar seconds , and if the clock second is equal to mean solar seconds , the observed times will be and respectively , so that we shall have , as the ratio of the observed time of the experimental pendulum to that of the standard , , which is the actual time of the experimental pendulum in terms of that of the standard . In order to express this in lJnits more nearly equal to 1 second , may be multiplied by which will give the actual time of the experimental pendulum in terms of , the unit described above . The finally tabulated times of the experimental pendulum will be given by\mdash ; time bservations ancidences Prof. Pointing , and described by Dr. Horton in the paper referred to above . One or two modifications in the procedure have however been made in the present case . The method as used will be understood the following description . Suppose the pendulum which is to be timed the flashin apparatus to be working , we shall observe , on looking through the telescope , whenever a flash occurs , two images of it in the field of view . One of these , due to the fixed mirror , will have a constant positio1i in the field , the other , due to the mirror attached to the pendulum , will in general be seen in a new position each second . The fixed mirror should be adjusted that when pendulum is vertioal , the two images are seen to be in the same line and partially overlapping . Now suppose that at some instant a perfect coincidence of the images occurs . If there is no special relation between the period of the pendulum and that of the flashes , the moving image will then appear to dart about the field in an erratic manner . After a time it will occupy a position near to the fixed image , but probably not exactly coinciding with it . Let this occur seconds after the first coincidence . At this instant the pendulum be nearly vertical , and if it is moving in the same direction as when the first coincidence occurred it will have executed almost , but not quite , exactly a whole number , say , of swings . Suppose it to have passed a little beyond its central position , so that the actual numbel of swings is , where is a small fraction . In this case the pendulum may be said to be gaining on the flashes . In seconds the pendulum will have executed Again , in another seconds the moving image will appear a little further from the zero ( or fixed ) , and so on . After a time the image will reach its maximum distance from the zero , and at that installt the pendulum will be at one extremity of its swing , and it will have ained one-quarter of a complete period on the flashes . The image will then begin to return towards the zero . When it reaches it , the pendulum will have gained half a complete . The image will then pass along to the other extremity of its range , and again eturn to the zero . We will suppose that an exact coincidence then occurs . At that in stant the pendulum will have ained exactly one complete swing on the flashes , and the observation will terminate . All the flashes except those occurring at intervals of seconds will , of course , have been ignored . Let the total number of periods of seconds each be , then we know that the pendulum will have executed swings in seconds , and its time of swing is thus . In general , however , exact coincidences do not occur , and it is necessary to observe two successive positions of the image , one on each side of the zero , the observation , should a perfect coincidence not occur . In order to enable these distances to be estimated , scales , slightly illuminated , are used in the eye-pieces of the telescopes . There are two sources of error in practice which need attention . In the first place , an error may arise due to an irregularity of the flashes caused in the following way . The clock pendulum is fitted with a platinum projection , which cuts through a fine stream of mercury and so makes contact each time it passes its mid-position . Now , should the projection or the mercury stream be slightly displaced laterally , so that contact always occurs when the pendulum is a little to one side of its mid-position , it is evident that the contacts will take place at unequal intervals . Alternate contacts will , however , take place at two-second intervals . Thus in the actual observations must always be an even number ; this ensures freedom from error due to the above cause . Again , the images in the field of view may not exactly coincide when the pendulum under observation is in its central position , and in this case the true zero is not accurately indicated by the fixed image . would be of little importance if the amplitude of the pendulum remained constant . But , as this is not the case , an error is introduced if we take the fixed image as representing the zero . This error is practically eliminated by two independent ( but overlapping ) observations of the time , one being started with a coincidence which occurs while the pendulum is moving towards the observer , and the other with one which occurs when the pendulum is in opposite phase . The mean of these times is to be taken as the observed time . The actual procedure is as follows :First , the experimental pendulum is set on its lower knife-edge and set into motion ; the standard is also started . After 10 or 15 minutes the two observations on the experimental pendulum are commenced , and then the two on the standard . In due course the experimental observations are completed , the pendulum stopped , and set on its upper and restarted . After a few minutes two observations on it commenced ; these are completed , and finally the two standard observations are completed . The value of for each of the six observations is then recorded- ecords are also kept of initial and final amplitudes , of the readings of the thermometers and of the barometer , ' and of a maximum and minimum thermometer ( in the mornings only ) kept in the case to show the range of temperature during the previous 24 hours . 1910 . ] Mass to Weight for a 0037 The filling of the bob is an important operation . As has been shown , slight variations in the position of the centre of gravity are in themselves unimportant , but errors are introduced by changes in the nloment of inertia - of the bob about an axis its centre of gravity . With reasonable care these can be rendered small . The substances used are red lead and uranium oxide . To the latter , however , it has been found necessary to add a small proportion of nagnesium oxide , to render it similar to the red lead in packing properties . The method of packing finally adopted is as follows : substance is divided into three equal portions by weight , and one of these is put into the bob . The bob is then tapped underneath , to cause the substance to nearly settle down into the lower third of the bob . Then a flat disc of brass is lowered on to the substance , and on this is placed a distance piece , which is pressed down until its top is exactly level with the rim of the bob . By this means the substance is htly compressed into a definite volume into the lower part of the bob . The disc , etc. , are then removed and the second poltion of the substance is put into the bob , and a similar process oone through , . a shorter distance piece . Finally , the remainder of the substance is put in and tapped down as before , and pressed home by means of the lid of the bob , which is then secured by its nut , care being taken to always screw down this llut to the same extent . Greater accuracy of packing could be attained by the stages of the process , but the three have been found to be sufficient for the purposes of this experiment . As regards the amplitudes of oscillation , these were practically identical in the several experiments . The initial and final amplitudes were\mdash ; Standard pendulum Exp. pendulum , upper K.E. lower K.E. 5 . Experim Results . In Table I some constants of the pendulum are given . They have been carefully determined , *though strict accuracy is not essential in the case of quantities which lemain constant throughout the whole series of experiments . Table II summarises the records of observations of the final experiments . Two experiments were usually made in a day , one in the morning and one in the afternoon . The substance was usually changed once day after the morning orvation.table , alues fthese constants Ixperiments taries , espect tumbers in the table actually cosition osubstance hssumed i 338 Mr. L. Southerns . Determi ' 910 . ] Mass to Weight for a Radioactive Substance . S39 are given for the standard and for the upper and lower knife-edge observations on the experimental pendulum . The values of and , and the number of swings gained or lost during the observations , are as follows:\mdash ; Standard pendulumains 1 swing . . pendulum , upper ains 1 swing . lower K.E. : , loses 2 The position of the bob is given in each case , ndicates n position , and a position somewhat lower than the normal lnd different in the different cases . The other columns of the table require no special explanation . The observed times , as obtained from the values of by the method which has previously been explained , are given in Table . Three sets of corrections are also given in the table . has been shown , it is only necessary to correct for variations from the normal conditions under which the experiments are made . The normal temperature is taken to be C. and the pressure . In the first place , corrections given for deviations in the temperature of the experimental pendululn from These are obtained in a manner which has been described in section The coefficient of expansion is taken to be . Taking approximate values of for upper and lower knife-edges , we have for upper knife-edge sec. for lower , , , , Thus for a rise of 1o C. we reduce the times by the above quantities . Correctione are next given for variations in the pressure . In order to obtain these it is necessary to know the increments of the values of I and in the expression for the time of swing of the pendulum under consideration . Thus , for example , in the case of the experimental pendulum swinging about its upper knife-edge , we have say . From Table I we see that Now , from a knowledge of the dimensions of the apparatus , it is easy to calculate with sufficient accuracy the produced in I and by an increase of pressure of 1 cm . of mercury . In making this calculation , regard must be paid to the points mentioned on p. 330 . In the above case , an increase of pressure of 1 cm . gives rise to an increase of I of 167 , and a decrease of of . Thus the new time will be given by , so that we have of tloe Ratio of \mdash ; $ 1910 . ] Mass to for a which is found to mean that the increase of pressure causes an increase of represented by units in the last place of decimals tabulated . Therefore , to reduce the observed times to times for pressure , it is necessary to deduct units from the last } place for each eentimetre of pressure . greater than 76 . In the case of the knifeunits are to be deducted , and in the case of the standard , 4 units . The effect of a fall of 1o C. in the temperature of the air is to that of an increase of pressure of 1 cm . as 76 : 285 . The ection s given in ) table for changes of atmospheric temperature are based on this fact . Table The corrected times are given in Table , together with the " " tabulated times In these , as was explained on p. 334 , the clock errol . S are elinlinated , and the times of the experimental pendulum are expressed iu invariable units closely approximating to seconds . The tabulated times can now be plotted , and the characteristic lines obtained for the two substances . We may first , however , determine the amount by which they will be separated on the supposition that the theory given at the of the paper holds true . We first require the approximate mass of radium equivalent in the radioactive substance used . The mass of uranium oxide is 1015 grammes , and assuming the composition to be given by , we shall have 860 gramrnes of urimium , corresponding to 811 grammes of radium . The extra mass attached to each ramme of radium is ramme . This gives 62 milligrammes for 806 rammes * Week ending Apri116 . Week ending Apri ] 1910 . ] Mass to Weight for Substance . 343 6 . It is evident from the diagrams that the characteristic lines for the two substances are identical within the limits of experimental error . In the experiments exhibited on the first diagram , the accurate method of packing ' was not in use , and the weather conditions were not quite so favourable as they were . the week following . In the second oram , the of the better system of packing , and also of the more uniform weather which prevailed , are well shown . The dotted lines are drawn ] to the experimental characteristic lines , so as to show the distance which should separate the lead and uranium lines , according to the theory . In the more accurate , the deviations from the line are not greater than 1 in 600,000 on the times . The results indicate that the ratio of mass to weight for uranium oxide does not differ from that for lead oxide by more than 1 part in 200,000 . It remains to show that inaccuracies in the crhing of the bob are not likely to cause appreciable errors . Following the method of p. 339 , we have for the normal time from the upper Now , suppose we add gramme to the bob , the increase in I ( the numerator ) will be about 196 , and the increase in Mh ( the denominator ) about . Thus , for the new time , we have which gives or , which is an increase of 1 in 2,000,000 , and is therefore negligible , which is also the case if the lower knife-edge be considered , though the effect is somewhat greater , , about 1 in 300,000 . It is , of course , easy to reduce the errors to smaller dimensions than these by careful weighing . An effect which caused considerable trouble the experiments may be briefly referred to . A rod of nickel steel was first used on account of its small coefficient of expansion . Sometimes for two or three days satisfactory results would be obtained , then the characteristic line would suddenly take up a new position to the left of the old one . This took place time after time , the line always moving parallel to itself in the same direction . A rod of tool steel exhibited the same error . It appeared to be due to magnetic effects . The rods became magnetised by induction in the earth 's field , and no doubt this magnetisation was assisted by the movements of the pendulum when it was transferred from one knife-edge to the other , and the removal and readjustment of the bob . The cast-iron bracket was probably concerned in the matter . The rod of the standard pendulum was also magnetic , but it remained untouched during the whole course of the experiments , and gave rise to no difficulty . It had , at any rate , settled down to a The pendulum was sensitive to sudden variations of the weather . It would be a great advantage to enclose the apparatus in a case kept at constant temperature and pressure . A somewhat improved method of removing and replacing the bob is also desirable . In conclusion , the writer wishes to express his best thanks to Prof. Sir J. J. Thomson for his unfailing kindness throughout the course of this investigation . On the Spontaneous Crystallisation the Melting Freezing Point Curves of JMixtures of Two Substances which form Mixed possess Minimum or Eutectic Freezing Point.\mdash ; IVIixtures of Azobenzene and Benzylaniline . By Miss F. ISAAC , formerly Research Fellow of Somerville College . ( Communicated by Principal H. A. Miers , F.R.S. Received June 21 , \mdash ; Read June 30 , 1910 . ) CONTEN TS . PAGK Crystalline Form of Benzylaniline and Azobenzene 345 Microscopic Examination of Azobenzene and Benzylaniline crystallised from Fusion 346 Mixtures of Azobenzene and Benzylaniline 347 The Freezing Point Curve 348 The Melting Point Curve 348 Analysis of the Mixed Crystals Microscopic Examination of Mixtures of Azobenzene and Benzylaniline crystallised from Fusion The Supersolubility Curve , or Curve of Spontaneous Crystallisation 355 ( 1 ) By the Method of Sealed Tubes ( 2 ) From Observations of the Refractive Indices of Liquid Mixtures 367 Nature of the Crystals separating on the Supersolubility Curve 360 Thin Sections cut from Solidified Mixtures of Azobenzene and Benzylaniline 366 Conclusion The behaviour of mixtures of naphthalens and -naphthol has already been investigated , and the freezing melting point curves and the curve of

rspa_1910_0079

0950-1207

On the spontaneous crystallisation and the melting and freezing point curves of mixtures of two substances which from mixed crystals and posses a minimum or eutectic freezing point. \#x2014;Mixtures of azobenzene and benzylaniline.

344

369

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Miss F. Isaac|Principal H. A. Miers, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1910.0079

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1910_0079

10.1098/rspa.1910.0079

Thermodynamics

Chemistry 2

Thermodynamics

]\gt ; 344 Miss F. Isaac . llisation , etc. , of Mixtures very steady state by the time the final experiments were made . some irregularity took place when new knife-edges were used , due no doubt to the wearing off of some slight " " burr\ldquo ; left on the edge during sharpening . : ! - The pendulum was sensitive to sudden variations of the weather . It would be a great advantage to enclose the apparatus in a case kept at constant temperature and pressure . A somewhat improved method of removing and replacing the bob is also desirable . In conclusion , the writer wishes to express his best thanks to Prof. Sir J. J. Thomson for his unfailing kindness throughout the course of this investigation . On the Spontaneous the Melting Freezing Point of Mixtures of Two Subst ances which form Mixed Crystals possess a Minimum or Eutectic Freezing Point.\mdash ; JPixtures of Azobenzene Benzytniline . By Miss F. ISAAC , formerly Research Fellow of Somerville College . ( Communicated by Principal H. A. Miers , F.R.S. Received June 21 , \mdash ; Read June 30 , 1910 . ) CONTEN TS . PAG13 Crystalline Form of Benzylaniline and Azobenzene 345 Microscopic Examination of Azobenzene and Benzylaniline crystallised from Fusion 346 Mixtures of Azobenzene and Benzylaniline 347 The Freezing Point Curve 348 The Melting Point Curve 348 Analysis of the Mixed Crystals Microscopic Examination of Mixtures of Azobenzene and Benzylaniline crystalhsed from usion The Supersolubility Curve , or Curve of Spontaneous Crystallisation 356 ( 1 ) By the Method of Sealed Tubes ( 2 ) From Observations of the Refractive Indices of Liquid Mixtures 357 Nature of the Crystals separating on the Supersolubility Curve 360 Thin Sections cut from Solidified Mixtures of Azobenzene and Benzylaniline 366 Conclusion The behaviour of mixtures of naphthalene and -naphthol has already been investigated , and the freezing melting point curves and the curve of 1910 . ] of Two which form Mixed Crystals , etc. spontaneous crystallisation for these mixtures described . * These substances were found to form a continuous series of mixed crystals , on a curve of Type 1 , the melting and freezing points of all the mixtures lying between the melting points of the pure substances . The behaviour of mixtures of monochloracetic acid and naphthaleue was also ated , for it was stated by Cady that these substances form mixed crystals of Roozeboom 's Type 5 , whose melting and freezing point curves exhibit a minimum or eutectic point . Experiments were therefore made with these substances with the object of determining the form of the curve of spontaneous crystallisation , or supersolubility curve , for mixtures of this type . No sign of the formation of any mixed crystals observed , however , in a lengthy series of expeliments , and it was shown that naphthalene and monochloracetic acid give the ordinary -shaped point curve for the solutions of two substances in each other , similar to that already obtained for mixtures of salol and betol , S the only new feature being introduced by the existence of three modifications of monochloracetic acid . The monochloracetic acid and naphthalene mixtures having thus failed as an example of mixed crystals possessing a minimum 01 ' eutectic point , other attempt was made to obtain a pair of substances with convenient melting points which form mixed crystals and possess the melting and freezing point curves with minimum eutectic point characteristic of Roozeboom 's Type 5 . Azobenzene and benzylaniline were chosen for this purpose , the present paper deals with mixtures of these substances . CRYSTALLINE FORM 0F BENZYLANILINE AND AZOBENZENE . Benzylaniline , ) been described by Jaeger obtained transparent colourless crystals from a solution in methylalcohol . He found the crystals to be monoclinic , with axial ratios\mdash ; and The habit is elongated along the -axis , the plane of the optic axes being ( 010 ) . The axial dispersion is strong , with Azobenzene , , has been described byBoeris , and by Calderon . ' Journ. Chem. Soc 1908 , vol. 93 , 1 , p. 927 . Phil. Trans 1909 , , vol. 209 , p. 33 Journ. Phys. Chem 1899 , vol. 3 , p. 127 . S 'Roy . Soc. Proc 1907 , , vol. 79 , p. 322 . ' Zts . fur Kryst 1907 , vol. 42 , p. 265 . . fur Kryst 1901 , vol. 34 , p. 301 . 'Zts . fur Kryst 1880 , vol. 4 , p. 234 . solution in acetic ether , which he describes as monoclinic , with axial ratios\mdash ; and The plane of the tic axes is perpendicular to ( 010 ) , and nearly parallel to ( 001 ) , and there is considerable axial dispersion , . Jaeger*points out hat , it is possible by a suitable choice of ametral faces to obtain similar axial ratios for the crystals of benzylaniline and azobenzene , ( Azobenzene Benzylaniline : yet this would require an unnatural position for the crystals , high indices for some of the forms observed , so that the relation between the two substances is a somewhat distant one . Jaeger gives the ] ting points of pure azobenzene and benzylaniline as and . He also gives the melting points of a few mixtures of these substances , which he states form mixed crystals and show a minimum eutectic point . He obtained mixed crystals of azobenzene and benzylaniline from solution in alcohol and chloroform as small red needles , which were strongly pleochroic , but unsuitable for crystallographic investigation . gives the melting point of azobenzene as , while PickeringS gives Nfixtures of azobenzene and benzylaniline have also been investigated by Bruni and Gorni and by Garelli and Calzolari ; these authors do not , however , oive any poin ts for actual mixtures , but state that azobenzene and benzylaniline form mixed crystals , and exhibit abnormal cryoscopic behaviour . MICROSCOPIC EXAMINATION or AZOBENZENE AND BENZYLANILINE BYSTALLISED FROM FUSION . In the present investigation azobenzene and benzylaniline were first examined under the microscope as a thin film crystallised from fusion on a microscope slide under a cover glass . . cit. 'Zts . fur Kryst 1907 , vol. 42 , p. 265 . 'Zts . fur Kryst 1880 , vol. 4 , p. 234 . S PhiL Mag ( 5 ) , 1895 , vol. 39 , p. 610 . 'Real . Accad . dei Lince 1899 , vol. 8 , pp. 454 and 470 . 'Real . Accad . dei Lincei , ' 1899 , vol. 8 , p. 579 , and 'Gazetta , ' 1910 . ] of Two Substances form Mixed , etc. 347 Azobenzene appears as stout radiating prisms and irregular plates of a fine orange colour . The plates and most of the prisms are stl.ongly pleochroic , the ours being and yellow . The extinction of the prisms is usually straight or nearly so , but on some it is oblique with angles ranging to about . Many of the prisnoe do not become dark at all , but show a strong red and green coloration about the position of extinction , . to strong dispersion of the optic axes . With convergent , some of the prisms with straight extinction show an interference figure resembling that of brookite , with a positive acute bisectrix in the centre of the field . The optic axial plane is parallel to the length of the prisms , and the dispersion , the crystals being nearly uniaxial for red light . The plates commonly show , in sodium light , hyperbolic bands indicating the htly o lique emergence of an obtuse bisectrix or third mean line . These appearances agree with the description of the crystals given by Boeris , prismatic outlines being due to a vertical or oblique position of the thin tabular crystals . Benzylaniline , examined in the same way , showed stout colourless blades growing radially from centres , with approximately straight extinction . In convergent light the needles show a wide angle ative bisectrix , nearly central , the axial plane being perpendicular to the length of the needles . In some of the needles a optic axis is visible at the edge of the field . The plates and needles of azobenzene and benzylaniline obtained from fusion on the microscope slide rarely possess angles measurable under the microscope , their being rounded or ragged . fo1med in drops of azobenzene dissolved in benzene or alcohol were also examined under the microscope . They were rhombs with an angle of and diagonal extinction . Viewed in these rhombs owed obtuse bisectrix or third mean line . Drops of benzylaniline dissolved in toluene or ether gave needles with angle of approximately,.the extinction being always parallel to the length of the needles . Viewed in convergent light these needles showed a normally bisectrix , both optic axes being visible . MIXTURES OF AZOBENZENE AND Mixtures of azobenzene and benzylaniline were next investigated , and the freezing and melting point curves for these mixtures were determined . 348 Miss F. Isaac . Crystallisation , etc. , of Mixtures [ June The Freezing Point Curve . To obtain the freezing point curve the mixtures varying in concentration from 100 per cent. azobenzene to 100 per cent. benzylaniline were enclosed in sealed glass tubes . Each mixture was heated in a water bath until it was completely melted , with the exception of one or small crystals at one end of the tube . These crystals were watched with a lens as the temperature of the bath was lowered , until a temperature was reached at which equilibrium was found to exist between them and the liquid mixture . This temperature , at which the crystals neither grew nor dissolved , was taken as the freezing point of the mixture . This method has been fully The results obtained appear tabulated below:\mdash ; These freezing points , when plotted on the concentration-temperature diagram , give the ordinary -shaped freezing point curve , with a minimul ) or eutectic point at for the mixture 81 per cent. benzylaniline , 19 per cent. azobenzene . On the side which shows excess of benzylaniline this curve is almost a straight line , but on the side showing excess of azobenzene the curve is slightly concave towards the concentration axis . The Melting Point Curve . To obtain the melting point curve the same tubes were used as in the experiments on the freezing point curve . The tubes containing the various mixtures were heated in turn and shaken until the crystals had completely nlelted . Each tube was then cooled , and the liquid mixture allowed to 'Journ . . Soc 1908 , vol. 93 , 1 , p. 931 . 1910 . ] of Two Substances Hixed Crystals , etc. 349 solidify completely . As with all substances forming mixed crystals , the solid first deposited differs in composition from the original liquid , and as the temperature continues to fall , different mixed crystals form , whose composition approximates more and more nearly to that of the liquid , until the very last mixed crystals that form should have the exact composition of the original liquid taken . Crystals of this composition , therefore , have a lower melting point than any of those previously deposited . When the mixture was completely solid the tube was immersed in a cold water bath , the of which was raised very slowly while the solid mixture was watched carefully with a lens . At first the mixtnre is quite compact and solid , but when the temperature has been raised to a certain point some of the crystals are seen to begin to melt ; parts of the mixture appear slightly sticky ; and , on further raising the tenlperature very slightly , if the tube be inverted a little liquid stream starts down the sides . This point is taken as the melting point of a mixture whose composition is the same as that of the original liquid taken . The melting point curve thus obtained agrees very approximately with some later experiments described on pp. 352-4 , in which the point curve was obtained directly by analysis of the mixed crystals . Each experiment was repeated several times , and the temperatule at which melting was first observed was very carefully noted . All the points are thus etermined with rising temperature , the following being the tabulated results:\mdash ; When plotted on the concentration-temperature diagram these points glve the complete point curve . all mixtures of azobenzene and benzylaniline . As will be seen from the , part of the melting VOL. LXXXIV.\mdash ; A. 2 benzylaniline , and per cent. azobenzene per cent. benzylaniline , start melting at the same temperature , . Hence , no mixed crystaJs are deposited on the side of the eutectic weak in azobenzene , only pure benzylaniline , which grows as soon as the temperature given by the point curve is reached , until the mixture reaches the eutectic composition , the rest of the liquid solidifies as a mixture of pure benzylaniline with the mixed crystals containing 35 per cent. azobenzene and 65 per cent. benzylan iline , whose melting point is . This result is confirmed by the ) icroscopic examination of the solidified mixtures as described below . On the other side of the eutectic , however , in mixtures containing excess of azobenzene , a series of mixed crystals are formed which contain from 100 per cent. to 30- per cent. of azobenzene . As has been shown above a mixture of approximately 81 per cent. benzylaniline 19 per cent. azobenzene freezes at , where the curve exhil ) a eutectic point . A mixture of this composition , therefore , melts and freezes very approximately at the same temperature . This is the invariant point , and on either side of it different solids exist in equilibrium with the liquid . At this point four phases can co-exist , namely , mixed crystals containing 35 per cent. of azobenzene , pure benzylaniline , liquid solution , and vapour . The melting point curve was not at first obtained in the form here described . In the first experiments , the flat part of the curve which extends from 65 to 100 per cent. of benzylaniline , appeared only to extend from 65 to 85 percent . of benzylaniline . Mixtures containing between 85 and 975 per cent. benzylaniline , which were allowed to solidify spontaneously in a sealed tube and were then reheated , appeared to start melting at temperatures varying from to , instead of at , as subsequently found . As plotted , therefore , the point curve pointed to the existence of two series of mixed crystals , one on each side of the eutectic . there careful experiments showed , however , that mixed crystals do not really separate on the side of the eutectic containing excess of benzylaniline , but pure benzylaniline only . Experiments made under the microscope by examining the crystals from drops of these mixtures on a slide , showed that the hrst Stals separating from mixtures more than 81 per cent. of benzylaniline are pure white in colour , and show no trace of the orange colour of the azobenzene , and are therefore probably pure benzylamline . But , if pure benzylaniline only is first deposited from these mixtures until the euteotic composition is reached , relnaining liquid will solidify as a mixture of pure benzylaniline with mixed crystals of composition 35 per cent. azobenzene 65 per cent. benzylaniline . All.these mixtures , therefore , since they contain some proportion of mixed crystals of this composition , should start at . As has been stated , this melting point was not at first noticed ; but , in some later experiments , it was found that if the tubes containing the ; mixtures with , and 10 per cent. of azobenzene wele melted so as ' ; to leave a few small crystals in the tube , and then allowed to solidify slowly at not too low a temperature , on tubes a slight elting does occur at . On the other hand , if these same tubes eated until the mixtures are completely liquid , and are then cooled and shaken till they crystallise spontaneously at a low temperature , no can be detected at , but only at from to This discrepancy may , perhaps , be due to the fact that in the latter case the mixtures have crystallised spontaneously in the tubes at temperatures considerably lower than their freezing points . The pure benzylaniline may have formed so suddenly and rapidly that the eutectic composition is overshot , so much benzylaniline coming out of solution that the remaining liquid contains a highel percentage of azobenzene than the eutectic , and consequently forms mixed crystals containing more than 35 per cent. azobenzene , which have higher melting points than . When , however , the same mixtures are allowed to solidify slowly after inoculation with benzylaniline , as stated above , the true point is obtained . In connection with this point it may here be mentioned that it was found possible later on , in some experiments described below , to separate the very first crystals which formed spontaneously in the mixtures of azobenzene and benzylaniline containing small peroentages of azobenzene . If pure benzylaniline is first deposited from these mixtures , the melting point of the crystals which first form should be , the melting point of the pure benzylaniline . It was found that the crystals thus separated from all mixtures on the benzylaniline side of the eutectic , after being washed with benzene to get rid of the mother liquor , all melt at . Thus the first crystals forming spontaneously from all these mixtures have the melting point of pure benzylaniline , and consequently no mixed crystals are formed on this side of the eutectic , but crystals of pure benzylaniline only , in the usual manner of mixtures of two substances which yield the oldinary -shaped point curve . In the experiments made to determine the freezing point curve , the mixtul.es were enclosed in sealed glass tubes , and the temperature of equilibrium was obtained between the liquid and a few small crystals of unknown constitution . If no nlixed crystals are formed on the side of the eutectic showing excess of benzylaniline , the point curve on this part mixture and pure benzylaniline . This was proved to be true by some further experiments , in which mixtures containing 5 , 10 , and 15 per cent. of azobenzene were placed in open test tubes , immersed in a water bath and inoculated with a minute crystal of benzylaniline . The equiliblium points so obtained were found to agree with the freezing point curve obtained above . Th Melting Point Curve Obtained by Analysing the Mixed Crysta:ls . The method of experimenting described above for obtaining the melting point curve appears to be somewhat rough and unsatisfactory ; in order , therefore , to check and confirm this ourve , the melting points of mixed crystals of known composition were determined as follows:\mdash ; Mixtures of azobenzene and benzylaniline of various compositions were dissolved in benzene in a beaker , and the liquid was stirred regularly by means of a water motor while the benzene evaporated slowly . The liquid inoculated with a minute mixed crystal , and as evaporation proceeded a crop of small crystals in equilibrium with the solution was slowly deposited and whirled about in the liquid . When a sufficient quantity of crystals had formed , the solution was filtered off by means of an air pump , and the crystals obtained dry on the filter in a small platinum cone . The crystals were then powdered in a mortar and placed in an exhausted desiccator for several hours to dry off the last traces of benzene . Since these crystals represent a small crop grown from , and in equilibrium with , comparatively large volume of solution , they may be taken to be very approximately homogeneous . If this is so , when placed in a capillary tube they will melt at an approximately constant temperature , and this was found to be usually the case . When the temperature was not quite constant , but extended through a range of 1o or , the mean was taken to represent the true melting point . The melting point for any crop bein ascertained , the crystals were next analysed in order to find their composition . The analysis was carried out by extracting the benzylaniline from a known weight of the crystals with dilute hydrochloric acid , the azobenzene being left undissolved . Three extractions in warm acid were found sufficient to dissolve all the benzylaniline , and the pure azobenzene left behind was dried and weighed . In this manner the composition of the original crystals was obtained . These experiments were repeated with a considerable number of different solutions of azobenzene and benzylaniline in benzene , each solution giving a different set of homogeneous mixed crystals . From these experiments it 1910 . ] of Two Substances uhich form etc. is possible , therefore , to plot the point curve for the azobenzenebenzylaniline mixtures , since the composition and melting point of each homogeneous crop of mixed crystals are known . The following are the details of these experiments:\mdash ; These results , when plotted on the concentration-temperature diagram , should give the melting point curve for the azobenzene-benzylaniline mixtures , each set of crystals giving a point on the curve . Ihese points are all shown on the diagram by . It will be seen that some of these points lie slightly above ) point curve obtained , though , the whole , the new experiments may be considered to confirm the original curve fairly well . The later experiments seem to show , however , that the melting point curve , as plotted from the original experiments , is htly too low . This result might have been expected from a consideration of the method employed , for it was assumed that the last drop of the liquid to solidify gives crystals having the original constitution of the liquid . This would , no doubt , be the case if the cooling of the liquid were sufficiently slow , so that as the mixed crystals grew there was cient time for the equilibrium to be maintained by a continuous the crystals and the liquid . But if the cooling is not sufficiently slow it is probable that the readjustment is incomplete , so that the last mixed crystals formed contain a slightly percen tage of benzylaniline than the original mixture . These crystals would , therefore , have a slightly lower melting point than those having the composition of the liquid . The later experiments , in which the mixtures were analysed , tend to sho that this is the case , although the discrepancy is very , and does not appear to amount to more than approximately 1o of temperature . The , points for azobenzene and benzylaniline obtained above and . On compariug these values with those previously obtained , and agree more nearly with those of Calderon and Pickering , who give the melting point of azobenzene as and respectively . The slightly lower values obtained in these experiments would seem to indicate that in all probability some small amount of impurity exists in the substances used in this research . We may also compare the melting points obtained by Jaeger for the few mixtures of azobenzene and benzylaniline he examined with those obtained above . Jaeger 's values :It will be seen that these values for the rnelting points are considerably higher than those indicated by the diagram . Microscopic mination of tures of Azobenzene and Benzcy tandine ystallised from Fusion . A great number of drops of different mixtures were allowed to crystallise on the microscope slide at the temperature of the surrounding air , and the crystals were examined as they grew . Various mixtul.es , containing 10 , 20 , 30 , 30- , 40 , and 60 per cent. of azobenzene , were examined in this way . The crystal needles first forming in the 10 per cent. mixture were colourless , and some colourless crystals also appeared in the 20 per cent. mixture . The remaining mixtures gave only coloured needles . The crystal needles were always formed with their oblique ends rounded or ragged , so that it was impossible to measure their angles , and when the liquid drop has completely solidified they form a confused mass intersecting each other in all directions . In all the mixtures the extinction was either straight or inclined at 1o or to the length of the needles . Crystals grown from mixtures containing up to 30 per cent. azobenzene , when viewed in convergent light , usually showed both optic axes with the bisectrix nearly normal , although some of the needles showed only one optic axis on the edge of the field . 1910 . ] Two Substcmces lIixed C , etc. 355 Needles rown from mixtures containing over 30 per cent. azobenzene always showed one optic axis only on the of the field . The axial plane vays appears to be nearly perpendicular to the length of the crystal needles . That the rless crystals which first appear in the mixtures weak in azobenzene are pure benzylaniline , is indicated by their optical properties . The coloured crystaJs in the other mixtures are probably mixed crystals of various compositions . Some of these mixtures containing the proportions of Zobenzene are very viscous , and remain partly liquid under a cover glass at the of the room after crystallisation has first started on the oscope slide . Although these experiments were repeated several times , the results obtained do not appear to lead to very definite conclusions , the crystal eedles being always ill-formed , with ragged edges . The temperature at which the needles grew on the slide was about or , so that it was con- siderably lower than the temperature at any point of the freezing point curve . The conditions of growth are therefore quite different , and these lower temperatures the composition of the crystals separating from any liquid may differ from the composition of crystals from a similar drop at temperatures between the and melting point curves determined above . Supersolubilitly \ldquo ; of ontancons jstallisation . The freezing and melting point curves for mixtures of azobenzene and benzylaniline been determine an attempt was next made to plot the curve of spontaneous crystallisation for these mixtures , as has already been done for of naphthalene and -naphthol . Two methods of were employed , both of which have been used in the previous esearches with Prof. Miers on spontaneous crystallisation , . : ( 1 ) the method of sealed tubes ; ( 2 ) the measurement of the 1efractive indices of cooling mixtures . ( 1 ) Scaled Azobenzene , benzylaniline , and their mixtures were enclosed in sealed lass tubes which also contained some angular ments of corundtun to en sure friction . The tubes containing the various mixtures were then heated in a water bath with frequent shaking until all the crystals had completely melted . The water bath then allowed to cool slowly , and as the temperatme fell the tubes were continuously , either by hand or on a rocking apparatus placed within the water bath . With each mixture found that when the temperature had fallen to a certain point , a dense shower of crystals suddenly appeared in the tube and the whole mixture rapidly 356 Miss F. Isaac . , etc. , of Mixtures [ June 21 , became solid . The temperature at which the shower occurs depends upon the composition of the mixture , and was found to be approximately constant for each mixture . . The experiment with each tube was , in eneral , repeated several times ; the following table gives all the results obtained from 16 tubes treated in this manner:\mdash ; These results , when plotted on the concentration-temperature give the complete supersolubility curve , or curve of spontaneous crystallisa- tion , for azobenzene , benzylaniline , and their mixtules . Where there was a slight variation in the temperature of spontaneous crystallisation of a single tube , the temperature obtained has been always taken as the true temperature of spontaneous crystallisation ; in the other experiments the mixture must passed slightly into the labile state , probably in consequence of too rapid cooling . This curve , which is shown on the diagram , separates the metastable and labile areas for all mixtures of azobenzene and benzylaniline . Above this curve the mixed crystals cannot form spontaneously , although they after inoculation , but below it mixed crystals can , and do , form spontaneously in a shower . As will be seen from the diagram the supersolubility curve runs roughly parallel to the freezing point curve . On the left hand side of the eutectic composition it crosses the . point curve twice , and on the hand side of the eutectic it again crosses the melting point curve . Near the eutectic composition the supersolubility curve reaches a minimum , and for mixtures containing from 70 to 90 per cent. of benzylaniline the 1910 . ] of Two lohich forr Mixed ystals , etc. 357 supersolubility curve is very flat , temperatures of spontaneous crystallisation for these mixtures only varying about ( 2 ) The Refractive of \mdash ; An attempt was now made to verify the supersolubility curve just obtained by observing the sudden 'change in the index of refraction which takes place on the curve . This method has been used before to obtain the supersolubility curve for mixtures of salol and betol and for various aqueous solutions of salts , \amp ; The liquid mixtures were heated and placed iu the of the inverted goniometer and their refractive indices determined as they cooled the method of total reflection within a dense glass prism immersed in the liquid . With the aqueous solutions examined in this manner it was found that the refractive index rose steadily till the labile temperature reached . Here a dense shower of crystals occurred , which soon settled at the ) oltom of the goniometer trough , the refractive index afterwards continually the temperature fell . The mixtures of azobenzene and benzylaniline were examined in this manner from the time when the warn ] mixture was first placed in the until the dense shower occurred at the labile temperature . As with the mixtures of salol and betol already examined , it almost impossible to determine the refractive index beyond this point , to the }lsit of the shower , the crystals remaining suspended in the liquid instead of to the bottom of the as with the aqueous solutions of , and thus rendering the mixtures almost opaque . The mixtures of azobenzene and benzylaniline examined contained to 100 per cent. of benzylaniline . In these it was found that the index rose gradually and as the temperature fell , until the dense labile shower of crystals occurred . Mixtures containing more than 50 per cent. of azobenzene were not examined , as they were somewhat viscous , and consequently intense concentration streams arise , which cause ritiesn in the index-temperature curves , and also because their temperatures of spontaneous crystallisation render them unsuitable for use in the goniometer trough . As the mixtures cooled in the trough they were con tinually by means of a small platinum vane driven by an electric motol . The liquid mixtures being somewhat deep red in colour , it was found that the monochromatic light of the sodium flame was nearly absorbed , and that the edge of the shadow total internal reflections could hardly be seen . White light was therefore used to illuminate the prism , a piece of ' Roy . Soc. Proc 190 , vol. , p. 322 ; Jourll . Chem. Soc 1908 , vol. 93 , p. 384 . occurring in the mixtures at the labile temperature is always accompanied by a considerable rise in temperature . The following are the general results of the experiments on the refractive indices of mixtures of azobenzene and benzylaniline . Experiment l.\mdash ; Azobenzene per cent. Benzylaniline The index rose from at to at . A dense shower occurred at and the temperature rose to Experiment 2.\mdash ; Azobenzene per cent. approx. Benzylaniline The index rose from at to at . A dense shower occurred at , the temperature rising to Experiment 3.\mdash ; Azobenzene per cent. approx. Benzylaniline \ldquo ; The index rose from at to at . A very dense shower occurred at , the temperature rising to Experiment 4.\mdash ; Azobenzene per cent. Benzylaniline The index rose from at to at . A shower of crystals occurreJ at and the temperature rose to Experiment 5.\mdash ; Azobenzene per cent. Benzylaniline The index rose from at to at . A shower of crystals occurred at and the temperature rose to Experiment 6.\mdash ; Azobenzene per cent. Benzylaniline The index rose from at to 1.62937 at . A slight shower began to form spontaneously at and became gradually denser without change of temperature . Experiment 7.\mdash ; Azobenzene per cent. approx. Benzylaniline , , The index rose from at to at . A shower of crystals occurred at and the temperature rose to Experiment 8.\mdash ; Azobenzene per cent. Benzylaniline The index rose from at to at . A shower occurred at the temperature rising to and the index . At the index had fallen to 1910 . ] of form . 359 Experiment 9.\mdash ; The same mixture wa used as iu Experiment 8 . The index rose frolu at to at . A dense shower occurred at , but no more readings for the index were possible . The temperature rose to Experiment 10.\mdash ; Azobenzene per cent. zylaniline The index rose from at to at . A shower of , occurred at and the temperature rose to 20 The index fell again during the shower and reached Experiment 1].\mdash ; Azobenzene per cent. approx. Benzylaniline The index rose from at to at dense shower of btals occurred at this temperature and no more readings were possible . The temperature rose to Experiment 12.\mdash ; Azobenzene per cent. Benzylaniline The index rose from at to at . A of crystials occurred at this temperature and the index fell with rise of temperature , reaching at Experiment 13.\mdash ; tzobenzene per cent. Benzylaniline The index rose from at to at . A dense shower occurred at , the temperature rose to and the index fell to at temperature . Experiment 14.\mdash ; Azobenzene per cent. Benzylaniline The index rose from at to at ystals first appeared at and a dense shower occurred at , the temperature then rising to From experiments 1 , 4 , 5 , 6 , 8 , 10 and 13 , in which the exact composition of the mixtures is known , it is possible to ascertain the refractive index of any given mixture at any temperature . The results of all these experiments , taken ether , may be expressed by curves drawn with concentrations as abscissae and temperatures as ordinates , the refractive index being constant for each curve . Such curves were drawn for the following values of index : , 1624 , . They were found to be very approximately straight lines , equidistant and parallel to each other , and inclined to the concentration axis at an angle of , the scale chosen being such that 10 per cent. on the concentration axis corresponds to on the temperature axis . , if a line be drawn on the concentrationtemperature perpendicular to these lines of constant index , and , therefore , inclined at an angle to the concentration axis , the refractive The curves of constant index are shown on the , and from these it is possible to plot the ] series of observations of refractive indices obtained in the above experiments . ( See p. 363 . ) These experiments give a number of curves , numbered 1 to 14 on the diagram , the number of the curve corresponding to the number of the experiment . The curves show slight irregularities , especia ] lie at high temperatures . These irregularities are probably due to concentration-streams , which are particularly marked when the liquid mixture is first introduced into the goniometer trough . On the whole , however , the curves go straight down the and show very iittle variation in concentration as the mixtures cool , until the labile shower occurs at points which lie very approximately on the supersolubility curve already obtained by the method of sealed tubes . These results , obtained from the refractive indices of the mixtures , therefore confirm those already obtained from the experiments with sealed tubes , by which the position of the supersolubility curve was first established . In two or three of the experiments , in which it was possible to trace the refractive index after the labile shower had un , it was found that the index attained a maximum value on the supersolubility curve and then fell again with rise of ) perature and approached the freezing point curve . This behaviour is seen in experiments 10 , 12 and 13 . In eIleral , however , it is not possible to trace the change of index with any certainty after the shower has occurred , the shower being usually so dense as to render the mixture opaque . The crystals which first separate from the mixtures during the showers were examined from time to time under the microscope , but no definite conclusions as to their nature could be drawn from the observations . The crystals were always needles and showed straight extinction . Their were never measurable under the microscope . An interference was usually visible ; sometimes both optic axes were seen with the bisectrix normal , and sometimes only one optic axis was visible , surrounded by , the birefringence being always positive . of the Crystats on the bility C The supersolubility curve hayincr been determined by the above experiments , an attempt was now made to ascertain the composition of the crystals which first form spontaneously on the supersolubility curve for various mixtures . In order to do this for any mixture it is necessary to separate the first crystals which form in labile shower . 1910 . ] of Two Substances which form Crystals , etc. 361 )aratus was deyised by Prof. Bowman , A wide tube A is drawn out at the lower end to forul -tube , the end of which is bent again and passes through a into the tube D. This -tube is immersed in a large -bath E. Another tube passes the of the iube and connects it with the vacuum flask and air pump . By means of the tap this connection may opened or closed at will . At the bottom of the tube A is a porcelain filter-plate covered with a filter-paper . The liquid to be experimented upon is placed in the -tube at a high temperature , the water-bath having been previously heated . The liquid in the -tube is stirred continuously and steadily by means of a plunging irrel , driven by an electric motor . By far the greater part of the liquid 1nixture is contained in the wide part A of the -tube , and is allowed to cool very slowly in the water-bath . As soon as the liquid reaches the labile temperature a shower of crystals begins to form in the tube A. The tap is then immediately turned and the liquid mixture bucked off into the tube leaving the first crystals that form in the shower dry and free from mother liquor upon the filter-paper in A. A thermometer was placed in the waterbath , which was kept stirred throughout the experiment by the glass stirrer G. The melting point of the crystals left in the tube A was then obtained from time to time under the microscope , by which means the first melting . at the edges of the als were easily detected . It is necessary to catch the shower in the U-tube at once so as to separate the first crystals that form . If the tap connecting the tube , A with the vacuum flask is not turned immediately the first crvstals appear , too much solid forms in , and the filter-paper is left with a large mass of crystals on it , instead of only the first few crystals which form . Sometimes the liquid mixture solidifies at the narrow upper end of the -tube when running off into . and this prevents the mother liquor from being properly drawn away from the first crystals on the filter . Usually , , if the mixture is very carefully watched , it is possible to isolate the first crystals of the labile shower , and though they are always extremely small and brittle needles they have clear sharp , and appear quite free from the mother liquor . The following results were obtained with this apparatus , the crystals being always examined in capillary tubes as stated above . 1 . Mixture containing 40 per cent. benzylaniline ; 60 per cent. azobenzene . \mdash ; This mixture was placed in the -tube at about and cooled slowly in the water-bath whilst it was stirred continuously . It crystallised spontaneously very suddenly at a somewhat high temperature , , and it was found extremely difficult to draw off the mother liquor with sufficient rapidity to ensure the first crystals that formed being left clean on the filter . The experiment had therefore to be repeated several times before any definite result was obtained . At , however , the liquid was drawn off , a few of the very first crystals of the labile shower on the filter . When examined in a capillary tube these showed a definite point at . The shows thali mixed crystals whose point is have a composition approximately 35 per cent. benzylaniline , per cent. azobenzene . This , therefore , appears to be the composition of the crystals separating spontaneously from a liquid mixture containing 40 per cent. benzylaniline and 60 per cent. azobenzene . Another experiment with the same liquid mixture yielded a larger crop of crystals on the filter . These appeared to be quite dry and free from mother liquor , but the melting point of different samples did not appear to be quite the crystals melting at , and . The composition of these crystals would appear therefore to vary from 36 per cent. benzylaniline with 64 per cent. , to 34 per cent. benzylaniline with 66 per cent. azobenzene . 2 . Mixture containing . per cent. benzylaniline ; 50 per cent. azobenzene . 1910 . ] of Two Substances which , etc. 363 containing 50 per cent. azobenzene with 50 per cent. benzylaniline . 3 . Mixture containing 61- ) per cent. benzylaniline ; 35 per cent. azobenzene . \mdash ; This mixture was placed in the -tube at and stirred steadily . A shower of crystals began to form at the labile temperature , and the first crystals were easily separated , since in this mixture the shower does not form so suddenly throughout the liquid as is the case with mixtures containing a higher of azobenzene . Three samples were examined in capillary tubes and found to melt at temperatures between and their composition therefore varying from per cent. benzylaniline with per cent. azobenzene , to 61 per cent. benzylamline with 39 per cent. azobenzene . 4 . Mixture per cent. benzylaniline ; 20- per cent. azobenzene . \mdash ; This mixture was placed in the -tube at . At a shower began to form in the tube . This was separated from the rest of the liquid and the crystals examined in capillary tubes . They were found to start melting at . The capillary tubes must therefore contain some mixed crystals of constitution 65 per cent. benzylaniline , per cent. azobenzene , which melt at , and the limit beyond which mixed crystals are not formed , rest of the mixture in the capillary tubes presumably pure benzylaniline . Another expeliment was made with the same mixture by the same method . In this experiment it was noticed that the shower began to form at with a very few small needle-shaped crystals and radial groups , and a thick shower did not come down immediately . These small crystals were separated in the usual way and washed with a few } ) of benzene while still on the filter in the -tube , the benzene being at once drawn off by means of the filter pump . They were then examined under the cope and placed in capillary tubes . Some of them were pure white in colour , and some showed traces of the orange colour of the azobenzene . The colourless crystals in the capillary tubes when slowly heated in a water-bath showed no sign of melti1lg till the temperature was raised to , the . point of pure benzylaniline . The crystals which showed some sign of the azobenzene colour , however , all began to melt very slightly at . It would therefore appear that the first crystals to 1910 . of which . form Mixed Crystals , etc. 365 form spontaneously from a mixture containing } ) cent. benzylaniline and 25 per cent. azobenzene consist of a mixture of pure benzylaniline and mixed crystals containing 35 per cent. azobenzene with 60- per cent. benzylaniline . 5 . Mixture containing per cent. benzylaniline ; per cent. azobenzene.\mdash ; This mixture also was placed in the -tube at and stirred as it cooled from this temperature to in hours . A slight shower commenced at , and was immediately separated from the rest of the liquid . The crystals thus obtained showed some of the colour of the azobenzene , and examined in capillsry tubes to melt at . They therefore probably contain some proportion of the mixed crystals of composition 35 per ceut . azobenzene , 65 per cent. benz.ylaniline . The experiment was repeated in the same way , but in this case the first crystals at were washed several times with benzene while still on the filter in the -tube . When examined in capillary tubes these crystals did not melt till the temperature was raised to , and under the microscope they appeared to be pure white in colour . Pure benzylaniline , therefore , apparently first separates spontaneously from this mixture , and if the crystals are freed from mother liquor by vashing with benzene , the point of pure benzylaniline is attained . 6 . Mixture containing 90 per cent. benzylaniline ; cent. azobenzene . \mdash ; This mixture was placed in the -tube at and cooled very A slight shower commenced at , the crystals of which were easily separated by means of the yacuum pump . The crystals were small radial groups . They were washed with benzene whilst still on the filter in the -tube , the benzene being at once drawn off with the vacuum pump . These crystals were colourless , and when placed in capillary tubes melted at the melting point of pure benzylaniline . If , however , the crystals were not washed with benzene before they were examined , they appeared to be yellowish in colour , and showed signs of melting at . This would be accounted for by the presence of the mother liquor the crystals . 7 . Mixture per cent. benzylaniline ; per cent. azobenzene.\mdash ; This mixture , placed in the -tube apparatus at about cooled in the same manner , gave a shower of crystal needles and radialgroups at the labile temperature , . These were easily separated since the shower takes some time to thicken . They were washed two or three times with a few drops of benzene whilst still on the filter in the -tube , and placed in capillary ) did not melt until the temperature was raised to . They were also quite colourless , and were therefore apparently pure benzylaniline . VOL LXXXIV.\mdash ; A. ) 366 Miss F. Isaac . llisation , etc. , xtures [ June 21 , From these experiments it will be seen that in general , with mixtures which contain a larger amount of azobenzene than the eutectic composition , the crystals which first separate spontaneously on the supersolubility curve contain a larger percentage of azobenzene than does the original mixture . In general , for such mixtures , the supersolubility curve was found to lie above the melting-point curve . From the results obtained , efore , with these mixtures , we see that the composition of the first crystals separating spontaneously at any point on the supersolubility curve is very approximately given by drawing a line from this point parallel to the concentration axis to meet the melting point curve . The point in which the line so drawn meets the melting point curve gives the approximate composition of the crystals which have first separated from the mixture under examination . With mixtures which contain a larger amount of benzylaniline than the eutectic composition , however , the crystals which first separate have been shown above to be pure benzylaniline . In the case of mixtures which approximate to the eutectic composition , it has been shown that the crystals first are frequently a mixture of pure benzylaniline with mixed crystals of 35 per cent. azobenzene and 65 per cent. benzylaniline , the limiting composition . Thin Sections from Mixtures of Azobenzene and Benzylaniline . An attempt was made to study the structure of a few of the solidified mixtures under the microscope . To do this thin sections were made from the mixtures that had solidified completely in glass tubes . The glass tube was broken and the solid rod of mixture removed . Discs and longitudinal sections were cut from this with a fret-saw , and then ground on ground-glass plates until they were sufficiently thin and transparent for microscopic examination . Sections were cut in this way from the following mixtures:\mdash ; 1 . Mixture containing 30 per cent. azobenzene and 70 per cent. benzylaniline.\mdash ; This mixture crystallised spontaneously while shaken continually in a sealed tube . When ground into thin sections showed a large quantity of yellow rod-shaped crystals small in size , and distributed irregularly all over the , also some radial groups growing from centres . These are probably mixed crystals of the limiting composition , i.e. with 35 per cent. azobenzene and 66 per cent. benzylaniline . The rest of the section is filled up with large colourless crystals of presumably pure benzylaniline . Under the microscope these exhibit ophitic structure and extinguish in large patches all over the slide , and have probably grown at rest after the shower of mixed crystals has occurred . This mixture was not ground into thin sections until it had been solid in a glass tube for several weeks . 2 . Mixture containing 10 per cent. azobenzene and 90 per cent. benzylaniline.\mdash ; This mixture also crystallised spontaneously while shaken continually in a sealed tube . This 1910 . ] of Substances for , etc. 367 section showed a mass of small white crystaIs , with small yellow crystals filling up the spaces between them . No regular arrangement could be observed , and the were all more or rod shaped . After this section had been left for four weeks at a temperature of about , it was observed that a new growth was taking piace at the surface of the section . formed thin rods could be seen quite clearly , ving out of the solid , the rods being both yellow and white in colour . 3 . lsIixture containing per cent. azobenzene and per cent. benzylaniline.\mdash ; CrystaFised pont tneously . Sections cut from this mixture large , pure white crystals of benzylaniline , growing as large compact masses which exti u together , and also as large radial groups . Small rod-shaped yellow fill up the gaps . After these sections had been kept for a few weeks at about also showed tinct signs of egation . Jder the high of the microscope thin rods can be seen growing up all over the surface of iihe sections . 4 . Mixture containing 5 per cent. azobenzene and per cent. niline.\mdash ; Crystallised spontaneously while shaken continually . Thin sections cut from this mixture much the appearance of the sections of ( 3 ) above , but the Cl.ystals are much smaller and arranged over the slide . After keeping sections for some weeks at a temperature , they thin rods growing up over their urface when examined under the high power of the microsoope . The study of the thin sections seems to indicate that , in mixtules wea in zene , changes take place in the solid solutions when they iven sufficient ti1ne . It be seen this up , or ation , does appeal to occur in sections ( 1 ) above , but it is to be noted these secticn were not ground until the mixture had been solid for some weeks at tlJe emperature of the room , . about . It is probable , therefore , the change had already place before the section round , and that equilibrium had already been established between the solid solution and the benzylaniline at this temperature . The sections ground within a few hours of having soJidified , so that the structures oserved would correspond to equilibrium at the temperatures ooiven by the supersolubility curve ; since , presumably , sufficient time had not elapsed for them to attain equilibrium at the temperature of the room . Hence , begin to show themselves later in the solid section , readjustment of the components of the mixed crystals taking place until is finally established at the ordinary air temperature . After the lapse of three winter months these sections were all examined under a high power . lt was found that they had all undergone considerable further , and very little of their original structure was recognisable . Sections ( 1 ) , which hree months before showed no sig of breaking up , had now entirely , and were riddled with minute crystal needles , both yellow and colourless . It was also noted that in 368 of which form Mixed , several of the sections the small newly formed needles were arranged in parallel positions over the surface . Conclusion . The results obtained iu this researcl ] may be thus summarised:\mdash ; 1 . The freezing and point curves for mixtures of azobenzene and benzylaniline have been determined , and it has been shown that these substances possess a minimum or eutectic point at for the mixture per cent. azobenzene and 81 per cent. benzylaniline , and form a series of mixed crystals on one side only of the eutectic , viz. , that with excess of azobenzene . This is , therefore , a limiting case of oozeboom 's Type 5 , in which two substances , A and , possess freezing and melting point curves which exhibit a minimum eutectic point , and form two series of mixed crystals , . mixed crystals excess of , and mixed crystals containing excess of B. 2 . The point curve has been confirmed by actual analysis of the mixed crystals . 3 . The supersolubility curve , or curve of spontaneous crystallisation , has been determined for these mixtures by two methods : ( 1 ) by noting the temperature at which a liquid mixture of known composition crystallises spontaneously in a sealed tube ; ( 2 ) by noting the tempel.ature at which a known liquid mixture attains its highest refractive index , and gives a dense labile shower when placed in the trough of the inverted goniometer . By these methods it has been shown that each mixture possesses a definite temperature of spontaneous crystailisation . The supersolubility curve shows a minimum for liquids having approximately the eutectic composition , and runs approximately parallel to the freezing point curve . It crosses the melting point curve three times as shown in the 4 . The nature of the mixed crystals which first separate spontaneously from any liquid mixture on the supersolubility curve has been investigated . The composition of such crystals been determined by separating them from their mother liquor and finding their elting points . 5 . A few thin sections have been ground from the solid mixtures in the neighbourhood of the eutectic , and their structures examined . These stl.uctures do not appear to be permanent , and after the lapse of some months they had completely changed , new crystal needles having appeared all over the sections . These changes , however , appear to be very gradual and to take place with change of temperature . Distribution of in Space . The analysis of these mixtures was carried out in the Balliol and inity Laboratory , Oxford , by permission of Messrs. Nagel and Hartley , to whom I am much inciebted for their kind help and advice . I also take this opportunity of expressing my grateful thanks to Principal H. A. Miers and to Prof. Bowman for the helpful criticism and dvice they have given me throughout the course of this research . On thoe bility of a Distribntion of the Stars in Space . By F. W. , F.R.S. ( Received July 9 , 1910 . ) In a recent paper*Prof . Pearson obtains the following results:\mdash ; ( i ) If when denotes the parallax of a star , and be the standard deyiabion , ' square root of the mean square devi tion of a series of values of from the mean ; theJl , for a uniform distribution of stars in space , ( ii ) If be the mean magnitude of all stars down to and those of magnitude , then , and 1 . The first of these results is compared with the values of , obtained from a list of 72 parallaxes of stars given in Newcomb 's ' The Stars : A Study of the Universe , ' and with those of 163 stars given in 'Trans . Yale Univ. Observatory , ' Vol. II . For Newcomb 's stars and for the Yale stars , The inference that these stars are not evenly distributed in space may be obtained more easily . the Yale stars there ( ' Trans. Yale Univ. Observatory , ' Vol. II , p. 200-)\mdash ; 17 stars with parallax to and 30 , , , , , , With a uniform distribution , or 136 stars , may be expected to parallaxes from to , if there are 17 with parallaxes from to ; and a larger number than 136 between limits and ' Roy . Soc. Proc , vol. 84 , pp. 47\mdash ; 70 .

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On the improbability of a random distribution of the Stars in Space.

369

371

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

F. W. Dyson, M. A., F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1910.0080

en

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1910_0080

10.1098/rspa.1910.0080

Tables

Astronomy

Tables

]\gt ; Distribution of in Space . The analysis of these mixtures was carried out in the Balliol and inity Laboratory , Oxford , by permission of Messrs. Nagel and Hartley , to whom I am much inciebted for their kind help and advice . I also take this opportunity of expressing my grateful thanks to Principal H. A. Miers and to Prof. Bowman for the helpful criticism and dvice they have given me throughout the course of this research . On thoe bility of a Distribntion of the Stars in Space . By F. W. , F.R.S. ( Received July 9 , 1910 . ) In a recent paper*Prof . Pearson obtains the following results:\mdash ; ( i ) If when denotes the parallax of a star , and be the standard deyiabion , ' square root of the mean square devi tion of a series of values of from the mean ; theJl , for a uniform distribution of stars in space , ( ii ) If be the mean magnitude of all stars down to and those of magnitude , then , and 1 . The first of these results is compared with the values of , obtained from a list of 72 parallaxes of stars given in Newcomb 's ' The Stars : A Study of the Universe , ' and with those of 163 stars given in 'Trans . Yale Univ. Observatory , ' Vol. II . For Newcomb 's stars and for the Yale stars , The inference that these stars are not evenly distributed in space may be obtained more easily . the Yale stars there ( ' Trans. Yale Univ. Observatory , ' Vol. II , p. 200-)\mdash ; 17 stars with parallax to and 30 , , , , , , With a uniform distribution , or 136 stars , may be expected to parallaxes from to , if there are 17 with parallaxes from to ; and a larger number than 136 between limits and ' Roy . Soc. Proc , vol. 84 , pp. 47\mdash ; 70 . 370 Improbability of Distribution of the Stars in But no inferences can be drawn from these figures as to the distribution of the stars in general . These particular stars were selected for observation largely on account of their great proper motions . This criterion was successful in leading to the discovery of 17 very near stars . 2 . The formulae , and , are immediately deducible from the proposition that for a uniform distribution of stars , and assuming no absorption of light , the total number of stars down to magnitude is given by In this well-known formula , is the ratio of ' the amount of received from two stars which differ by one nitude . A formal proof of the fomlula may be given as follows:\mdash ; Let be the number of stars contained in unit volume , of magnitude 7 ' or hter , as seen from unit distance . A thin spherical shell of radius will contain of such stars . Now if a star is of magnitude at unit distance , its magnitude at distance is . Thus equals the number of in the shell which , seen from the centre , appear to be of nitude Therefore the total number of stars down to nitude m is given by . Thus , where Therefore 3 . Writing this in the form or ; and , similarly , Thus Prof. Pearson 's formulae follow directly from the law and no assumption is made with to the form of . The assumption is , however , made that the stars extend to infinity and that there is no absorption of light in space . 4 . Now in the table quoted by Prof. earson from the ' Harvard Annals , ' the numbers of stars as far as nitude 7 roughly agree with the formula Conditions for Discontinuous Motion in . 371 from which and are deducible , values which with those found by Prof. Pearson . 5 . It does not seem to me that 's catalogue of double stars can be used as a basis for a discussion of the departure of the actual distribution of the stars from a random distribution . As far as magnitude , Hussy and Aitken have made systematic search for all double stars . Beyond this tYnitude no systematic search has been made . Further , the definition of a double star is a very elastic one . Thus on page 1 of Burnham 's catalogue , Andromedae with a companion of magnitude at a distance of is counted as a double star . Two faint stars of magnitude or at this distance would not be classified as double , and the raphs taken for the Astrogra } ) contain many such stars . The in By G. I. TAYLOR , B.A. , Trinity College , ( Communicated by Prof. Sir Joseph Larmor , Sec. R.S. Received July 11 , 1910 . ) The possibility of the propagation of a surface of discontinuity in a was first considered by Stohes*in his paper " " On a Difficulty in the Theory of Sound This paper begins with a physical interpretation of Poisson 's integral of the equation of motion of a in one dimension . The in question is ; and it represents a disturbance of finite amplitude moving in a gas for which the velocity of propagation of an infinitesimal disturbance is is the velocity of the in the direction of the axis . It is shown that the parts of the waves in which the velocity of the gas is travel forward with a velocity , and that there is in consequence a tendency for the crests to catch up the troughs . After a certain time , and at a certain point in space , the value of will become negatively infinite ; a discontinuity will then occur , and Poisson 's will cease to apply . Stokes then leaves the subject of oscillatory waves and proceeds to consider whether it is possible to maintain a sharp discontinuity in a gas which obeys Boyle 's law . His meant , slightly modified by Lord Rayleigh , is as follows:\mdash ; Suppose that a travelling discontinuity can exist . Give the whole gas 'Phil . Mag 1848 , vol. 33 , p. 349 ; 'Collected Papers , ' vol. 1 .

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0950-1207

The conditions necessary for discontinuous motion in gases.

371

377

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

G. I. Taylor, B. A.|Prof. Sir Joseph Larmor, Sec. R. S.

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6.0.4

http://dx.doi.org/10.1098/rspa.1910.0081

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1910_0081

10.1098/rspa.1910.0081

Fluid Dynamics

Tables

Fluid Dynamics

]\gt ; Conditions for Discontinuous Motion in . 371 from which and are deducible , values which with those found by Prof. Pearson . 5 . It does not seem to me that 's catalogue of double stars can be used as a basis for a discussion of the departure of the actual distribution of the stars from a random distribution . As far as magnitude , Hussy and Aitken have made systematic search for all double stars . Beyond this tYnitude no systematic search has been made . Further , the definition of a double star is a very elastic one . Thus on page 1 of Burnham 's catalogue , Andromedae with a companion of magnitude at a distance of is counted as a double star . Two faint stars of magnitude or at this distance would not be classified as double , and the raphs taken for the Astrogra } ) contain many such stars . The in By G. I. TAYLOR , B.A. , Trinity College , ( Communicated by Prof. Sir Joseph Larmor , Sec. R.S. Received July 11 , 1910 . ) The possibility of the propagation of a surface of discontinuity in a was first considered by Stohes*in his paper " " On a Difficulty in the Theory of Sound This paper begins with a physical interpretation of Poisson 's integral of the equation of motion of a in one dimension . The in question is ; and it represents a disturbance of finite amplitude moving in a gas for which the velocity of propagation of an infinitesimal disturbance is is the velocity of the in the direction of the axis . It is shown that the parts of the waves in which the velocity of the gas is travel forward with a velocity , and that there is in consequence a tendency for the crests to catch up the troughs . After a certain time , and at a certain point in space , the value of will become negatively infinite ; a discontinuity will then occur , and Poisson 's will cease to apply . Stokes then leaves the subject of oscillatory waves and proceeds to consider whether it is possible to maintain a sharp discontinuity in a gas which obeys Boyle 's law . His meant , slightly modified by Lord Rayleigh , is as follows:\mdash ; Suppose that a travelling discontinuity can exist . Give the whole gas 'Phil . Mag 1848 , vol. 33 , p. 349 ; 'Collected Papers , ' vol. 1 . uniformly at this speed . Let and be the corresponding densities , and the corresponding pressures . The equation of continuity of mass is . ( 1 ) ! The equation of conservation of momentum is . ( 2 ) If and be given , these two equations determine and Against this theory , however , Lord Rayleigh* raised the objection that the equation of energy , , cannot , in general , be satisfied simultaneously with ( 1 ) and ( 2 ) . In a recent note he adds a remark that it is possible that energy might be lost at the discontinuity , but it cannot be supposed that energy is gained . Lord ayleigh further points out that the energy lost must be converted into heat , and that this complication must be taken into account . This has been done by C. and by Hugoniot , S but their equations have the same as those of Stokes , in that they contain no indication that the motion represented by them is irreversible . In the case considered by Stokes it is evident that the motion is in fact , it is only the front of a compression that can possibly travel unchanged . For , if for an instant the sharp discontinuity were to disappear , leaving a small transition layer in which the elocity might vary continuously from to , then the back part of the layer would travel forward relatively to the front part with a velocity . Hence if exceeds any such transition layer will become obliterated owing to the greater velocity behind , and the discontinuity will thus be maintained . This is the case of the front of a wave of condensation . If , however , the wave is wave of rarefaction , that is , if is less than , then the layer of transition will get wider , and the sharp discontinuity will not be re-established . The object of this paper is to discuss in detail what actually does occur at a discontinuity , and to determine , in the general case of a gas whose chal'acteristics are known , whether a discontinuity obtained by the method Stokes is a physically possible feature . 'Theory of Sound , ' vol. 2 , p. 41 . . Soc. Proc , 1908 , vol. 81 , p. 449 . ' Phil. Mag 1893 , vol. 35 , p. 317 . S See ' Hydrodynamics , ' note on p. 466 , 3rd edition $ 1910 . ] for It is evident that a plane of absolutely sharp or nlathematical discontinuity cannot occur in any real When , owing type , there sudden compression or rarefaction of the material in any boundary , modified physical laws must come into operation whose effect is to prevenlt abrupt discontinuity from being formed . Some clue to the nature of the processes involved in this case is afforded by the kinetic theory of gases ; for when the in velocity is very sudden , the molecules which are moving faster will penetrate anJong those which are moving more slowly , and an irreversible ledistribution of velocities will ensue . This ests that heat conduction and viscosity are , in the case of a real gas , the causes of the production of dissipative heat ; it will be shown that under certain conditions they are also sufficient to produce permanence of type in the layer of transition . Consider a continuous disturbance of permanent type in a cras whose characteristic equations are known . Give the whole such a velocity that the disturbance is to rest ; the motion is then steady . Let A and be two planes which move with the gas , let and , be the pressure , density , velocity , and internal of mass of the gas at A and respectively . Since , the temperature , is a function of and , and is a known function of , and , therefore may be regarded as a function of } ) tjndent variables and The equation of continuity of matter is The rate of gain of momentum between and is The equation of momentum for the gas between A and is therefore where X and X ' are the viscous normal forces which act over the planes and A respectively . The work done on the between A and in a small interval of time is The increase of its kinetic energy in time is The increase in internal energy in the same time is ( E-E ' ) The amount of heat conducted away from the mass of between A and in time is , where and are the rates which heat , measured in mechanical units , is conducted across the planes and A. The equation of energy for the gas between A and is therefore abscissa . If and are the points which represent the state of the gas at the two ends of the transition layer in which the velocity changes from to , then the state of the . that layer are represented by the points on some curved line joining and D. It will be possible by means of equations ( 4 ) and ( 5 ) to determine of X and so that any given lin joining and may represent the state of the in the transition layer ; but the motion so represented will not be thermodynamically possible unless the coefficients of conduction and viscosity are both positive . If represents distance in the direction in which the gas is , these conditions become X and must have opposite and must have opposite Hence at the front of a condensation X is positive and is negative while for a rarefaction X is ative and is positive . Construct curves NI and to represent the relations obtaining between and when and when respectively . Lt , and represent the pressures at points on , and corresponding to a particular value of the density . The equation to is obtained by dropping X from ( 4 ) , and is and since ( 4 ) yives therefore Similarly it can be shown that 1910 . for Discontinuous in Gases . 375 In a condensation therefore and , and in a rarefaction and Also where is the specific heat at constant volume ; and must be of the same as ; hence in a condensation , and in a rarefaction Now the equations to the lines and depend only on the relations which exist between pressure , density , temperature , and internal , that is on the characteristic equations of the gas , and not at all on its viscosity or its conductivity ; for if either X or is small the other can be eliminated . Hence if a discontinuity is specified by the equations two uniform states between which it lies , and it is desired to find out whether it is thermodynamically possible , the lines and joining and , which are the points representing the states of the on the two sides of the discontinuity . If the line lies above the line ( see diagram ) so that is greater than then a condensation is possible . If the line lies below the line a rarefaction is possible . If the line cuts the line at any point between and , neither is possible . The only special case of any importance is that of a perfect whose characteristic equations are , where is the ratio of the specific heats . The general criterion is as above ; but if we also assume constant conductivity and viscosity , the circumstances can be followed out in detail . In this case it ma } be shown that X and Substituting these values in equations ( 4 ) and ( 5 ) , and * See Rayleigh 's ' Theory of Sound , ' vol. 2 , p. 315 . 376 Conditions ecessary for tinuous Motion in From these two equations , together with the equations , the quantities and may be eliminated . The resulting equation is where and It may be written in the form where If either or may be solved in the form , whele and are the roots of If , however , neither nor vanish , ( 6 ) cannot be solved in finite but if be small compared with an approximate solution can be obtained . If be the greater of the two roots of , the solution is By substituting and their values and remembering that is small compared with , it may be shown that ( ) which is positive . Hence ( 7 ) represents a condensation ; for when approaches approaches , and when approaches approaohea . From ( 7 ) it possible to calculate approximately the thickness of the transition layer . It is evident that the distance between the planes where the velocities are and , is infinite ; but to obtain some idea of the extent of the transition layer consider the thickness of the layer in which On the Radium Content the velocity changes from to these vahles for in ( 7 ) and the values of , and for air , there is obtained and oximately . In the case of waves of percussion it is known that the differs appreciably from that of sound . In that case would be considerable and its reciprocal would be small , so the motion would closely approximate to an abrupt discontinuous one . In the case of ordinary sounds , however , the relative velocities of air in different parts of a wave are small , so that would be compared with a nothing in the nature of a sharp discontinuity would ever be established . the Radium Content of By the Hon. B. J. STRUTT , F.R.S. , Professor of Physics , Imperial of Science , South Kensington . ( Received July 16 , 1910 . ) In a fonner paper measurements of the amount of radium in ) sentatiye fneous rocks . In the reduction of these measurements value of the equilibrium ratio between radium and uranium iven by utherford and Boltwood was used , which has subsequently been corrected by those authors . My results were reprinted with the necessary amendment by Eve and McIntosh . Subsequent to the publication of my first paper other experimenters have made similar measurements , with results in most cases substantially the same . S Prof. J. Joly , however , has arrived at values considerably . His results are most conveniently referred to in his book " " ndioactivit ) and * O. E. Meyer , ' Kinetic Theory of Gases , ' English edition , p. 292 . ' Boy . Soc. Proc , vol. 77 , p. 472 . Phil. Mag August , 190 p. 231 . S See Eve and McIntosh , . cit. Far and orance , ' Phil. } ' November , 1909 , p. 812 . Schlundt and Moore , ' U.S. Geol . Survey Bull vol. . Fletcher , ' Phil. Mag July , 1910 , p. 36 .

rspa_1910_0082

0950-1207

On the radium content of basalt.

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Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

the Hon. R. J. Strutt, F. R. S.

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http://dx.doi.org/10.1098/rspa.1910.0082

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1910_0082

10.1098/rspa.1910.0082

Tables

Chemistry 2

Tables

On the Radium Content the velocity changes from -fui + -fv2 to TV'i 4-values for u in ( 7 ) T Qmi \#151 ; S M(\#171 ; i \#151 ; 2 log , 9 , Substituting these and inserting the values of 7 , p , p , and k for air , 7 = 1-4 , p = 1-3 x 10"3 , 1*9 x 10~4 , / c = -1'6^\#151 ; * J ( 7\#151 ; 1 ) there is obtained ( Qwi\#151 ; S)/ M = 022 and T = W2)-1 approximately . In the case of waves of percussion it is known that the velocity differs appreciably from that of sound . In that case \#151 ; u2 would be considerable and its reciprocal would be small , so that the motion would closely approximate to an abrupt discontinuous one . In the case of ordinary sounds , however , the relative velocities of air in different parts of a wave are small , so that T would be large compared with a wave-length , and nothing in the nature of a sharp discontinuity would ever be established . On the Radium Content of Basalt . By the Hon. R. J. Strutt , F.R.S. , Professor of Physics , Imperial College of Science , South Kensington . ( Received July 16 , 1910 . ) In a former paperf I gave measurements of the amount of radium in representative igneous rocks . In the reduction of these measurements a value of the equilibrium ratio between radium and uranium given by Rutherford and Boltwood was used , which has subsequently been corrected by those authors . My results were reprinted with the necessary amendment by Eve and McIntosh . ! Subsequent to the publication of my first paper other experimenters have made similar measurements , with results in most cases substantially the same . | Prof. J. Joly , however , has arrived at values considerably higher . His results are most conveniently referred to in his book " Radioactivity and * O. E. Meyer , ' Kinetic Theory of Gases/ English edition , p. 292 . t ' Roy . Soc. Proc./ A , vol. 77 , p. 472 . + ' Phil. Mag./ August , 1907 , p. 231 . S See Eve and McIntosh , loc. cit. Parr and Florance , ' Phil. Mag./ November , 1909 , p. 812 . Schlundt and Moore , ' U.S. Geol . Survey Bull./ vol. 395 , p. 26 . Fletcher , ' Phil. Mag./ July , 1910 , p. 36 . On the Radium Content of Basalt . Geology " ( Constable , 1909 ) . The discrepancy is most marked in the case of basalts , for which he finds a value of 4'9 x 10~12 gramme radium per gramme of rock . My own results average about 06 x 10-12 , as also do those of the other experimenters . Prof. Joly does not find much difference between acid and basic rocks . Other experimenters have all found that acid rocks tend to be considerably richer . I have made some additional measurements on basalts , in order , if possible , to clear up the cause of this discrepancy . Special attention was paid to a point which had perhaps not been adequately considered in the earlier investigation . When the rock has been fused with sodium carbonate , and the product extracted with water , the aqueous solution obtained usually develops a precipitate on prolonged boiling . Formerly , this precipitate was allowed to remain in the alkaline liquid . In the present experiments it was filtered off and added to the acid liquid , in which it readily dissolved . After extracting the sodium carbonate melt with water , the residue was formerly dissolved in hydrochloric acid , any silica which separated being allowed to remain in the liquid . In the present experiments this , too , was filtered off , and fused again with soda , the treatment being repeated if necessary , until everything had been got into solution . It was thought possible that the undissolved matter might be prejudicial to complete extraction of the emanation . But no such effect seems traceable in the results , and the trouble of preparing the solutions is greatly increased . In other respects the method of experimenting was the same as before . The standardisations were carried out with several different analysed specimens of uranium ores , with fairly concordant results . The mean values obtained from several readings with each rock were as follows:\#151 ; Description . Radium per gramme , in grammes x 10"12 . Coarse-grained basalt . Hightown , near Belfast 0T6 Fine-grained basalt . Oelberg , Siebengebirge 0*33 Fine-grained basalt . Tobermory , Mull 0-35 Olivine basalt . Talisker Bay , Sky 0-57 These results are even lower than those obtained before for similar rocks . The actual material is different , except in the case of the last rock on the list , which gives about the same result as before.* * This was the only one of the original basalts examined of which I had enough left for examination . Rate at which Helium is Produced 379 Thus the difference between my results and Prof. Joly 's is somewhat emphasised . I should have regarded my results , if they stood alone , as sufficiently conclusive , though it is impossible to help feeling disconcerted by want of agreement with so distinguished an experimenter . It is perhaps possible , after all , that the difference is due to his having met with exceptional specimens . Measurements of the Rate at Helium is Produced Thorianite and Pitchblendewith a Minimum Estimate of their Antiquity . By the Hon. E. J. Strutt , F.E.S. , Professor of Physics , Imperial College of Science , South Kensington . ( Keceived July 23 , 1910 . ) S 1.\#151 ; Introductory . The method of deducing a minor limit to the age of minerals from an examination of their radioactive properties has , up to the present time , depended on a measurement of the amount of helium they now contain , and on an indirect calculation of the rate at which it is being produced by the radioactive matter within them . There is not now much uncertainty about this calculation . Nevertheless , considering the fundamental importance of the question of geological time , it is not superfluous to determine in some favourable case by direct volume-measurement of the gas how much helium is produced per gramme of the mineral per annum , in order to see how long the quantity found in the natural mineral would take to accumulate , and to check the method of calculation to which we must still resort where the much more difficult direct method is impracticable . A mineral suitable for such experiments must be obtainable by the kilogramme , and very radioactive , so as to give a measurable quantity of helium in a few months . The minerals selected have been thorianite ( two varieties ) and pitchblende\#151 ; practically the only ones available . Some account of preliminary work was given in a former paper.* Much more elaborate and satisfactory experiments have since been carried out . These will now be described . * ' Roy . Soc. Proc. , ' A , vol. 83 , p. 98 .

rspa_1910_0083

0950-1207

Measurements of the rate at which Helium is produced in Thorianite and Pitchblende, with a minimum estimate of their antiquity.

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388

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

the Hon. R. J. Strutt, F. R. S.

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http://dx.doi.org/10.1098/rspa.1910.0083

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10.1098/rspa.1910.0083

Thermodynamics

Atomic Physics

Thermodynamics

Rate at which Helium is Produced 379 Thus the difference between my results and Prof. Joly 's is somewhat emphasised . I should have regarded my results , if they stood alone , as sufficiently conclusive , though it is impossible to help feeling disconcerted by want of agreement with so distinguished an experimenter . It is perhaps possible , after all , that the difference is due to his having met with exceptional specimens . Measurements of the Rate at Helium is Produced Thorianite and Pitchblendewith a Minimum Estimate of their Antiquity . By the Hon. E. J. Strutt , F.E.S. , Professor of Physics , Imperial College of Science , South Kensington . ( Keceived July 23 , 1910 . ) S 1.\#151 ; Introductory . The method of deducing a minor limit to the age of minerals from an examination of their radioactive properties has , up to the present time , depended on a measurement of the amount of helium they now contain , and on an indirect calculation of the rate at which it is being produced by the radioactive matter within them . There is not now much uncertainty about this calculation . Nevertheless , considering the fundamental importance of the question of geological time , it is not superfluous to determine in some favourable case by direct volume-measurement of the gas how much helium is produced per gramme of the mineral per annum , in order to see how long the quantity found in the natural mineral would take to accumulate , and to check the method of calculation to which we must still resort where the much more difficult direct method is impracticable . A mineral suitable for such experiments must be obtainable by the kilogramme , and very radioactive , so as to give a measurable quantity of helium in a few months . The minerals selected have been thorianite ( two varieties ) and pitchblende\#151 ; practically the only ones available . Some account of preliminary work was given in a former paper.* Much more elaborate and satisfactory experiments have since been carried out . These will now be described . * ' Roy . Soc. Proc. , ' A , vol. 83 , p. 98 . 380 Hon. R J. Strutt . Rate at which Helium [ July 23 , The great difficulty of the problem lies in the small quantities of gas which have to be dealt with . In this respect the conditions are far more onerous than in determinations of the helium production by radium ; for a quantity of radium equivalent in activity to a ton of pitchblende or thorianite may be placed in a small vessel , and the helium developed in a given time extracted and measured . In the present investigation , the entire bulk of the original mineral has to be handled , and not merely the radium present in it . It is impracticable to work with more than a few kilogrammes in this way , thus the quantity of helium which can be obtained in , say , six months is small indeed . Assuming the difficulty of the measurement of small volumes got over , there remains another not less serious . The helium initially present which has accumulated in geological epochs is perhaps 500 million times what the experimenter can grow under his observation . Thus , to make the experiment satisfactory , it is necessary to remove the helium so perfectly that not more than one part in 5,000 millions of the original stock remains . This could never be done if the mineral were allowed to remain in its original solid condition . For solid minerals only yield their helium slowly and partially by heating.* It is essential , therefore , to get the mineral into solution , and to filter off any slight undissolved residue with the most scrupulous care . Prolonged boiling will then remove helium with the necessary completeness . It is important to use thick filter paper . Fine particles of undecomposed mineral may otherwise get through the pores . The importance of avoiding this will be understood when it is stated that the presence of 1/ 1000 of a milligramme of undecomposed thorianite was altogether inadmissible in my experiments . Much trouble was incurred through a failure to adopt this precaution in the earlier attempts . The necessity for dissolving the mineral raises a theoretical question of some importance . Can we be really sure that this does not affect the rate of helium formation ? I shall briefly discuss this question , chiefly for the convenience of those who approach the subject from a standpoint of general scientific interest , rather than as students of radioactivity . Nearly all the evidence we have at the present time points to the conclusion that the rate of radioactive change is unalterable by anything that man can do . It is true that a few experimenters have thought that they could detect changes in radioactivity at high temperatures , but the experiments of Bronson , f which have been pushed further than any others , reveal no such effect up to * Unless , indeed , very high temperatures are used , which would introduce many other difficulties . t ' Boy . Soc. Proc. , ' A , vol. 78 , p. 494 . 1910 . ] Produced in Thorianiteand , etc. 1600 ' C. The calorimetric experiments of Curie and Dewar showed no loss of heating effect in radium at liquid hydrogen temperatures . As the development of heat is quantitatively accounted for by the expulsion of a-particles ( helium atoms ) with a high velocity , it cannot be doubted that the helium emission is unaltered at these temperatures . More directly relevant are the experiments of Moore , * who found that radium emanation , dissolved in water , decayed at the same rate as when in the gaseous condition . As the decay is the direct consequence of the emission of a-particles , it is clear that here also helium formation is independent of circumstances , and , in particular , of whether the radioactive body is in solution or not . Lastly the method is only applicablef if we assume that the rate of helium production has been the same throughout the whole geological period which it is sought to measure . What is there to be said in defence of this assumption ? The critic will naturally object that the radioactive matter present is necessarily diminishing in quantity as it generates helium and other nonradioactive products to which it may give rise . There must , therefore , have been more of it at the beginning of the geological period considered than at the end , and consequently more rapid production of helium . The method as here applied is only valid if it can be shown that this diminution is unimportant in the period considered . A simple argument goes far to establish this for thorianite . This mineral is a dense substance , consisting almost entirely of the parent radioactive bodies , uranium oxide and thorium oxide . We cannot suppose that there was ever much more of these bodies in the thorianite crystals than at present , for they do not contain much inactive matter of any kind , which can be assumed to represent the debris of the decayed radioactive bodies . Apart from this simple argument , we have a good indirect estimate of the rate of decay of uranium , J which shows that it is unimportant in the periods here dealt with . The decay of thorium is almost certainly slower still . The other chief line of objection which can be taken is that the rate of formation of helium depends on the physical condition of the radioactive matter . This objection has already been considered . S 2.\#151 ; Experimental . The thorianite used was dissolved in nitric acid , and most of the excess of acid driven off by evaporation . A slight insoluble residue then remained , consisting in the main of zircon which had been mixed with the thorianite . * ' Roy . Soc. Proc. , ' A , vol. 80 , p. 597 . t At least , in the simple form with which alone this paper deals . f Boltwood , ' Amer . Journ. Sei./ June , 1908 , vol. 25 , p. 506 . VOL. LXXXIV.\#151 ; A. 2 D Hon. R. J. Strutt . Rate which Helium is [ July 23 , This residue was filtered off and rejected . It would no doubt have been preferable to reject nothing , but much additional trouble would have been incurred in getting it into solution . The quantity of residue was insignificant and its activity much less than that of an equal weight of the original thorianite . Two kinds of thorianite were used in the experiments , one the ordinary variety , the other that specially rich in uranium , from the Galle district . Besides the experiments on thorianite some were made on pitchblende . This mineral was treated with nitric acid , and the solution preserved separately . Pitchblende contains sulphides which were oxidised by the nitric acid . This led to precipitation of barium , radium , and lead as sulphates . The insoluble residue was boiled with large excess of sodium carbonate to expel sulphuric acid , and , after washing , again treated with nitric acid . After one or two repetitions of this process nothing but inactive sand remained . This was rejected . The solution obtained after the sodium carbonate treatment was , of course , kept separate from the original nitric acid solution . The helium obtained from these separate solutions was all measured together . The various solutions were stored in vacuous round-bottomed flasks arranged as shown at a in fig. 1 . A tall tube b serving as a reflux condenser was sealed to the neck of the flask , and was continued in a narrow tube c , with recurved end dipping down into a basin of mercury . The whole arrangement was fastened to a rod stand , and could be put away during the intervals allowed for the helium to be generated . When it was desired to collect the gas the liquid was boiled , taking care to raise the temperature slowly so that no violent bumping occurred . When vapour of appreciable pressure had formed over the liquid , boiling would proceed quite quietly , provided the solution was not too strong . Boiling was continued by the application of a gentle heat , which did not raise more steam than could be condensed by the vertical tube , with simple air cooling.* The dissolved gases were expelled from the liquid , and accumulated in the upper part of the apparatus . They could be collected by increasing the heat under the flask , so as to wash them out with steam into a test tube inverted over the recurved end of the narrow delivery tube . It was found that the nitric acid solutions invariably gave some nitric oxide , and a much smaller quantity of nitrogen . I have not paid special attention to the origin of this nitrogen , but it is certainly not atmospheric , as the absence of neon in the helium collected proves . It may be due to * A fan was sometimes used to cool the tube , but without much advantage . decomposition of nitric acid by radioactive bodies , but I have not tried whether it can be got from nitric acid only . The gas collecting tube was half filled with oxygen , and some caustic potash floated on the surface of the mercury . Thus the nitric oxide was oxidised and absorbed . The excess of oxygen , carrying nitrogen and helium , was drawn into a gas burette and thence passed into a quartz tube full of mercury with melted phosphorus at the top . The oxygen was burnt , and nitrogen , containing a small proportion of helium , remained . The flasks usually contained about 3 litres of solution , in which about 600 grammes of thorianite was dissolved . The nitrogen from each of them amounted to a fraction of a cubic centimetre , and served conveniently to carry the helium , in itself too little for pneumatic trough manipulation . The final isolation of helium was effected by cooled charcoal . The apparatus used is shown in fig. 2 . The gas is introduced into a gas pipette a with a twoHon . R J. Strutt . Rate at which Helium [ July 23 , way stopcock , and thence into the exhausted apparatus . It is followed up with mercury as far as the point b. After standing for some time over the cooled charcoal in c , it is drawn into the large vessel d , where it comes into contact with more cooled charcoal in the annexe ; is then heated to drive off any occluded gas , and allowed to cool . Ultimately/ is closed , and d is fdled with TO MERCURY PUMP mercury so as to compress the residual helium into the capillary . The arrangements for doing this are sufficiently obvious from the figure ; is a piece of very fine thermometer tubing 0T64 mm. diameter . The upper end , instead of being fused up , was closed by drawing a thread of melted sealing-wax into it . This gave an approximately plane end to the tube at right angles to its length , so that the volume of gas was calculable from the measured length it occupied , and the pressure . The latter was measured by taking the 1910 . ] Produced in Thorianiteand Pitchblende , etc. 385 difference of level between the mercury in h and in by a cathetometer , and subtracting it from the barometric height.* The capillary depression in g ( 4'9 cm . ) was allowed for . The actual pressure was about 20 cm . of mercury , and the length of tube occupied by the largest volume of helium generated under observation 7'3 mm. The length by the column of gas was measured by a microscope with ocular scale , or , when too long for that , by a mirror glass scale , estimating to 1/ 10 mm. The apparatus lent itself very conveniently to spectroscopic observation of the gas , as a check on purity . Two strips of tinfoil on the capillary , at 2 or 3 cm . apart , were connected to an induction coil , and the pressure was reduced by lowering the mercury until the gas filled that part between the strips . When the helium was pure a bright yellow glow was observed , which became bluish with the slightest admixture of nitrogen . The spectroscope was , indeed , scarcely needed . It was observed that if any trace of nitrogen remained it was rapidly removed by running the discharge for a short time , notwithstanding the absence of metallic electrodes , to which such actions are usually attributed . The volume of gas was , of course , diminished by this process ; but , when once the nitrogen was gone , no amount of further sparking would diminish the volume of helium . A correction to the measured volume is necessary , on account of the small quantity of helium which necessarily remains in the two charcoal vessels . This fraction was determined , once for all , by starting with pure helium introduced into cl and measured . Connection was then made to c and c , both previously exhausted and cooled . Cutting off these connections , the volume was measured again in g. It was found to be diminished by about 1/ 10 part . The validity of the measurements depends , of course , on the assumption that no part of the very small volume of helium obtained is absorbed by the charcoal , under the conditions of the experiment . Although the absorption of helium at low pressures has been shown by Dewar and others to be very small , it was thought advisable to make direct tests . This was done as follows : A small quantity of helium was very largely diluted with oxygen , so as to form a standard mixture ( of arbitrary composition ) . This was placed in a graduated tube , and 1 c.c. of it drawn into the apparatus . The helium contained measured 5'5G x 10-6 c.c. , a volume comparable with the smallest obtained in the helium experiments . Seven cubic centimetres more of the mixture was then taken and most of the oxygen removed with phosphorus . The residue was added to the gas already in the apparatus , and the total helium ( from 8 c.c. of mixture ) measured as 4-73 x 10~5 c.c. , 8-5 times that * h was open to the atmosphere during the volume measurements . 386 Hon. R. J. Strutt . Rate at which Helium is [ July 23 , from 1 c.c. This proved that no appreciable absorption took place . For , if there had been a slight absorption , it would have told much more on the small volume , and would have disturbed the ratio . Further evidence on this point will be given immediately . S 3.\#151 ; Results of First Seines.\#151 ; Thorianite from Galle ; the variety rich in uranium . Three flasks ( numbered 4 , 5 , 6 ) set up , each containing 680 grammes in solution . Experiment . Volume of helium . Initial blank test of all three flasks , P3 invisible After 205 days ' standing\#151 ; Flask No. 4 C.C. X 10-6 . \lt ; 1-0 15 -5 34 -9 45 -9 2-9 24 -3 \lt ; 1-0 * Flask No. 4 +No . 5 Flask No. 4 + No. 5 + No. 6 Blank test of all three flasks , Ds conspicuous After standing 129 days more , all three flasks Final blank test , D3 invisible From these experiments\#151 ; f 8*18 x 10~5 c c Rate of production from all three flasks , per annum \#166 ; \lt ; g.gg ^q_5 c'c ' Mean ... ... ... 7'54 x 10~5 c.c. Rate of production per gramme of Galle thorianite , per annum ... ... ... ... ... ... ... ... ... ... ... ... ... 3-7 x 10~8 c.c. Helium initially present , per gramme ... ... ... ... . . 9-3 c.c. Time required to produce this ... ... ... ... ... ... ... 2'50 x 108 years . Second Series.\#151 ; Ordinary thorianite containing 13T0 per cent. U3O8 , and 72'65 per cent. Th02 . Three flasks ( numbered 2 , 3 ) set up , each containing 510 grammes . Experiment . Volume of helium . Initial blank test of all three flasks , D3 doubtful c.c. x 10~6 . \lt ; 0-5 After standing 141 days*\#151 ; Flask No. 1. . 5-0 Flask No. 1 + No. 2 11 3 Flask No. 1 + No. 2 + No. 3 16-5 Final blank test of all three flasks \lt ; 0-5 * As a matter of fact , the flasks were not all boiled out at quite the same time on this occasion . The numbers given are slightly corrected to compensate for this , so that the results can be studied more easily . 1910 . ] Produced in Thorianiteand , etc. 387 From these experiments\#151 ; Rate of production from all three flasks per annum 4'27 x 10-5 c.c. Rate of production per gramme of ordinary thorianite 2*79 x 10~8 c.c. Helium initially present , per gramme ... ... ... ... . 7*8 c.c. Time required to produce this ... ... ... ... ... ... . . 2-8 x 108 years . Pitchblende , from Joachimsthal , 353 grammes . Dissolved ( see above , p. 382 ) in two separate flasks , which were always boiled at the same time , and the gases treated together . Experiment . Volume of lielium . Blank test , Dq invisible c.c. X 10~6 . \lt ; 0-5 2 -0 9-0 After 61 days ( not a good experiment ) After 294 days ( good experiment ) The last experiment is the only one on which stress can be laid . It gives Helium per gramme pitchblende , per annum ... ... ... . . 3T6 x 10 ~8 . The pitchblende experiments were not carried so far as those on thorianite , on account of the much greater difficulties of preparing the solution . The best experiment , however , was a very satisfactory one . The helium measured may be exhibited graphically as a function of the Number of flasks . Fig. 3.\#151 ; ( 1 ) Gall thorianite . ( 2 ) Ordinary thorianite . 388 Bate at which Helium is Produced etc. number of flasks emptied , in those cases where the contribution of each was added successively , and shows fair proportionality ( fig. 3 ) . This is additional evidence that no appreciable helium was lost in the charcoal , otherwise the first flask would have apparently yielded less than its due contribution . S 4.\#151 ; Discussion of Results . It now remains to compare the rate of formation of helium observed with that calculated theoretically . For the calculation I refer to ' Boy . ' Soc. Proc. , ' A , vol. 81 , p. 276 , and vol. 83 , p. 97 . Mineral . . U8Og . Per cent. Th02 . Per cent. Helium production per gramme per annum . C.c. x 10~8 . Observed . Calculated . Thorianite . Grille district ... 24 -50 65 -44 3-70 3-46 Ordinary thorianite 13 -10 72 -65 2-79 2-55 Pitchblende 37 -6 None 3-16 3 -44 The calculation is clearly justified by the direct observations , and can in future be employed with confidence in its substantial correctness . The present experiments leave , I think , no doubt whatever that some specimens of thorianite are as much as 280 million years old . I will take this opportunity of summarising the data in my previous papers* with regard to the duration of geological time , as deduced by the indirect method . With the verification of this method now presented , I feel justified in stating them numerically without the qualifications before insisted on . Mineral . Geological horizon . Minimum age . Sphaerosidenite from Rhine provinces Haematite , Co. Antrim Oligocene Eocene Years . 8,400,000 31,000,000 150.000 . 000 710.000 . 000 Haematite , Forest of Dean Sphene , Renfrew Co. , Ontario Carboniferous limestone ... Archaean These are minimum values , because helium leaks out from the mineral , to what extent it is impossible to say . Summary.\#151 ; The rate at which helium has been and is being produced in thorianite has been measured directly with reasonable accuracy , and is found to be in agreement with the rate calculated indirectly . The helium now found in one sample examined would take 280 million years to accumulate . Similar measurements have been made with pitchblende . * ' Hoy . Soc. Proc. , ' A , vol. 81 , p. 272 ; vol. 83 , p. 96 ; vol. 83 , p. 298 .

rspa_1910_0084

0950-1207

Observations on the anomalous behaviour of delicate balances, and an account of devices for increasing accuracy in weighings.

389

391

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

J. J. Manley, Hon. M. A. Oxon.|Prof. E. B. Elliott, F. R. S.

abstract

6.0.4

http://dx.doi.org/10.1098/rspa.1910.0084

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10.1098/rspa.1910.0084

Measurement

Thermodynamics

Measurement

389 Observations on the Anomalous Behaviour of Delicate , and an Account of Devices for Increasing Accuracy Weighings . By J. J. Manley , Hod . M.A. Oxon . , Daubeny Curator , Magdalen College , Oxford . ( Communicated by Prof. E. B. Elliott , F.R.S. Received June 21 , \#151 ; Read November 10 , 1910 . ) ( Abstract . ) Many observers have drawn attention to the small irregularities that are frequently exhibited by delicate balances . The consequent inconveniences appear to have been felt chiefly by those who have been engaged in atomic weight determinations , the measurements of the mean density of the earth , the standardisation of weights , and work of a like nature . Of those who have thus been hampered during their researches we may mention the names of such well-known investigators as Miller , Thorpe , Pointing and Phillips , and Dixon and Edgar . In this paper an account is given of experimental work that was carried out with the object of elucidating the causes of the variations in the resting-point of a balance . Through the kindness of the agents of various balance makers , the author was enabled to experiment with a number of new instruments of high grade and of different types . It appeared probable that the possible causes of the fluctuations in the resting-point were due to ( 1 ) Side-slipping of the central knife-edge upon its supporting plane . ( 2 ) Differential and continued flexure of the beam after loading . ( 3 ) Lateral displacement of one or more knife-edges . ( 4 ) Small variations in the temperature of the two arms of the beam . Each of the four possibilities is investigated in detail both experimentally and theoretically . It is shown that the anomalous behaviour of a balance is due almost , if not quite entirely , to causes ( 3 ) and ( 4 ) , and that causes ( 1 ) and ( 2 ) are , for all practical purposes , inoperative . Experiments were conducted by means of a differential bolometer placed within the ordinary balance case . They revealed the existence of slight but rapid and almost continuous fluctuations in the temperature of the air immediately surrounding the beam . These fluctuations cannot be detected by even very delicate mercury-in-glass thermometers ; for such thermometers VOL. LXXXIV.\#151 ; A. 2 E 390 Anomalous Behaviour of Delicate , etc. are too sluggish to respond to them , and record a mean temperature only . When the pans are being loaded or unloaded , the variations in the temperature of the two arms are , as we should naturally expect , largely increased ; and if a weighing is effected immediately after the necessary weights have been placed upon the pan , there is considerable uncertainty as to the true weight of the object under measurement . For accurate weighing , the final observations should not he taken before some 10 to 15 minutes have elapsed after loading . Other experiments appear to prove that the knife-edge blocks require , not infrequently , some little time to take up a normal position for a given load . Balances which have their knife-edges attached to the beam in a certain manner often show this kind of defect somewhat markedly . When it is required to determine the mass of a body with the highest degree of accuracy , it is necessary to fatigue the balance-beam by allowing it to swing freely for some time after the object and weights have been placed upon the pans . The time required to reduce a balance to a normal condition in this way , depends both upon the instrument and upon its load . It was found that some balances may he completely fatigued within a few minutes , while others require a more prolonged period . So far as T am able to judge from my own observations , it appears that from 10 to 20 minutes are generally sufficient for the purpose . Any abnormal temperature effects that may he produced whilst the pans are being loaded will also die away during the time required for fatiguing the beam . It ; was also found that the resting-point changes in a perfectly regular manner with an increase or decrease in the temperature of the beam . The magnitude of the change depends upon the type of the balance and its load ; also , two different balances of the same type and by one maker may have totally different temperature coefficients . The temperature coefficients appear to be best represented by an equation of the form M = Mi ( 1 \#177 ; a / 3t2 ) , in which M and Mi are respectively the true and apparent masses , and \#171 ; and / 3 are factors which must be determined for different loads and for each balance . It is also shown that a distinct advantage is gained and some marked irregularities avoided , by surrounding the beam with an extra inner case consisting of metal , wood , and plate glass . By the introduction of this device , the beam is permanently screened from heat ladiations and The Damping of Sound Frothy Liquids . 39 ] , convection currents , even when the ordinary shutter of the balance case is lifted . An additional advantage is gained by placing a differential bolometer within the inner or beam case ; for we are then enabled to ascertain , at any time , whether the temperature of the two arms is uniform or not . Some few of the numerous results are represented graphically rather than in tabular form . In this way the facts to which it is desired to draw attention are brought out more clearly and prominently . The dispositions and forms of the apparatus used are shown in diagrams ; the efficiencies of the various forms of knife-edges employed in balances are also discussed . The Damping of Sound by Frothy Liquids . By A. Mallock , F.R.S. ( Received May 26 , \#151 ; Read June 23 , 1910 . ) The fact that a tumbler containing a frothy liquid gives a dull sound when struck is familiar to every one , but I cannot find that any explanation of the rapid damping of the vibrations , which is indicated by the character of the sound , has been published . The converse case , namely , that of waves propagated through a gas in which small solid or liquid spheres are disseminated , has received considerable attention , and the results deduced , which agree with observation , are to the effect that although the presence of small obstacles does cause some damping , it is very small in amount . I think there can be little doubt that the excessive damping in the case where the obstacles are gaseous , and the intervening spaces filled with liquid , is due to the augmentation of the distortion of the latter caused by the variation of pressure acting mainly on the volume of the gas . When no gas bubbles are present in a liquid transmitting vibrations , distortion accompanies changes of pressure , but the rate at which shear takes place is of the order amplitude -r- wave-length , and in liquids the velocity of transmission is large , and also the wave-length in cases where the frequency is that of an audible note . On the other hand , if bubbles of gas are present the variation of pressure acts almost entirely on the volume of the gas , and scarcely at all on the relatively incompressible liquid . Thus , if S , fig. 1 , be part of the surface of

rspa_1910_0085

0950-1207

The damping of sound by frothy liquids.

391

395

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

A. Mallock, F. R. S.

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6.0.4

http://dx.doi.org/10.1098/rspa.1910.0085

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10.1098/rspa.1910.0085

Fluid Dynamics

Thermodynamics

Fluid Dynamics

]\gt ; The 'ing . Soumd by Frothy 39 ] convection , even when the ordinary hutter of the balance case is lifted . An additional is gained by a differential bolometer within the inner or beam case ; for we are then enabled to ascertain , at any time , whether the temperature of the two arms is uniform or not . iome few of the numerous results are represented graphically rather in tabular form . In this way the facts to which it is desired to attention are brought out more clearly and prominently . The dispositions and forms of tlJe apparatus used are shown in diagrams ; the efficiencies of the various of knife-edges employed in balances also discussed . The by By A. LLOCK , F.R.S. Received Eead June The fact that a tumbler containing a frothy liqnid gives a dull sound when struck is familiar to every one , but 1 cannot find that any ) of the rapid of the vibrations , which is indicated by the of the sonnd , has been published . The co yerse case , namely , that of waves propagated in which small solid or liquid spheres are disseminated , ] attention , and the lesults deduced , which agree with observation , are to the effect that although the presence of small cles does cause solle ( lanlping , it is very in amount . I think there can be little doubt that the excessive dampin in the where the obstacles are aseous , intervening filled with liquid , is due to the augmentacion of the distortion of the latter the variation of pressure acting mainly on the volume of the When no ( bubbles are present in a liquid ) tions , distortion accompanies changes of pressure , but the rate which shear takes place is of the mplitude , and in liquids the velocity of qsion is large , and also the in cases the frequency is that of an audible note . On the other , if bless of gas are present the variation of pressure acts almost entirely on the volume of the gas , and scarcely at all on relatively incompressible liquid . Thus , if , be part of the surface of 392 . A. Mallock . [ May 26 , a bubble at the mean pressure , which under the variation of pressure its radius from OS to OS ' and OS ' ' , the liquid in the element whose mean position is AB changes from to , and the difference of and is a measure of the distortion caused by the For a criven variation of volume the distortion riation of as the radius of the bubble diminishes . It must be assumed that is never large to make the pressure or radius of the he much from their mean values . The nature of the stress to which a non-viscous liquid in a vibrating cylindrical vessel is exposed depends on the ratio of the wave-length in the iquid to the transverse dimensions of the vessel . If this ratio is the stress in the liquid is one of shear only , the compression and dilation at all points being neutralised by the symmetry of the motions of the vibrating walls . If , however , the velocity of propagation is so slow that the diameter ot the vessel is a considerable fraction of a wave-length , there will be pressure in the liquid as well as distortion , and it is only variation of which will the ping action of gas bubbles effective in the way supposed . It may be remarked that the velocity of transmission of a wave in mixed fluid , such as a liquid containing bubbles , is the same as it would be in a homogeneous fluid of the same density and mean e.lasticity . Thus , and being the mean density and elasticity of the mixture , if the volume , density , and elasticity of the liquid and are respectlvely , and , and if , the velocity of transmission is , and , if is the variation of stress . Hence , in terms of E2 , Also so that 1910 . ] The of Sd Frothy Liqu ids . Thus , if the is air , mi-xture This has a minimum when , which makes very nearly unity in the case of a water and air mixture . The form of the velocity curve is shown in , in which the abscissa ; the value of It will be seen that a very small quantity of liquid , when distributed as in froth , lowers the velocity of transmission enormously , and that the velocity rises to that of sound in . when the volume of air is about 1/ 800 of the hole . When is less than 2 , the mixture begins to take the nature of a froth . The velocity rises actually as the quantity of air diminishes , , of course , ultimately ( and sensibly when ] million ) the velocity of ation in water . As before mentioned , it is only altel.ations in the volume of the n1ixture which produce excessive dissipation of the of the vibrations , and the haracter of the action may be examined by the dissipation for the case of a spherical bubble of gas surrounded by a sphere of viscous , but The Dampimg of by Liquids . incompressible fluid , subjected over its outer surface to a harmonic radial displacement of given amplitude . Let and be the radii of the sphere and enclosed bubble respectively , and let be the amplitude of the vibration at ; also let be the period of vibration and Since the liquid is incompressible , the amplitude at is , and if is the thickness of a spherical shell of mean radius when the liquid is at rest ; and its thickness at time when vibration is going on , , and this quantity differentiated with respect to time is proportional to the rate of shear . The rate of shear is therefore to \ldquo ; and for a shell of thickness , the speed with which the spherical faces approach or recede one another is ; and the force required ( over the whole shell ) to cause shear at this rate is proportional to The work done ( as far as it depends on viscosity ) in time is proportional to , and substituting , and taking account of the tangential , as well as the radial , ariations in the dimensions of the shell , it will be found* that the dissipation in . the work done in overcoming the viscous reaction , is dr . , t.herefore , from to , and to the dissipation hout the whole sphere one complete period is . The whole of vibration in the liquid and bubble is Hence the ratio of the work dissipated in time to the hole energy in the liquid is 3 , or ( since and ; also , for vity , putting for ) , we Thus the efficiency of the bubbles in damping vibrations increases rapidly , as their diameter and the distance between them ( measured by ) uinish . The damping viblation is proportional to the period but for a constant time is indepelldent of , the reduction for all periods bein ; in the atio of when . The increased * See Lamb 's 'Hydrodynamics , ' S Determination ofof effect when the bubbles are small is borne out observation , but it is difficult to make quantitative periments in these cases . When the proportion of air to water is large the mixture becomes a froth that is a ) of bubbles separated ] thin films of liquid . The problem of ting the viscous reaction in such a mixtul.e is one I not attempted to solve . iment , however , that froth is a most efficient agent in This may be shown in a simple and stliking } as follows : prepared a sufficient quantity of fine grained froth in a flat dish soap and water , take a wine lass or tnnlblelhich gives a clear lnusical note when uck . Dip the month of the glass into the froth ' about a quartel of an inch and withdla it . A thin . of froth will be left lound , perhaps , 1 or 2 . Small as this quantity of froth is be found suflicient to damp the ibration so as to depl i the sound of an . musical character . the ) ) of ) ) By ( Communicated by Lord Rayleigh , O. I. , F.B.S. Received , \mdash ; , 1910 . As addition to my ) aper , pnblished in the ' on the determination of the of } , I to set the ving remarks the ) of the value of tension it formed water-surface , tances 1 of ) the determination of Prof. P. Lenard has , in a } ) ) telv published : deterrnined of a recently ) wRter-hurface } of tion o falling drops , and has this tension found vahles n hich are greater than those found by other methods . this , as vell ils the results of experiments blished in former he concludes recently formed -surface very tension , hich , ever ' Phil. Trans , 1909 , vol. 209 , p. 281 . Sitzun gsber . Heidelbel.ger Akacl . lVis .-nat . Kl . . 1910 , Ann. 188 vol. 30 , p.

rspa_1910_0086

0950-1207

On the determination of the tension of a recently formed water-surface

395

403

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

N. Bohr|Lord Rayleigh, O. M., F. R. S.

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6.0.4

http://dx.doi.org/10.1098/rspa.1910.0086

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10.1098/rspa.1910.0086

Fluid Dynamics

Tables

Fluid Dynamics

]\gt ; Determination ofof effect when the bubbles are small is borne out observation , but it is difficult to make quantitative periments in these cases . When the proportion of air to water is large the mixture becomes a froth that is a ) of bubbles separated ] thin films of liquid . The problem of ting the viscous reaction in such a mixtul.e is one I not attempted to solve . iment , however , that froth is a most efficient agent in This may be shown in a simple and stliking } as follows : prepared a sufficient quantity of fine grained froth in a flat dish soap and water , take a wine lass or tnnlblelhich gives a clear lnusical note when uck . Dip the month of the glass into the froth ' about a quartel of an inch and withdla it . A thin . of froth will be left lound , perhaps , 1 or 2 . Small as this quantity of froth is be found suflicient to damp the ibration so as to depl i the sound of an . musical character . the ) of ) By ( Communicated by Lord Rayleigh , O. I. , F.B.S. Received , \mdash ; , 1910 . As addition to my ) aper , pnblished in the ' on the determination of the of } , I to set the ving remarks the ) of the value of tension it formed water-surface , of ) the determination of Prof. P. Lenard has , in a } ) ) telv published : deterrnined of a recently ) wRter-hurface } of tion o falling drops , and has this tension found vahles n hich are greater than those found by other methods . this , as vell ils the results of experiments blished in former he concludes recently formed -surface very tension , hich , ever ' Phil. Trans , 1909 , vol. 209 , p. 281 . Sitzun gsber . Heidelbel.ger Akacl . lVis .-nat . Kl . . 1910 , Ann. Pllys . 188 vol. 30 , p. Mr. N. Bohr . Determination of the [ Aug. 22 , in the course of a very short time ( fraction of a second ) decreases considerably . He remarks that this result is in agreement with experiments published in my paper mentioned above . I shall , however , in the following try to explain the reasons why I cannot in these conclusions . The determination of the surface-tension published in my paper cited was carried out by the method of jet-vibrations , the theoretical founda- tion of which method , as well as of the method used by Prof. Lenard , is due to Lord As to the closer ation of vibration of the , especially with regard to the satisfaction of the suppositions made in the theoretical treatment of the enon , a great number of vibrations , commencing just at the orifice and in the most stable . extending to a distance of more than cm . from this ( the velocity of the jets was about 425 cm . ) , were examined b.v my experiments . hese measurements showed that the was nob the same everywhere , but that , advancing from the orifice , it increased in inning rather rapidly and thereupon more slowly until finally from a of about 20 cm . from the orifice and as far as the stability of the jet allowed the measurin , , the became practically perfectly constant . tables , This result consequently showed the existence of certain irregularities of the phenomenon , which arise in the mation of the jet , and which are rapidly ( in about see . ) extinguished ( loc. cit. , p. 309 ) . These irregularities partly be thought to inate from possible variations of the value of the surface-tension in the time immediately after the formation of the surface , partly from irregularities of a more mechanical ( hydrodynamical ) character . Since the last-mentioned irregularities , as explained in my former paper , must decrease rapidly on emoval from the issue of the jet , the result of the showed } the surface-tension , in evcry case from about second after mation o the sulface , and as long as it was possible to investigate the tension by the used method , was sensibly constant . This constant value was considered as ' Roy . Soc. Proc 1879 , vo1 . .39 , p. 71 . Prof. Lenard remarks in last paper that the mechanical irregularities certainly must decrease , but cannot , even far from the orifice , completely ( lisappear , on account of the resistance of the air against the movement of the jet . As , however , the effect of the air reRistance removing from the orifice very rapidly will ecome constant , we see that an influence of this resistance on the phenomenon will not affect the above conclusion of the constancy of the surface-tension , but it can only cause an nlteration of the value found for this constant tension . As to the question of the magnitude of the influence of the air resistance , I mention here an unpublished experimade during my first investigation . Around jet , at a distance of about 10 cm . from the orifice , was placed large and carefully worked iris diaphragm , so 1910 . ] of a the sought value for the surface-tension , it was in every case the only one which could be compared with values found by other methods , in which the investigated surfaces always have been much older than second . Concerning the question of a possible variation of the surface-tension the time from the formation of the surface until some second later , it seems to me that my nents do not any reason to conclude an existence of such a variation , there being , as we shall see , objection in explain ing the found variation in the wave-length by ) of the velocity-differences veen concentric parts of the jet produced by friction during its formation , by which the central parts receive a ) velocity than the parts nearer the surface . These velocity-differences decrease , removing from the issue , on account of the viscosity in the jet : the mean velocity of the jet eeping constant , this effects that the velocity of the outer parts increases at the same time as velocity of the central parts decreases . That the are shorter close to the orifice than at a greater distance from this has always seemed to me to be a natural consequence of the velocity of the surface ( the outer parts ) here smaller and the waves in question surface-waves ( the velocity of the vibrating liquid-particles is beconling smaller } from the , and is in the axis of the jet ) . In his above-cited paper ( loc. p. 4 ) , Prof. Lenard , however , is of the opinion that the innel mixture\mdash ; produced uing the motion , on accoun of the mutual ] of the concentric parts of the jet\mdash ; will an apparent increase of the mass , and a thereby prolongation the time of vibration and increase of the For the closer examination of this question , I have therefore made the direct calculation of the assun ) ption that the different concentric parts of the jet are with diffferent velocities . that the jet just passed through the centre of the diaphragm . This was at first open , so that a free space of 5 cm . ( the opening of the diaphragm cm . ) surrounded the jet . hereupon the diaphragm was closed , so that the free space between the jet and the diaphragm was not more than some mm. , and at the same time a wave-su1nmit of the jet at a distance of 30 cm . from the orifice was fixed in a telescope help of reflection ill the surface of the jet . It was then observed that the mentioned summit during the closing of the diaphragm was displaced only little ( less than This simple experiment was repeated several times with exactly the result . As such a closing of the diaphr . must increase the resistance of the air to a considel able degree , completely stopping the mass of set in motion by the jet ( the jet produces sensible blast ) , the experiment , in my opinion , shows very distinctly that the resistance cannot any appreciable influence on the results . As will be show in the following , an air resistance would besides introduce a correction of lalue of the surface-tension , the sign of which would be opposite to that supposed by Prof. . N. Bohr . Determination of the [ Aug. 22 , The equations of motion of an incompressible non-viscous fluid unaffected by extraneous forces , are , ( 1 ) and , ( 2 ) in which are the components of the velocity , the pressure , the density , and In the problem in question the motion will be steady . Putting and supposing that , and are so small that products of them , and quantities of the same order of nitude , can ) ected in the calculations , we from the equations ( 1 ) . ( 3 ) Introducing polar co-ordinates and ) , and the vadial and tangential velocity and , w by help of the relations from ( 3 ) , assuming to be a function of . only . , ( 4 ) and . ( o ) that , and have the form get from ( 4 ) . ( b ) In the case is con stant , the solution of ( 6 ) , subject to the colldition to be imposed when , is ( 7 ) in which is the syml ) of the Bessel 's function of order . . ( 8 ) we get from ( 6 ) . ( 9 ) 1910 . ] Tension of a ecently f We will now suppose that , in which the constant is the mean velocity of the jet , and a quantity small compared with c. In this case is small , and terms of the same order of onitude as , we from ( 9 ) . ( 10 ) In the experiments the numerical value of will be a very small quantity\mdash ; the laroeo in comparison to the diameter of the jet\mdash ; in order not to complicate the formulae , will therefore in the calculation of only use the first term of the expression for . This ooives the solution of ( S ) becomes The motion being finite for , we have Integrating by part we get . ( 11 ) Let us suppose that the equation of the surface is The yeneral surface condition whence we quantities of the same order of , as by the equations ( :3 ) In the ] ) anner } further , if the principal of ) and Calling the surface-tension , the dynan ical surface-condition will ) const . From this we the same approximation as before and From ( 12 ) get , and ( 8 ) , ( 13 ) 400 Mr. N. Bohr . rmination of the [ Aug. 22 , From ( 13 ) we get . by help of ( 11 ) and with the same approximation as used in the calculation of This equation is , except the last term , the solntion given by Lord ayleigh . We therefore see that the effect of the velocity-differences between concentrical parts of the jet consists in an exchange in the formula for the wave-length , of the mean velocity of the jet by an " " effective mean velocity We see from that the greater is , the nearer the effective mean velocity will be to the velocity of the surface , which is explained by the fact that the greater ( the number of waves on the circumf.erence of a section of jet ) is , the rapidly the velocity of the vibrating liquid particles will decrease , moving from the surface towards the axis of the jet . It can now be shown that will be smaller than , if the velocity of the jet\mdash ; which will be the case in the experiments\mdash ; is greatest in the middle ( continually decreases approaching the surface ; being the mean velocity of the jet , we have , and in the case in question further where . From this we Ctet f ( in the experiments ) . After seen the velocity-differences in question will produce a variation of the wave-length in the same direction as found by the experi- lnent , we shall further see how the decrement of the variation of the can also be explained by the manner in which the ences will decrease . In order to show this , we shall use the four experiments quoted in the table , . cit. , p. 310 . In the table below is the mean radius of the jet , the velocity ( calculated from the mean adius and the discharge ) , and under the indication , the difference etween the wave-length , measured between the wave-summits and the constant value to which the wave-leno.thso were tending , diyided by the difference between the wave-length , measured between the sunnnits II and III , the mentioned constant value ( in these differences introduced the small corrections for the curvature of the jet and for the -amplitudes mentioned in the table , loc. cit. , p. 311 ) ; under the 1910 . ] Tension of recently formed ce . 401 indication is quoted the difference between the mean value of the of the summits and and the mean values of the II and III . Further , under the indication is quoted the between the variations of the wave-length in two places corresponding to a time-interval of 1/ 100 sec. ( calculated on the assumption that the variations decrease after an exponential law ) . Un der the indication is finally quoted the ratio between the velocity differences in the jet in two places corresponding to a time-interval of 1/ 100 sec. , calculated from the theoretical formula , I. II . a 5 . 0.59 0 . 0 . 0.59 0 . 0 . 0.59 0 . 0 . 0.59 0 . 0 . 0.59 0 . 0 . 0.59 0 . 0 . 0.59 0 . As will be seen , the calculated and found values for the decrement of the variation of the wave-lengths with regard to the order of magnitude , and more was not to be expected from such an approximate calculation . It is thus not justified to expect that the distribution of the velocity in jetsections so close to the orifice could be completely expressed by the term in formula on p. 298 . After having now seen that my experiments do not give any reasons the conclusion of the existence of a variation in the surface-tension durinero the first time after the formation of the surface , we shall proceed to mention the values for the surface-tension of a recently formed water-surface found by Prof. Lenard by his fations of the vibrations of falling drops . The surfaces there investigated must , in my opinion , be considered as much older than the surfaces investigated by my experiments , on account of the of the time used for the formation of the drops . Prof. Lenard remarks in his last paper [ loc. cit. , p. 11 , note ( 18 ) ] , that this time\mdash ; amounting from to sec. in his first paper , and from to sec. in his last\mdash ; will contribute only a very little to the age of the surface of the drops , new surface continually being formed during this time . This circumstance does 0.08010 4.30 0.54 0 . Determination of ension of Water-Surface . not , however , seem to me sufficiently to justify the neglecting of this , in this connection , very time . I should rather be inclined to agree with the opinion set forth in his former PaPer , according to which the time for the formation of the drops is considered a measure for the age of the surface ( loc. cit. , p. 233 ) . A comparison between the experiments of Prof. Lenard ( ibid. , p. 236 ) and of Lord Rayleigh* on the surface-tension of a solution of soap seems also distinctly to show that the time of formation of the drops has a great influence on the condition of the surface . By the experiments of Lord Rayleigh with vibrating jets , the surface-tension of a solution of soap , 1/ 100 second after the formation of the face , was thus found to be very near to that of pure water ; while Prof. Lenard by experiments with vibrating drops ( tinl of formation greater than sec. ) finds the surface-tension of a soap solution of corres ondincr s ( 1 : 1000 ) less than half that of water and rather near the value of the surface-tension of a soap solution . It appears , from the preceding , that the high values of the tension of a recently formed water-surface and the rapid decreasing of this value , which Prof. Lenard has found by his experiments , are not in agreement with the result of my previous peliments , because the tension of water-surfaces of lower ag than those ated by Prof. Lenard have been found much smaller and pelfectly constant within the time teryal ( from to second after the uion of the surface ) during which the method allowed the determination of ension . The cause of the great deyiation between the results found by the method of drop-vibration and those found by the method of jet-vibration must , in opinion , be sought in the circumstance that sufficient regard as to the influence of irregularities of ) character , arising from the disement of the drops , is scarcely taken by the drop method . The investigation of the influence of such irregularities seems also much more difficult vibrating drops than vibrating jets , the investigation by the latter very much facilitated by the perfectly steady character of the phenomenon . these , I might call attention to the good agreement between the value of the tension of a water-surface second old dine / cm . at found in my paper , and values of the tension of a water-surface found by statical methods dine / cm . at 'Roy . Soc. Proc 1890 , vol. 47 , p. 281 . As to the result found by other methods , I might refer to the discussion in my former paper . 'Wied . Ann 1895 , vol. 56 , p. 45 Obse ? of the C. , . This agreement ceems to show that the tension of a water-surface already only second after the formation of tlJe surface ( and according to what is discussed in the present probably earlier ) assumed the nt value which the tension , if contaminations are kept , will very time . Tidal of , 1907 . SIR . , F.P.S. ( Received ) tember 2ovember 1 , 1910 . ) The } ) resent iation undertaken at the request of hackleton ; the expense of the eduction rayed by hinl , and this paper is now to Society by his pelmission . ultimately be republished as a contribution to the volume of the sical results of the expedition . The first section , describing the method of is by Janles Inrray . The second section explains the reduction of the vatiollS and gives a comparison veen the new results and those ined by the " " Discovery\ldquo ; in ) . The section is devoted to the of certain remarkable oscillations of mean sea-level and to speculations as to their cause and I.\mdash ; ON T11E IETHOD Early in June , , preparations were for the erection of tideauge , the most feature of which to be a made from modified raph . ious delnys and lnishaps it was not the nliddle of July that the completel in its form , and the continuous record which was carlied on for more than three months , subject only to the loss of half an ekly , while the : was being Dr. Iackay undertook the erection of instrument , the ratus was devised by the joint gestions of . David , fackay , lawson , Murray , while . Day did the mure delicate part of the work , nanlely . the alteration of the raph . 'Math . es Termeszettud 1885 , vol. 3 , p. 54 ( Budapest ) .

rspa_1910_0087

0950-1207

The tidal observations of the British Antarctic expedition, 1907.

403

422

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Sir George Darwin, K. C. B., F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1910.0087

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1910_0087

10.1098/rspa.1910.0087

Tables

Meteorology

Tables

]\gt ; Obse ? of the C. , . This agreement ceems to show that the tension of a water-surface already only second after the formation of tlJe surface ( and according to what is discussed in the present probably earlier ) assumed the nt value which the tension , if contaminations are kept , will very time . Tidal of , 1907 . SIR . , F.P.S. ( Received ) tember 2ovember 1 , 1910 . ) The } ) resent iation undertaken at the request of hackleton ; the expense of the eduction rayed by hinl , and this paper is now to Society by his pelmission . ultimately be republished as a contribution to the volume of the sical results of the expedition . The first section , describing the method of is by Janles Inrray . The second section explains the reduction of the vatiollS and gives a comparison veen the new results and those ined by the " " Discovery\ldquo ; in ) . The section is devoted to the of certain remarkable oscillations of mean sea-level and to speculations as to their cause and I.\mdash ; ON T11E IETHOD Early in June , , preparations were for the erection of tideauge , the most feature of which to be a made from modified raph . ious delnys and lnishaps it was not the nliddle of July that the completel in its form , and the continuous record which was carlied on for more than three months , subject only to the loss of half an ekly , while the : was being Dr. Iackay undertook the erection of instrument , the ratus was devised by the joint gestions of . David , fackay , lawson , Murray , while . Day did the mure delicate part of the work , nanlely . the alteration of the raph . 'Math . es Termeszettud 1885 , vol. 3 , p. 54 ( Budapest ) . Sir G. Darwin . Observations of the [ Sept. 27 , The ( fig. 1 ) shows the chief parts of ) apparatus and their relations to one another . The ice is shown in section , with the tripod and apparatus erected on it . A weight , consisting of a box filled with stones , rests on the sea bottom . A piece of iron tubing is let through the ice vertically and fastened . It is filled with paraffin oil , the object of which is to prevent the wire frozen in , an idea used with success by the fficers of the " " Discoverv.\ldquo ; A wire is taken from the weight on the sea bottom , passed through the oil-filled iron tube , over the pulley , and fixed to the end of the baml ) ] ever E , where it is kept FIG. 1 . taut the smaller weight F. The pulley is suspended from a tripod of bamboo poles , of which two legs are shown . The long lever works on a spindle at , and its short end I is connected by a cross-piece with the pen of the barograph . The details of this part are too small to be shown in this diagram , and will be illustrated in another figure . From this diagram there are omitted several parts , such as the guides which prevent the long lever from . during a blizzard , which are not essential to the understanding of the instrument . The barograph was of necessity covered by a box to keep out the snow . The lever entered through a slit in the end of the box , and an ement of canvas kept the snow out . The box containing I 1910 . ] British Expedition , 190 the barograph was raised on a little mound of snow , in order to the lever equal play above and below , or in other words , to allow of the mean seillevel recorded about half-way up the drum . Of course the mean level had to be asceltained by a little observation . The second is plan on a ' scale of the part of the apparatus . The circle A is the drum of the raph ; is the pen making the tracing on the is the axle on which the lever bearing the pen works . This is continued beyond the axle to a distance rather greater than that of the part bearing the pen . This end of the level is made much heavier than the other . The bamboo lcver , of which only a small is shown , is borne on axle , which is in line with the axle in the of course quite unconnected ith it , outside the glass box of the . Attached to the end of the bamboo is a stout wire , bent round so that it passes under the eud 1 ) of the pen lever , which rests upon it by its own weight , rises and falls with it , but , being quite free fronn it , is 1lot affected by any vibration of the ) under the influence of the wind . The bnrograph pen has , of course , been uncoupled from the aneroid capsules , which are not indicated in the plan . Dr. Mackay , with much assistance from Prof. David , had the set up , all but the part , by June . In order to utilise the facilities we now had for noting the changes of level , the recording instrument to be finished , ) devised a simple arrangement for the amount of the tide . It was simply inclined plane on which a paper marked with lines an inch apart pinned . On this there slid a heavy block of wood which was ched to the end of the wire over the pnlley . A lead pencil inserted a hole in the block of wood , which was kept in position by two uides . VOL. LXXXIy.\mdash ; A. Sir G. Darwin . Observations of the [ Sept. 27 , This erement is shown in fig. 3 , which is drawn in perspective . The pulley A is suspended from the tripod , B. The wire is attached to the wood block , which slides on the inclined board between the guides , F. The pbncil is fixed so as to project a little below the block of wood ; . is the line traced by the pencil . This simple device was not intended to give anything but a straight line but it was hoped by frequent inspections to ascertain tlJe turn of the-tide , and Dr. Mackay kept one night , and the gauge at intervals of about an hour . to a general slackness of the parts of the instrument the line traced was not a straight line , but a zigzag one , which proved of much greater interest . The pencil in descending did not follow the same course as it made going up , but swerved a little , and thus we the first indications of what we believe to be seiches , at any rate of regular oscillations of much shorter intervals than those of the tides . The tracing obtained thus accidentally was too vague to enable us to count with certainty the number of periods per hour , but at any rate it demonstrated oscillations of a period of a few minutes and an amplitude of a few inches . A number of records were taken in this rough manner till July 3 , when the wire was found to be broken . A new situation was then selected for the tide-gauge , nearer the house , about 100 yards from shore , where the depth was 13 fathoms . The ice being now of considerable thicknes@ , it was with no little labour that Dr. Mackay , with the help of Mr. Marston , got a new hole made to put the weight down . 1910 . ] , 1907 . By July the completed at the place , this tinle with the attachnlent . A preliminary record got from July to 11 , the instrument then stopped for readjustment . On July 14 it was stat led , and ran ithout mishap till nearly the end of Octol ) Prof. David usually the papers eekly . It was impossible to do this in the field , as it required bare The raph 1 therefore disconnected and carried to the house , where a new paper ) put on and ink put in the pen . The whole did not take more than half an hour . The scale on which the curve traced was about one-nineteenth of end of the lever feet and the short end inches . The alue of the factor of reduction of amplitude has therefore been taken to be 7/ 132 or One of the first for a complete week was analysed . The curve appeared a simple one with maximum , but a slight of the minima indicated that other elements were present . The showed that there was a tide . have ing two xima daily . The whole of the tide highest about feet . The reatness of it surprised us , as the tide Cl.acks usually difference of of not more foot to feet . This have been because the free edge of the crack not room to sink to the full exteJlt of the but on botton ] , and the ice then to the level part . Towards the end of Octobcl the tripod down dtll i a and the wire was snapped . The ice was by this ti1ne so thick that it was found iolpraccicable to cut another hole to put a weight ( so the observations were discontinued . The curve traced on the drum very frequent indications of seiches the form of but the scale so and the clock-motion so slow that these indications wel.eblurl.ed and useless study . It and would lave been , to substitute a cloc of about 10 times the speed to a allendar 1ecord swhich had with us , but it late i11 the season before we coudd try it , the ) of the put a stop ) the attempt . II.\mdash ; THE 0F TIDAL The motion ot the ice the tively to the -bed transmitted to the ] ) means a lever , as ined it is very neally exactly the of the arc turl ) the lever which to have been meaSUl.ed . it is the arc itself is recolded on the curvilinear scale on the . The turned Sir G. Darwin . Observations of tloe [ Sept. 27 , by the lever is , ever . sufficiently small to permit us safely to the correction in strictness required for the conversion of arcs to chords , and the arcs have been accepted as giving the changes of water level with sufficient accuracy , The tidal record extended from July 14 to October , 1908 , but the sheet which bore the record from October 12 to 18 is missing , and the record actually treated ends with October 11 . It was possible by means of a few interpolations to obtain an unbroken record from . astronomical time of July 14 to 23 . of October 11 . About an hour was generally lost once a week , while the paper was being changed : but it was always easy to complete the curve over this short interval by a pencil line , and this was regarded as equivalent to the actual curve . On September 13 the pen failed to mark , but the curves on the 12th and 14th were unusually regular in character , so that a good interpolation the 13th was easily obtained . The following is a list of the interpolated and the hours are given inclusively in astronomical time : July 14 , . to 3 . ( extrapolated ) ; July 19 , 19 . to 23 . ; September 12 , 17 . to 23 . ; September . to 23 . ; October 11 , 22 . and 23 The errors of the clock do not seem to have been great to demand attention , and in fact , they are not always noted on the rams . The clock was kept to apparent time , and was reset as the equation of tinle changed sensibly . the scheme of reduction assumes that mean time has been used . This error may be taken into account with sufficient by certain changes in the true longitude of the place of observation , which was E. The observations were broken into three groups of a month each , for which the epochs were : ( 1 ) , July 14 ; ( 2 ) , August 13 ; ( 3 ) , September12 , To allow for the equation of time the longitude for the first month was taken as 6 . of time or 1o 30 ' further east than in reality ; in the second month the longitude was arded as correct , and in the third it was shifted 10 to the west . The correction for the last month is less satisfactory than for the other two , because at that time of year the equation of time is rapidly , and differs considerably at the beginning and end of the month . The unit adopted the height was 1/ 10 of an inch of the scale on the drum . Since 1 inch on the drum corresponds to inches of water , the heights as derived from the harmonic analysis of the readings were converted to inches on multiplication by 1910 . ] , 1907 . For the tides the observations were also as apperGainingl to a period of three months , without regard to the equation of time ; a similar treatment was also extended to the tides , K2 , , and as will be explained more fully hereafter . The reductions were made , under my supelvision , by . F. Finch with apparatu in the first instance the three months were discussed independently . The semidiurnal tides were derived from months of 30 days , and the diurnal tides from months of 27 days . In this treatment it is necessary to assume that the phase of the tide is the same as that of and that the amplitude of K2 is 3/ 11ths of that of . Similarly , we must assume identity of phases for and , and that the amplitude of is of that of The following are the results:\mdash ; July 1Sept . in . in . in . in . in . in . in . in . in . in . in . in . in . in . in . in . in . in . in . in . in . in . in . in . in . in . in . in . in . in . in . in . in . in . in . in . in . in . in . in . in . in . Sttme inas f in . in . Sttme inas f in . in . Sttme inas f in . in . Sttme inas f in . in . Sttme inas f in . in . Sttme inas f in . in . Sttme inas f in . in . Sttme inas f in . in . Sttme inas f in . in in . in . in . in . in . 30- In these results there appears to be some evidence of a the season advances , such as was noted in case of the ionS made by the " " Discovery\ldquo ; in , and I shall retul'n later to subject . But in the case of the tides , this easily arise from an erroneous assumption as to the heights and phases of and relatively to those of and respectively . It is therefore advisablo to discuss these tides without making the assuml ) tions which necessary when each month is treated independently of the others . * . Soc. Proc 1892 , vol. 52 , p. 345 , or ' Scientific ) , Paper 6 . 'National Antarctic Expedition , 1901\mdash ; 4 , Physical -ations ' ( 1908 ) , p. 3 ; ' Scientific Papers , ' vol. 1 ( I907 ) , Paper 12 . Sir G. Darwin . Observations of the [ Sept. 27 , In explaining my , I adopt the notation of my paper " " On an Apparatus for the eduction of Tidal Observations . The heights and phases of the tides are denoted respectively pair of harmonic constituents for diurnal tides , when 27 consecutiye days are analysed , are denoted by . , and the theory shows that . Similarly , when consecutive days are analysed , and when denotes the mean value for the month of the ratio of the cube of the sun 's parallax to his mean parallax , the pair of semi-diurnal constituents are given ) . In each single month independentl . , we assumed , but we now no ake that supposition . If we put ; ; , are known functions , and each month ives the pair of equations\mdash ; Thus the three months afford six equations for the determination of which the and phases of and are easily found . Again , if we put ; ; ; each month gives for the semi-diurnal tides the pair of equations\mdash ; ; ' Roy . Soc. Proc 1892 , vol. 52 , pp. : or ' Scientific Papers , ' vol. 1 ) , Paper 1910 . ] Expedition , 1907 . and the three months si equations for from which the heights and phases of and are easily found . On solving the dinrnal group of equations by least I find inches , inch , . The ratio of to is , instead of the 3 assumed from theoretical considerations in the separate treatment of the months , but the phases are virtually identical . The similar treatment of the semi-diurnal group gives inch , inch , The ratio of to is , instead of , as assumed from theory . It thus appears that the theoretical hypotheses considerably in and results probably more in accordance with the truth will be obtained from the several months if we assume With these assumptions the three months now give\mdash ; 2 . 3 . in . in . in . in . in . in . in . in . in . in . \mdash ; \mdash ; The appearance of ressive s change in this of tides has now almost disappeared , although the nlonth is slightly discordant from the other } It is interesting to note that , in the result of the treatment by least squares , ( for ) is practically identical with ( for P ) , but ) there considerable between and ( for ) . The difference between the phase of hich we may tnke as by and that of riven by is very their difference of speeds is not reat . Itence we should expect that a small difference of speed in a tide old 1 sensible erence in phase . If phase varies sinlply as difference of speed , shall have the results : Speed of speed of per hour ; ) ) Speed of speed of per Sir G. Darwin . Tidal Observations of the [ Sept. 27 , Hence we ought to find , As a fact , we find , and thus the direction of the diffel.ence of phases is such as was to be expected , although the amount is not satisfactory . With tides of such small amplitude , however , and with only three months on which to rely , the amount of agreement is all that is to be expected . The results of the analysis for the tides M2 and , when the months are taken independently , are above . If , however , we neglect the equation of time , the whole period of three months may be treated as a single group of observations . In this way I obtain for inches , If we take the three values of each of the quantities from our previous results , and form means of these functions , we obtain inches , The latter method has the that it takes the equation of time into account ; the former is somewhat more likely to eliminate casual inequalities . We may safely . take ) inches , , as very near the truth . Similarly the whole series when treated for the tide gives inches , But the means of the three values of , give the somewhat discordant esult inches , I should have expected the two uations to be closer together , as was case with , and I think we must accept inches , as as nearly accurate as is possible from our data . In the reduction of the ' Discovery\ldquo ; obsel.vations it was known that there had frequently been a small change of the zero point in consequence of the shift the ship , and I did not think it was worth while to attempt 1910 . ] British , 1907 . to combine the several nlonths by least squares so as to separate the tides , from K2 , and from P. I llow think that it was a pity that the attempt was not made to separate them , and therefore I have bnck to the old work and discussed the numbers by least squares with the results iven below . In the course of this revision it appeared that there had been a small mistake in the value assigned to for each month , which , however , made little change in the values vned to the tide , and did nothing to remove the considerable discrepancies between the results from each of the 12 months . FINAL TABLE or ESULTS F\ldquo ; ] ] THERE )ITII C VlTlf \ldquo ; \ldquo ; ' \ldquo ; ' ' \ldquo ; new reduction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . \mdash ; \mdash ; ( ( Tilllrod , \ldquo ; 1908 . ( . ' \ldquo ; new duction . in . K. in . in . K. in . in . in . in . in . in . in . in . in . in . in . in . in . 3 OS2 in . in . :3 in . in . The eeluent between these sets of constants , ctednced observations taken at places some 25 miles apart , seems to be very . The later ations were taken furtl ) . north than the earlier ones , and the greater value of in the more nherly series is a reality , The two days of observation made by Dr. Wilson in 1904 close to the ( Nimrod\ldquo ; station with our present results in indicating a htly increased value of ) sc1ni-diurnal tide . In discussing the : \ldquo ; tides , I was led to suspect that thele semi-diurnal lines to the northward , but that the node for nearer than ) . The fall in the amplitutlo of anrl possibly the amplitude has to increase previously to its decrease to the zero value at node . The ratio of to for " " Nimrod\ldquo ; is , and for ) " " the former value is more nearly normal thau the latter . Sir G. Darwin . ) oj the [ Sept. 27 , The sums of the of , are respectively inches for Nimrod\ldquo ; and for " " Discovery The smns for are inches for : ' Nimrod\ldquo ; and inches for Discovery Thus for " " Nimrod\ldquo ; the greatest diurnal tides are times as great as the greatest semi-diurnal tides , while for " " Discovery\ldquo ; the greatest diurnal tides are times as as the reatest semi-diurnal tides . This emphasises the importance of the semi-diurnal tides as we penetrate to the south . It should be remarked that the difference of phase of from that of in the new reduction for " " Discovery\ldquo ; is not in accordance with the theoretieal considerations adduced in support of the corresponding difference for " " Nimrod However , too much stress should not be placed on results crived from these very small tidal oscillations . On the whole , I conclude that we now know the tidal constants at this part the Antarctic Ocean with as much accuracy as is desirable , and I reler the reader to the discussion the " " Discovery\ldquo ; observations for the conclusions which may be drawn from the values found . In discussing the " " DiscoveT)\ldquo ; obseryations , I saw reason to suspect a lemarkable seasonal , in the amplitude and phase of the tide ; it is therefore to see whether these new observations tend to confirm conclusion . The results in my previous aper were discussed by means of curves , but I will now merely examine the matter numerically . The results for each month which has been reduced , , 12 fcr Discovery\ldquo ; and 3 for Nimrod may be held to appertain to the middle ( of the month under consideration , that is to say 15 days after the correepoch . The following table exhit ) the values of and for each of the Date . inches . 2.41 2 . 2 . 1.56 1.21 inches . Apr. 21 , 1903 191 May 24 , 1933. . 220 27 , 1902 . . June 20 , ) . . . . . 229 30 , 1908. . . . 233 , 1903 . . 2.41 * 29 , 1908 Aug. 8 , 1902 . . * 28 , 1908 29 , 2.18 Sept. 7 , 1902 * 27 , 1908 . . 2 . . 8 , 1902 1.74 28 , 1.56 Nov. 28 , 1902 inches . Apr. 21 , 1903 191 May 24 , 1933. . 220 27 , 1902 . . June 20 , ) . . . . . 229 30 , 1908. . . . 233 , 1903 . . 2.41 * 29 , 1908 Aug. 8 , 1902 . . * 28 , 1908 29 , 2.18 Sept. 7 , 1902 * 27 , 1908 . . 2 . . 8 , 1902 1.74 28 , 1.56 Nov. 28 , 1902 inches . Apr. 21 , 1903 191 May 24 , 1933. . 220 27 , 1902 . . June 20 , ) . . . . . 229 30 , 1908. . . . 233 , 1903 . . 2.41 * 29 , 1908 Aug. 8 , 1902 . . * 28 , 1908 29 , 2.18 Sept. 7 , 1902 * 27 , 1908 . . 2 . . 8 , 1902 1.74 28 , 1.56 Nov. 28 , 1902 inches . Apr. 21 , 1903 191 May 24 , 1933. . 220 27 , 1902 . . June 20 , ) . . . . . 229 30 , 1908. . . . 233 , 1903 . . 2.41 * 29 , 1908 Aug. 8 , 1902 . . * 28 , 1908 29 , 2.18 Sept. 7 , 1902 * 27 , 1908 . . 2 . . 8 , 1902 1.74 28 , 1.56 Nov. 28 , 1902 inches . Apr. 21 , 1903 191 May 24 , 1933. . 220 27 , 1902 . . June 20 , ) . . . . . 229 30 , 1908. . . . 233 , 1903 . . 2.41 * 29 , 1908 Aug. 8 , 1902 . . * 28 , 1908 29 , 2.18 Sept. 7 , 1902 * 27 , 1908 . . 2 . . 8 , 1902 1.74 28 , 1.56 Nov. 28 , 1902 inches . Apr. 21 , 1903 191 May 24 , 1933. . 220 27 , 1902 . . June 20 , ) . . . . . 229 30 , 1908. . . . 233 , 1903 . . 2.41 * 29 , 1908 Aug. 8 , 1902 . . * 28 , 1908 29 , 2.18 Sept. 7 , 1902 * 27 , 1908 . . 2 . . 8 , 1902 1.74 28 , 1.56 Nov. 28 , 1902 inches . Apr. 21 , 1903 191 May 24 , 1933. . 220 27 , 1902 . . June 20 , ) . . . . . 229 30 , 1908. . . . 233 , 1903 . . 2.41 * 29 , 1908 Aug. 8 , 1902 . . * 28 , 1908 29 , 2.18 Sept. 7 , 1902 * 27 , 1908 . . 2 . . 8 , 1902 1.74 28 , 1.56 Nov. 28 , 1902 inches . Apr. 21 , 1903 191 May 24 , 1933. . 220 27 , 1902 . . June 20 , ) . . . . . 229 30 , 1908. . . . 233 , 1903 . . 2.41 * 29 , 1908 Aug. 8 , 1902 . . * 28 , 1908 29 , 2.18 Sept. 7 , 1902 * 27 , 1908 . . 2 . . 8 , 1902 1.74 28 , 1.56 Nov. 28 , 1902 inches . Apr. 21 , 1903 191 May 24 , 1933. . 220 27 , 1902 . . June 20 , ) . . . . . 229 30 , 1908. . . . 233 , 1903 . . 2.41 * 29 , 1908 Aug. 8 , 1902 . . * 28 , 1908 29 , 2.18 Sept. 7 , 1902 * 27 , 1908 . . 2 . . 8 , 1902 1.74 28 , 1.56 Nov. 28 , 1902 inches . Apr. 21 , 1903 191 May 24 , 1933. . 220 27 , 1902 . . June 20 , ) . . . . . 229 30 , 1908. . . . 233 , 1903 . . 2.41 * 29 , 1908 Aug. 8 , 1902 . . * 28 , 1908 29 , 2.18 Sept. 7 , 1902 * 27 , 1908 . . 2 . . 8 , 1902 1.74 28 , 1.56 Nov. 28 , 1902 Apr. 21 , 1903 May 24 , 1933. . 27 , 1902 . . June 20 , ) . . 30 , 1908. . . . , 1903 * Aug. 8 , 1902 * t. 7 , 1902 * 27 , 1908 . . . 8 , 1902 Nov. 28 , 1902 Apr. 21 , 1903 May 24 , 1933. . 27 , 1902 . . June 20 , ) . . 30 , 1908. . . . , 1903 * Aug. 8 , 1902 * t. 7 , 1902 * 27 , 1908 . . . 8 , 1902 Nov. 28 , 1902 Apr. 21 , 1903 May 24 , 1933. . 27 , 1902 . . June 20 , ) . . 30 , 1908. . . . , 1903 * Aug. 8 , 1902 * t. 7 , 1902 * 27 , 1908 . . . 8 , 1902 Nov. 28 , 1902 Apr. 21 , 1903 May 24 , 1933. . 27 , 1902 . . June 20 , ) . . 30 , 1908. . . . , 1903 * Aug. 8 , 1902 * t. 7 , 1902 * 27 , 1908 . . . 8 , 1902 Nov. 28 , 1902 l5 1910 . ] British . , 1907 . 15 months , together ) the dates to hich the be held to applv . The new results are marked an asterisk . In order to.judge of the ression in the should note that the mean for the norChel n is , and for the southern is Hence we , perhaps , to reduce the three " " Nimrod viz. , , in the proportion of The corresponding as so reduced are written in parentheses after the actual numbers . The proin the heights appears to be fairly consistent , but that of the phases is not so clear . The phase of the of the " " \ldquo ; months is some 15o awa . from what we should expect if the ressive c is an actuality . If we convert this into lime , it means that the should be changed by half an hour to fit into the supposed ) ression . The middle month fits into its place fairly well , but the ]ater for he third month should be shifted some 40 minutes . Such changes are not , ever , large , when we consider that the range from high to low water is only about 5 inches . On the whole , I should ay that the new results do not tend to confirm the truth of the progressive change in marked , but they can hardly be held to invalidate it . If we examine the results of the three months for the tides , find some traces of a seasonal progression , for the are ; but the progression of phases is again not clearly marked , for . I was not able to detect any evidence of in the case of the tide as observed by the " " Discovery III.\mdash ; ON EICHES ] THE TARCTlC O In the course of the reduction of the tidal dail heights of the water were computed , so as to furnisb a of the summations necessary in the monic analysis . the arduon . conditions under which the observations were it seemed well 10 test series of , so to tletect any accidental shift in of the gauge which have curled . tuuately , no snch examination of the ' Discovery\ldquo ; observations had out , ) it was well known that there had been frequent of to the shift of the ship . It did not occur to me that a illnstlatiun oi ' mean sea-levels , to be ) to some}l hat of might give indications of vorthy of 1lotice . A cursory examination of a table of the daily } uf series at once revealed considerable inequalities . paper on the changed once a week , yet there no of discontinnity , and the observers did not think reaso1l to ] ) Sir G. Darwin . Observations of the [ Sept. 27 , : each paper and the next . of daily mean sea-levels was accordingly plotted , as on a reduced scale in the firm line of fig. 4 . I was surprised to see a somewhat regular rise and fall of the water with a period of about three days , for nearly five weeks on end . Although the rise and fall was interrupted , this seemed to be a fact worth looking into . A line drawn so as to bisect the zigzags clearly undergoes changes considerable amount , for which it is only possible to guess the causes . Distant barometric and distant gales may be responsible for most of the effect . There are also probably annual and semi-annual meteorological tides , fortnightly and monthly astronomical tides , and some small inequality with a period of a fortnight due to the residual effects of the tides of short period . But these obviously could not produce the shorter zigzags , so that we may consider these as being embroidered , to use M. Forel 's phrase , on a slowly variable curve . Local barometric must affect the mean sea-level , and pressure lbove the mean will correspond with depressed sea-level , at the rate of about inches of water to one of mercury , and . Mr. James Murray has given me the mean barometric heights both in a tabular and in a graphical form . The means of pressure are given in civil t.ime , while those of sea-level were computed according to astronomical time . I therefore made a estimate from the curve of the mean pressure according to the latter time . The mean pressure for the 90 days of observation was then found , and a correction was applied to the sea-levels at the rate of 14 inches of water to one of mercury above or below the estimated mean . A rather high value for ths correction is taken , because it seemed desirable to give the barometric changes every possible chance of mnulling the sea changes ; and further , because , by the use of the factor 19 ( instead of ) , the zigzags had been very slightly gerated . In any case , the correction is quite exact enough for such a rough allowance for barometric pressure as is possible . The corrected mean sea-levels are shown in the dotted curve of fig. It will be seen that the zigzags are ensibly diminished , but not annulled , that in one or two places a new maximum or minimum has been introduced . We may conjecture that distant barometric changes and distant ales n have annulled some maxima and minima which vould otherwise have been visible . For servations of this uncertain kind mathematical treatment for the detection of partially veiled periodicity seems inappropriate . I have therefore only examined zigzag for maxima and minima and have noted these incidences in the following table . In five cases a mark of is 1910 . British Antnrct Expeditio 1907 . 417 Sir G. Darwin . Tidal of tloe [ Sept. 27 , added because another observer deny the existence of a maximum or minimum which I conceived to be there , but partially masked by the general rise or fall of an ideal line bisecting the zigzags of the dotted line . In the second column of each half of the table I give the differences between the dates in days , and these numbers will give the period of the suspected inequality . TABLE MAXInA AND MINISIA 0F MEAN SEA-LEVEL CORRECTED F0R PRESSURE , 1908 . Periods Maxima , in days . July 16 Aug. 2 2 Sept. 2 2 Oct. 1 Periods Minima . in days . July 14 Aug. 3 Sept. 1 Oct. 2 The intervals between successive maxima are as follows:\mdash ; 1 of 1 of 5 1 of Total of 27 periods days . 5 of Mean period days . 4 of 7 of 8 of lti If we suppose the intervals of , 5 , and were really double periods , with masked maxima there were 30 periods , and the mean becomes days . I 910 . ] , 1907 . intervals between the minima as 4 of of 8 1 Total of periods S9 } 13 of Mean period } of of If the intervals of five ) really double periods with masked ulinima interyening , there ) eriods and the mean period becomes days . Taking both estinlates as of equal we a mean interval of days , or allowing for possible masked nlaxima or minima , as explained nbove , of days . I think then that there is some evidence of the existence of an oscillation with period of about three days . In a paper in the 'Philosophical azine ' Tanuary , , lIessrs . Honda , Terada , and Isitani discuss " " of Oceanic Tides\ldquo ; or sea-seiches . These seiches occur in , and they find that the pel.iod depends on the size and depth of the bay . In some bays the period is fairly constant , but in others it changes " " continuously and through certain They that for a bay of and depth the main period is iven by the , where is ravity . The period as so computed is snbject to a correction due to the opening into the sea , but only now want a very estimate of the period , correction be ected . The formula is the sam as that for the period of the unin odal seiche in a lake of length . The authors in fact regard the cnd of the as lesenlbling the end of a lake , while the seaward is equivalent to the middle of the lake . Accordingly the second half of the lake , whichvould stretch out into the sea , is suppressed . The formuhx gives results in accordance with the seiches observed in many } ) anese bays , and they remal'k that bays are sometimes disturbed by seiches of shorter pel.iod , which they transverse seiches from side to side of the bay , just if it an enclosed basin . In none of the exalnples given by these authors has the seiche a period at all comparable with of which we have reason to suspect the existence in the Antarctic Sea , that aft'ords no reason for to apply the theory to such prolonged oscillations . In most inland . lakes the seiches.have periods of 10 minutes to one or two hours , yet in Lake Erie the seiche is found to have a period of hours , while in the Lakes of A 20 Sir G. Darwin . Tidal Observations of the * and Huron conjointly a seiche of 45 hours is suspected . * Thus we have justification the application of the th eory to oscillations of very long period . In the case of the Antarctic Sea , if there is a great bay running far back into the Antarctic continent behind the ice barrier , its length and depth are quite unknown . Hence there are elements of great uncertainty in the application of the theory . It seems likely , at any rate , that the bay extends for a considerable distance , and speculations have even been made as to whether there may not be an arm of the sea to the Weddell Sea almost dialnetrically a whakwas supposed to be a continent . It , perhaps , be thought that the thick ice of the barrier would serve to damp out cillations of sea-level ; but , unless , indeed , the sea is solid to the bottom , I conceive that the ice would behave like an elastic skin , ind would hardly exercise any damping effect on oscillations with a period of more than an hour or two . It seems almost impossible that the remarkable changes of sea-level which are obseryed should arise from errors of observation , and if they exist at Backdoor , the sea the barrier must necessarily also partake of the motion . If the sea rises and falls . the barrier itself , must moye with it ; and it may be suspected that it is subject to a true tidal lise and fall . If we accept the existence of a sea-seiche with a period of three days , the formula gives indication as to the length and ) of the bay behind the barrier . We cannot assume the sea to be very shallow , because if it were so it would ineyitably be frozen solid to the bottom . Moreover , shallow sea would certainly be broken up by shoals , so that it could not oscillate as a single ystem . A little consideration shows that to produce a seiche of three days the bay must be of enormous length , and for the reasons assigned it would be useless to assume it to be very shallow . The few soundings near the barrier give depths of between 200 and 300 fathoms , and perhaps a somewhat smaller depth might suffice to allow of the required seiche . I propose to guess the length of the bay and to find what depth of sea is required to produce a seiche of three-day period . I guess then that the bay behind the barrier stretches past the South Pole and a little to the east of it as far as latitude . Such an inlet would have a length of to of latitude . It seems likely that if it is really an arul of the sea th.ough to Weddell 's Sea , with a constriction about the place where we place the end of the bay , the seiche would be much the same . * Dr. Anton Endros , Peterm nn 's Geograph . Mitteilungen , ' Heft II , 1908 . 1910 . ] Expedition , 1907 . Tile 1 of supposed bay in centimetres will be ) or 30 times , and these I take as two assumed values of . On the multiplications I find that will be cm . or cm . The period of oscillation is three days , or sec. ; also is 981 . Thus , numbering our two alternatives as ( 1 ) and ( 2 ) ( 1 ) Whence ( 1 ) cm . cm . thoms . fathoms . Thus a sea of from].00 to l50 fathoms in such an immense bay as has been conjectured would oscillate a pel'iod of three , and ) obssl'ved results are seen to be consistent with the existence of a deep inlet , almost or quite cutting the Antarctic continent in two . Such a conclusion is interesting , but it would llot be to attribute to it a of probability , because there are elements of uncertainty on every side . In view of the interest of our result it has seemed well to reverG to the observations made by Captain Scott 's expedition , notwithstanding the known uncertainty in the zero of the . I therefore examined days of the " " \ldquo ; record , , 113 days of 1902 and 62 days of 1903 . correction has been applied for barometic pressure , and thus periodic inequalities have doubtless sometimes been masked by contem } ) oraneous changes of pressure , and by the shift of zero . I should expect to find rather a ) ortion of long intervals between consecutive maxima and minima than in the imrod \ldquo ; results as reduced for pressure . I found , in fact , on analysing the in the way already plained th amongst the periods as deduced from maxima , there were : 2 of , lof , 10 of 5 , lof and amongst the periods , as deduced from minima , there were\mdash ; lof , lof 5 , lof Taking maxima and minima together there were 83 periods to 323 days , thus giving a mean period of days . But if we postulate that periods from 7 days to days were leally double periods with masked maxima or minima , and that the LXXXIV.\mdash ; A. 2 Observations of the British 9-day period is really triple , we get 105 periods for 323 days , with a mean of days . These results are generally confirmatory of the preceding ones , but seem to indicate a slightly longer period . In this rough examination there is undoubtedly a danger of finding a false periodicity under the influence of unconscious bias . I thought it advisable therefore to examine other tidal records , for it } be possible to perceive periodicity even in cases where there was but small likelihood of its real existence . Colonel Burrard then kindly sent me tables of daily mean sea-levels for the year 1880 from May 1 to June 30 and from October 1 to ember 3 for Aden , Karachi , Madras and Port Blair , Andaman Islands . These old observations were chosen because it had been usual at that time to have each daily mean " " cleared\ldquo ; of the residual effects of the tides of short period , and thus one slight source of error was obviated . I also oceeded in the case of Aden to deduct the tides of long period , but as this correction clearly made no difference in the kind of inequality I was looking for , I did not carry out that laborious task in the other cases . The tabulated numbers were then plotted out in a number of curves . An inative investigator possibly fancy he could detect signs of periodicity with a period of two or three days at Aden and at Port Blair , but as the range from crest to hollow was not more than inch , it seems safer to say that no periodicity could be traced . In the curve for Madras there are considerable , but it seemed impossible even to imagine any periodicity . At Karachi there does seem to bc an inequality with a period of two to three days and a of two or three inches . A succession of waves with three to five crests one after the other is observable at several parts of the curve . It seems quite likely that sea-seiches may exist in the Indian Ocean , and Karachi would be well placed for observing them . These Indian results were not corrected for barometric pressure , and it may be worth while hereafter to submit them to a more systematic examination . For the present , however , I am satisfied with the c , onclusion that periodicity is not to be seen in all cases , and that the oscillations of mean sea-level in the Antarctic Sea are many times as great as those in the Indian Ocean and Bay of Bengal . Thus it seems unlikely that imagination is responsible for the existence of the Antarctic sea-seiches , and we may ope that the investigations of Captain Scott 's second expedition will throw some further light on the subject , and possibly also on the existence of a deep bay behind the barrier .

rspa_1910_0088

0950-1207

On a mistake in the instructions for the use of a certain apparatus in tidal reductions.

423

425

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Sir G. H. Darwin, K. C. B., F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1910.0088

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1910_0088

10.1098/rspa.1910.0088

Tables

Meteorology

Tables

]\gt ; On a Mistake in the structions for the Use of a C in Reductions . By Sir G. H. , K.C.B. , ( Received November 4 , \mdash ; Read November 10 , 1910 . ) apparatus is describe in the ' Proceedings ' of the Royal Society , vol. p. Collected Scientific Papers . I first correct an obvious misprint in fig. 3 , where is inserted in place of In S6 the incidence is determined of the exact mean solar hours of a day amongst the hours of a special time scale , when the- . of solar . time is assumed to fall within half a special hour of an exact hour of special time . from this 12 . of solar time we proceed upwards by Stlb r 1 , hours of solar time , but in special time , . to the integral special hours when necessary so as to make that integral number lie between and inclusive . Similarly we proceed downwards adding 1 , 211 hours of solar time expressed in special time , and nilarl reduce the integral number of special hours so that it shall lie betn'een and 23 . There are thus in the schedule , 12 above the ldle and 11 below . If denotes an . solar hour , an exact special hour , and an error expressed in special time , each line of the schedule is of the forlu both and are whole numbers lying between and 23 The frequency of the error is ated , and is to conform to a certain law which is identically the same for each special hour from to 23 inclusive . Each harmonic tide goes its period times ( with equal to 1 , 2 , 3 , 4 , or 6 ) in its appropriate special day . The height of the water is supposed to be observed at the exact solar , and the problem is to determine the error in the result when the observations are deemed to appertain to the corresponding exact hours of special time . M. M. H. van wrote to me from the opinion that my procedure was erroneous , and I to find that his suspicion is well founded . tely the error thus introduced is nificant as regards practical tidal work . I will not explain how I came to go wrong , but will consider the correct procedure and show how the rules of computation must be amended . 424 Sir G. H. Darwin . in the Instructions for [ Nov. 4 , Let denote the speed of any one of the harmonic tides expressed in degrees per mean solar hour . Then since we may without loss of enerality take the amplitude of the tide as unity and the phase as zero , the 24 observations at the mean solar hours will be 24 values of corresponding to equal to , 1 , 2 23 , and as before is one of the numbers 1 , 2 , 3 , 4 or 6 . We equally well have proceeded from and it is on this account that the phase is immaterial for our discussion . We have to translate ncot into special time . By the definition of a special day , when translated becomes per special hour , and by the edule of incidence becomes , thus we have . In my paper I virtually wrote as , and as , so that was error reduced to angular measure at the rate of per special hour . Hence the function to be considered , where is subject to a certain known law of frequency , say . It was at this point that I made the mistake , for I erroneously considered the function . The required mean value of is clearly to be determined from the fraction The integral in the denominator was found correctly , but that in the numerator was because of the wrong sign of under the cosine . The factor in the result which was given as must be corrected so as to stand as It is proved that is equal to , where The correct final result is . The was correct , but the term in was given in the paper with the wrong Accordingly the paper may be corrected by changing the sign of every term involving and in the computation forms the co1Tections in have been applied with the wrong although the numerical values remain correct . Copies of the computation forms have been sold by the Cambridge Scientific Instrument Company for use with the apparatus , and I shall try to 1910 . ] the Use of Certain } Tidal . 425 reach the purchasers circular out that all the corl'ections on p. 12 of the forms which involve been systematically applied with the signs . I notice on p. 13 under the heading a mispl.int of instead of , but the number nttached , viz. , is correct , except of course as to its sign . The correction of the phases derived from the erroneous instl.uctions may be at once effected without recurring to the computations by adding to each twice the value ) ulated in the paper for the corresponding If this note should be seen by } one concerned who may not reccive a circular I him to notice the correction . It has already been remarked that the error is practically insignificant . The only tide in which it could possibly be appreciable is M2 , and since in this case the correction is equivalent to one minute of time in high water , the mistake caused by the erroneous instructions httS been minutes of time or 1o in . Even for M2 the discrepancies in from year to year are often as great or reater than , and in the smaller tides they are frequently far greater ; moreover the solar group of tides has been unaffected by the mistake . practically the error is of little importance , it is clear that it to be corrected . * See ' Roy . Soc. Proc , p. , or ' Scientific Papers , ' loc. , p. 241 .

rspa_1910_0089

0950-1207

On the sequence of chemical forms in stellar spectra.

426

432

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Sir Norman Lockyer, K. C. B., F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1910.0089

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10.1098/rspa.1910.0089

Atomic Physics

Astronomy

Atomic Physics

426 On the Sequence of Chemical Forms Stellar Spectra . By Sir Norman Lockyer , K.C.B. , F.R.S. ( Received October 17 , \#151 ; Read November 24 , 1910 . ) [ Plate 6 . ] Introduction . In the Bakerian Lecture , 1873 , * after summarising the observations of stellar spectra and my laboratory researches which had been made up to that time , I wrote : " I have asked myself whether all the above facts cannot be grouped together in a working hypothesis which assumes that in the reversing layers of the sun and stars various degrees of celestial dissociation are at work . " The phenomena revealed by the spectroscope seemed to afford a demonstration of the validity of Prout 's hypothesis , for so far as the stellar spectra were then known , hydrogen seemed to be the chief constituent of the hottest stars as judged by the extension of the spectrum into the ultra-violet . In a letter to M. Dumasf I wrote . " Plus un est chciude plus son spectre est simple . " The idea that stars with different spectra were entirely composed of different chemical elements gave way to one in which the chemistry was a function of temperature only , the chemistry of all stars having the same basis . I should here state that from the first I have used the term temperature as including electrical effects.^ In 1888 , in another Bakerian Lecture , S I brought together the various eye observations of the spectra of stars , comets , and nebulae which had been made by others up to that time , and showed that the discussion suggested the hypothesis that all celestial bodies are , or have been , swarms of meteorites , and that the difference between them is one of condensation only . This hypothesis , instead of locating the highest temperature at the commencement of the evolution as demanded by Laplace 's hypothesis , placed it much later . Hence bodies of increasing temperature were demanded as well as bodies of decreasing temperature . In 1892|| I gave an account of the work carried on up to that year in the Solar Physics Observatory on the photographic spectra of stars , and I laid * ' Phil. Trans. , ' vol. 164 , Part 2 , p. 480 et seq. t ' Comptes Rendus , ' 1873 , vol. 77 , p. 1347 . % ' Roy . Soc. Proc. , ' 1874 , vol. 22 , p. 372 . S ' Roy . Soc. Proc. , ' vol. 44 , p. 1 et seq. || 'Phil . Trans. , ' vol. 184 , pp. 675\#151 ; 726 . On the Sequence of Chemical Forms Stellar Spectra . 427 before the Royal Society a classification of stars based on the then known chemistry and the extension of the spectra into the ultra-violet so far as it could be determined when glass prisms and lenses were used . I divided the stars into groups and sub-groups , and pointed out that , as more photographs became available , the sub-groups would in all probability become divisible into species . By 1897 the problem had entered into a new stage . I had in the meantime published the complete spectra of the cleveite gases , including helium , which Ramsay had run to earth , * and by the use of a large coil had discovered a new series of lines , which I termed " enhanced lines , " in the spectrum of iron.f By the continuation of this work most of the unknown lines in the spectra of the stars were identified , and stars were found the spectra of which contained the enhanced lines of various metallic elements without the arc lines . The research could therefore be continued on a much wider basis . This was done , and 1897 I laid before the Society a memoir on the chemistry of the hottest stars . | At the end of that memoir I wrote : " The above conclusions , based on laboratory , solar , and stellar evidence , all tending in the same direction , may be regarded as the result obtained so far in regard to the ' celestial dissociation ' which I pictured to myself in 1873 . I claim that each step in the work has demonstrated the truth of that hypothesis more and more , and that we can now acknowledge that the phenomena of the inorganic world are dominated by an evolution not less majestic , although more simple , than that now universally accepted in the case of organic nature . " More recently ( 1905)S I have checked the chemical classification by studying the physical condition of stars , using a calcite-quartz optical train to obtain photographs of the extension of the spectra of each chemical group of stars into the ultra-violet on the same plate and under equal conditions of atmosphere and altitude . I found absolute parallelism between the two series of photographs . This , of course , confirmed the prior chemical results . It is to be remarked that the study of temperature effects in the stars is much more simple and effective than their study in the laboratory , as in the laboratory the effects produced at low temperature are always present , while in the hotter stars , the lowest temperatures where the phenomena observed are produced , may be taken as anything between 5,000 ' and 20,000 ' C. There is thus a complete shielding from the effects produced at low temperatures . * * * S * ' Roy . Soc. Proc. ' 1895 , vols . 58 and 59 , several papers . + ' Roy . Soc. Proc. , ' vol. 60 , p. 475 . X 'Roy . Soc. Proc. , ' vol. 61 , p. 148 . S ' Roy . Soc. Proc. , ' A , vol. 76 , p. 145 et Sir N. Lockyer . Sequence of [ Oct. 17 , Recent Work on the Classification of Stars . The more recent researches with better photographs and with increased knowledge of the changes in spectra have enabled me to carry the classification into finer details , and to observe with greater certainty the heat levels at which various chemical forms are predominant . By the term " chemical forms " I mean the molecular grouping , as I termed it 40 years ago ( or the corpuscular grouping , as perhaps it may be called now after the recent discoveries of J. J. Thomson , Becquerel , Curie , Bamsay , Butherford , and others ) , associated with a special group of lines made visible or more obvious by an increase of temperature in the spectrum of a so-called element which , in the spectrum of a star , is seen without the low temperature effects for the reason above stated . In order to make clear the diagrams in which the new results are shown , we may consider a series of furnaces in the spectra of which , on the dissociation theory , the hottest gives the final result of the simplification brought about by temperature . In each furnace we shall have , as shown by Erankland and myself in 1869 , * the chemical form produced in greatest quantity by each temperature indicated by the most widened line , while in the complete spectrum of the mixture of vapours in each furnace the relative thickness of lines will be an indication of the percentage composition ! qud the various chemical forms . The Chemical Forms a Various Heal Levels . With regard to the spectral lines of the various chemical forms now in question , we have:\#151 ; Metals . Enhanced lines^i These are seen separately in stellar spectra . Arc lines J Hydrogen . Pickering 's series ' ! These are seen almost geparateiy . Ordinary series J Silicium.\#151 ; Four groups of lines have been made out , some seen separately . Carbon.\#151 ; Two groups of lines seen separately . Sulphur.\#151 ; Two groups of lines seen separately . Nitrogen.\#151 ; Two groups of lines seen separately . Fig. 1 shows the various heat horizons at which , in the stars , each chemical form is most predominant ; I deal only with the series of stars of rising temperatures . The range of each form is also shown . From the furnace analogy we may conclude that at these horizons , owing to the * ' Roy . Soc. Proc. , ' vol. 17 , p. 288 . t 'Phil . Trans. , ' 1872 , vol. 163 , p. 639 . 1910 . ] Chemical Forms in Stellar Spectra . heat conditions , each form predominates in turn , owing to a balance between the effects of association and dissociation . It is most important to observe that in no case is there any break along the line of range , or a double maximum . In this we have most cogent evidence of the continuous working of a law . As we ascend in temperature we find one form giving way to another . B fist e I f O .1 2 So S0 2 -S S c JB *2^ a 4= x 4= 3 $ e ( LtflOZO(/ )(/ )X\lt ; 0 S c V Z WQ . ill ! 9is \amp ; \#163 ; c e \#163 ; M % \#163 ; * ^ \#163 ; % i ill ! fli-5 fo p _ Argoniaa A ( frPuRPt\#187 ; ) \#165 ; Ainitamiaa\#169 ; ( \#163 ; Orioni\#187 ; ) Alnitamian(i ) ( K Orioni* ) Crucian . ( / Orionis ) Rigelian . ( p Orion is ) Cygnian ( a Cygni ) Polarian . ( a Ur** . Minonig ) Aktebarian . ( \#171 ; Taur\#187 ; ) Antarian ( oHlrcuus ) Fig. 1.\#151 ; Showing the heat levels at which the various chemical forms predominate , and also the range through the stellar groups . The new results , while entirely in harmony with the old ones , enable us to recognise better than before the stellar demonstration of that celestial dissociation which was first glimpsed in 1873 . It must be borne in mind that the record at present is very incomplete . Many of the rarer elements have not yet been studied , the regions in the red and ultra-violet have yet to be explored ; only the brighter stars give us spectra which can be discussed in detail . Sir N. Lockyer . On the Sequence [ Oct. 17 , Special Study of the Stars . In the classification and catalogue of 470 of the brighter stars published in 1902 , * I divided the stars into 16 groups . I had previously stated that sub-divisions must come with better photographs and more knowledge . The new work has enabled me to make a step in this direction . Already the Alnitamian stars have been divided into four species . The facts on which this advance is based are shown in fig. 2 , in which the various Alnitamian stages are shown in relation to stars higher and lower in temperature , so that the sequence of phenomena may be more completely followed . ASCENDING SIDE Alnitamian ( DO ( l Oaionis ) ALNITAtflAN(Bl ) ( tOWONlS ) ALNITAMIAN( ! I ) ( c-OrioniO ALNlTAMIAN(Iy ( K 0RI0NI8 ) Crucian ( Blu.atr.ix ) Riceuan a r O v ! I E % I \#163 ; ii i \amp ; c I ! \#163 ; O T Z \#163 ; ' ? 5 * ' Fig. 2.\#151 ; Showing the sequence in intensity of typical lines of various chemical forms through the spectra of some of the higher-temperature stars . Stars with Peculiar Spectra . The continuation of these researches into the finer details of stellar spectra , in conjunction with laboratory work , is certain to afford help in other directions , notably that dealing with stars showing peculiar spectra . * Publications of the Solar Physics Committee . Chemical Forms in Stellar Spectra . 1910 . ] The Henry Draper Memorial researches , under the strenuous direction of Prof. Pickering , have already made us acquainted with a large number of such spectra ; unfortunately most of them are of stars so faint as to be beyond the instrumental means at the disposal of the Solar Physics Observatory . They therefore are not included in the catalogue . But the delicate changes in the spectra of four Alnitamian stars above recorded really provide us with cases of peculiar spectra , and we have now run home the causes of the peculiarities . In e Orionis we have a predominance of silicium IV , in k Orionis a predominance of oxygen , in i Orionis a predominance of proto-hydrogen , representing three different temperatures at which these particular chemical forms are produced at the expense of others , which have been driven out of existence by the rise of temperature . The larger the number of chemical forms produced by the dissociation at work , the more numerous must be the minute changes in the spectra if we can only study and record them . In the Alnitamian stars we are dealing with increasing temperatures . On the hypothesis put forward in 1888 the stars with rising temperature are much less condensed\#151 ; are much nearer the nebular stage\#151 ; than those on the opposite descending arm of the temperature curve ; in these latter only can we postulate such a restricted region of absorption as that lying above the photosphere of the sun , which is certainly reducing its temperature and approaching extinction . This view has been strengthened by the recent researches of Prof. Eussell , Director of the Princeton Observatory , on the parallaxes , brilliancy , proper motion and spectral types of stars.* He concludes that there ought to be two distinct kinds of red and orange stars greatly differing in condensation , and that " in the intermediate stages the star would be hotter , passing through orange and yellow to white , and back to red as it approaches extinction . " In spite of these different conditions , however , so much are they dominated by temperature that it is temperature and not the other conditions which is effective in producing the spectrum , so similar are the spectra at equal temperatures , whether their temperature is rising or falling , that without the guidance afforded by the different behaviour of the hydrogen lines it would be difficult in the case of the hotter stars to separate the two series . ( See Plate 6 , fig. 3 . ) We have already , in a research on the spectrum of e Ursae Majoris , found another star with a peculiar spectrum ; this star , unlike Alnitam , is cooling . Its temperature is such that the spectrum of proto-chromium is considerably more developed than in stars of either higher or lower temperature . * ' Amer . Phil. Soc. Proc. , ' 1910 , vol. 49 , p. 230 . 432 On the Sequence of Chemical Forms in Stellar Spectra . Other variations from the normal Sirian type in the case of this particular star are the absence of the strong barium line X 4554'2 and the weakening of r 4198*2 the silicium II lines \lt ; The strengthening in e Ursse Majoris of the proto-chromium lines and the absence of the barium line are indicated in Plate 6 , fig. 4 . Other Possible Causes of Peculiarity . In some stars ( a Andromedse , g Leporis , 0 Aurigse and a Canum Venati-corum ) the peculiarity arises from the presence of sets of lines not yet revealed in the laboratory . The question arises whether some of the other peculiarities may not arise from the fact that we are dealing with close doubles . Atomic Weights Involved . I must point out that the chemical forms thus far traced in the stars are associated with the so-called elements having a relatively low atomic weight , and also that , while the evidence for oxygen and nitrogen is now complete , so far the series of atmospheric gases discovered by Kamsay have not been found . My best thanks are due to Mr. Baxandall , A.R.C.Sc . , First Assistant , for the determination of most of the wave-lengths of lines involved in the discussion and for the examination of the photographs . The more recent stellar photographs have been taken by Messrs. Baxandall , Butler , Rolston , Moss , and Goodson . The enlargements for purposes of comparison have been made by Mr. Wilkie . DESCRIPTION OF PLATE . Showing the variation in thickness of the hydrogen lines and the similarity of the finer lines in stars of about the same heat level , but on different sides of the stellar temperature curve . Comparison of two Sirian spectra ( one of normal type , the other peculiar ) , showing the increased prominence of proto-chromium lines and the absence of the barium line 4554'2 in e Ursae Majoris ( peculiar ) . Fig. 3.\#151 ; Fig. 4.\#151 ; Lockyer . Roy . Soc. Proc. , A. 84 , Plate 6 . Ha . r Fig. 3 . Barium spark . a Oanis Majoris . Sirian spectrum ( normal ) . e Ursae Majoris . Sirian spectrum ( peculiar ) . ( Jr spark . Or arc . Fig. 4 .

rspa_1910_0090

0950-1207

A spectroscopic investigation of the nature of the carriers of positive electricity from heated Aluminium phosphate.

433

449

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Frank Horton, M. A., D. Sc.|Sir J. J. Thomson, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1910.0090

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rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1910_0090

10.1098/rspa.1910.0090

Thermodynamics

Electricity

Thermodynamics

A Spectroscopic Investigation of the Nature the Carriers of Positive Electricity from Heated Aluminium Phosphate . By Frank Horton , M.A. , D.Sc . , Fellow of St. John 's College , Cambridge . ( Communicated by Sir J. J. Thomson , F.R.S. Received October 24 , \#151 ; Read November 10 , 1910 . ) The emission of ions from incandescent solids has been studied by many investigators . The value of e/ m , the ratio of the charge to the mass , for the carriers of negative electricity was first measured by Sir J. J. Thomson* in the case of a carbon filament heated in a high vacuum . Other observers have since determined the value of this quantity for the negative ions emitted by different incandescent solids , and all agree that the carriers are negatively electrified corpuscles identical in mass from whatever substance they are produced . The investigation of the nature of the carriers of positive electricity emitted by glowing solids presents greater difficulties , owing to the variability of the amount of the positive ionisation produced under different conditions , the causes of which are not yet fully understood . The first measurements of the value of the specific charge of these ions were made by Sir J. J. Thomson , f who found \#151 ; 104/ 25 for the positive ions from a heated iron wire . Later , experimenting with a strip of platinum foil which had already been heated for some hours in a high vacuum , he obtained the value e/ m = 104/ 27 for the majority of the carriers of positive electricity from that metal . The positive ions thus seem to have the same mass , about 26 times that of the hydrogen atom , in the two cases . This value suggested to Sir J. J. Thomson that they might be molecules of CO or of N2 , either of which has a mass about 28 times that of the hydrogen atom , so that it would be impossible to distinguish between these two gases by a determination of e/ m alone . When a luminous discharge was passed through the residual gas in the tube after the experiments with platinum , the band spectrum of carbon monoxide was obtained , and it was concluded that molecules of this gas acted as the carriers of positive electricity from the glowing metal . Measurements of the value of e/ m for the positive ions from platinum and from carbon have been made by a more elaborate method by 0 . W. Richardson , :\#163 ; who finds in the case of these elements values very t * ' Phil. Mag. , ' 1899 , V , vol. 48 , p. 547 . + 'Conduction of Electricity through Gases , ' Camb . University Press , 1906 , p. 148 . t ' Phil. Mag. , ' 1908 , YI , vol. 16 , p. 740 . Aote.\#151 ; In a paper published since this was written Richardson and Hulbirt ( ' Phil. Mag. , ' VI , 1910 , vol. 20 , p. 245 ) have found the values of m/ H for the positive ions from 434 Dr. F. Horton . Nature of Carriers of Positive [ Oct. 24 , nearly the same as those obtained by Sir J. J. Thomson . The values of the ratio of the mass of the carriers to that of an atom of hydrogen given by Richardson 's method are\#151 ; For platinum ... ... ... m/ H = 25*7 , For carbon ... ... ... . m/ H = 27'6 . Richardson found that the ions appeared to be quite homogeneous and independent of the temperature of the hot body . He mentions that the values obtained are nearly those required by the molecular weights of nitrogen , oxygen , or carbon monoxide , but he sees no reason for supposing the substances experimented on should give out one or other of these gases . As Richardson states , it is possible that the ions arise from some impurity common to all the materials which have been examined , and he suggests that positively charged sodium atoms would have a value of e/ m sufficiently near the values mentioned above . This impurity theory seems difficult to reconcile with the facts that the positive leak from glowing platinum decays with continual heating , but can be restored by exposing the wire to a luminous discharge or by heating it in an atmosphere of any of the commoner gases . On the other hand , if the positive ionisation is caused by an evolution of absorbed gas , it is possible that the passage of a luminous discharge near the wire would lead to reabsorption , or that the same effect would be brought about by heating the wire in an atmosphere of the gas , but one must admit that it is difficult to see why the value of e/ m for the positive carriers should be the same whatever gas is used . As a matter of fact , the gas most copiously emitted by a metal when heated is hydrogen , and the values of e/ m obtained for the positive carriers make it quite certain that they are not atoms or molecules of that gas.* The spectrum of carbon monoxide can nearly always be obtained in a vacuum tube when the pressure is very low . Its presence is generally \#166 ; considered as being due to dust in the tube or to grease used in lubricating taps in connection with the apparatus . If a tube gives the CO spectrum , the bands generally obscure the spectrum of any other gas which may .a large number of metals . These values are approximately the same in each case , the mean being 25*3 . * In a paper published after this was written Garrett ( 'Phil . Mag. , ' YI , 1910 , vol. 20 , p. 582 ) describes an experiment in which he obtained the value = 9700 for " the lightest positive ? ions present " when aluminium phosphate was heated on a platinum strip in a vacuum . This corresponds with a mass about equal to that of the hydrogen atom . Some hydrogen would be evolved from the heated platinum , and this gas would no doubt be ionised . It would seem , therefore , that Garrett was measuring the specific charge of these ions , which were not detected in Richardson 's experiments , and probably iorm a small proportion of the total ionisation . 1910 . ] Electricity from Heated Aluminium Phosphate . 435 be present in small quantity . It therefore seemed desirable to attempt a spectroscopic investigation of the nature of the carriers of positive electricity from incandescent solids , taking the greatest possible precautions to avoid contamination with substances which might give rise to the spectrum of carbon monoxide . The Method of Experiment . Certain salts , when heated either in air at atmospheric pressure or in a good vacuum , give a much larger emission of positive ions than is obtained by heating metals or carbon . The behaviour in this respect of a large number of substances was investigated by Sir J. J. Thomson , * and he found that , of the substances experimented on , the greatest effect was given by aluminium phosphate . This salt was therefore used as the source of the positive ions in the experiments which are about to be described . Some preliminary observations were first of all made to get some idea of the amount of the carriers of positive electricity which might be expected to be set free in an hour from a platinum strip covered with aluminium phosphate and heated in a good vacuum , in order to see if it were likely that they could be detected spectroscopically . With this object in view the current which could be obtained between a platinum strip covered with aluminium phosphate and a surrounding electrode was measured when the strip was at a bright red heat . The quantity of ions required to carry this current was then calculated on the assumption that each ion carried a charge equal to that of a monovalent ion in electrolysis . With a strip of platinum , 25 cm . long and 5 mm. wide , it was found that a current of 10-5 amperes could easily be obtained , and by adjusting the temperature of the platinum strip the current could be kept at this value . In one hour this current would liberate , electrolytically , sufficient hydrogen gas to fill a vessel of 1 c.c. capacity at a pressure of 3 mm. of mercury and a temperature of 0 ' C. If the ions produced from the heated phosphate are monovalent and are capable of existing separately in the uncharged state ( unlike the electrolytic hydrogen ions , two of which when discharged combine to form a molecule ) , the quantity produced by a current of 10~5 amperes in one hour would , if confined in the same vessel in the gaseous state , exert twice this pressure at the same temperature . Here we are not assuming that the positive ions from heated substances owe their origin to electrolysis , only that they carry the same charge as the electrolytic hydrogen ion , and the calculation shows that they could be collected in a small vacuum tube at a pressure sufficiently high to allow of a spectroscopic examination of them being made . * 'Canib . Phil. Soc. Proc. , ' 1907 , vol. 14 , p. 105 . 436 Dr. F. Horton . Nature of Carriers of Positive [ Oct. 24 , In the actual experiments the small collecting vessel was cooled in liquid air while the current was being passed from the aluminium phosphate to the surrounding electrode . The connection with the rest of the apparatus could then he closed , the liquid air removed , and when the condensed gas had vaporised its spectrum could be examined . In the earlier experiments a small vacuum tube with aluminium electrodes was used to collect the gases liberated , but the spectrum obtained always contained lines which were thought to be those of gases ( chiefly hydrogen ) given out by the aluminium electrodes . Small platinum electrodes were next tried , but these too , though better than those of aluminium , were unsatisfactory , and were finally discarded in favour of an electrodeless vessel . A ring discharge in a spherical vessel was used , for it was found to be brighter and more easily worked than the ordinary electrodeless discharge in a straight vacuum tube . In order that the volume of the collecting vessel should not be unduly large it was made by blowing a bulb of about 2 cm . diameter , and then heating the bottom of this and sucking it inside the bulb to within about 1'5 mm. of the outer wall , thus giving a vessel of very small capacity . Preliminary experiments with vessels of this kind showed that with six or eight turns of wire round the bulb a bright ring discharge could be obtained if the gas pressure was between 0'08 mm. and 1 mm. of mercury . The apparatus used is diagrammatically represented in the figure . The glass used in its manufacture was first of all carefully cleaned with chromic acid to remove grease , and the whole apparatus when completed ( but before the platinum strip P was sealed in ) was again cleaned out with hot concentrated nitric acid , and afterwards with chromic acid , and finally with distilled water . The anode P was prepared in the following manner:\#151 ; A strip of platinum foil , 25 cm . long and 5 mm. wide , was cut , and its ends welded on to thick platinum wire terminals Ti , T2 . The whole was then boiled for some hours in concentrated nitric acid to clean it and to remove hydrogen . It was then washed with distilled water , suspended in a clean tube , and heated by an electric current to bright redness for about an hour . It was covered with a uniform layer of aluminium phosphate by making a thin paste of the latter with distilled water , dipping the strip into this paste , and then warming it gently by means of the electric current until quite dry . This process was repeated several times until the strip was completely covered with aluminium phosphate . It was then sealed into the apparatus . In the diagram K is a thin sheet of platinum foil bent into a tube of slightly smaller diameter than the glass tube A ( about 2'5 cm . ) and joined 1910 . ] Electricity from Heated Aluminium Phosphate . 437 to the platinum wire C for connection to a battery of accumulator cells . The aluminium phosphate covered strip , P , hangs inside the platinum tube without touching it , and the current between the strip and the tube can be measured by means of a d'Arsonval galvanometer . The connection to the mercury pump , McLeod gauge , drying tubes , and carbon tube for producing a very low vacuum by cooling in liquid air is shown in the figure . This To Pump OOOOOO connection could be broken by raising the mercury in the cistern of the barometer tube D. B is the bulb for collecting any substance evolved during the passage of the discharge in the tube A. This bulb was about 2 cm . in external diameter , and the distance between the two walls was about l-5 mm. It was connected by capillary tubing to the discharge tube A , the connecting tubing being as short as possible . This connection could be cut off by means of the mercury column E. The bulb B could be surrounded by liquid air for the purpose of condensing any evolved gases which could be liquefied by VOL. LXXXIV.\#151 ; A. 2 H 438 Dr. F. Horton . Nature of Carriers of Positive [ Oct. 24 , cooling to that temperature . A small coil of six turns of insulated flexible wire , such as is used for electric lamps , was made to fit the bulb . It could be slipped over B with its axis in the plane of the paper as indicated in the figure . The ends of the coil were connected to the outside coatings of two large Leyden jars , the inside coatings of which were connected to an induction coil with an electric valve in series . An adjustable spark gap was arranged between the two inside coatings , and as sparks passed across this gap they were accompanied by a ring discharge in the bulb B. The spectrum of the discharge was viewed by means of a Hilger direct wavelength spectroscope . The apparatus was evacuated by means of a mercury pump , and was then left for some time to make sure there was no leakage anywhere . The conditions under which the ring discharge could best be obtained were then investigated , experiments being made at different low pressures and with varying lengths of air gap between the sparking knobs . It was found that the ring discharge was at its best when the pressure in the bulb was between OT mm. and 0'5 mm. , although it could sometimes be obtained with the pressure as low as 0*03 mm. This seemed very satisfactory , and showed a distinct advantage over the ordinary vacuum tube arrangement , in which , at these low pressures , the luminosity of the discharge is very faint . The spectrum of the ring discharge through the residual gas in the apparatus was carefully observed . It was found to be the elementary line spectrum of air , consisting of a large number of nitrogen lines with some lines of oxygen and the hydrogen red line . Five or six lines of the mercury spectrum were also present . The gas pressure in the apparatus was then reduced as low as possible by means of charcoal cooled in liquid air , and the tube A was then cut off from the pump and charcoal tube by raising the level of the mercury cistern in connection with the barometer D. The temperature of the platinum strip P was raised to over 1000 ' C. by connecting its terminals to the town alternating current supply through a set of resistances which could be varied so as to adjust the current to give the required temperature in the strip . The bulb B was immersed in liquid air to condense anything liquefiable at that temperature which was given off by the heated strip . After about two hours the heating current was cut off , the connection at E was closed , and the liquid air was removed . G-as to a pressure of about 5 mm. developed in the bulb B , and , as this pressure was too great to give the electrodeless ring discharge , it was lessened by reopening the connection at E and allowing some of the gas to escape into the main tube A. The ring discharge was then easily obtained and its spectrum showed many of the brightest nitrogen 1910 . ] Electricity from Heated Aluminium Phosphate . 439 lines , also the hydrogen red line very brightly and several of the mercury lines . A few lines of carbon were also measured , the double red line A 6584 , 6579 being particularly brilliant . The existence of nitrogen lines in this spectrum was taken as showing that all the air had not yet been got rid of . It is probable that the warming up of the glass apparatus during the heating of the strip had driven off some of the air which is known to cling to the walls of an exhausted tube , and that it was this which was producing the nitrogen lines in the spectrum . The hydrogen line was probably from gas evolved by the heated platinum strip . Before the experiment proper could be performed it was obviously necessary to get rid of this liberation of gas on merely warming the glass apparatus . The connection to the pump , etc. , was again opened and the whole apparatus was again evacuated by means of the charcoal tube cooled in liquid air . The above experiment was then repeated and the spectrum of the condensed gas again observed . The nitrogen lines were now much fainter , and on repeating the evacuation and heating several times they completely disappeared . It was found that the amount of gas collected while the platinum strip was maintained at a high temperature became gradually less , but although the heating was repeated some 8 or 10 times , on each occasion for about two hours , it was found that some gas could always be collected . The lines measured in the spectrum of this gas are given in the first column of the table on p. 440 . When all the air had been got rid of , the effect of having a measured current passing from the heated aluminium phosphate to the surrounding cylinder was investigated . The platinum strip covered with aluminium phosphate was earthed . The positive terminal of a battery of small accumulator cells was also earthed , and the negative terminal was insulated and connected through a d'Arsonval galvanometer to the platinum cylinder surrounding the strip . The vacuum having been made as good as possible , the apparatus was isolated from the pump and the platinum strip was raised to a temperature of about 1000 ' C. A difference of potential of 120 volts was then established between the earth-connected end of the strip and the cylinder . The bulb B was surrounded with liquid air and the discharge allowed to go on for about two hours . During this time the galvanometer deflections were read at intervals of about a quarter of an hour . The deflections were not steady , but tended to decrease . This was prevented by gradually increasing the temperature of the platinum strip . The mean of the galvanometer deflections corresponded to a current of 8'4 x 10"6 amperes , a current sufficient to liberate by electrolysis 2'5 c.c. of hydrogen gas per hour , measured at 0 ' C. and at a pressure of 1 mm. of mercury . 440 Dr. F. Horton . Nature o Carriers of Positive [ Oct. 24 , At the conclusion of this run the bulb B was separated by the mercury cut-off from the rest of the apparatus , and the spectrum of the ring discharge in the collected gas was examined . It was found to consist of practically the same lines as the spectrum of the gas collected by simply heating the aluminium phosphate without the negative potential being applied to the surrounding cylinder . The lines measured , together with their intensities , are recorded in the following table . Most of them have been identified as being due to carbon , oxygen , hydrogen , or mercury :\#151 ; Lines measured in the spectrum of the gas collected after the sixth heating of platinum strip covered with aluminium phosphate . Intensity . Lines measured in the spectrum of the gas collected after current'of 8*4 x 10-6 amperes had passed for 2 hours between heated aluminium phosphate and surrounding electrode . Intensity . Lines identified as X. 6582 8 1 6582 10 / 65841 L 6579 J 6563 10 6563 10 6563 H 6152 1 6152 1\#151 ; 5 6152 Hg 6096 3 6097 3 5890 10 5890 10 5889 Hg 5878 1 5791 1 5791 1\#151 ; 4 5791 Hg 5771 1 5771 1\#151 ; 4 5770 Hg 5696 5 5696 4 5679 4 5679 5 5679 Hg 5663 2 5663 2 5662 0 5649 2 5649 1 5649 C 5640 1 5640 1 5641 0 5460 2\#151 ; 10 5460 10 5461 Hg 5427 3 5427 2 5427 Hg 5206 3 5206 2 5207 O 5152 2 5152 2 5152 c 5146 8 5146 5 5145 c 5133 6 5133 5 5133 0 4940 3 4940 3 4924 2 4924 2 4925 0 4907 2 4907 2 4907 0 4891 1 4891 1 4892 0 4850 5 J4706 [ 4700 4700 4 b 4700 3 d \ ' 4675 1 ? 4676 0 4660 1 ? 4662 0 | 4650 8b 4648 8 4649 0 4641 3 b 4640 3 b J4642 ' 14639 j 4593 3 b 4593 2d / 4597 ] 14591J / 4417 ] Lr\gt ; 4416 3 b 4418 4 \ 4415 J 4357 4 4359 Hg ! / 4352 1 A 4350 1 b 4352 2 14349 J ? u 4270 6 b 4270 2 4267 c b signifies that the line was blurred , not sharp . d signifies that the line was thought to be a double one . 1910 . ] Electricity from Heated Aluminium Phosphate . 441 The wave-lengths in the last column were taken from Kayser 's ' Handbuch der Spectroscopie/ those of mercury lines being from the observations of Eder and Valenta , the carbon lines by Gramont , and the oxygen lines by Neovius . On first taking away the liquid air the pressure in the bulb B was too low for the ring discharge to pass . This began as the bulb warmed up , and it was noticed that the mercury lines were the last to appear in the spectrum . , These always brightened up considerably as the tube was worked , owing to the increasing vapour pressure of the mercury which had been condensed in B during the first part of the experiment . It was found that the brilliance of the ring discharge could be considerably reduced by surrounding the bulb B with iced water to keep it cool . In the spectrum , under these conditions , the lines marked as mercury were all greatly diminished in brightness , most of the weaker ones disappearing . The unidentified lines also disappeared , except A 4940 , which became very faint . The carbon , oxygen , and hydrogen lines remained , but were of slightly diminished intensity . It has been stated that , in the first experiments which were made , instead of using the ring discharge to test the spectrum of the gas collected , a small vacuum tube of the ordinary kind was employed . In these experiments the spectrum obtained showed the hydrogen red and blue lines and some of the brighter lines of the secondary hydrogen spectrum* together with the band spectrum of carbon monoxide . The hydrogen lines became brighter as the vacuum tube was worked , which seemed to suggest that this gas was coming out of the electrodes . It was for this reason that the tube was discarded and the electrodeless bulb used . From the table it appears that the oxycarbon spectrum was not due to the metallic electrodes , for the lines of carbon and of oxygen point to the presence of an oxide of carbon in the gas collected . In order to see if this supposition were correct , the apparatus shown in the figure was modified by putting a small vacuum tube of the ordinary shape , but without electrodes , in connection with the bulb B. The small tube had its ends covered with tinfoil , which was bound on by insulating tape and then waxed over . On repeating the experiment and observing the spectrum of the gas collected in the two tubes , it was found that whereas the ring discharge gave the lines of carbon and oxygen , the ordinary electrodeless discharge gave the band spectrum usually attributed to carbon monoxide . It is probable that this difference is due to the decomposition of the carbon monoxide by the ring discharge . This is similar to the result obtained with air . It has been mentioned that the spectrum of the ring 442 Dr. F. Horton . Nature of Carriers of Positive [ Oct. 24 , discharge through the residual air in the apparatus , before the platinum strip had been heated , was the " elementary line spectrum " of air , whereas the spectrum obtained from air at a low pressure in an ordinary vacuum tube is a series of bands due to nitrogen . The difference between the two spectra is probably due to the dissociation of the nitrogen molecules at the higher temperature of the ring discharge . The ring discharge is an oscillatory discharge from Leyden jars , and the production of line spectra under these conditions is in accordance with the general rule that increasing the amount of energy in the discharge by the introduction of capacity into the circuit has the effect of increasing the number of lines in the spectrum obtained . This increase is usually greatest at the blue end of the spectrum , as , for instance , in the case of argon . In the present case of carbon monoxide I was unable to change the band spectrum of the ordinary electrodeless discharge into the line spectra of carbon and oxygen by placing a Leyden jar and spark gap in parallel with the tube , although Smithells* has found that with a vacuum tube with electrodes , at low gas pressures , this change takes place as the spark gap is gradually widened . The difficulty of sending a heavy discharge through the electrodeless tube probably accounts for this change not occurring in these experiments . It might here be mentioned that the difference between the spectrum of the ring discharge and the ordinary vacuum tube spectrum of carbon monoxide is in agreement with the theory of Sir J. J. Thomson as to the origin of line spectra and band spectra . According to this theory , banded spectra are due to the vibrations of electrical doublets , each consisting of a negatively charged particle bound to a positively charged particle inside the atom or molecule , whereas line spectra are produced by the vibrations of small negatively charged corpuscles outside the atom . It does not seem improbable that the extra energy of the ring discharge should lead to a splitting up of the electrical doublets inside the CO molecule , liberating electrons which , by their vibrations , give rise to the lines obtained in the spectrum of the ring discharge . The fact that the gas collected when a continuous current is passing from the heated aluminium phosphate to the surrounding cylinder gives the same spectrum as the gas obtained when no external E.M.F. is applied , might bb taken as indicating that the positive ions have escaped collection , or that they are present in such small quantity as not to produce any change in the spectrum observed , were it not that we have already seen that the total quantity of electricity carried by these ions * ' Phil. Mag. , ' 1901 , VI , vol. 1 , p. 476 . 1910 . ] Electricity from Heated Aluminium Phosphate . 443 during the experiment is so great that it might reasonably be expected that they are produced in sufficient quantity to be detected by the spectroscope . We must take it that the positive ions are present in the collected gas in sufficient quantity for their spectrum to be observed , and I think these experiments show that they consist of molecules of carbon monoxide or of oxygen . Although no oxygen lines were visible in the ordinary vacuum tube discharge through the collected gas , it must be remembered that these lines do not show up when oxygen is mijced with nitrogen , and they would probably also be obscured by the presence of carbon monoxide . We cannot , therefore , be sure that the oxygen lines obtained in the spectrum of the ring discharge are entirely due to the effect of that discharge on the carbon monoxide gas , although this would be a satisfactory explanation of their presence . On the other hand , the carbon lines in the spectrum of the ring discharge are probably due entirely to the carbon monoxide , for carbon in the gaseous condition could only be present in the bulb at the instant of dissociation of that gas . In this connection it should be mentioned that there was no noticeable deposition of carbon in the bulb , so that the dissociation into carbon and oxygen must have been followed by a complete recombination of these elements when the ring discharge was stopped . Carbon monoxide and oxygen are two of the gases mentioned by Kichardson as possible carriers of the positive charges from the point of view of their molecular masses . The entire absence of nitrogen lines from the spectrum of the gas collected in these experiments seems to preclude the possibility of the positive ions consisting of nitrogen . If they do consist of a*n elementary substance , it would be more in accordance with the nature of positive ions from other sources if they are atoms and not molecules . In ordinary electrolysis we have the atoms of elementary substances acting as the carriers of the electric charges , but in certain cases we have also compound radicals , consisting of groups of atoms , acting as the carriers of the positive charge . There seems to be no reason why , in the case of the discharge of electricity from a glowing solid , the positive ion should not consist of CO , a compound radical acting like an atom , for we know that this group plays the part of an atom in many chemical reactions . Five of the lines recorded in the table on p. 440 are there not attributed to any element . It may be that these , together with other lines only faintly visible and not measured in these experiments , form the spectrum of the carriers of positive electricity from heated aluminium phosphate , but I am inclined to think that they are due to some other cause . Each of the lines 6097 , 5878 , 5696 , 4940 , 4850 , corresponds to a line in the secondary spectrum of hydrogen , but the corresponding secondary hydrogen lines are 444 Dr. F. Horton . Nature of Carriers of Positive [ Oct. 24 , very faint , except in the case of 4849 , which is of intensity 4 . In my experiments the line 4850 was only observed in one set of experiments . The other four lines were always seen , and I am inclined to attribute their presence to mercury , although they are not lines which are usually seen in the mercury spectrum . Like most of the mercury lines observed in these experiments , they increased in brightness as the tube warmed up with continual working , and like all the fainter mercury lines , they disappeared when the bulb was kept cool in iced water while the spectrum of the discharge was being observed . Some time ago the writer* drew attention to five lines in the red and orange regions of the mercury spectrum which , though generally invisible , were obtained very brightly when a luminous discharge from a glowing lime-covered cathode is produced in mercury vapour . Since then the spectrum of mercury has been more closely studied , and it has been found that when the ordinary vacuum tube discharge , with capacity in parallel , is taken in mercury vapour at a very low pressure , a large number of new lines come into prominence . These lines ( and the red and orange lines referred to above ) may not be due to mercury vapour in a normal condition , but may be produced by something formed from mercury by the passage of the electric discharge through its vapour\#151 ; some new arrangement of corpuscles which again becomes mercury when the discharge ceases . Two experiments which have recently been made seem to support this view . The first of these is an experiment described by Dr. H. Brereton Baker at a recent lecture at the Royal Institution^ If oxygen is allowed to enter a mercury lamp immediately after the current has been cut off , it is found that a considerable quantity of mercuric oxide is formed , although the temperature is much lower than that at which mercury vapour in a normal condition combines with oxygen . Evidently the ionised mercury vapour remaining in the lamp has different chemical properties from mercury vapour in the ordinary atomic condition , and the spectrum given by this vapour may depend upon the nature and extent of the ionisation . This view is also supported by the recent experiments of Ladenburg on the absorption spectrum of hydrogen . Ladenburg found that when light from a hydrogen vacuum tube was sent through a long tube containing hydrogen gas , no absorption took place unless the gas in the long tube was also conveying an electric current , in which case marked absorption of the hydrogen red light was obtained . It looks , therefore , as though the hydrogen red line were given out by some arrangement of corpuscles not * ' Camb . Phil. Soc. Proc. , ' 1908 , vol. 14 , p. 501 . t See ' Nature , ' 1910 , vol. 84 , p. 388 . 1910 . ] Electricity from Heated Aluminium Phosphate . 445 present in hydrogen in the ordinary condition , but manufactured from the gas by the passage of the electric current . In the case of mercury we have a vapour of high atomic weight , and one which is very easily ionised , and it would seem that new corpuscular arrangements might be formed more readily than in the case of hydrogen . That the brightness of different lines given by mercury vapour varies enormously under different conditions is well illustrated by the intensities given in the table on p. 440 by the brightness of the yellow line A 5889 in the spectrum of the electrodeless ring discharge , at a time when the two yellow lines X 5770 and X 5791 , usually so prominent in the mercury spectrum , were only faintly visible . I think it is probable , therefore , that the lines X 6097 , 5878 , 5696 , and 4940 are due to the passage of the electrodeless ring discharge through the mercury vapour present in the discharge tube . Conclusion . It has been pointed out that from the magnitude of the total quantity of electricity carried from the heated aluminium phosphate to the surrounding electrode we are justified in assuming that the positive ions are set free in sufficient numbers for their spectrum to be observed . The spectroscopic evidence shows that carbon monoxide , hydrogen , mercury vapour , and possibly oxygen are present in the apparatus , all of these , with the exception of mercury , being liberated by the heating of the platinum strip covered with aluminium phosphate . The values of e/ m for the carriers of positive electricity obtained by Richardson make it certain that these carriers cannot be atoms or molecules of hydrogen or mercury ; and in this paper reasons have been given for thinking it doubtful whether oxygen is really present in the free state in the tube . Richardson 's values of e/ m make the mass of the carriers considerably greater than that of the oxygen atom , and I think it is more likely that the ions , if they consist of an elementary substance , are atoms , not molecules . The fact , too , that oxygen is strongly electro-negative in character would seem to be against its acting as a carrier of positive electricity . The conclusion arrived at is , therefore , that the positive ions are molecules of carbon monoxide . The mass of these molecules is very near to that required to fit in with the value of the specific charge obtained for the positive ions from iron , platinum , and carbon . We are assuming that the carriers of positive electricity are the same in the case of aluminium phosphate , an assumption which seems to be justified by the experiments of Brown , * who has shown that the kinetic energy of these ions is the same as that of the ions from metals . * * Phil. Mag. , ' VI , 1909 , vol. 18 , p. 649 . 446 Dr. F. Horton . Nature of Carriers of Positive [ Oct. 24 , The question arises , is this carbon monoxide evolved from the heated aluminium phosphate , or is it produced from the glass walls of the apparatus ? In the experiments which have been made to determine the value of the specific charge and the kinetic energy of the carriers of positive electricity from heated substances , there can be no doubt that relatively large amounts of carbon monoxide were present in the apparatus used . In the experiments described in the present paper the utmost care was taken to have the whole apparatus free from traces of dust or grease or anything which might give rise to carbon monoxide gas . With glass cleaned in the same way as the apparatus used in these experiments , the writer has had vacuum tubes containing mercury heated so that the spectrum of the electric discharge through the vapour might be observed , and only after long continued heating has the spectrum of carbon monoxide appeared . In the case of these mercury vacuum tubes the inner surface of the glass became broken up by continued sparking from the surface of the mercury while the discharge was passing , and this might be expected to allow any gas occluded or dissolved in the glass to escape into the vacuum tube , and probably accounted for the CO spectrum which was sometimes seen in tubes that had been worked for several weeks . In the present experiments no such breaking up of the glass surface occurs , and it would he much more difficult for gas to escape into the tube from inside the glass . The gas occluded on the surface would be got rid of during the first few heatings and evacuations . It must , however , be mentioned that the experiment was tried of heating up the glass by means of a Bunsen burner while the aluminium phosphate remained cold , and it was found that a small amount of gas could be collected in the bulb cooled in liquid air and this gas gave the carbon monoxide spectrum , but the amount of gas collected in this way was not nearly so much as when the aluminium phosphate was heated . In heating the apparatus from outside with the Bunsen flame parts of the glass were no doubt made much hotter than when heated by the radiation from the glowing platinum strip , and gas occluded on these parts might thus have been removed . It would be much easier to imagine that the CO spectrum is due to the heating of the glass than that it is evolved from the aluminium phosphate , for the carbonates used in the manufacture of glass might be expected to evolve COa , which in a vacuum tube gives the same spectrum as CO , the reason for this being , according to Liveing* that the carbonic acid gas dissociates into carbon monoxide and oxygen and the former acts as the carrier of positive electricity through the tube . I tried to estimate whether more gas was produced in the apparatus when a current was passing from the heated * ' Camb . Phil. Soc. Proa , ' 1904 , vol. 12 , p. 338 . 1910 . ] Electricity from Heated Aluminium Phosphate . strip to the surrounding electrode than when the latter was insulated , but I was unable to come to any definite conclusion . The experiment could easily be performed by having a small McLeod gauge in immediate connection with the discharge tube A or the condensing bulb B. In these experiments , however , the apparatus was designed to have as little surface of glass as possible , in order to avoid trouble from the occluded gas . Reference has already been made to the fact that the spectrum of the gas collected is the same whether it is obtained when the aluminium phosphate is heated without an external electric field being applied from the battery of cells , or with a current passing from the strip to the surrounding electrode . In the first case it might be thought that no ions would be set free , but the liberation would still go on for a short time . Sir J. J. Thomson found that aluminium phosphate evolves positive ions when heated without the application of any electric field , and it must be remembered that in the present experiments the phosphate was heated by an alternating current , which would cause it alternately to drive out and to draw back positive ions . If the surrounding cylinder is so near to the heated strip that the positive ions reach it before the potential difference between the electrodes is reversed , they would give up their charges to the cylinder and be set free in an uncharged condition . Other ions emitted by the heated phosphate would , no doubt , discharge themselves to the sides of the glass tube , and , perhaps , to the mercury in the adjacent barometer tube . That positive ions were shot , off in this way and charged up the surrounding platinum cylinder was proved by connecting this to earth through the galvanometer . On heating up the phosphate by the alternating current a large deflection was obtained , the current passing across the tube being about the same as when the saturation E.M.F. was applied from the cells . When the electrode surrounding the platinum strip is insulated , as in the experiment from which was obtained the spectrum recorded in the first column of the table on p. 440 , the ions would cease to be emitted from the heated strip after the surrounding electrode had become charged to a certain potential , depending upon the maximum positive potential attained in the strip . As already stated , experiments made to see whether more gas was evolved while the current was passing across the tube than when the cylindrical electrode was insulated led to no definite result , but the fact that the gas collected in each case gave the same spectrum may , perhaps , be due to ions being condensed in both experiments , although the number collected would be very much greater while the current was running than when the cylinder was insulated . If carbon monoxide gas is evolved from the heated aluminium phosphate , and if it is molecules of this evolved 448 Nature of Carriers of Positive Electricity . gas which act as the positive ions , it would follow that much more gas is evolved while the current is passing from the heated electrode than when the surrounding cylinder is insulated , or else that a larger percentage of the molecules of the evolved gas is ionised when the heated phosphate is at a higher positive potential than the surrounding cylinder than when this is not the case . That carbon monoxide should be evolved from metals and from aluminium phosphate when heated seems very mysterious . It is well known that many metals , notably platinum and palladium , evolve hydrogen when strongly heated , but the presence of this elementary gas can be more readily accounted for than could the presence of a compound like carbon monoxide . I believe that , for some unknown reason , the aluminium phosphate used in these experiments did evolve some ( at least ) of the gas which gave the carbon monoxide spectrum , but it is difficult to believe that this gas is also emitted by all the materials heated in the kinetic energy experiments of Brown . However , there can be no doubt that carbon monoxide was present in the apparatus used by Brown , and even if it were not in the first place evolved by the substances experimented on , I think it may still have acted as the positive ion as indicated by the uniformity of the results obtained . Ho doubt the molecules of carbon monoxide would more readily act as carriers of positive electricity from a substance if they came from inside that substance than if they only got in contact with its surface . How carbon monoxide has the property of readily diffusing into carbon and into a number of metals ; it is also not easily dissociated by heat or by the electric discharge.* When a metal is heated in an atmosphere of carbon monoxide , molecules of the gas would be continually entering and leaving the surface of the metal . Many of those leaving would , as a rule , be ionised and carry away a positive charge , but this leakage of positive electricity could be prevented by an opposing E.M.F. , which would cause the molecules escaping with a positive charge to diffuse back again into the metal . The question arises , why does this not happen to other gases when present in the apparatus ? I should have expected it would happen to some extent , especially in the case of a strongly electro-positive gas such as hydrogen ; but hydrogen would be present in the molecular condition , and ions usually consist of atoms when an elementary substance is concerned . The CO radicle , though compound , acts as an atom in many chemical combinations . It would appear also to have a greater affinity for positive electricity than * J. N. Collie , ' Chem. Soc. Journ. , ' 1901 , vol. 79 , p. 1063 . Colour-Blindness and Trichromatic Theory of Colour Vision . 449 any of the ordinary gases , as is evidenced by the readiness with which the spectrum of carbon monoxide shows up in vacuum tubes , often to the total exclusion of the spectrum of other gases which are known to be present . If the view that the positive ions from heated substances are molecules of carbon monoxide is correct , it would mean that a substance -which of itself evolved this gas when heated would probably have a greater positive leak than one which did not do so . A large emission of positive ions would also be expected to be obtained from a substance which had a strong affinity for negative electricity , and would thus more readily allow the molecules of gas to escape with a positive charge . This is probably a property of phosphorus at high temperatures , for Sir J. J. Thomson has shown that the phosphates as a class emit large amounts of positive electricity when heated . The author wishes to take this opportunity of thanking Prof. Sir J. J. Thomson for his interest in these experiments , which were carried out in the Cavendish Laboratory , Cambridge . Colour-Blindness and the Trichromatic Theory of Colour Vision . Part II.\#151 ; Incomplete Red or Green Blindness . By Sir W. de W. Abney , K.C.B. , D.Sc . , F.R.S. ( Received October 5 , \#151 ; Read December 8 , 1910 . ) In Part I of this subject* I treated of complete colour-blindness in its relation to the trichromatic theory of colour vision . In this communication , which is a continuation of that published , I deal with incomplete colourblindness and its relation to the same theory . The number of cases of incomplete red or green blindness is larger than those where the colourblindness is complete . In cases of incomplete colour-blindness so far as they have come under my examination the sensation curves of the red and green sensations are similar ( in a mathematical sense ) to those existing in normal vision , that is to say , if in the normal ( say ) red curve an ordinate of one colour indicates a perception of " a " red , and for the incomplete red-blind a perception of " b " red , then in any other position in the spectrum the proportion of normal to incomplete red-blindness is as b. This * ' Roy . Soc. Proc. , ' A , 1910 , vol. 83 .

rspa_1910_0091

0950-1207

Colour-blindness and the trichromatic theory of colour vision. Part II.\#x2014;incomplete red or green blindness.

449

464

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Sir W. de W. Abney, K. C. B., D. Sc., F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1910.0091

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1910_0091

10.1098/rspa.1910.0091

Optics

Tables

Optics

]\gt ; Colour-Blindness and Theory of Colour Vision . 449 any of the ordinary gases , as is evidenced by the readiness with which the spectrum of carbon monoxide shows up in vacuum tubes , often to the total exclusion of the spectrum of other ases which are known to be present . If the view that the positive ions from heated substances are molecules of carbon monoxide is correct , it would mean that a substance , which of ; itself evolved this gas when heated would probably have a greater positive leak than one which did not do so . A large emission of positive ions would also be expected to be obtained from a substance which had a strong affinity for negative electricity , and would thus more readily allow the of gas to escape with a positive charge . This is probably a property of phosphorus at temperatures , for Sir J. J. Thomson has shown that the phosphates as a class emit amounts of positive icity when heated . The author wishes to take this opportunity of thanking Prof. Sir J. J. Thomson for his interest in these experiments , which wele carried out in the Cavendish Laboratory , Cambridge . Colour-Blindness and the of Colour Vision . Part II.\mdash ; Incomplete Red or Green Blindness . By Sir W. DE W. ABNEY , K.C.B. , D.Sc . , F.R.S. ( Received October 5 , \mdash ; Read December 8 , 1910 . ) In Part I of this subject*I treated of complete colour-blindness in its relation to the trichromatic theory of colour vision . In this communication , which is a continuation of that published , I deal with incomplete colourblindness and its relation to the same theory . The number of cases of incomplete red or green blindness is than those where the colourblindness is complete . In cases of incomplete colour-blindness so far as they have come under my examination the sensation curves of the red and green sensations are similar ( in a mathematical sense ) to those existing in normal vision , that is to say , if in the normal ( say ) red curve an ordinate of one colour indicates a perception of " " \ldquo ; red , and for the incomplete redblind a perception of " " \ldquo ; red , then in any other position in the spectrum the proportion of normal to incomplete red-blindness is as . This 'Roy . Soc. Proc , 1910 , vol. 83 . 450 Sir W. de W. Abney . -Blindness the [ Oct. fact leads to a far-reaching conclusion . It tells us that the place of maximum luminosity travels in the case of red-blindness from Standard Scale No. to S.S.N. 46 . A reference to Table I will show why such travelling of maximum luminosity takes place . To take two examples , a table ( Table II ) and diagram of luminosity curves for eyes which only perceive one-third of the red sensation and one-third of the green sensation is given . In the first the maximum is closely at S.S.N. 48 5720 , and in the second at S.S.N. 51 5922 . The maximum at S.S.N. 49 is when the red sensation is about two-thirds of the normal , and at S.S.N. ( 47 ) 5658 when it is about one-tenth of the normal , at S.S.N. 46 when there is no red sensation . In the green-blind when there is no green sensation the maximum is closely at S.S.N. 52 By observing the position of maximum luminosity we can form an approximate diagnosis of the amount of the defect and as to the sensation in which the defect exists . Suppose that we have a luminosity curve taken by ( say ) an incompletely In this communication as in the last the white light which forms the spectrum is from the crater of the positive pole of the arc light . If any other source of light be used the maxima will not be in the same positions as those given . 1910 . ] Trichromatic Theory of Colour Vision . 451 red-blind eye the question comes whether we can find the exact amount of deficiency that exists or , at all events , approximate to exactness . If by any means we can make the ordinates of the curve obtained of proper height when compared with those of the normal vision curve ( which Table the Composition of the different Rays of the Spectrum in Terms of Luminosity of the Three Sensations . A is ; Red lithium , ; Blue lithium , , ll2 ; Sir W. de W. Abney . Colour-Blindness and the [ Oct. 5 , Table II.\mdash ; Showing incomplete Red and Green Blindness . we usually make 100 ) we can then compare all the ordinates of the former with those of the latter , both being on the same scale . If the trichromatic theory holds good then the difference between the ordinates of the two curves ' should , at every place ( except maybe in blue ) , in the case of incomplete redblindness , give a curve which is mathematically similar to the normal red sensation curve . The ordinates of this curve compared with the ordinates of the normal red sensation curve will give the amount of red sensation deficient in the incomplete red-blind eye . When the incomplete blindness is in the green sensation the same line of argument applies . 1910 . ] . Theory of I give two cases , one of incomplete red- and the other of blindness . The measures were taken several years , nd before I ] ) worked out the three sensation curves of my own ( normal ) eye . Without knowing whether a comparison of the luminosity of the spectral coloul . S to my own eye with the same white which they used for comparison purposes would be of any value , in some cases I made observations at the same time and recorded the readings . These I shall refer to later . I must here point out that owing to differences in the ) sorption by the macula lutea in different eyes the blue sensation curve may not always be capable of the same treatment as the green or red sensation curves . But from the red end of the spectrum to about S.S.N. 40 this variation will not appreciably the results . In Table III we have the case of the incompletely red-blind eye . The ordinates of luminosity as measured are iven in Column III . We have to obtain a factor by which to multiply the numbers in this column to make it compare with the luminosity of normal vision given in Table I. Table III.\mdash ; Showing W. Curves . Let us take S.S.N. 's 58 and 46 in the first instance . The normal luminosities of these S.S.N. 's are 21 and 87 ( see Table 1 ) , and for W. and 92.5 . See " " Colour Photometry Part 3 , ' Phil. Trans 1800 . VOL. LXXXIV.\mdash ; A. 2 I 454 Sir W. de W. Abney . Colour-Blindness and the [ Oct. 5 , From these we can form two equations , putting for the reduction of W. 's total luminosity curve and for the reduction of his red sensation curve , the right-hand members of the equations being formed from the red sensations of these two scale numbers given in Table I. The left-hand member of the equations is the diffel.ence between the ordinates of the normal and redblind curves at these scale numbers , which should be equal to the right-hand member . 21\mdash ; From these we find and . Making the factor by which the normal red sensation has to be multiplied in order to give the amount of this sensation that is present in W. 's colour sense , and from these equations . That is when his curve is multiplied by , the difference between the ordinates of his curve and those of the normal give a curve which is five-sixths of the normal B.S. curve . Taking two other positions , viz. , S.S.N. and 44 , we obtain the following equations:\mdash ; S.S.N. 50 S.S.N. 44 From this we obtain . Taking the mean of , we get and ; that is , W. has only or closely This number has been used in the table to compare the red sensation curve of the table with that of the incomplete blind . Column I is the S.S.N. , II the wave-length , III the luminosity of the colour-blind , the Column from the Table I ; is ( Column -Column V ) , and Column . reduced from Table I. It will be seen that after the have been deducted from the reduced luminosity , we have a residue which gives ( within limits of error of observation ) the same numbers as those given by . In this case , then , the incomplete blin luminosity curve indicates the truth of the trichromatic theory , and also of the sensation curves of Table I obtained by the author . The nearer to complete colour-blindness , the greater the necessity for accuracy in the determination of the luminosity curves . In the next table is given a determination of a case of incomplete greenblindness , N. 1910 . ] Theory oj Colour Vision . 455 Table 's Curves . Taking S.S.N. and 46 , we form the equations as before ; but from Table I we use the green sensation luminosity\mdash ; S.S.N. 52 S.S.N. 46 S7From these we find and Other pairs of equations can be formed by , , S.S.N. 's 5 and 38:\mdash ; S.S.N. 52 S.S.N. 38 From which we and We may take as approximately , which tells us the green sensation felt is only about one-tenth of the normal . [ The green sensation is shown in the table as of the normal . ] S 456 Sir W. de W. Abney . Colour-Blindness and the [ Oct. 5 , This method can be used in what at first sight appear to be complicated cases , but it was not possible to use it before the sensation curves of normal vision had been worked out , as unless the composition of the colours in terms of sensation luminosity is known , must also remain unknown . A case which puzzled those who considered it , is shown in the . Soc. Proc May 14 , 1891 , vol. 49 . The figure is not well drawn , but the numbers given in the table of luminosities are correct . * The readings near the maximum were a little erratic , probably owing to the fact that at that part green was distinguished , the rest of the spectrum being grey or brownish-grey . Using numbers on each side of the maximum to form our equations , the following are found to give the factors of reduction of the curve to compare it with the normal curve whose maximum is 100 . Taking S.S.N. and 40 , we form the first pair of equations from the minosities in Table I and that of N. W. luminosities . As before , the right hand of the equations are formed from the R.S. numbers in Table I. This gives Another pair of equations can be formed from S.S.N. 's 54 and 44\mdash ; which give From S.S.N. 's 52 and 42 we get which make From S.S.N. and 46 we get which make From S.S.N. 's 60 and 38 we get which make The mean of the different values of And that of the different values of is For the sake of simplicity , we may take the values as , that is , ( the red sensation ) is of the normal , . In Table III these values are employed . It also , in Column , gives the theoretical curve derived from Table I containing the colour equations . * At S.S.N. 42 , 82 was a misprint for 72 . 1910 . ] Trichromatic Theory of Colour Vision . Columns and ether , we see that at the position of maximum luminosity the theoretical values differ fionl those obtained from the , the mean of taken . Had the evidently low been omitted when calculating the mean , the two would tallied well . A further examination of these two columns also the violet end of the spectrum the luminosity values by N. W. are much than the normal curve ives . The luminosity of the blue sensation is very small compnred with the luminosities of the red and green , and is ) as far ( say ) as S.S.N. 30 , but from S.S.N. 25 to the violet end the luminosity of the blue sensation plays a and part in the total luminosity of each number . We have already found the factor of the red seusation part of the normal violet ) . If then from the sity values obtained by N. W. , we subtract . reduced red sensation , and also hole of . green sensation , the residuc will be dne to the blue scnsation , which can be compared with that in normal vision . Sir W. de W. Abney . Colour-Blindness the [ Oct. 5 , Taking her readings from S.S.N. 25 to , we obtain the following result:\mdash ; If we lay down the luminosities shown in a curve , and draw a freehand curve between the points , we get as ordinates , and the resulting ordinates of N. W. 's blue sensations are six times larger than those of the normal curve . It appears likely that the blue sensation is the same as the normal , and that the green sensation is reduced to one-sixth of the normal and the red to one-twenty-fourth . These facts give a very good clue to the naming of the colours of the spectrum as iven in the paper referred to . One more example of the application of the formula to complete redblindness may be given . At p. 466 , 'Roy . Soc. Proc 1910 , where the first part of this subject is treated of , we have the luminosity curve of X taken direct in Column IX of the table . We can apply the formula as in the other cases . Taking S.S.N. and 40 , 50 gives Here and . That is , as , the colour-blindness to red is complete . Taking S.S.N. 's 52 and 38 , we get and 38 Here again and , and from this pair the same deduction is made , We can now discuss the plan of calculating directly the amount of colour sensation which exists in an incompletely colour-blind eye . The method is adapted also for the completely colour-blind . Suppose a person with normal vision and the person whose colour-vision is defective each make luminosity measures of the same spectrum colours , the comparison white light in each case being the same . ( The luminosity , it must be remembered , is measured by sectors placed in the path of the white beam . ) Now the luminosity of the white light to the colour-blind is less than to normal eyed by exactly the amount due to the defect in one sensation . Hence , when the colour-blind 1910 . ] Theory of Colour Vision . makes an observation , he is the comparison with a lower of white than does the observer with normal vision . If the white light were to both equally luminous their would give two curves of such a character that the difference in ordinates would be a direct measure of the defect as in the previous method . As the white is less luminous to the colour-blind , we have to find to what extent the ordinates of his curve have to be altered . Let be the factol iving the amount of his deficiency in one sensation , and let and be the component luminosities of the red , green , and blue sensations of the ray which is to be measured . Reverting to Table I the total luminosities of these three sensations in the whole spectrum of white light to normal vision are closely as 580 , , and 3 . It will be seen that the blue luminosity has but small effect , and the red and the green are nearly as 7 to 3 , when the luminosity for the normal eye is 10 . In those rays of the spectrum which contain the defective sensation the luminosity of this sensation must be multiplied by a factor the reading for the normal to be , and for the colour-blind , then we can make an equation which will contain To the red-blind remains tmaltered , is negligible , so that we get the equation in the form , ( i ) from which can be determined . When there is no green sensation in the colour , as when the slit is at any scale number below 58 , the equation becomes . ( ii ) For a green-blind remains unaffected , and the equation ( i ) becomes , ( iii ) and equation ( ii ) becomes . ( iv ) Supposing , which is the case when the colour-blindness to red or green is complete , ( i ) ecomes or and ( iii ) becomes or [ is , of course , the luminosity from the normal curve Table I. ] ( iv ) becomes or 460 Sir W. de W. Abney . Colour-Blindness and the [ Oct. 5 , which shows that the readings in the red are larger for the green-blind than for normal vision . The following observations made by a well-known man of science are given in Table and show the application of both methods of procedure . Table \mdash ; Showing Z. Curves . We will ascertain the defect of red sensation by the first method , and then it by the second method . From the table we take the scale numbers 52 and 46:\mdash ; From this S.S.N. 's 50 and 66 give This makes From S.S.N. and 40 From this Taking the mean of these factors , 1910 . ] Theory of } Here we have the defect in the red sensation is ; therefore , he must have only . of normal vision . Using formula ( i ) , at S.S.N. the luminosity of the normal vision is 8 , and of the colour defective 1 ) . At another place in the red the were 25 and 16 . At the nornud and colour-blind were 50 and 34 . In this case and ? . The equation then becomes This makes Again , at the two ) were and 53 . The equabion is then This gives Finally , at the are and 6 The eqnation is This makes The mean of the re , sults gives as the factor by to reduce the sensation of this incompletely red-blind . The factor derived from the first method was . This example that both nlethods the same result . I have worked out sensation factors from nunlerous other luminosity curves as made Sronl the observations of pletely colour-blind persons , So far , I have not met with any caso . to which these methods , founded on the normal colonl sensations , as shown in Table I , will not ] . Any small deviations which are shown , are readily accounted for by erl.ors in the somewhat difficult of luminosity . Whatever may be the nature of the visual receivin , whether it be . chetnical , there seems to be no reason why similarity in the sensation curves of the blind , compared with of the normal curves , should not ays be maintained . It is probable that , taking the and of the different points in the spectrum curves , the normal visual sensation curves can be calculated . 462 Sir W. de W. Abney . Colour-Blindness and the [ Oct. 5 , I now give a determination of the amount of incomplete colour-blindness which existed in a recent case that came before me for examination . In addition to ordinary tests I employ , and of which I shall have to say something in another communication , the inosities of two points in the spectrum were determined by the ] -blind ( Jn . ) and myself . It was found by the examination that he was red-blind to a certain extent , and afterwards the amount was determined by the two sets of observations . At S.S.N. 34 Jn. 's luminosity was 21 , that of A At S.S.N. 34 the sensation luminosities from the table were E.S. G.S. and at S.S.N. The following equations were formed to determine the defect in red sensations:\mdash ; From which , the factor of defect , was , or was the amount of his red sensation , and , the factor by which to reduce the luminosity , was Next using my determinations of the luminosity , the following equations were obtained , where is the factor for B.S. existing in Jn. 's sensation:\mdash ; The mean of the two gives as the factor and agrees with the preceding determination . It is to be noticed that the blindness must be to the red , for if we form equations by the first method , supposing greenblindness , with the same numbers we get This makes a minus quantity , which is impossible . Again , with the second method we should have , with S.S.N. We get larger than unity . There is at leaSt one other method by which the amount of visual defect in a colour sensation can be determined , but this is dependent on the colours * In both cases the mean of several observations was taken . 1910 . ] Theory of which go to form white . This and the colours perceived by the colour-blind and by normal vision I have reserved for a future communication . There may be some investigators who are a rade of artificial light such as paraffin , candle , or the glow lamp . They do not differ much from one another , so I have thought it be of use if I ooave the luminosity curve of the spectrum of the light emitted by paraffin ( crystal oil ) . I have also shown the luminosities in terms of , and B.S. in Table . It will be noticed that the maximum of R.S. is at S.S.N. 54 instead of at S.S.N. 52 , as is the case if the arc is used , and the maximum G.S. is at S.S.N. 48 instead of at S.S.N. 46 , as also is the case for the arc light . Table\mdash ; Luminosity Curves of the Spectrum of aParaffin ( Crystal Light . This indicates the extreme care that must be taken in securing a good luminosity curve of the spectrum of the employed for investigations before any deductions as to observations are made . In a paper recently presented to the Royal Society on the subject of Lord Rayleigh . Sensibihty of the [ Nov. 26 , colour-blindness there are several misapprehensions of what the trichomatic theory can or cannot explain . One very glaring misapprehension is that this theory cannot explain the matching of a bluish green by a mixture of red and blue . This is one of the most easy matches to make by the green-blind , for the green of the normal curves is absent to the green-blind , and the curves at this point are red and blue ( see S.S.N. 34 , Table I , which is a blue-green ) . Hence a mixture of red and blue to the green-blind will match what is blue-green to normal vision . There are other points on which there are misapprehensions , and they will be dealt with in another communication which I propose to offer . On the Sensibility of the Eye to of -length in the Yellow of the By Lord RAYLEIGH , O.M. , ( Received November 26 , \mdash ; Read December 8 , 1910 . ) Dr. has introduced a method of classifying colour-vision by the number of separate parts or divisions in the spectrum within each of which the observer call perceive no colour difference . Movabl screens are provided in plane of the spectroscopic telescope , by which the part admitted to the eye is limited and the limits measured in terms of wave-length . Beginning at the extreme visible red , more and more of the is admitted until a of colour ( not merely of bri htness ) is just perceptible . This gives the first division . The second division starts from the place just determined , and is limited in the direction of shorter by the same condition . In this way the whole spectrum is divided into a number of contiguous divisions , or patches , which Dr. Edridge-Green terms monochromatic . It will be observed that the delimitation of these patches includes an arbitrary element depending on the point from which the start is made\mdash ; in this case the extreme red . " " Tested with this instrument a normal individual will , as a rule , name six distinct colours ( viz. , red , orange , yellow , green , blue , violet ) , and will mark out by means of the shutters about 18 monochromatic patches . Occasionally we come across individuals with a greater power of differenhues , to whom , as to Newton , there is a distinct colour between the 'Roy . Soc. Proc , 1910 , vol. 82 , p. 458 , and earlier writings .

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On the sensibility of the eye to variations of wave-length in the yellow region of the spectrum.

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Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Lord Rayleigh, O. M., F. R. S.

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10.1098/rspa.1910.0092

Optics

Tables

Optics

464 Lord Rayleigh . Sensibility of the [ Nov. 26 , colour-blindness there are several misapprehensions of what the trichomatic theory can or cannot explain . One very glaring misapprehension is that this theory cannot explain the matching of a bluish green by a mixture of red and blue . This is one of the most easy matches to make by the green-blind , for the green of the normal spectrum curves is absent to the green-blind , and the overlapping curves at this point are red and blue ( see S.S.N. 34 , Table I , which is a blue-green ) . Hence a mixture of red and blue to the green-blind will match what is blue-green to normal vision . There are other points on which there are misapprehensions , and they will be dealt with in another communication which I propose to offer . On the Sensibility of the Eye to Variations of Wave-length in the Yellow Region of the Spectrum . By Lord Rayleigh , O.M. , F.R.S. ( Received November 26 , \#151 ; Read December 8 , 1910 . ) Dr. Edridge-G-reen* has introduced a method of classifying colour-vision by determining the number of separate parts or divisions in the spectrum within each of which the observer can perceive no colour difference . Movable screens are provided in the focal plane of the spectroscopic telescope , by which the part admitted to the eye is limited and the limits measured in terms of wave-length . Beginning at the extreme visible red , more and more of the spectrum is admitted until a change of colour ( not merely of brightness ) is just perceptible . This gives the first division . The second division starts from the place just determined , and is limited in the direction of shorter wave-length by the same condition . In this way the whole spectrum is divided into a number of contiguous divisions , or patches , which Dr. Edridge-Green terms monochromatic . It will be observed that the delimitation of these patches includes an arbitrary element depending on the point from which the start is made\#151 ; in this case the extreme red . " Tested with this instrument a normal individual will , as a rule , name six distinct colours ( viz. , red , orange , yellow , green , blue , violet ) , and will mark out by means of the shutters about 18 monochromatic patches . Occasionally we come across individuals with a greater power of differentiating hues , to whom , as to Newton , there is a distinct colour between the * ' Roy . Soc. Proc. , ' B , 1910 , vol. 82 , p. 458 , and earlier writings . 1910 . ] Eye to Variations of Wave-length . blue and violet , which Newton called indigo . Such individuals will mark out a greater number of monochromatic patches , from 22 up to 29 . The limited number of monochromatic patches which can be marked out in this way is at first surprising when we consider how insensibly one part of the spectrum seems to shade into the next when the whole of the spectrum is looked at . The number and position of the patches present , however , great uniformity from one case to another . " Being curious to know into what class my own vision would fall on this system , I was glad to be tested by Dr. Edridge-Green last July . The number of patches proved to be 17 , a little short of the number he lays down in the passage above quoted as normal . The slight deficiency appears to be in the high violet . I have known for some years that I required more light in the violet to measure interference-rings than did my assistant , Mr. Enock , and that the deficiency of sensibility was greatest for my right eye , used with Dr. Green 's apparatus . The limits of the actual patches were as follows :\#151 ; . 780\#151 ; 635-|\#151 ; 624\#151 ; 612\#151 ; 603\#151 ; 595\#151 ; 586\#151 ; 576\#151 ; 560\#151 ; 541\#151 ; 521\#151 ; 509\#151 ; 500\#151 ; 489-1\#151 ; 477\#151 ; 462\#151 ; 443\#151 ; 426 . Thus in the region of the D lines a patch including wave-lengths between 595 and 586 did not manifest a difference of colour . The interval between the D lines on the above scale being 0'60 , it appears that my " monochromatic patch " was 15 times this interval . While it is undoubtedly true that in this way of working no colour-difference was perceptible as the eye travelled backwards and forwards over the patch , my experience with colour discs and other colour-mixing arrangements made me feel certain that under more favourable conditions I could discriminate much smaller differences of wave-length . Special experiments have since proved that I can in fact discriminate by colour between points in the spectrum as close together as the two D lines . In order to compare two colours with advantage it is necessary that each should extend with uniformity over a considerable angular area , and that the two areas should be in close juxtaposition . The requirements of the case are sufficiently met by a colour-box ( after Maxwell ) such as I described nearly 30 years ago.* In this form of apparatus a second slit , placed at the focus , allows a narrow width of the spectrum to pass ; but instead of regarding the transmitted portion with an eyepiece , the eye is brought close to the slit and focussed upon the prism , which thus appears uniformly lighted with such rays as the second slit allows to pass . The light thus * 'Nature , ' 1881 , vol. 25 , pp. 64\#151 ; 66 ; 'Scientific Papers , ' vol. 1 , p. 543 . See also 'Nature , ' August 18 , 1910 . Lord Rayleigh . Sensibility of the [ Nov. 26 , presented is of course not absolutely homogeneous ; it includes a mixture of neighbouring spectrum rays , the degree of purity augmenting as the slits are narrowed . With the aid of a refracting prism of small angle ( set perpendicularly to the dispersing prisms ) the field of view is divided into two parts which correspond to any desired colours according to the situation of the two primary slits . For the present purpose these primary slits lie nearly in one straight line , inasmuch as the two spectrum colours to be compared are close together . A detail of some importance in delicate work may here be mentioned . It is known that in many cases , e.g. in lantern projection , the spectrum lines corresponding to a straight primary slit are sensibly curved . Mr. Madan proposed many years ago to cure this defect by counter-curving the primary slit . In the kind of instrument under discussion it is desirable to retain straight primary slits , but there is nothing to forbid curvature of the second or eye slit , which is a fixture , and such curvature is necessary for the most effective working . A deficiency in this respect , or in focussing , may entail objectionable changes of colour as the eye moves about behind .its slit . The simplest way of making the adjustment is to illuminate a somewhat narrow primary slit with soda light and to fit the jaws of the secondary slit to the image thus obtained and examined with a lens as eyepiece . In making the observations on sensitiveness , one primary slit , as well as the eye-slit , remains fixed , the position being chosen so as to provide yellow light from the neighbourhood of D. The second slit can be moved as a whole while retaining its width . The shutters necessary were cut from thin zinc sheet and were held by sealing or soft wax , in a manner which need not be minutely described . The movements of the shutter which carries the second slit were measured by callipers . The procedure is quite simple . If the colours seen are strongly contrasted , the movable slit is displaced until the difference is moderate . Marks may then be given ; 0 , denoting that the difference is uncertain ; Ri , that it is just distinct in the direction of making the second patch the redder ; Gi , that it is just distinct in the opposite direction . Similarly , R2 , G2 , denote differences in the two directions which are more than distinct , and so on . After each observation worth recording , the position of the movable slit is measured . One further precaution ought to be mentioned . In making a decision when the difference of colour is slight , care should be taken that the brightnesses are nearly equal . When , as in my experiments , daylight is employed , the passage of clouds may cause a disturbance in this respect , even if the two primary slits are of equal width . The interposition of a 1910 . ] Eye to Variations of Wave-length . 467 piece of ground glass a little behind the primary slits is usually a remedy . But this reduces the illumination , and it is sometimes preferable to adjust the brightness otherwise . It may be done conveniently by cutting off some of the light on the preponderating side by the interposition of one or more strips of glass held at varying angles of obliquity . In this manner , as the result of sets of observations made on several days , it was found that a movement of the second slit through 0T5 mm. was sufficient to carry the variable colour from being distinctly redder than the standard to distinctly greener . Ho doubt the result might have been arrived at quicker with a more refined apparatus , in which the movements of the slit were controlled and measured by a micrometer screw , but I do not think it would be any more certain . Probably the distance is something of an over-estimate . In several of the measurements included , the distinctness of the difference was unnecessarily pronounced . We may conclude that the eye is capable of appreciating without fail a- difference of situation represented by 007 mm. It remains to interpret the result in terms of wave-lengths . By allowing light to enter at the eye-slit , or rather at a narrower slit superposed upon it , a spectrum is formed at the other end whose scale has to be determined . It appeared that the distance from D to E was 7 mm. The difference of wave-length between these lines is 62'3 . The perceptible difference is 1/ 100 of this , corresponding nearly enough to the difference between the I ) lines . I think I am safe in saying that I could distinguish the colours of the two D lines if favourably presented to the eye . This degree of sensitiveness , though not higher than I had expected , is a little difficult to reconcile with the monochromatic appearance of a portion of the spectrum 15 times wider . I suppose that the gradual character of the transition is an obstacle to the recognition of differences . The question of angular magnitude may also enter . Ho doubt a very small apparent magnitude would be unfavourable . It is possible that in Dr. Green 's apparatus an eyepiece of higher power , with a corresponding augmentation in the intrinsic brilliancy of the source of light , would allow of an increase in the number of distinguishable patches . The experiment would be worth a trial . It will be seen that the existence of " monochromatic patches " in the spectrum is far from meaning that the eye is incapable of making chromatic distinctions within their range . I do not infer from this that the results of the method are without significance . Undoubtedly it is possible by means of it to classify col our-vision , and such a classification cannot be without interest , even if we fail as yet to understand exactly what it means . 468 Sensibility of the Eye to Variations Wave-length . In conclusion , I will remark that those who lay great stress upon the number of principal colours recognised by any particular eye seem to me to overlook too much the colours not represented in the spectrum . To most of us white is a sensation quite as distinct from any other as yellow can be . In my estimation purple has a better claim than orange to be reckoned a principal colour . The fact , too , that dark orange reveals its character so little as to be called by another name ( brown ) seems to indicate that these distinctions are not of fundamental importance . On the Determination of the Chief Correlations Collaterals in the Case of a Simple Population Mating at Random . By E. C. Snow , B.A. , Biometric Laboratory , University College , London . [ This paper is published in ' Proceedings , ' Series B , vol. 83 , pp. 37 55 . ]

rspa_1910_0093

0950-1207

On the determination of the chief correlations between col\#xAD;laterals in the case of a simple Mendelianp population mating at random.

468

468

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

E. C. Snow, B. A.

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10.1098/rspa.1910.0093

Optics

Biography

Optics

468 Sensibility of the Eye to Variations Wave-length . In conclusion , I will remark that those who lay great stress upon the number of principal colours recognised by any particular eye seem to me to overlook too much the colours not represented in the spectrum . To most of us white is a sensation quite as distinct from any other as yellow can be . In my estimation purple has a better claim than orange to be reckoned a principal colour . The fact , too , that dark orange reveals its character so little as to be called by another name ( brown ) seems to indicate that these distinctions are not of fundamental importance . On the Determination of the Chief Correlations Collaterals in the Case of a Simple Population Mating at Random . By E. C. Snow , B.A. , Biometric Laboratory , University College , London . [ This paper is published in ' Proceedings , ' Series B , vol. 83 , pp. 37 55 . ]

rspa_1911_0001

0950-1207

Address of the President, Sir Archibald Geikie, K. C. B. at the Anniversary Meeting on November 30, 1910.

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482

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Sir Archibald Geikie, K. C. B.

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10.1098/rspa.1911.0001

Biography

Atomic Physics

Biography

Address of the President , Sir Archibald , at the Anniversary Meeting on November 30 , 1910 . The year which has passed since our last Anniversary will be memorable in our annals for the losses which death has brought upon the Royal Society . First and most conspicuous is the decease of our Patron , His revered Majesty , King Edward VII . During his brief but eminently beneficent reign , His Majesty continued to manifest the same interest in the advancement of science which he had always shown before his accession to the Throne . We mourn that a life so devoted to the cause of peace and progress should have been cut off so soon . King George Y has honoured us by stepping at once into his father 's place as Patron of the Royal Society , and has subscribed his name in our Charter-book . His Majesty as Prince of Wales found many occasions to show his appreciation of science , and his interest in its progress . We feel confident that under his enlightened rule the advancement of Natural Knowledge will continue to receive his support and encouragement . The deceased Fellows are : Dr. Ludwig Mond , died December 11 , 1909 . Dr. Shelford Bidwell , died December 18 , 1909 . Sir Charles Todd , died January 28 , 1910 . Edward Saunders , died February 6 , 1910 . Sir Robert Giffen , died April 12 , 1910 . Sir William Huggins , died May 12 , 1910 . John B. N. Hennessey , died May 23 , 1910 . C. Greville Williams , died June 15 , 1910 . The Rev. Robert Harley , died July 26 , 1910 . Dr. Sydney Ringer , died October 14 , 1910 . The deceased Foreign Members are : Prof. Friedrich Ivohlrausch , died January 17 , 1910 . Prof. Eduard F. W. Pfluger , died March 17 , 1910 . Prof. Alexander Agassiz , died March 28 , 1910 . Prof. Stanislao Cannizzaro , died May 10 , 1910 . Prof. Robert Koch , died May 27 , 1910 . Prof. Giovanni Schiaparelli , died July 4 , 1910 . Dr. Melchior Treub , died October 3 , 1910 . On the list of Foreign Members of the Society we have thus to mourn the loss of no fewer than seven illustrious names . Of these there is none which we VOL. LXXXIV.\#151 ; A. Anniversary Address by Sir A. [ Nov. 30 , more deeply regret than that of Alexander Agassiz . His frequent visits to Europe brought him into closer personal contact with the Fellows of the Royal Society than is usually possible for our Foreign Members . Only last summer he came once more among us with apparently little diminution of his characteristic capacity for work . But it was his last public appearance , for he died a week or two afterwards on his homeward passage across the Atlantic . His genius for original research , the unwearied activity with which he pursued those lines of enquiry to which he specially devoted himself , and the generous prodigality with which he placed his ample fortune at the service of science in the investigations which he led and inspired , placed him at the head of the oceanographers of his day . Year after year he traversed , dredged , and sounded the ocean through many different latitudes , bringing back from each cruise enormous collections of material , which went to increase the treasures of that Museum of Comparative Zoology which his father had planned at Harvard , and to which he himself had devoted the strenuous energies of his life . Besides adding much to our knowledge of the fauna of the deep , he ever had an eye for the great physiographic problems which the oceans , their coasts , and their islands present . The pile of goodly volumes in which his incessant labours are chronicled form one of the most remarkable monuments which have been reared in our day by the genius , enterprise , and enthusiasm of a single man . By the death of Stanislao Cannizzaro , at the ripe age of 84 , Italy has been deprived of her foremost chemist , and science has to regret the loss of one of her illustrious students , who by his generalisations on chemical combination did so much to place modern chemistry on a sound basis . It happened that at the time of his death the senior Secretary of the Boyal Society and myself were in Rome as delegates of the Society to the meeting of the International Association of Academies . We were glad to avail ourselves of the opportunity of attending the funeral of our deceased Foreign Member . It was a touching sight to find that in the class-room where he had so long taught and where his diagrams were still hanging on the walls , the coffin had been placed on his lecture-table and was guarded by a body of his students , who bore it thence on their shoulders , through a dense crowd of mourners to the hearse . Representatives of science from far and near followed the body to the grave . A veteran astronomer has passed away in Giovanni Schiaparelli . From the time of his discovery of the planet Hesperia , made when he was only six and twenty years of age , he prosecuted an active and successful study of the heavens , extending over some forty years at the observatory of Milan . 1910 . ] Anniversary Address by Sir A. Geikie . 471 His notable identification of the orbits of meteors with those of comets , his minute delineation of the surface of the planet Mars , and his subsequent studies of Mercury and Venus , have made his name a household word in astronomical science . In Robert Koch we have to deplore the loss of one who conferred inestimable benefits on the science of bacteriology . To him we owe the isolation of the tubercle bacillus , the proof that it is the cause of tuberculosis , and the product , tuberculin , for the treatment of this calamitous disease . He has made modern bacteriology possible by his elaboration of methods for the culture of bacilli . Friedrich Wilhelm Koiilrausch , who died in January last , in Ins ' seventieth year , will be remembered for his investigation of the methods of measuring magnetic and electrical quantities , for his laborious researches into the conducting power of electrolytic solutions , which formed the foundation of the modern electrolytic theory of solution , and for the great service which he rendered by insisting on the necessity of practical instruction in the laboratory for the teaching of physics . In Melchior Treub botany has lost an esteemed and eminent worker . A master of technique , with high intellectual gifts , he attacked many important problems and materially advanced knowledge in the diverse domains of plant physiology , cytology , morphology and geography , presenting his results with great lucidity and grace of style . His scientific work was mainly done while he was engrossed in the official duties of Director of the Buitenzorg Botanic Garden in Java : duties performed for nearly thirty years with such success that the practical benefits which resulted from them to pharmacology , forestry and tropical agriculture are comparable with his scientific contributions . His sympathies were as wide as his interests ; and his memory will live in the work which he helped others to achieve as well as in his own . Coming now to the losses from our Home List during the year that has passed , we have to mourn the death of one of the great historical figures of the Royal Society\#151 ; Sir William Huggins . It would be out of place in this brief address to attempt even a summary of the achievements of his distinguished career , but on this anniversary occasion our thoughts naturally turn to the recollection of the salient features of that career which shed such lustre on the Society . Soon after the invention of spectrum analysis as.a practical method of investigation was accomplished , only fifty years ago , by Kirchhoff and Bunsen , Huggins resolved to devote himself to the application of this new method to astronomical problems , and , as we all know , he thereby laid the foundations of the wonderful science of astrophysics . His early observations of the spectra of the stars , made before any of the apparatus . 472 Anniversary Address by Sir A. Geikie . [ Nov. 30 , now so appropriate for such purposes had been evolved or even thought of , showed his close application and the exquisite refinement of his appliances . In rapid succession he informed us of the similarities in constitution between some types among the fixed stars and our own Sun , and of the marked differences shown by other types , thus leading on to the great fundamental subject of the classification of the stars and initiating the discussion of the order of their evolution . The early application of photography to the spectra of objects whose light is so feeble demanded wonderful patience and skill : it was rewarded with an immediate crowd of physical results in the registration of spectra far beyond the visible limit in the violet , among which the recognition of the second spectrum of hydrogen may be recalled . So , too , at a later time , when the four lines of the ordinary spectrum of this gas were shown by Balmer to belong to a very definite algebraic series , which ought to include numbers of other lines whereof laboratory experiments showed no trace , it was Huggins who called in the aid of the celestial laboratory of the stars and pointed to the exact succession of the missing lines in the spectra of certain stars\#151 ; thereby infusing new zeal into the efforts of theorists to unravel the secret of the origin of the spectrum . When the same refined appliances were turned to the scrutiny of the nebulae , which are spread over such vast regions of the sky , the news soon came that the problem raised by William Herschel and his successors had now been definitely solved by the discovery that these nebulae were not all clusters of stars , but that some of them shone as masses of glowing gas . In solar work reference may be made to Huggins ' proposal to render the flame-prominences visible in open day by great optical dispersion , and also , though the result was less satisfactory , to his persistent attempts to photograph the solar corona by aid of coloured screens . But perhaps the most brilliant of his achievements was his early conception , undeterred by full knowledge of the difficulties which had to be faced , that it might be possible to measure the velocities of approach or recession of the stars by spectroscopic means . In a masterly investigation he proved to the world that his expectation was well grounded , and that the development of instruments specially adapted for this new outlook into astronomy demanded vigorous prosecution . His other laboratory work , all designed for the elucidation of astronomical problems , can only be referred to , such , for instance , as his research into the nature of the luminosity of radium salts . Sir William Huggins was elected into the Boyal Society as far back as 1865 . During his long association with us he took the keenest interest in the affairs and the success of the Society . He was repeatedly elected into the Council , where his total length of service amounted to no less than sixteen 1910 . ] Anniversary Address by Sir A. years . He served as Vice-President for four years , and we count it as one of the distinctions of the Society in our time that he Held the office of our President for five years . Thus , not merely for the lustre reflected from his high reputation in science , but for the personal service which he so willingly and effectively rendered in the conduct of its business , the Eoyal Society gratefully and affectionately cherishes his memory . But , great as was his position in scientific discovery , it is within the personal knowledge of most of us that in character he was equally great . His was an ideal life , dedicated throughout to the sublime science for which he did so much , and during many years happy in the devoted companionship and co-operation that eased , and at the same time stimulated , the arduous work of a solitary astronomer . Dr. Ludwig Mond will be remembered not only for his eminence in chemistry , which was recognised by his election into this Society , but for the indomitable courage and sagacity with which he brought his discoveries into successful practical operation on a commercial scale , and not less for the well-considered and large-hearted liberality wherewith he dispensed the wealth which rewarded his success . The Eoyal Society has good cause to cherish his memory as that of a genial Member who took an active interest in its affairs , affording it at all times the benefit of his business experience , and ever ready to aid financially any of its enterprises which seemed to him to stand in need of assistance . By his will also he has left a munificent benefaction whereby the Society will ultimately be enriched . The other deceased Fellows on the Home List are Dr. Shelford Bidwell , Sir Eobert Giffen , the Eev . Eobert Harley , Mr. John B. N. Hennessey , Dr. Sydney Einger , Mr. Edward Saunders , Sir Charles Todd , and Mr. C. Greville Williams . The Eeport of the Council now presented to the Fellows contains a record of the main features of the work of the Society for the past year . To one or two parts of this work I wish to make brief allusion . It will be seen that , acting on the recommendation of the President and Council of the Society , the Government of this country has agreed to continue its subscription to the International Association of Seismology for six years more , up to the end of March , 1916 . This prolongation of the adhesion of Great Britain is eminently desirable , in order that time may be allowed for the consideration of the best means of securing effective international co-operation in seismological observation and enquiry . In this branch of science our country has a special interest , for it was here that modern observational seismology was begun many years ago , and that the first network of observing and registering 474 Anniversary Address by Sir A. Geikie . [ Nov. 30 , seismological stations was established over the face of the globe . To the wide experience , great practical skill , and unwearied enthusiasm of our .colleague , Dr. John Milne , the establishment and maintenance of that network of stations have been entirely due . With but little financial assistance from outside , he has borne the whole burden of the organisation , as well as of the voluminous correspondence which it entails with all parts of the world . The valuable service which he has thus rendered to the study of earthquakes has been universally recognised , and there is a widespread conviction that the system of observing stations which he has created is worthy of being made a national undertaking . The whole question of the future of seismology in this country must soon be seriously considered . Meanwhile , I would express my own personal hope that means will be found to place on a more permanent footing the work which Dr. Milne has originated and conducted , and to carry it on as successfully as in the past , but with an enlarged staff and more generous financial aid . The Fellows are aware that for many years past the Society , at the request of different departments of Government , has undertaken the investigation of various diseases with the view of ascertaining their cause , and , if possible , of suggesting methods of treatment and cure . Chief among these enquiries is that of the appalling disease Sleeping Sickness . From the Report of the Council it will be seen that , although much important information has been obtained in Uganda , the investigation has had to be extended beyond the limits that originally seemed to be requisite , and that probably much still remains to be done before the conditions can be definitely stated in which trypanosome diseases are spread in tropical Africa . The work of those enquirers who are busy in London endeavouring to discover an effective drug for the treatment of trypanosomiasis is still in progress , with results which are so far encouraging for further investigation . One of the most important statements in the Council 's Report is that which has reference to the Gassiot Committee and the future of Kew Observatory . The arrangement therein detailed was the subject of long and careful enquiry and discussion . The Gassiot Committee has now been reconstituted and enlarged so as to make it an effective scientific body of advice in regard to magnetic , seismological or other geophysical observations which are to be conducted under the direction of the Meteorological Office . Fellows of the Royal Society should be aware that they are divisible into two classes , those who were elected before 1878 and those who were elected after that year . The distinction is a pecuniary one . The older group paid \#163 ; 10 of entrance fee and an annual subscription of \#163 ; 4 , which they still .continue to pay . They are a dwindling band which now numbers only 571910 . ] Anniversary Address by Sir A. The second and younger group , by the institution of what is called the Fee-Beduction Fund , are relieved of the payment of an entrance fee and their annual contribution is reduced to \#163 ; 3 , the remaining \#163 ; 1 being paid out of that Fund . When this arrangement was made it seems to have been calculated that the original capital sum of \#163 ; 10,111 5s . ( which was raised by voluntary contributions ) , with the invested interest accruing from it , would yield an annual income of \#163 ; 600 , which was estimated to be sufficient to meet the highest demand that was likely to be made on the Fund . But these calculations have proved erroneous , partly no doubt on account of the fall in the rate of interest and partly also because younger men have been elected into the Society than was formerly the case , so that the increase in the participators in the benefit of the Fund has not been balanced by deaths to the extent anticipated . Consequently now , thirty years after the foundation of the Fund , the income , instead of amounting to \#163 ; 600 per annum , has only reached \#163 ; 467 4s . 9 while the payments this year should be \#163 ; 474 , viz. , \#163 ; 150 in respect of fifteen entrance fees and \#163 ; 324 towards the annual contributions of 324 Fellows elected since 1878 and still living . There is , thus , this year , for the first time a deficit , which amounts to \#163 ; 6 15s . The excess of the sum which should be paid beyond the income of the Fund will increase annually , though at a diminishing rate , and will probably ultimately amount to about \#163 ; 50 . It is obvious , therefore , that some new arrangement will require to be made . The Fellows elected since 1878 might be called upon to increase their annual subscriptions , but such a call would probably be felt to be both inconvenient and undesirable . An alternative would be to increase the capital of the Fund , and this would undoubtedly be the more acceptable solution of the difficulty . If the Treasurer could be put in possession of a sum of at least \#163 ; 1,000 he would be placed in a satisfactory position in regard to this portion of the Society 's finances . So long as the deficit remains small the excess of income could be devoted to the increase of the capital , and consequently the sooner the sum required is obtained the better . I commend this matter to the consideration of the Fellows ; among whom there are doubtless many who will be as glad to contribute substantial sums as were the original founders of the Fund . MEDALLISTS , 1910 . Copley Medal . The award of the Copley Medal has this year been made to one of our own countrymen , who has been more than fifty years a Fellow of the Boyal 476 Anniversary Address by Sir A. Geikie . [ Nov. 30 , Society . Sir Francis Galton 's life has been one of ceaseless activity in many varied departments of intellectual effort . Few of us can remember how he began as an enthusiastic explorer and geographer , " urged , " as he confessed , " by an excessive fondness for a wild life , " and with " the love of adventure " as his chief motive . He chose South Western Africa as the theatre of his exploration , penetrated into regions where no European foot had preceded him , and brought back with him a vivid impression of the scenery , physical geography , natural history , and ethnology of Damaraland and South Ovampoland . He embodied his observations in an interesting volume of travel published in 1853 . That work showed that he was no mere hunter after game or seeker of adventure , but a shrewd and observant traveller , with his eyes open to every distinctive natural feature in the countries and their inhabitants . His experience in these African journeys led him to plan and to publish in 1854 his well-known and admirable hand-book , the " Art of Travel , " which , as a pioneering treatise in the practical methods of scientific exploration , has proved of inestimable service to the travellers of the last half century . Sir Francis at an early period of his career was led to interest himself in meteorology , which , as a science of observation , was then in its earliest infancy . With much labour and skill he constructed weather-charts , and discussed meteorological statistics . His zeal and success in these studies led to his being chosen a member of the Meteorological Council at its origin , and he remained in that position until the Council was superseded in 1901 by the Meteorological Office . He likewise acted as Chairman of the Royal Society 's Committee of Management of Kew Observatory from 1888 till 1900 , when the work of this Committee became merged in that of the National Physical Laboratory . But it was not only in geography and meteorology that Sir Francis Galton manifested his versatile energies . He was much interested likewise in biological studies , especially in regard to questions of relationship and heredity . As far back as 1871 he began what has proved to be a voluminous and important series of contributions to these subjects . From his first paper , " Experiments in Pangenesis , " down to his last volume on " Eugenics , ' his successive papers have shown a continuous development of ideas and conclusions . He was led from his early ethnological enquiries into the mental peculiarities of different races , to discuss the problems of Hereditary Genius , from the fundamental postulate that " a man 's natural abilities are derived by inheritance under exactly the same limitations as are the form and physical features of the whole organic world . " To obtain further data for the discussion of this subject , he carried out the elaborate statistical 1910 . ] Anniversary Address by Sir A. enquiries embodied in his " English Men of Science . " Confident in the results of these researches , he proceeded after the manner of " the surveyor of a new country who endeavours to fix in the first instance , as truly as he can , the position of several cardinal points . " His results iff this quest were given in his " Inquiries into Human Faculty and its Development , " published in 1883 . A further contribution was made by him in 1889 , when his work on " Natural Inheritance " appeared . His subsequent papers and essays on " Eugenics " have still further stimulated enquiry into a subject of such deep interest and transcendent importance in all efforts to improve the physical and mental condition of the human race . It has seemed to the Council fitting that a man who has devoted his life with unwearied enthusiasm to the study and improvement of many departments of natural knowledge , whose career has been distinguished by the singleness and breadth of its aims , and by the generosity with which he has sought to further them , should receive from the Royal Society its highest award in the Copley Medal . i Rumfokd Medal . The Eumford Medal has been awarded to Prof. Heinrich Eubens in recognition of the value of his researches in radiation . For many years he has been engaged in the experimental investigation of optical radiations of very long wave-length . In the course of this work he elaborated , in conjunction with Prof. E. F. Nichols , a method of isolating pencils of nearly homogeneous rays , using the fact that a non-metallic substance reflects very copiously waves of the same length as those to which it is opaque . If then a pencil of rays of mixed wave-lengths is reflected several times to and fro between mirrors of the same kind of substance , the rays finally emerging ( the " Reststrahlen " ) have the " wave-lengths of the kinds of light which the substance refuses to transmit . The light of other wave-lengths has been transmitted freely at each incidence , and by a sufficient number of reflections is ultimately removed from the pencil . By using different substances as reflectors , Prof. Eubens has isolated infra-red light of various wave-lengths up to as much as 96/ i , or about 0T of a millimetre ; while , on the other hand , purely electric waves have been produced of wave-lengths as small as 2 millimetres . He has thus enormously extended our knowdedge of the infrared spectrum . Moreover , in conjunction with colleagues , he has investigated the absorbing and reflecting powers of substances for these long wave-length rays . He has shown that , for radiation of wrave-length even less than ten times the wave-lengths in the visible spectrum , the reflecting and absorbing powers Anniversary Address by Sir A. [ Nov. 30 , of metals and alloys are determined by their electric conductivities alone , in accordance with Maxwell 's theory . It followed from Maxwell 's own observations on the absorption of gold-leaf for visible light that agencies more complex than tonductivity must be involved for these shorter wave-lengths . Prof. Eubens has recently applied to the measurement of the long infrared wave-lengths a quartz interferometer , and among other results , he has found that the refractive index of water , for waves of length about 82/ / , , is of the same order as for waves in the visible spectrum , while for the shortest Hertzian waves yet examined , about 2000/ / , , it is as high as 9 . These examples will serve to illustrate how much Prof. Eubens has already done to bridge the gap between optical radiations and electric waves produced by direct electric agency , and how much more is to be expected from him in the investigation of the interval still remaining in which such fundamental changes of properties take place . Eoyal Medals . The awards of the two Eoyal Medals given annually by our Patron the King have received His Majesty 's approval . One of these Medals has been assigned to Prof. Frederick Orpen Bower in recognition of the great merit of his contributions to morphological botany , of which department of science he is the acknowledged leader in Great Britain . Prof. Bower 's early studies in this field ( 1880\#151 ; 82 ) , on the genera Welivitschia and Gnetum , were marked by the discovery of the true nature of the two persistent leaves in . The next period of his work was given to a study of the morphology of the leaf . He developed in 1884 the idea of the phyllopodium or leaf-axis , and discussed in 1885 the apex of the leaf in Osrnunda and Toclea . This latter study was cognate to subsequent researches , the results of which were given in 1886 in a review of " Apospory and Allied Phenomena . " This work , of much intrinsic interest , is important as having led its author to formulate the views advanced in 1890 in a memoir on " Antithetic as distinguished from Homologous Alternation [ of Generation ] in Plants . " Another memoir , published in 1889 , on " The Comparative Examination of the Meristems of Ferns as a Phylogenetic Study , " prepared in the light of the then received belief that the leptosporangiate ferns are the more primitive , was followed in 1891 by a discussion of this question in which Prof. Bower advanced morphological reasons for reversing the hitherto accepted phylogenetic order . The new conclusion has proved to be in accord with palseobotanical results , and marked another distinct step in the advancement of botanical science . 1910 . ] Anniversary Address by Sir A. Geikie . 479 During the third period of his work , 1892\#151 ; 1908 , Prof. Bower 's papers , including an important series on the spore-producing members , have resourcefully maintained the antithetic doctrine , and have afforded a striking instance of the advantage of a well-considered working hypothesis as a guide to investigation . The career of morphological research here outlined has been recently crowned by the publication ( 1908 ) of a book on " The Origin of a Land Flora , " which is one of the " most important contributions to the advancement of Natural Knowledge , published originally in His Majesty 's dominions , " within the period prescribed in respect of the award of Eoyal Medals . The other Eoyal Medal has been adjudged to Prof. John Joly , who is eminent in two branches of science , geology and physics . This combination of studies has proved to be reciprocally fruitful to both departments . It was from his mineralogical interests that he was led to devise the steam calorimeter , which has enriched physics with an apparatus of high refinement . The use of this method was extended by him to the direct determination of the specific heats of gases at constant volume , a measurement dealing with minute quantities of heat under circumstances quite beyond the capabilities of the usual forms of calorimeter . Among many contributions to standard physical data , which are accepted and in use , may be instanced his determination of the density of saturation of steam . His meldometer , primarily intended for determining the melting points of mineralogical and geological specimens , has been the means of providing data for use in thermometry . He has devised and applied a method of determining the change of volume of rocks and other substances on fusion , which is a datum of primary importance for cosmical theories . He has carried out a refined research , with negative results , on the possibility of minute change of mass ( as distinguished from weight ) accompanying chemical combination . His recent extended investigations of the occurrence of radioactive substances in materials from various strata have been utilised for fundamental geological discussions . Of other useful inventions which he has introduced , one of the best known is the translucent block photometer . Prof. Joly has made important contributions to the subject of colour photography , and devised some years ago a three-colour system in which all three colours are present on the same plate in the form of fine parallel lines or small dots . He has also contributed substantially to the theory of biological processes , such as the ascent of sap in vegetation . Eeference may likewise be made to his suggestive memoir on the Age of the Earth based upon a discussion of the chemical constitution of the Ocean . Anniversary Address by Sir A. . [ Nov. 30 , Davy Medal . The Davy Medal has been assigned this year to Prof. Theodore W. Pochards , as a mark of appreciation of the value of his work in the determination of the atomic weights of the elements . His researches on this subject have not been surpassed in comprehensiveness by those of any other chemist . He has himself determined the atomic weights of no less than 14 elements , and many other atomic weight determinations have been made under his direction and superintendence . The accuracy of the numbers obtained is certainly much higher than that which has been attained by any previous series of researches , and it is impossible to speak in too high tetms of the ingenuity , the unremitting labour , and the masterly manipulation which Prof. Eichards has brought to bear on his investigations . In addition to this work on atomic weights , Prof. Eichards has made many important contributions to physical chemistry , and it is probably no exaggeration to say that he has done more to raise the standard of accuracy in physico-chemical work than any other living chemist . Theoretical contributions to this branch of science are comprised in a series of papers on " The Possible Significance of Changing Atomic Volume , " in which he suggests a relation between the energy of the atoms and their compressibilities . In order to test his hypothesis , he has made a long series of investigations on the compressibility of elements and compounds . He has determined this constant for nearly all the solid and liquid elements , and he has shown that the compressibility is a periodic function of the atomic weights . In electro-chemistry , Prof. Eichards has made important determinations of the electro-chemical equivalent of silver , and he has supplied some of the most rigorous proofs of the universality of Faraday 's Law . Darwin Medal . To Mr. Eoland Trimen , who was for many years Curator of the South African Museum , in Cape Town , the Darwin Medal has been awarded . His official position , and the duties it involved , enabled him to do admirable work in African zoology . His name will always stand with those of Bates and Wallace in the establishment and illustration of the theory of mimicry . In addition to his researches on that subject , he has done admirable systematic work , his descriptions of insects , especially the Lepidoytera rhopalocerct , being models of accuracy and literary style . He , furthermore , rendered the greatest assistance to Charles Darwin , especially in his work on orchids\#151 ; assistance the high value of which is acknowledged in a long series of that great naturalist s published letters . 1910 . ] Anniversary Address by Sir A. Geikie . Sylvester Medal . The Medal which perpetuates the name and mathematical prowess of James Joseph Sylvester has this year been assigned to Dr. Henry Frederick Baker , in recognition of his work in the Theory of Functions , wherein he has shown himself to be a profound analyst . His book on the Abelian Functions , published in 1897 , is a classic , and probably no better guide to the analytical development of pure mathematics has appeared during the last three-quarters of a century . While basing the argument of the work on the methods of Eiemann , he never loses sight of the arithmetical ideas which we owe to Ivronecker , Dedekind , and Weber , or of the geometrical notions brought to light by the labours of Clebsch , Gordan , Noether , and Klein . The critical insight which was thus in evidence marked him out a few years ago as the editor of Sylvester 's Collected Papers . This work , which , with the approaching issue of the fourth and last volume , may be said to be complete , has been necessarily a difficult task , which besides making demands upon the resources of an accomplished mathematician has entailed no little editorial labour . Dr. Baker , by explanatory and critical observations , and by frequent ameliorations of the text , has done much to assist mathematical students . His scholarly work has resulted in a faithful record of the course of Sylvester 's thought . It seems eminently fitting that the Sylvester Medal should be given to one who has erected so lasting a memorial to the great mathematician . Hughes Medal . To Prof. John Ambrose Fleming the Hughes Medal has been awarded . For thirty years he has been actively engaged in researches in experimental physics , chiefly in the technical applications of electricity . He was an early investigator of the properties of the glow lamp , and elucidated the unilateral conductivity presented in its partial vacuum between glowing carbon and adjacent metal , a phenomenon which has been linked up recently with the important subject of the specific discharges of electrons by different materials . He has published in the scientific and technical press , and in technical textbooks , many admirable experimental investigations and valuable expositions in the applications of electricity , as , for example , to electric transformers and wireless telegraphy . Of special interest and value for theory were the important results concerning the alterations in the physical properties of matter , such as the remarkable increase in the electric conductivity of 482 Mr. A. Mallock . Influence of Viscosity on [ Oct. 10 , metals , when subjected to very low temperatures , which flowed from his early collaboration with Sir James Dewar in investigating this domain . In recent years he has taken a prominent part in the scientific development of telegraphy by free electric waves . Influence of Viscosity on the Stability of the Flow of Fluids . By A. Mallock , F.R.S. ( Received October 10 , \#151 ; Read November 24 , 1910 . ) No part of the theory of hydrodynamics is more difficult than that relating to stability , and even were the conditions which determine the limits of stability thoroughly and satisfactorily investigated , only the fringe of the problem would be touched , for the chief interest in the cases presented by real fluids lies in the character of the motion after instability has been established . In some restricted dynamical problems an inverted pendulum ) the system passes from an unstable to a stable configuration , and the whole process can be traced . With fluid motions , however , this is not the case , and there is no more prospect of tracing the course of a particle of fluid in an unstable flow than of following an individual molecule of gas in its various encounters with its neighbours . Nevertheless , the direction and speed in a region of unstable flow is not in general a mere matter of chance , but rather one of periodic variation , though the periods involved are not in most cases definite , in the same sense as are the periods of stable systems , but are in character more nearly allied to the intervals which separate the times of activity of a geyser\#151 ; intervals , that is , whose constancy depends on the uniformity of the rate at which energy is supplied or withdrawn from the fluid . In all the streams , whether of gas or liquid , met with in nature , the conditions are in general those of instability , and it is only in certain cases , and by taking considerable precautions , that an approximately stable flow can be maintained , and where this is accomplished the stream-lines are of the electric type . Although it is impossible by mathematical analysis to follow in detail the motion in an unstable flow , the general character may , in many cases , be traced , and the object of the present note is to apply an observation made by

rspa_1911_0002

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Influence of viscosity on the stability of the flow of fluids.

482

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Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

A. Mallock, F. R. S.

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6.0.4

http://dx.doi.org/10.1098/rspa.1911.0002

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rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1911_0002

10.1098/rspa.1911.0002

Fluid Dynamics

Geography

Fluid Dynamics

482 Mr. A. Mallock . Influence of Viscosity on [ Oct. 10 , metals , when subjected to very low temperatures , which flowed from his early collaboration with Sir James Dewar in investigating this domain . In recent years he has taken a prominent part in the scientific development of telegraphy by free electric waves . Influence of Viscosity on the Stability of the Flow of Fluids . By A. Mallock , F.R.S. ( Received October 10 , \#151 ; Read November 24 , 1910 . ) No part of the theory of hydrodynamics is more difficult than that relating to stability , and even were the conditions which determine the limits of stability thoroughly and satisfactorily investigated , only the fringe of the problem would be touched , for the chief interest in the cases presented by real fluids lies in the character of the motion after instability has been established . In some restricted dynamical problems an inverted pendulum ) the system passes from an unstable to a stable configuration , and the whole process can be traced . With fluid motions , however , this is not the case , and there is no more prospect of tracing the course of a particle of fluid in an unstable flow than of following an individual molecule of gas in its various encounters with its neighbours . Nevertheless , the direction and speed in a region of unstable flow is not in general a mere matter of chance , but rather one of periodic variation , though the periods involved are not in most cases definite , in the same sense as are the periods of stable systems , but are in character more nearly allied to the intervals which separate the times of activity of a geyser\#151 ; intervals , that is , whose constancy depends on the uniformity of the rate at which energy is supplied or withdrawn from the fluid . In all the streams , whether of gas or liquid , met with in nature , the conditions are in general those of instability , and it is only in certain cases , and by taking considerable precautions , that an approximately stable flow can be maintained , and where this is accomplished the stream-lines are of the electric type . Although it is impossible by mathematical analysis to follow in detail the motion in an unstable flow , the general character may , in many cases , be traced , and the object of the present note is to apply an observation made by the Stability of the Flow of Fluids . 483 . 1910 . ] the late Mr. Froude to the explanation of some of the commonly occurring phenomena of instability . At the meeting of the British Association at Bristol in 1875 , Froude showed , * among other experiments , one in which a jet issuing horizontally from an aperture in a vessel of water impinged symmetrically on a similar aperture in a vessel standing near the first ( fig. 1 ) . The water in the Fig. 1 . first vessel ( A ) was maintained at a uniform level , and by providing an outflow in the second vessel ( B ) at a slightly lower level , the stream from one to the other could be maintained indefinitely , nearly the whole of the outflow from A entering B at the speed due to the head . A small but definite loss of fluid , however , occurred at the entrance to the aperture in B , giving rise to the appearance shown at P in fig. 1 . It will be seen that the loss is confined to a thin layer at the outer surface of the jet\#151 ; to that part of the jet in fact which was in contact with or close to the walls of the-passage from which it issued ; and Froude pointed out that this was to be explained by the loss of velocity suffered by the outer part of the jet from surface friction and viscosity , for the fluid which has had its velocity lowered without having its pressure raised has had its potential degraded , and is therefore incapable of ever agaiu entering a region where the pressure is greater than that due to its diminished velocity . The degradation of potential by viscous action gives the explanation of a very large number of natural phenomena , some of which are on a large scale , but before giving examples it * Presidential Address to Section G. 484 Mr. A. Mallock . Influence of Viscosity on [ Oct. 10 will be convenient to examine the nature of viscous degradation more closely . Suppose a stream of fluid flowing in a parallel channel with a velocity v \#151 ; ( uniform over the whole section to begin with ) has its velocity over a certain thickness near the walls reduced from v to 6v by the action of surface friction and viscosity ; the pressure is not altered in the layer , hut the height to which its velocity can carry it is reduced from ^/ H to -fOW = so that H'/ H = 6~ . Now suppose the channel to contract ; the stream-line pressure diminishes as the velocity increases , and there is nothing to prevent the degraded surface streams from retaining their surface position . If , however , the channel expands so as to make the stream-line pressure greater than H ' , the degraded streams must have their onward flow diverted or reversed , and in either case the conditions of continuity will produce a change of flow in the central streams , different , not only in degree , but in kind , from any change due to the expansion of the electrical stream-lines . Thus it will be seen that according to whether the electrical stream-lines are convergent or divergent , the results in the presence of viscous dissipation are of widely different characters . When the electrical stream-lines are convergent , the actual path of the retarded streams may be nearly the same as if viscosity were absent ; but with divergent electrical flow this is impossible , if the divergency is such as to raise the pressure anywhere above that which is due to the speed of the degraded streams . There is a difficulty in many real phenomena in distinguishing between the secondary currents arising from the conditions of continuity due to the diversion or reversal of the degraded streams , and the degraded streams themselves . Some sort of an eddy is necessarily formed , and although it would be too much to say that all eddies in real fluids are formed in this way , the following examples in which the explanation does apply will be sufficient to show how far-reaching the effect of degraded potential is , and how large what may be called the secondary effects of viscosity are , compared with those which appear in the initial stages of instability investigated by mathematicians :\#151 ; ( 1 ) It is well known that in many tidal waters ( e.g. the English Channel ) the stream continues to run in mid-channel after it has turned inshore . In this case the shallow water near the shore is more retarded than the midchannel surface streams , and thus since the level of the water is not affected by viscous retardation , the degraded inshore stream is unable to hold up against the tidal gradient after this has reached some definite value ( fig. 2 , a\#151 ; -f).The same reasoning applies to all the fluid which is near enough to the boundary of the channel ( whether bed or shore ) to be sensibly 1910 . ] the Stability of the Flow of Fluids . influenced by surface friction , and there can be no doubt that the tidal current along the bed of the channel is also reversed before that on the surface . In many tidal rivers this is known to be the ease from actual observation . Fig. 2 , a\#151 ; f.\#151 ; Diagrammatic plan of the direction of flow in a viscous fluid oscillating in a rectangular channel during one half period , c and refer respectively to the times just before and just after the epoch of maximum wave slope . ( 2 ) I have watched the same phenomenon in a canal under the following circumstances:\#151 ; When a lock is being filled a stream is created in the canal , and as the lock fills this stream is gradually retarded and the water level at the lock rises in consequence above the mean level of the canal by an amount depending on the velocity of the stream ( among other things ) . The stream in the canal is , of course , from the surface friction , slower at the sides than in the middle , and the side current there is reversed by the excess of head at the lock long before the central stream has ceased to flow in its primary direction . I have seen this reversal more than a quarter of a mile above a lock in a canal whose width did not exceed 30 feet . The opposite directions of the side and central streams imply a vorticity in the fluid , and constitute together ( including the reversal over the bed ) a single long eddy . This is in itself unstable , and secondary eddies are formed along its length as in fig. 2 , g. These , however , are generally difficult to observe , for the stream to begin with contains eddies of the same character , which tend to mix the layers at different distances from the VOL. LXXXIV.\#151 ; A. 2 L Mr. A. Mallock . Influence of Viscosity on [ Oct. 10 , boundaries , and it is on this account the speed of rivers is more uniform over the cross-section than it would be were the flow lamellar . Fig. 2 , g.\#151 ; Diagrammatic vertical section , showing the eddies in a current flowing in a rectangular channel . ( 3 ) Another very typical case mentioned by Froude is the inward spiral motion which occurs near the bottom of a flat circular vessel while water rotating in it is coming to rest , which is made apparent by the way in which small objects are carried towards the centre . Near the sides and floor the degraded streams are unable to describe plain circular orbits from lack of sufficient velocity to withstand the pressure due to the motion of the less retarded fluid , the result being that the centre of curvature of the orbit is shifted and the stream deflected inwards . The inward stream over the floor necessitates an upward central current and a slow outward flow at a higher level giving rise to a circulation such as is showm in fig. 3 Fig. 3a.\#151 ; Diagrams showing in plan the spiral current near the floor , and in section the vertical circulation set up when a viscous fluid which has been rotating in a circular vessel is being brought to rest by the action of the stationary boundaries . Fig. 3 b.\#151 ; Plan and section of a vortex in a viscous fluid flowing from a central hole in a circular vessel . 1910 . ] the Stability of the Flow of Fluids . The same phenomenon has been treated by Prof. James Thomson ( ' Roy . Soc. Proe . , ' 1876 ) , who explained in this way the formation of banks of gravel and pebbles which are found on the inside of the bends of quickly flowing rivers . In the slower tidal waters of estuaries the curious conformation of sand banks is a result of the same kind of action . ( 4 ) As another example suppose fluid to be flowing from a circular hole in the floor of a large vessel in which the level at a distance from the outlet is maintained constant . If the fluid is without rotation the flow to begin with is purely radial . A flow of this character is unstable , and even the smallest angular velocity given to the mass will increase as the flow proceeds and ultimately the fluid itself will form a vortex , at the free surface of which the orbital velocity is that due to the difference of level between the point considered and the surface at a distance ( fig. 3\amp ; ) . The effective area of the outlet is then determined by the difference of the diameters of the outlet and the tubular vortex surface at the floor level ( viz. , AB \#151 ; CD in the figure ) . If the liquid is devoid of viscosity AB \#151 ; CD = 0 and the outflow ultimately ceases , but with a viscous fluid AB \#151 ; CD is always finite and the ultimate condition is reached when the energy in the fluid discharged is equal to the work expended in viscous dissipation within the vessel . ( 5 ) Cases analogous to ( 3 ) and ( 4 ) occur in meteorology . The ordinary barometric depressions of large area may be considered as vortices undergoing viscous dissipation whose only store of energy is the kinetic energy due to velocity . These correspond to the circulation of liquid in a closed vessel as in example ( 3 ) . The loss of velocity near the ground necessarily causes the degraded streams to turn inwards towards the centre , and the conditions of continuity demand that near the centre there must be an upward current . Whirlwinds , waterspouts , dust storms , and perhaps tornadoes have part of their energy in the potential form due to denser air lying for a time unstably over air which is lighter , and which when disturbed rushes up a chimney as it were of its own formation . These are analogous to ( 4 ) . In both cases the inward slope of the spirals followed by the current depends on the amount of degradation which the stream has undergone ; but for ordinary meteorological depressions the upward central current is a secondary effect of the degraded circulation , whilst in whirlwinds , etc. , it is the primary cause . ( 6 ) Similar considerations apply to slowly oscillating liquid . The simplest case is that in which the fluid completely fills a long prismatic box oscillating about an axis parallel to the edges of the prism . The motion of the fluid far removed from the ends is then two-dimensional . The electric stream lines of the fluid in these circumstances are known , and it is not necessary for the present purpose to define them by symbols . Mr. A. Mallock . Influence of Viscosity on [ Oct. 10 , The relative velocity of the fluid and the solid boundary is a maximum through the planes parallel to the axis of rotation and passing normally through the middle of each side ( if the prism is a regular polygon ) and a minimum through the planes bisecting the angles . The general character of the flow is shown by the dotted lines in ; fig. 4 a.In a perfect fluid the velocity and pressure are of course connected in the usual way . If the fluid is viscous , consider the motion of two elements which start from A and B respectively and which in the absence of viscosity would follow the paths AC and BD . Here A moves from a region of low towards a region of higher pressure , while B travels from a higher towards a lower pressure . Figs. 4a and 4b.\#151 ; Slow circulation set up in a viscous fluid completely filling a rectangular prismatic box oscillating about the axis of the prism . In Fig. 4a , A C B D is a stream line of perfect fluid referred to the boundary considered as stationary . Owing to viscous retardation the paths AC ' and BD ' will both be shorter than AC and BD , but while there is no reason ( except such as may he imposed by the conditions of continuity ) that D ' should not lie on BD , it is impossible that C ' should lie on AC , for at all points along this path the pressure is greater than the head equivalent to the degraded velocity of the particle which starts from A. The actual path AC ' must therefore lie inside and be more curved than AC . In the next quarter of an oscillation C ' will return not to A but to A ' outside A and D ' to B ' inside B. The result of the first half of an oscillation is that a certain amount of 1910 . ] the Stability of the Flo w of Fluids . fluid will be carried inwards from the angles towards the centre of the prism and outwards from the centre towards the middle of the sides . The same process will go on in the succeeding half oscillation and if continued will give rise to a slow circulation such as is shown by the arrows in fig. 4 ( 7 ) An important case is that of the initiation of eddies in a stream flowing past an obstacle . Let the obstacle be a lamina . As is well known there are two forms of mathematical solutions of this problem , one of which makes the stream-lines similar curves both up and down stream ( electric flow ) while the other involves a surface of discontinuity on the down stream side . As far as this portion of the flow is concerned , neither of the solutions represents even approximately what is observed to take place in real fluids , though the discontinuous form is not so far removed from the facts as is the electric flow . The form of the discontinuous surface of theory is determined by making its curvature such that , while fulfilling the conditions of continuity , the pressure just outside the surface and throughout the space within it is that of the fluid at a distance , the velocity just outside the boundary being that of the general stream and zero inside , fig. 5 . Fig. 5.\#151 ; Discontinuous flow of a perfect fluid past a lamina at right angles to the stream . If the lamina were devoid of surface friction , and the liquid free from viscosity , this form of flow would be possible , though unstable . In the actual case the fluid which is in contact with the up stream surface of the lamina is degraded and reaches the edge with a velocity insufficient to follow the theoretical curve . The result is that the fluid as it passes the edge is necessarily deflected inwards behind the down stream face of the lamina . The subsequent motion cannot be followed by analysis . Observation , however , shows that the flow is not steady but of a periodic character , the actual period being determined by the velocity of the stream , the magnitude of lamina , and the angle between it and the general direction of flow . Tigs . 5 a,5 b,5c indicate the periodic structure of the wake in the case of a long lamina at right angles to the stream . The inflow past the edge initiates a small eddy , about half of the fluid Mr. A. Mallock . Influence of Viscosity on [ Oct. 10 , Figs. 5a , 56 , 5c.\#151 ; Diagram illustrating the periodic formation of eddies in a viscous fluid under the same conditions as in Fig. 5 . involved being derived from the wake ( or dead water behind the lamina ) and half from the stream . The eddy continues to grow , and the conditions of continuity demand a current in the interior of the wake in the contrary direction to that of the outside stream to supply part of the fluid required for its formation . When the diameter of the eddy exceeds a certain fraction of the width of the lamina , the access of a sufficient supply from the central wake is impeded , and the full-grown eddy then leaves its position close to the lamina and travels down stream , while a fresh eddy is being formed in the same way at the edge . The general structure of the wake , therefore , consists not in a mass of dead water separated from the stream by a surface of discontinuity , but of a central current opposite to that of the stream bordered by a series of eddies at definite distances from one another . It may be mentioned that the eddies just spoken of may be in the same state of growth at either edge , or be formed alternately ( fig. 6 ) . In the latter case the full-grown eddy occupies nearly the whole width of the lamina , and the wake consists of a trail of eddies alternately right-handed and left-handed . 1910 . ] the Stability of the Flow of Fluids . 491 How far the diameter of the full-grown eddy remains directly proportional to the width of the lamina it would be difficult to say . I have observed this proportionately up to a width of 20 cm . , but would it be true when the width was as many kilometres ? Under dynamically similar conditions it should be . Fig. 6.\#151 ; Diagram showing the alternate formation of right-handed and left-handed eddies in a viscous fluid . ( 8 ) When the obstacle is not a lamina but a cylinder , the character of the wake is not greatly altered , and the eddies may be formed either simultaneously or alternately . In the alternate formation , the flow past the obstacle is more rapid round that side on which the eddy is growing than on the other , and the stream line pressure therefore less . Hence the force acting on the obstruction is not in the direction of the stream , but has a lateral component urging the obstruction towards that side . ( 9 ) If the cylinder is a stretched string with a period of its own , and if the velocity of the stream is such that the period of eddy formation approaches the natural period of the string , it will be seen that the applied force is in the right phase to maintain a vibration when once started . This is the explanation of the action of the iEolian harp and many allied phenomena . * ( 10 ) The whistling of the wind is also a result of the periodic formation of eddies , but in this case the pitch of the note is in general dependent only on the velocity of the wind and the dimensions of the obstacle and not a coincidence of periods , and a sound will be produced whether the formation of the eddies is synchronous or alternate . Many more examples might be given , but those already cited are sufficient to illustrate the far-reaching effects of the viscous degradation of potential , and of the principle to which Froude called attention , as explaining the difference in the behaviour of a viscous fluid , according to whether the motion is towards regions of increasing or diminishing pressure . i

rspa_1911_0003

0950-1207

Optical dispersion : an analysis of its actual dependence upon physical conditions.

492

523

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

T. H. Havelock, M. A., D. Sc.|Prof. Sir Joseph Larmor, Sec. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1911.0003

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1911_0003

10.1098/rspa.1911.0003

Tables

Atomic Physics

Tables

]\gt ; Optical Dispersion : An Analysis of its Actual Dependence upon Physical Conditions . By T. H. HAVELOCK , M.A. , D.Sc . , Armstrong College , Newcastle-on-Tyne . ( Communicated by Prof. Sir Joseph Larmor , Sec. . Received October 10 , \mdash ; Read November 24 , 1910 . ) CONTENTS . PAGE 1 . Introduction 492 2 . Refractive Index and Physical State 494 3 . Temperature Variation : Organic Liquids 496 4 . Carbon Disulphide and Water 497 5 . Organic Liquids ( Falk ) 500 6 . Variation under Pressure 602 7 . Artificial Double Refraction in Liquids 502 8 . Temperature Variation in Solids 605 9 . Change from Vapour to Liquid 508 10 . Absolute Values of the Variable 509 11 . Dispersion Formulae : Absorption Maxima 512 12 . Displacement of Absorption Maxima by Pressure and Heat. . 617 13 . Summary 522 1 . Introduction . The influence of a transparent medium upon light passing through it may be ascribed to two factors ; one is the existence , in each individual molecule or particle , of vibrating parts with certain natural frequencies , and the other is the physical condition of the aggregation of molecules composing the medium . Suppose that a typical vibrating part is an electrified particle of charge and mass , whose free vibrations are given by equations of the type Let X be the corresponding component of electric force in the incident light wave . The impressed force , to be supplied on the right-hand side of ( 1 ) for the actual motion , is not simply , but has an additional term to express the effect of the surrounding molecules ; the simplest conception of this effect indicates a term directly proportional to the ayerage polarisation of the surrounding molecules at each instant . Hence , instead of ( 1 ) , we have an equation . Optical : its upon Physical . 493 As regards the numerical value of the co-efficient , little can be said beforehand on theoretical grounds ; certain considerations , iven in the present connection by Lorentz and by Larmor , indicate that for gases and liquids should be approximately The i1lvesGigation is an attempt to extract from available experimental data , information about the numerical value of and its variation with changing physical conditions . The problems concerned are those of optical dispersion in isotropic oeolotropic media , and the changes produced by varying density , pressure and temperature , or by the action of extel.nal electric or magnetic fields . attempt is made to explain the intimate mechanism of these phenomena , that is , the physical process by which the value of is altered ; rather , the term is used as a possible means for the various effects under one formal scheme , at least for a first approximation . The method is , in to the usual procedure of . absorption effects by a term in into equation without thereby completely the physical process involved in absorption . If we ignore the effect of molecules in equation ( 2 ) , that is , if we put zero , the dispersion formula which can be deduced is of the type where is the refractive index of the medium for wave-length is a constant associated with the ) rating e of type , and is pro- portional to the number of such ) unit volume , is the corresponding to the natural frequency of the same type , and the summation 2 extends over all the types . Again , if we put to we obtain a dispersion formula In both cases , if we assume the quantities to be proportional to the density , and divide either of equations ( 3 ) ftnd ( 4 ) , we obtain on the -hand side a quantity dependent only upon the constitution of the individual molecule ; the expression on the other side also be independent of the physical conditions of regation . In this two relations refractive index density arisen , namely constant ; constant . ( 5 ) These relations have been the subject of numerous . The Dr. T. H. Havelock . Optical : its [ Oct. 10 , second one gives generally a better reement with the facts , especially in cases of change of state from vapour to liquid ; however , when the refractive indices at different temperatures and under different pressures are compared , it is found that neither relation expresses all the facts ; these cannot be ascribed merely to change of density . We then fall back upon simply asserting that the quantities and in ( 3 ) or ( 4 ) must vary with the physical conditions , or , in other words , the natural frequencies of the individual molecules must be affected by pressure , temperature , or external action on the medium ; for a small variation one would obtain from ( 3 ) a dispersion formula . ( 5 ) This in fact has generally been the procedure in previous investigations . In colitrast to this method , we shall consider here to what extent the facts can be expressed in terms of two variables , the density and the quantity without changes in the inherent molecular frequencies . It has been remarked that the cause of the reement between the second relation in ( 5 ) and experiment must be looked for partly in the fact that is not exactly equal to , partly also in changes that take place in the interior of the particles when a body is heated or compressed . ; these changes causing a variation in the value of the coefficients in equation ( 2 ) Without denying that both these are probably true contributing causes , it seems of interest to examine separately the former supposition , especially as it has been ignored in favour of the latter as sole cause . 2 . ' and Physiced Conditions . If we retain the quantity we can deduce a dispersion formula like ( 4 ) but with on the left hand side . The coefficients are proportional to the ) of vibrating parts of given type in unit volume ; if we make the usual assumption that they are proportional to the density and if we divide through by , we have . ( 6 ) On the hand we have now , supposition , a function of the wave-length and the constitution of the individual particle ; hence for a given wave-length and for all physical conditions of the aggregation of particles , we should have const . * H. A. Lorentz , ' The Theory of Electrons , ' p. 147 . 1910 . ] Actnal Dependence Condition It may be noted that if we divide hout by we }vrite this relation as const . This has been used as a generalised form of ( 5 ) ; but it clearly nores the dependence of upon the physical conditions , and has in fact been no more successful than the simplel relation . The formula in ( 7 ) may be put more conveniently as const . ( 9 ) Now we have no means of independently , so this relation cannot be verified directly . obtain numerical values of we shall have to fi-x its value in some condition ; ) so , we can deduce a diffel.ence- equation which can be put to the test of experiment . If the suffixes 1 and 2 denote values in two different states of a medium composed of sinlilar individual particles we have Hence ) . ( 10 ) Thus , for two physical states , the difference in is constant for by supposition is independent of the , hence the left-hand side of ( 10 ) is a function only of physical conditions such as temperature , pressule , density , and so forth . two relations given previously in ( 5 ) are special cases of ( 10 ) iven by ) and ; so that if either of the formul held , the constant in ( 10 ) would have the value zero or respectively . Two special forms of ( 10 ) for small changes should ) noted , that is , when it may vritten deonstant . First , if the ) ressure is constant and the temperature the independent variable , we have const . , ( 11 ) where coefficient of cubical expansion . Secondly , if the temperature is constant and the pressure varies , COIlSC . where coefficient of compressibility . Dr. T. H. Havelock . Optical Dispersion : its [ Oct. 10 , From ( 11 ) we have . ( 13 ) Thus if is a positive quantity it is possible for the temperature variation to change from positive to negative ; this would occur for a wave-length at which the index of refraction equals . We shall examine now the relations ( 10 ) , ( 11 ) , and ( 12 ) . Where special reference is not made , the data used have been taken from Landolt and Bornstein ( ' Physikalisch-Chemische Tabellen ' ) or from Winkelmann ( ' Handbuch der Physik 3 . Temperature : Organic Liquids . A preliminary comparison may be made by using a set of liquid organic compounds which have been examined in a similar manner by Voigt* ; the data are taken from the collection in his paper . Voigt adopts the hypothesis that thermal or mechanical deformation produces a change in the natural frequencies of the vibrations within the molecule in addition to the effect due merely to the change of density ; he gives expression to this change by tabulating for different wave-lengths the values of a quantity defined by . ( 14 ) Apart from a few exceptions , due probably to inaccurate data , Voigt finds . that for liquids is positive and increases regularly with decreasing length . Now if we compare ( 14 ) with ( 10 ) we see that is equal to ; it is possible then for to remain constant for different wave-lengths since , in general , and increase with decreasing wave-length . Table I shows the results of the calculations for the heat expansion of nine liquids , namely , those used by Voigt as a random selection from available data ; in each case the mean value of , that is of , is compaled with the value of , so that one sees the divergence from the simpler Lorentz formula . One may say that the general result of these calculations is favourable to the relation given in ( 10 ) ; such divergences as occur are ular in character , and are probably due in these cases to insufficient accuracy of the values of density and refractive index . Without laying too much stress on the actual numerical values , it appears that may be considered constant within the range of wave-lengths concerned in each case . * W. Voigt , ' Annalen der Physik ' ( 4 ) , 1901 , vol. 6 , p. 459 . 1910 . ] Actual Dependence Physical Conditions . More recent experiments are available in the case of }vater and carbon disulphide and we shall examine these no Table I. Aniline . . 1Ie Acet.vlene dibroll . Mean 005l6 ; Ethyl alcohol . . Mean C. . 413 408 407 415 Ethylene bromide . . Mean Benzene . Iean C ; Iodobenzene . . Mean Methylacou{te . . Mean . . 67 60 61 Thiophene . . Mean A. . 656 689 486 434 Vinyl tribromide . ) . . . . 589 486 434 4 . Disulphide Flatow* has examined in detail the dispersion of water and carbon disulphide , the absolute refractive index at and for several different temperatures ; he concludes that the relation const . is pproximately satisfied , and he has also calculated for each temperature a dispersion formula of the type in order to study ths variation of with the temperature . We shall consider dispersion formulae in a later section ; at pzesent use 's experimental results to the relation ( 10 ) . * E. Flatow , ' Annalen der Physik ' ( 4 ) , ) , vol. 12 , p. 498 Dr. T. H. Havelock . Optical Dispersion : its [ Oct. disulphide.\mdash ; We have measurements of at nine wave-lengths for the temperatures , and . The densities have been calcu- lated from the known expansion of , and with the value We are able in this way to form three sets of differences ; using the . notation the results are shown in Table II . Table II.\mdash ; Carbon Disulphide . mean values of and the changes in density , we have the following : ; ; ; ; ; As regards the constancy of , the results may be regarded as satisfactory , considering the order of accuracy that may be expected . Considerable deviations occur at the two smaller wave-lengths and . It must be remembered that here we approach the dominating region of absorption in the ultra-violet , which is in the neighbourhood of ; and it is known that also a minor region of absorption occurs between these two values , near , which is sufficient to cause slight anomalies in the refraotive index.* In the relation ( 10 ) absorption has not been taken directly into account , so deviations may be expected as one approaches a region of absorption . *W . Fricke , ' Annalen der Physik , ' 1905 , vol. 16 , 1910 . ] ldence uPhysical ) ditions . Another of expressing these results is by the alternative form ( 11 ) , the chances small and the pressure constant ; thus approximately Using the mean value of we filled the rate of of at iven by In this case we notice that remaius ative for all leno t Graphing respect to from we obtain practically the curveas that ooiven by Flatow as the esulC of his experiments ; in the visible region varies ouly slowly . but in the it diminishes very rapidly algebraically with decreasing . As oftrds variation with the temperature , it should be noted that both the numerical coethcients in would be slightly different for other nperatures . Water.\mdash ; We have observations at five temperatures , , and ; using the same of with the same notation , we have the results in Table III . Table III.\mdash ; Water . From these we ] ve for mean values and difference of densities : ; ; ; ; ; ; Dr. T. H. Havelock . Optical Dispersion : its It cannot be said that the results are very satisfactory when analysed in this ma1mer . On the other hand there is nothing decisive against the present theory ; for if has a slight regular decrease , and increase a little with increasing wave-length , while is ular . Further , if we make the calculations for the smallest wave-length used , we find small values for the four quantities , viz. , ; . Flatow himself , in calculating dispersion formulae , found greater deviations for wave-lengths between and ; owing to these appearing at all the temperatures , he concludes that they are not due to experimental inaccuracies , but possibly to a ected r of absorption . Another point in which water is peculiar in the present connection is the occurrence of a minimum density in the region considered ; as the constancy of , we see from the comparison of and that this fact makes a considerable divergence in this region . Taking the observations and calculations for water as they stand , one concludes that , although the results allow of the present interpretation , the evidence is more doubtful in character than for other substances examined . 5 . Organic Liquids . Falk* has ated in great detail the variation of refractive index with temperature for a series of liquid organic compounds , using the sodium line and the three hydrogen lines ; the density of each liquid was also determined at various temperatures . It was found that within the limits of experimental error , both the refractiye index for given wave-length and the density were linear functions of the temperature . For five temperatures from to , Falk calculated , for the four wave-lengths , the quantities , and ; each of these quantities shows given wave-length a small , but regular and continuous , change with the temperature , either increase or decrease . The quantity was also calculated , so as to give the best average results for the relation constant , for each liquid . For the present purpose , the data for the two extreme temperatures , and , have been used to calculate , t'ne difference in vaJue of for the two temperatures for each wave-length ; the results are shown in Table only substances which show regular variation in the values of are nitrobenzene and monomethylaniline . It is stated that owing to the oolour of the liquid the live ( 434 ) was too indistinct for measurements G. Falk , ' Journ. Amer . Chem. Soc 1909 , vol. 31 , p. 86 and p. 806 . 1910 . ] Actual Table Wave-length 656 . Dimethylaniline -Heptyl alcohol Diisoamyl Benzvl alcohol . 138 acid Isobutyl acetate lacetone Ethyl -butyrate Isoamyl acetate 141 ketone 97 itrobenzene . 122 Monomethylani ] in . . Benzyl cyanide. . 93 Benzaldehyde 99 to be made in these two cases ; thus the regular increase seelns clearly to be connected with exceptional absorption . For all the other substa1lcGs it can at least be said that is no increase or decrease of with decreasing wave e , so that it is permissible to the variations as accidental . In the previous section we noticed that has meitHured the effect of temperatul.e ) the chnnge in , and fouud this increased ] decreasing in general . The same remark applies to the present collection of with one 01 two doubtful cases ; however , in about six the inctease is by the quantity ) for the line than for the 1 ) line . of this can be noticed in the column in the table ) , if we calculate the differencc in value of at and for alcohol ior the fonr , we the quence 0 ) , and ) . This tJht possibly indicate some eperimental e for observations with the line ; if not , it seemt ; a ious effect . The mean values in column of Table are eqnal to the lnea]lues of from relation ( 10 ) . We cannot as yet cnlate vnl for , but the numbers measure the rate of increase of temp erature . The VOL LXXXIV.\mdash ; A. 2 Dr. T. H. Havelock . Optical : its [ Oct. large value of for acetyl acetone may be noticed ; according to Falk , this substance is exceptional in the above collection , owing to its being a tautomeric mixture of two forms , the relative proportions changin with the temperature . Anotber point is that the isomeric substances , isobutyl acetate and ethyl -butyrate have practically the same rate of change for the product 6 . Prjssure Variation . As regards the change of refractive index with pressure , experimental data are not so numerous for liquids ; at least not a form suitable for the present analysis , for which obseryations are needed at various wave-lengths . In order to illustrate the alternative formula ( 12 ) , a set of observations on carbon disulphide is taken from a paper by and Zehnder . * The data are the values of for the , and lines , the , and the index for the sodium line . From the values for the sodium line we calculate the value of in relation ( 12 ) and obtain thus . ( 16 ) Estimating the values of for the other two lines we can calculate from this equation the values of . The results are shown in the Table Table Carbon Disulphide . 7 . Artificial Double Befraction in Liquids . In previous the present scheme was developed in a simple form in connection with artificial double refraction produced by mechanical strain or by the action of an electric or netic field . The formal basis of the theory is the supposition that the effects can be represented by an oeolotropic in the quantity . If the density remains constant and if the * W. C. Rontgen and L. Zehnder , ' Annalen der Physik , ' 1891 , vol. 44 , p. 24 . 'Boy . Soc. Proc , vol. 80 , p. 28 , 1907 ; also ' Phys. Rev 1909 , vol. 28 , p. 136 . 1910 . ] Actual Dependence upon Conditions . medium becomes doubly like a uniaxal crystal with and for principal refractive indices , the relation ( 10 ) becomes constant . ( 17 ) If the changes are small , with the refractive index for the isotropic medium at same density , we have -\mdash ; constant . This relation has ) confirmed by recent researches , at least as a first approximation for the double refraction induced in liquids by an electric or netic field ; reference may be made to the experimental and theoretical investigations of McComb , *Skinner , Cotton and Mouton , and atanson . the present aim is rather to include various phenomena a single fo1mal scheme than to analyse in detail the physical mechanism of each effect , a few remarks may be made in the present instance . All the relations such as ( 10 ) , ( 17 ) , and ( 18 ) have been developed by considering the medium as effectively all of optically isotropic particles ; all the changes which occur in the dispersion , whether isotropic or oeolotropic , are expressed in terms of two variables : the density and the quantity . In the previous work quoted the physical process was conceived of as a rearrangement of the particles in space . Cotton and Mouton prefer to regard it as an orientalion of anisotropic molecules , and they give a theoretical deduction of relations ( 17 ) and ( 18 ) which is said to rest on this hypothesis Now this assumption is possibly preferable for certain physical reasons , but it is not clear where it enters into the proof referred to above . In fact the proof is formally the same as ours , in that it ascribes the birefraction to a directional variation in the quantity ; the hypothesis of orientation enters in the assertion that it is the cause of these in and of course if the particles are to orientate under a ficld of force they must be in some way anisotropic . Perhaps one might reconcile the hypothesis of orientation and the theoretical of relation ) by the particles as in some way physically anisotropic but isotropic , just as one for instance the particles of a crystallinle substance which is optically isotropic ; then one cvht have the possibility * H. E. McComb , ' Phys. Rev 1909 , vo ] . 29 , C. Skinner , ' Phys. Rev 1909 , vol. 29 , A. Cotton and H. Mouton , ' Ann. de ChinL et de Phys 1910 , vol. 19 , p. 153 . S L. Natanson , ' Bull . de l'Acad . des Sciences , Cracovie , ' June , 1910 . Cotton and Mouton , toc . cit. ante , p. 217 . Dr. T. H. Havelock . Optical Dispersion : its [ Oct. 10 , of orientation without interfering with the simplicity of isotropy in the optical equations . If we wish to consider the parcicles as optically anisotropic , and the isotropy of the medium to be the result of averaging due to all possible orientations , we should have the following scheme . The equations of motion of a typical electron take , instead of ( 2 ) , the form , . ( 19 ) Suppose now the extreme case when all the particles are orientated the same way ; then we should have a crystalline medium with three principal refractive indices , and given by the equations . ( 20 ) On the other hand , if the particles are arranged at random in all possible directions , we should have an isotropic medium of index , for which we could write . ( 21 ) In general , if we adnlit optical anisotropy of the particles , this in itself would contribute directly to the observed double refraction , as well as indirectly through the alteration in the -quantities . One hypothesis would be to ignore the quantities , or make them all equal ; this would ascribe the doubly-refracting properties to the differences between . But the relation between these quantities does not seem obvious , except that the right-hand side of ( 21 ) is in some way an average of those in ( 20 ) . Another hypothesis , one by which the simple relations ( 17 ) and ( 18 ) are obtained , is to regard the right-hand sides of equations ( 20 ) and ( 21 ) as all the same function of the wave-length ; that is , we do , in effect , treat the molecules as if they were isotropic . Cotton and Mouton have also investigated variation of the induced 1910 . ] Actual Dependence upon Physical Conditions . double refraction with the temperature ; they find that in general the diminution is reater with increase of temperature than could be accounted for by the mere of density . This result was involved in one case in the calculation given by the present writer for carbon disulphide ; expressing the results of Blackwell in the form it was found that at and at So that , although the in ? is allowed for , there is in addition a decrease in C. With the present notation is , and if we take the average decrease veen the two temperatures we have It might be possible to connect this with the rate of of with the temperature for the isotropic medium ; but it would doubtless be necessary to examine in more detail the physical nature of the changes which occur . [ Since the above remarks were written , a note has been published ) angevin , dealing with the theory of electric and magnetic double refi.action from the point of view of molecular orientation ; the note records the results ined . Apparently the lnolecule is supposed to be anisotropic , but accou is taken of differences between electric , magnetic , and optical asymmetry ; action of the external field is to modify the distribution of the molecular axes in space . As ards t dispersion , it is stated that the relation ( 1S ) above is obtained under certain conditions . ] 8 . Vari(tion Sofi ds . Although one expects more complexity in the case of solid substances , it seems of interest to cxpress the erimental results by the same method as for liquids . It been well established that the eHect of temperatule on the disf ) ersion of solids is not merely due to the of density , and it is here especially that lecourse has been had to dispersion formulae showing in the natural resonance-frequencies . Glass . extensive researches of are available , and we choose three examples which have already been exalnine by Voigt . The Table shows the results:\mdash ; . cit. , p. . Langeviu , ' Comptes Rendus , ' August 16 , 1910 . C. Pulfrich , ' Annalen der Physik , ' 1892 , vol. 45 , p. 609 . Dr. T. H. Havelock . Optical Dispersion : its [ Oct. 10 , . Heavy Flint Glass , 2.810 O527 . Light Flint Glass , S40 . Crown Glass , In the above table , is the quantity calculated by Voigt in the manner referred to previously ( S3 ) ; for small changes the relation is , where is the cubical coefficient of expansion . Also the quantity of the present theory is given by . It appears that is negative and increases numerically with decreasing wave-length . For the heavy glass , the increase in the factor is not sufficient to ) teract the increase in , snd the quantity shows a regular increase ; in the other two glasses the effect is the other way and shows a ular decrease in the same direction . One must remember that glass is not a simple substance but is a complex mixture , a fact which is illustrated by its optical behaviour under mechanical stress . Further , Pulfrich considered that the observed changes in refractive index were connected with a variation of absorption in the ultra-violet region ; . Konigsberger*has also observed in solid bodies a displacement of this absorption region towards the longer wave-lengths with temperature . The direct influence of absorption has not been taken into * J. Konigsberger , ' Annalen der Physik , ' 1901 , vol. 4 , p. 796 . 1910 . ] Actual Dependence upon account in the present theory , so that one cannot say how the results would be modified thereby . Meantime , it appears that the variation of the -quantity must play a considerable part in a complete theory of the phenomena . Similar eneral remarks apply to the following calculations , which are tabulated here for comparison . Amorphous Qnartz . Observations on this substance have been made by Martens ; the from to . With the usual notation the following Table shows the results for some of the wavelengths . If the substance were the same as fused quartz or silica it would have a small coefficient of expansion ; whether this was the case or not , it appears that if we take to have the mean value for quartz , the values of show a remarkable constancy in this range . If we calculate the values of as before , we find it varies ularly from at 508 to at . We notice that is positive in this range . If we take the mean value of to be , and if we assume to remain constant , we can calculate when would become ative ; it would be zero when , that is , when approximately . As ? is at and at 656 , the wavelength in question would be large ; judging from the refractive index of ordinary quartz , it be in the neighbourhood of 5 , approaching a region of absorption in the infra-red . Table \mdash ; Amorphous Quartz . Fluor Spar Salt . observed the ariation of for eral substances , with rangiug from about to 589 * F. F. Martens , ' Berichte der Phys. Ges 1904 , p. 308 . F. J. heli , ' Annalen der Physik , ' 1902 , vol. , p. 772 . Dr. T. H. Havelock . Optical Dispersion : its [ Oct. 10 , All the curves obtained by graphing erainst show a towards smaller values of . The most striking result is that for rock salt , where varies from at 202 to at 643 . If we calculate the quantity in this case , we find that it varies only slowly in the visible region , having a value of about , but increases rapidly in the ultraviolet . If we use the value ' to calculate where sign , and estimate the wave-length from a dispersion formula , we obtain the position as ; the experimental curve cuts the axis at about 220 . Similar remarks apply to the calculations for fluor spar , where has a value of about in the visible region , but rises rapidly in the ultra-violet to at In the case of solids such as those examined above , we find that if we use the value of in the visible region to calculate a curve for , the curve so obtained falls below the experimental curve when the latter begins to vary rapidly in the ultra-violet . It is unnecessary to add further calculations of the same type , or one might examine data available from experiments on elastic deformation of solids , or from the double refraction of natural crystals and its variation with temperature and pressure\mdash ; probably with similar results . The general conclusion is that the variation of the quantity needs to be considered in each case , but the changes in solids are too complex to be brought under a simple scheme with only two or three variables . 9 . Changj Vapour to Liquid . In this region the relation has had its greatest success compared with the other simple formulae . Calculations for many substances have been given by from his data we calculate the quantity the present theory for six typical substances , including those for which the Lorentz formula shows most disagreement . Two wave-lengths are given , the Li and Na lines ; the data for the vapours are for a temperature of about , while the liquids vary etween and . Table VIII shows the values of , the differe1lces between values of for vapour and liquid , for the two wave-lengths ; the agreement between the second and third columns is as good as could be expected . The values of are given for comparison . * Briihl , ' Zeitschrift fur Phys. Chem 1891 , vol. 7 , 1910 . ] Dependence Physical Conditions . Table VlII.\mdash ; Values of 10 . A bsolnt of We have so far been concerned only with a difference equation , the quantity being equal to thus we ) tain a ition between the values of in two different states . If we wish to assign numerical values to , we must fix its value in some state . At first it might be advisable to follow the ordinary theory , and make equal to in the gaseous state . If we try this for carbon disulphide we can calculate from Table VIII the value of for liquid at : knowing the densities of the vapour and liquid , and putting , we obtain thus . This is less than the value of in the state ; but represents the additional force on a particle due to the molecules , so it seems preferable that should be greater for a substance in the liquid state th when gaseous . This result can be obtained by making very smadl for gases ; this is allowable , as , to the small values , there is no evidence to decide between the of constancy of the various forms or To make the matter definite , we decide provisionally to zero for gases , and for simplicity we fix the standard state as the gaseous condition supposed to be at and a pressure of 760 mm. With this assumption , the values of in the last column of Table VIII have been calculated . One cannot deduce much from the values , as the data for gases are possibly ]lot very accurate and the liquids are at various temperatures ; otherwise it might be of interest to trace , for instance , a connection between the values of and the chemical constitution of the substance . It may be lloticed that the " " specific refraction\ldquo ; is ; thus , for example , the value of for propyl iodide would give a corresponding divergence in the specific refraction ordinarily used . On the present scheme , anomalies in Dr. T. H. Havelock . Optical Dispersion : its [ Oct. 10 , molecular refraction might be ascribed , in part , at least , to the indirect effect of intra-molecular action specified by the -quantity . Air.\mdash ; Magri* has made observations on the refractive index of air at high densities ; he found that gave the best approach to constancy . In Table IX some of his results have been used to calculate ; in the column under are the values under the assumption that is zero in the standard state , while under are the values if is in that state . The column shows the value which should have in each case in order that should have always its value for unit density ; the last column gives the actual value of this quantity referred to unit density at C. The temperature for the first row is , while for the other it varies and . Assuming the experimental data to be sufficiently acucrate , the variations both in and are curious , rising to a minimum with increasing density , and then falling to approximately . It may be noticed how an apparently difference between and makes little in the in the last column . The resuJts given here are referred to later in S 12 . Table IX.\mdash ; Air . Carbon Disutphidc.\mdash ; By combininrro the observations of Flatow , referred to previously , with values of for the vapour , we can see how the value of varies with temperature and density . For the vapour , we know for one wave-length of the series used for the liquid , viz. , the lins 589 . If we use the data , and for the vapour , together with and for the liquid at , we find * L. Magri , ' Physikalische Zeitschrift , ' 1905 , vol. 6 , p. 629 . 1910 . ] Actual Dependence upon Physical Conditions . this value for all wave-lengths at , we can calculate the values for various wave-lengths at and ; the results for four cases are contained in Table X. There is a small regular increase in with rise in temperature , the density diminishes . Table X.\mdash ; Values of for CS ; the vapour we use , and for sodium light . Carrying out similar culations , we find the following series of mean values of for the liquid:\mdash ; It is of interest to compare with these some values for ice , which is a uniaxal crystal ; Pulfrich has measured the two indices ? and for various wave-lengths . Let and be the corresponding principal values of for ice at ; with the density ) , the table shows the values of for certain . absolute values of the indices:\mdash ; Ice . Now for water at , and wave-length 589 , we ; thus , if is the value for water at , we have the equations From these , with , we find and ) actual numbers would probably be modified with with which to compare ; however , it appears in the to the solid state is increased . 512 Dr. T. H. Havelock . Optical Dispersion : its [ Oct. 10 , 11 . Dispersion Formuloe : Absorption Maxima . It would seem possible to obtain values of by constructing dispersion formulae of a suitable type ; before examining a few cases it is necessary to consider certain points in regard to the wave-lengths for which absorption is a maximum . The argument may be given first for a simple formula , such as . ( 22 ) Consider the values of in the hbourhood of a " " resonance\ldquo ; wavelength , say ; suppose that this is sufficiently isolated so that we may take the other terms in ( 22 ) as constant , that is , we write . ( 23 ) From this equation is ative , and consequently imaginary , for the range of wave-length given by . If in ( 23 ) we regard as complex and equal to we should have zero , e.xcept within the above range , where it increases from zero at the lower limit to infinity at the upper limit . This effect is , of course , not a true absorption effect , but would mean that the medium refused to admit certain radiation within a definite of wave-length . If we now insert a term in the equations of the medium to represent absorption , we have instead of ( 23 ) , an equation . ( 24 ) Following the method used by Lorentz*for a similar equation with equal to unity , we write the last term of ( 24 ) as ; then we have Solving these , we obtain . ( 26 ) If we assume , further , the usual simplification , viz. , that is , we obtain finally the approximate result . ( 27 ) * H. A. Lorentz , ' The Theory of Electrons , ' p. 310 . 1910 . ] Dependence upon Thus the retention of does not affect the form of the result , and the deduction follows that the maximum of is in the hbourhood of that is , of the wave-length Returning to the dispersion formula ( 22 ) , the previous uluent is of the type which has been ] on when the quantities have been identified with absorption maxima experimental]y ; as far as the simple formula is concerned , these quantities are the upper limits of the ranges which is imaginal.y and are -lengths for which is infinite . If we turn now to the type of formula used in the previous worl we have . ( 28 ) In the neighbourhood of we now . ( 2 ! ) If we solve this for we find ( 30 ) with ; . The lower limit for which is inary is equal to while the upper limit is Thus both the limits of the of imaginary values il are ) the introduction of the quantity , a fact which was noticed by in optical dispersion . It is clear if we introduce term true absorption , the argument would follow the same lines from equation ( 30 ) as ; consequently , we led to lentif the absorption maxinlun with upper limit of the above in ( 31 ) . Witb a dispersion formula of type , the quantities sent true\ldquo ; resonance\ldquo ; wave-lengths to the individual atonn or molecule ; it not permissible to identify them with maxima of , or refleclion , which have been determined ) erinlenta ] the nlediuln as a whole . To J. rmor , ' Phil. Trans , 18 vol. 190 , p. 240 . Dr. T. H. Havelock . Optical Dispersion : its [ Oct. 10 , determine the latter , in any case , we must write the dispersion formula as in ( 29 ) , and the wave-length required is , instead of Numerical illustrations may be taken from two cases , where a dispersion formula of the type ( 28 ) has been used without taking account of this change . Cccrbon Disulphide.\mdash ; In the paper quoted , Flatow has calculated dispersion formula of the type for at various temperatures ; he finds to be about , varying slightly with temperature . There.is a region of absorption ranging from to with a maximum at approximately ; there is also a minor of absorption near . By a method of continued reflection , Flatow found a maximum at and concludes that the value of for agrees well with this for a natural frequency . He also states that a dispersion formula of the Lorentz-Planck type gives a value of for and consequently gives a worse agreement than the older form . In the latter calculation Flatow ignores the effect considered above , and also uses a specially simple type of formula , . But for carbon ulphide we must use at least a three-constant formula . Suppose , for comparison , we assume that is , and make the calculations with determining the constants from the data With sufficient approximation for the purpose we find the values Thus we find is . But this is not to be compared with the experimental data ; according to the previous argument , the quantity to be so used is in the present notation . Working this out for the above values we find the value , giving practically the same reement as the older formula . Rock Salt luorite . Larmor 's development of the present type of dispersion formula , to which reference was made above , Maclaurin*has deduced and illustrated the form . ( 32 ) R. C. Maclaurin , ' Roy . Soc. Proc , 1908 , vol. 81 , p. 367 . 1910 . ] Actual Dependence upon Conditions . For a given physical state of the medium this form is equivalent to above , with equal to ; however , the previous form is preferable when we wish to consider changes of dispersion for physical conditions , and it also enables us to separate out a quantity independent of these conditions . Maclaurin gives numerical calculations for two substances , rock salt and fluorite ; identifying with the dielectric constant , he uses ( 32 ) in the form A very close eement is shown between calculated and observed values over a range of ; in addition Maclaurin claims that and agree with the mean values of the best experimental data . Howevel the quantities and are identified directly with the observed of absorption or reflexion , : we calculate now what difference is by the argument of the present section , using Maclaurin 's values of the constants for the dispersion formula ( 33 ) . For rock salt we have\mdash ; Putting for in the last term of , we have , in the vicinity of , with Hence the required wave-length is given by , that . is , . The lower limit of the range for which is imaginary is or . We have seen it is the upper limit which , consistently with the similar ument for the simpler dispersion formula , should be identified with the experimental data . For the neighbourhood of find and result is that is imaginary between and ; bence if we use the erical values given above it is that should be compared with experiment instead of We may compare with this Paschen 's formula for rock salt of Sellmeier type ; this gives a natural wave-length of 60 in the infra-red and in its neighbourhood we have 5 . We find then that is imaginary between approximately and 60 ; the upper limit * F. Paschen , ' Annalen der Physik , ' , vol. 26 , p. 130 . Dr. T. H. Havelock . Optical Dispersion : its [ Oct. 10 , being compared with the absorption maximum , although Paschen regards as an open question how far the observed " " Reststralhen\ldquo ; maxima can be identified with the wave-lengths of the natural vibrations which dominate the dispersion in the infra-red . A smaller value of the constant would probably give a better agreement in this respect . In fact Maclaurin states that he tried at first equal to 2 ; he found then a fair agreement between calculated and observed values of but with the values of and as much below the observed values as they vere above them with an ordinary Sellmeier dispersion formula . As regards dispersion formulae in general , it should be remembered that we replace the actual substance by an ideal simplified medium with only two or three natural frequencies ; it may happen that.the actual substance has two or three very predominant regions of resonance , in which case there should be good agreement between calculated and observed positions for these . On the other hand it may be that there are two or three erions of equal value not far apart , and the calculated value would be a mean position . For instance , recent observations on rock salt show maxima at and It appears that the quality of the agreement between observed and calculated values of refractive index even over a considerable range is not sufficient in itself to decide between different hypotheses , and for instance to give reliable values of or In respect to the absorption regions in the infra-red , the dispersion often gives no more than a term , which we could make up from any number of places of selective absorption in the absence of further information ; numerical values are obtained only when we assume the definite simplification of a small number of natural frequencies and use the value of the dielectric constant . For fluorite Maclaurin gives the ] owing values : With the same notation as before , we find in the neighbourhood of that ; hence . Also near we have , and . The relative displacements are larger here owing to the larger values of than in the former case . If we used the value of obtained from these formulae we could calculate * Rubens and Hollnagel , ' Sitzungsber Berlin , 1910 . 1910 . ] Actual Dependence Conditions . equal to ; this wo11ld give for rock salt , and for fluorite . But the preceding argument indicates that the calculations need considerable revision . 12 . cement of We shall consider now the displacement of absorption maxima under varying physical conditions , illustrating this by calculations for three cases in which suitable data are available . Air.\mdash ; The first example shows the effect of of pressure and density in a , and we use Magri 's nents on air already examined in S10 . For a dispersion formula under ordillary standard conditions we have one obtained by C. . Cuthbertson*in the form ' ( 34 ) lere p is frequency . the density of air as we put this into a form suitable for present calcu1-ations and obtain ( 35 ) with . To make the calculations definite assume , as in S10 , that is zero in the standard condition , so that the quantity on the right of is invariant as regards physical conditions and depends only on the atomic or molecular constitution . In any other physical state the quantity on the left of ( 35 ) is altered so that we have The argument of the previous section shows that the observed 1naximum of absorption in any condition should be near the wave-length iyen by We obtain the following series of values of to the values of the relative density ) C. and M. Cuthbertson , ' . Soc. Proc 1909 . , vol. 83 , p. 170 . VOL. LXXXIV.\mdash ; A. 2 Dr. T. H. Havelock . Optical Dispersion : its [ Oct. 10 , Table XI.\mdash ; Air . variation of and of with the Ons may notice the slight initial increase of , then a sharp rise between the values of 15 and 40 for , followed by an approx imately steady rise . We see also that decreases steadily with increasing density , falling sharply from an infinite value in the initial } . No doubt the peculiarities af the lower values of are due largely to the assumption that is zero initially . Still it does not seem possible to obliterate them entirely by assigning some small positive value initially ; it is conceivable thaG there may be a stage at which the inter-molecular action specified by becomes suddenly appreciable . One may notice a possible analogy between the variation of in the present case and the pressure displacement of lines in an emission spectrum . 1910 . ] Actual upon Physical Conditions . Carbon Disulphide.\mdash ; We can make calculations for with the observations of Flatow and the values of refractive index obtained by Rubens for longer wave-lengths . If we know for a given wave-length for a physical state of the medium defined by and , the quantity is independent of physical conditions ; thus , by observations at various temperatures , we can form an average set of vahles showing this molecular dispersion . With the convention adopted for assigning numerical values to , this would in fact , the values of for the substance as a gas at and 760 mm. For reasons which have been indicated , it has not been thought advisable to try for a complete dispersion formula for this substance . However , four have been chosen , covering the range available , so as to form a four-constant formula to illustrate the present scheme . the values of given in S10 and the observations referred to above , we find 0.274 . 0.508 . 1.037 . 1.998 . Specific refraction Before proceeding , we may notice the corres o values of for the vapour ; using , we obtain for these four tYths in order the values . The values of were , of course , calculated with the help of the observed value of for the wavelength . The values of ? so calculated would be values for the vapour , on the assumption that the change from liquid to vapour involves only physical changes which can be expressed optically in terms of and ; for instance , if some of the regions of absorption or resouance in the liquid were due entirely to molecular ates which were dissociated in the aseous condition , then from this point of view the vapour would be optically a different substance . However , in most cases there does not appear to be an actual disappearance or creation of the principal dominating resonances , but only displacement and tion with changing conditions . use the data above to determine the constants of a formuIa . With sufficient approximation for our purpose , we find ' This gives a value of for . If we take the dielectric constant to ] ) given by ) for liquid CS we ) ffiin a mean value of for the left-hand side for vice ; this , we may replaco the term by a single equivalent bsorption region in the -red . We obtain in this a term ) Dr. T. H. Havelock . Optical Dispersion : its [ Oct. 10 , now , and . Experiment has shown that carbon disulphide has specially strong absorption in the region between and In any given state the maxima of absorption occur at wavelengths \fnof ; m and , given , as in the previous sections , by expressions like , when the dispersion formula has been put into a form suitable for the vicinity of the wave-length in question . Table XII shows the results for the as and the liquid at three temperatures . Table XII.\mdash ; Carbon Disulphide . 9.161 It is seen that is displaced towards the shorter wave-lengths with increasing temperature . This appears to be the general rule for liquids : in contrast apparently to the behaviour of solids . Water.\mdash ; We examine now in the same manner Flatow 's observations on water at five different temperatures ; the values of were calculated in S10 , from a certain value of for water vapour . Using these values we calculate the specific refraction for four wave-lengths ; the following table shows the values at the various temperatures and the mean for each wave-length . Table XIII.\mdash ; Values of for Water . Using the mean values and a density of for water vapour , with zero , we find the following values of for these four wave-lengths in order : ; the last value is of course the one which was used in order to calculate the values of for the liquid . *Cf . , ' Handbuch , ' vol. 3 , p. 350 . 1910 . ] Actual Physical Conditions . Using the meau values above , we calculate the constants of a dispersion formula of the type ( 37 ) and find ; ; ; The value of is ; we calculate now the values of near which occur the maxima of selective absorption in the ultra-violet at the various temperatures . The following table shows the data and the results for the liquid , usin , 0.33489 0.33361 0.3,3364 0.99233 0.98331 0.97191 0.1294 0 . 0 . 0 . In the formula for it is the product which occurs as the variable ; this decreases continuously in this case and we find a corresponding regular but very slight decrease in with temperature . result is in contradiction with that deduced by Flatow ; he calculated the constants of a Sellmeier dispersion formula for each temperature and a fairly increase in with rising temperature , the values anging from to approximately . There is , of course , no direct experimental evidence available in this case . In general the experimental data for the variation of absorption maxima with temperature are rather in charactel ; the results appear to depend on circumstances such as the homogeneity of the medium and the charactel , selective or general , of the absorption . It has been stated that in several cases , at least in the ultra-violet , nlaxima are displaced towards the shorter wave-lengths with increase of temperature for liquids , while for solids they move to the longer If we wish to study the in the we must Gplnce the term of the dispersion by the effect of one or more equivalent terms ; we try first a term . If we for the calculation the values of the dielectric constant iven by , namely at and 799 at , and if we use the colTcsponding values of iven above , we obtain a mean value of for the specific refraction for infinite -length ; hence and are given by . These give the values ) and . If , with the same notation as before , we form in order to find the approximate position of the absorption maximum , we find that ranges from about at to 55 at . This lalge variation is due to the large values of and , and these come directly 522 Dispersion : its Dependence upon Physical Conditions . from the normal value of the dielectric constant ; the only inference is that if we insist on bringing the dielectric constant in this case under the same scheme as the ordinary dispersion , one resonance in the infra-red is not sufficient . It is well known that Sellmeier dispersion formulae with the same assumption indicate as the approximate position , and the subject has been experimentally recently . Using ice , Trowbridge and Spence* find no metallic leflection between and ; with water , Rubens and Hollnagel obtain a similar result and also deduce that at the refractive index is of the same order of magnitude as in the visible spectrum . We may use this information in attempting to make up the term from two resonance terms , . To make the matter definite , we assume that is at 80 ; then , with this and the above data for the dispersion , we have the equations We have only three equations , with four unknown quantities ; but to illustrate the calculations we assume a value for , say 10 . Then , solving the equations approximately , we find Calculating now , as before , the positions of selective absorption corresponding to at the various temperatures , we find they range from at to at . The principal absorption corresponding to is far removed in the infra-red ; the results appear to 'be fairly consistent with the absorption of water , and they confirm at least the necessity for more than one selective absorption in the infra-red . 13 . Summary . The chief results of the previous investigation may be summarised briefly in the following manner:\mdash ; 1 . The formal scheme of the theory is the representation of the effect of the physical state of the medium upon its dispersion by means of two variables : the density , and a quantity expreseing an effect of surrounding molecules . 2 . A relation independent of is deduced , and is used as a test of the theory , namely , the difference of for any two physical states is independent of the wave-length . 3 . As the result of an analysis of available experimental data , it appears that the scheme is sufficiently adequate for gases , for liquids , and for changes of state from gas to liquid . For solid substances , the two variables and A. Trowbridge and B. J. Spence , ' Phys. Rev July , 1910 . Rubens and Hollnagel , . cit. The of Halley 's Comet . are not sufficient to express all the facts , but it seems that the term must at least be taken into account in a complete theory . 4 . It is shown that it is possible to include , either wholly or in part , the dispersion of artificial or natural double refraction in simple cases . 5 . By assigning a standard state for the medium , gas at and 760 mm. , for which is zero , numerical values of are obtained for various substances in different states . Anomalies in molecular refractivity are ascl'ibed , in part , to the variations in 6 . Using a type of dispersion formula involving and , it is shown that the positions of the absorption maxima depend upon these quantities as well as upon the frequencies of the natural vibrations of the molecule . The consequent displacement of the maxima for varying conditions of pressure temperature , and density are illustrated by analysing certain expel.imental data . of Halley 's Comet . By CHARLES P. , A.R.C Sc. , F.B.P.S. , F.R.A.S. ( Communicated by Sir Norman Lockyer , K.C.B. , F.R.S. Received November Read November 24 , 1910 . ) [ PLATE 7 . ] Owing to the interference it was inlpossible to for observations of the comet sp ectrum lfay from the Solar Physics Observatory at South Kensington . Sir Norman therefore obtained permission to occupy the site on Fosterdown , Caterhall , which already been selected as the future position of the Observabory . No observations of value were possible during the first three weeks of May on account of exceptionally bad weather ; but on May 23 and 26 photographs and visual observations of the spectrum were seeured . The spectrum was seen as a small nebulous clou to in diameter ; with a binocular the central htening due to the intense tellar nucleus became clearly visible . a whole the conlet was ) as conspicuous as a second nitude star , so that it was inter than had been expected . The curvature of the was not so that seen in Comet 1910 iving the appearance of an to the tail extension seen with moderate power . Photographs of comet were obtained with a lncycr camera of

rspa_1911_0004

0950-1207

The Spectrum of Halley's Comet.

523

526

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Charles P. Butler, A. R. C Sc., F. R. P. S., F. R. A. S.|Sir Norman Lockyer, K. C. B., F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1911.0004

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1911_0004

10.1098/rspa.1911.0004

Atomic Physics

Optics

Atomic Physics

The Spectrum of Comet . are not sufficient to express all the facts , but it seems that the term involving \lt ; r must at least be taken into account in a complete theory . 4 . It is shown that it is possible to include , either wholly or in part , the dispersion of artificial or natural double refraction in simple cases . 5 . By assigning a standard state for the medium , gas at 0 ' and 760 mm. , for which a is zero , numerical values of a are obtained for various substances in different states . Anomalies in molecular refractivity are ascribed , in part , to the variations in a. 6 . Using a type of dispersion formula involving and a , it is shown that the positions of the absorption maxima depend upon these quantities as well as upon the frequencies of the natural vibrations of the molecule . The consequent displacement of the maxima for varying conditions of pressure temperature , and density are illustrated by analysing certain experimental data . The Spectrum of Comet . By Charles P. Butler , A.R.C Sc. , F.R.P.S. , F.R.A.S. ( Communicated by Sir Norman Lockyer , K.C.B. , F.R.S. Received November 5 , \#151 ; Read November 24 , 1910 . ) [ Plate 7 . ] Owing to the interference of high buildings it was impossible to arrange for observations of the comet spectrum during May from the Solar Physics Observatory at South Kensington . Sir Norman Lockyer therefore obtained permission to occupy the site on Fosterdown Fort , Caterham , which has already been selected as the future position of the Observatory . No observations of value were possible during the first three weeks of May on account of exceptionally bad weather ; but on May 23 and 26 photographs and visual observations of the spectrum were secured . The spectrum was seen as a small nebulous cloud about 3 ' to 5 ' in diameter ; with a binocular the central brightening due to the intense stellar nucleus became clearly visible . As a whole the comet was about as conspicuous as a second magnitude star , so that it was much fainter than had been expected . The curvature of the head was not so sharp as that seen in Comet 1910 a , giving the appearance of an elongated arc perpendicular to the tail extension when seen with moderate power . Photographs of the comet were obtained with a Dallmeyer camera of Mr. C. P. Butler . [ Nov. 5 , 6 inches aperture and 5 feet focal length . The spectra were obtained with an ultra-violet spectrograph having a quartz lens of 2 inches aperture and 18 inches focal length , with an Iceland-spar prism of about 30 ' angle adjusted to avoid double refraction . Although it was not possible to give sufficient exposure to record the tail extensions , the photographs of the nucleus and coma present several interesting features which assume importance when considered in relation to similar observations recorded elsewhere . The chief of these is the intermittent occurrence of a secondary condensation some distance from the principal nucleus . A photograph exposed on May 23 from 9.20 to 9.50 p.m , shows no appreciable trace of duplicity in the nuclear matter , while on a photograph exposed on May 26 from 9.40 to 10.10 p.m. there is a very distinct secondary condensation well separated from the principal nucleus , in position angle 270 ' and about 65 " distant ( Plate 7 , figs. 1 and 2 ) . Similar appearances are described in the reports from other observers.* The colour of the head was pale lilac , being very similar to that of a vacuum-tube discharge in carbon compounds under feeble excitation without capacity . The tail was double and practically straight as far as it could be followed . On May 26 it was traced for about 8 ' to 10 ' from the head towards the south-east . The spectrum was observed visually on May 22 , 23 , and 26 with a direct-vision spectroscope . No appreciable differences in the relative intensities or positions of the bands were perceptible for this interval of three days . The nucleus showed a very strong continuous spectrum intensified by three bands in the yellow-green , green , and greenish-blue regions , presumably the usual cometary bands at XX 5635 ( int . 7 ) , 5165 ( int . 10 ) , and 4737 ( int . 7 ) . Other intensifications of the continuous spectrum of the nucleus were suspected , but their positions could not be estimated with sufficient accuracy for record ( fig. 3 ) . The spectrum of the coma surrounding the nucleus was seen to consist of these same three bands , extending the whole length of the slit . Careful examination failed to detect any continuous radiation in the coma spectrum . The spectrum of the tail could not be observed under the working conditions . It is to be noted that the general appearance of the spectrum was somewhat different from that seen in the ordinary fluted spectrum of carbon compounds . The maximum intensity appeared to be more nearly at the * ' Astronomische Nachrichten , ' vol. 185 , No. 4420 , June 17 , 1910 ; 'Comptea Rendus , ' vol. 150 , pp. 1496 , 1659 , June , 1910 . Butler . Roy . Soc. Proc. , A. 84 , 7 . Fig. 1 . Fig. 2 . 1910 , May , 23 d. 9li . 20 m. to 9h . 50 m. 1910 , May , 26 d. 9li . 40 m. to 10h . 10 m. ( Photographs of the Nucleus of Halley 's Comet . ) Fig. 3.\#151 ; Visual Observations of Spectrum , May 22 , 23 , 26 . HMHsHe Hs a Lyne . Comet spectrum enlarged vertically . Comet spectrum . 3884 4050( ? ) 4737 5165 5635 Fig. 4.\#151 ; Photograph of Comet Spectrum , with a Lyme comparison . ( Quartz-calcite Spectrograph , 2-inch aperture , 18-inch focu3 . ) 1910 . ] The Spectrum of Halley s Comet . centre of each band , being somewhat similar to that seen in spectra under medium pressures rather than to the more complicated fluted structure under low pressure with electrical excitation . This appears to be borne out by the photographic spectra , where the maxima seem to be practically images of the nucleus and surrounding nebulosity of the coma . This appearance , however , may also be explained as being the integration of the brightest terminal components of the usual flutings by the objective prism spectrograph . The weather conditions being so unfavourable it was only possible to obtain a photographic record of the brightest features of the spectrum of the nucleus . The three chief bands recorded visually are of course rendered of quite different relative intensities on the photographs , the least sensitive region of even the best isochromatic plates being the green . The photographic spectrum shows two very conspicuous bright bands , about wave-lengths 4737 ( int . 10 ) and 3884 ( int . 6 ) . with several other fainter bands at XX 4050 , 4360 , 5165 , and 5635 . Their relative intensities will be best understood from tl le accompanying reproduction of the spectrum obtained on May 26 ( fig. 4 ) . In enlarging the comet spectrum in one direction only , to provide a spectrum of sufficient width for reproduction , it is practically impossible to avoid introducing artificial lines due to the grain and minor imperfections of the plate . The bands noted as cometary bands , however , have all been found from the original negative , and are equally well shown on several enlargements . A small strip of the spectrum without vertical enlargement is given below for comparison ( fig. 4 ) . In view of the fact that other photographs of the comet spectrum obtained elsewhere at a different time show important differences of intensity to those photographed at Fosterdown , it is of interest to inquire whether such differences are ' physical and indicative of real changes in the cometary radiation , or whether they may be due to atmospheric absorption ( as has already been suggested by Deslandres ) or optical differences between the instruments and photographic plates employed . One of the chief differences noted is the relative inversion of intensity in the lines near XX 4737 and 3884 , as shown on photographs obtained in India on May 1 , 3 , 13 , and at Fosterdown on May 26 . The photographs at Fosterdown being taken with an instrument having a quartz-calcite optical train , consisting of a 2-inch quartz lens and Iceland-spar prism , specially adapted for recording radiations of short wave-length , these differences cannot be ascribed to instrumental absorption in the ultra-violet region . Owing to the close proximity of the comet to the earth during the period Mr. F. W. Aston . Distribution of [ Nov. 22 , about the time of transit , the aspect of the head and nucleus of the comet was rapidly changing from day to day . Before the transit the part of the head facing the sun was principally visible ; near the transit another part of the comet 's head was visible from the earth ; while after transit the hotter side of the coma would again gradually come into view . It is quite conceivable that this presentation of such different portions of the comet might exhibit notable differences of spectrum . From a series of preliminary experiments it has been found that very remarkable changes of intensity of these carbon bands may be brought about by simple variations of the conditions of volatilisation ; so much so , that this would probably serve as the more satisfactory reason for differences between various photographs of the comet 's spectrum , provided , of course , that any known instrumental or atmospheric differences are duly considered . I am indebted to Mr. J. P. H. Wilkie , photographer to the Observatory , for help in the preparation of the illustrations to this report . The Distribution of Electric Force in the Crookes Dark Space . By F. W. Aston , B.Sc. , A.I.C. , Trinity College , Cambridge . ( Communicated by Sir J. J. Thomson , F.R.S.\#151 ; Received November 22 , 1910 , \#151 ; Read January 12 , 1911 . ) Introductory . The electric force in the Crookes dark space and the negative glow has been the subject of a considerable number of investigations . The first determination was made by Schuster , * whose results indicate the presence of a positive charge of electricity , whose density decreases in geometrical progression as the distance from the cathode increases in arithmetical progression . Grahamj* found a curious drop in potential near the cathode , but Wehnaltt , repeating these experiments , was unable to find this drop of potential , and ascribes it to the fact that the exploring points were not in the direct line of the current . SkinnerS came to the conclusion that all the fall of potential occurs at the surface of the cathode . Recently , Westphal|| has made a careful series of observations with cathodes of different metals * ' Boy . Soc. Proc. , ' 1890 , vol. 47 , p. 526 . t ' Wied . Ann. , ' 1898 , vol. 64 , p. 49 . % 1 Ann. d. Phys. , ' 1903 , ( 4 ) , vol. 10 , p. 542 . S ' Phil. Mag , ' 1902 , 6 , vol. 2 , p. 616 . || 'Verhand . d. Deutsch . Phys. Ges . , ' 1910 , vol. 12 .

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The distribution of electric force in the crookes dark space.

526

535

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

F. W. Aston, B. Sc.|Sir J. J. Thomson, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1911.0005

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1911_0005

10.1098/rspa.1911.0005

Electricity

Tables

Electricity

]\gt ; Mr. F. W. Aston . The Distribution of [ Nov. 22 , about the time of transit , the aspect of the head and nucleus of the comet was rapidly changing from day to day . Before the transit the part of the head the sum was principally visible ; near the transit another parb of the comet 's head was visible from the earth ; while after transit the hotter side of the coma would again radually come into view . It is quite conceivable that this presentation of such diHerent portions of the comet might exhibit notable differences of spectrum . From a series of preliminary experiments it has been found at very remarkable changes of intensity of these carbon bands may be brought about by simple variations of the conditions of volatilisation ; so much so , that this would probably serve as the more satisfactory reason for differences between various of the comet 's spectrum , provided , of course , that any known instrumental or atmospheric differences are duly considered . I am indebted to Mr. J. P. H. Wilkie , photographer to the Observatory , for help in the preparation of the illustrations to this report . The Distribution of Electric Force in the Crookes Dark Space . By F. W. ASTON , B.Sc. , A.I.C. , Trinity College , Cambridge . ( Communicated by Sir J. J. Thomson , F.R.S.\mdash ; Received November 22 , 1910 , \mdash ; Read January 12 , 1911 . ) The electric force in the Crookes dark space and the negative glow has been the subject of a considerable number of ations . The first determination was made by Schuster , *whose results indicate the presence of a positive charge of electricity , whose density decreases in geometrical progression as the distance from the cathode increases in arithmetical progression . Grahamt found a curious drop in potential near the cathode , but Wehnalt , repeating these experiments , was unable to find this drop of potential , and ascribes it to the fact that the exploring points were not in the direct line of the current . SkinnerS came to the conclusion that all the fall of potential occurs at the surface of the cathode . Becently , has made a careful series of observations with cathodes of different metals * . Soc. Proc 1890 , vol. 47 , p. 526 . Wied . Ann 1898 , vol. 64 , p. 49 . 'Ann . . Phys 1903 , ( 4 ) , vol. 10 , p. 642 . S 'Phil . Mag , ' 1902 , 6 , vol. 2 , p. 616 . Verhand . . Deutsch . Phys. Ges , vol. 12 . 1910 . ] Elec Force in the Dark Space . in several gases , using a single exploring point , in which he finds a definite fall of potential\mdash ; e.g. about 80 volts for Al in \mdash ; at the surface of the cathode , the electric force a few millimetres away appearing from his curves nearly uniform . Now all these measurements were made by introducing sounds , i.e. metallic wires or points , into the discharge , the observers trusting to these up the potential of the gas by which they were surrounded . The danger of such assumption has been pointed out by Sir J. J. Thomson , * and for ents made inside the dark space it seems entirely unwarranted . Fortunately , however , there is an alternative method , which involves no doubtful assumptions , and does not introduce substantial obstacles into the discharge . Its simplicity and elegance cannot fail to appeal to anyone investigating this field of research . This method was suggested by Sir J. J. Thomson , and used by him recently in determining the potential distribution in the striated discharge it consists in a beam of cathode transversely through the discharge , the deflection of these being taken as a measure of the electric force at that point . It appeared to the author that this method might be used with advantage to determine the distribution of potential near the cathode under the conditions used by him in obtaining measurements of the length of the dark spaceJ these conditions being briefly:\mdash ; Electrodes in the form of circular discs filling the discharge tube , the latter being very much wider than the maximum length of the dark space , so that the effect will be comparatively small . Current density greater than that necessary to cover the with glow , and to cause the positive column to disappear . It was to be expected , from the numbers obtained in the above research , that the electric forces to be snred would rise as voloe per centimetre . Now it can be easily shown that , for an electron to attain suflicient velocity to cross a tube 10 cm . wide under such a force with a small deflection , it is necessary for it to fall a potential of about 20,000 volts . The principal problem to solve , crefore , was the design of a secondary tube , which , working at a pressure necessary to give a dark space of 2 to 3 cm . in the main tube , wonld deliver a homogeneous beam of cathode rays under a working polential responding to a centimetrc spark in air . ' ' Conduction of Electricity through Gases 2nd ed. , p. 531 . 'Phil . Mag Oct. , 1909 , vol. 18 , pp. 441\mdash ; 4Cl . . W. Aston , Roy . Soc. Proc 1907 , , vol. 79 . Mr. F. W. Aston . The Distribution of [ Nov. 22 , It only after a tedious and dispiriting investigation , in which a large number of forms of secondary tube were tried\mdash ; the whole apparatus having to be completely re-evacuated after each variation\mdash ; that the conditions were arrived at , when the rest of the research became comparatively easy . The arrangement of the apparatus is indicated in fig. 1 . The main tube is a cylindrical bottle 12 cm . wide , with windows cut in the sides , which the exploring ray is to pass . , and are three aluminium discs , just filling the tube , and kept at fixed distances apart by a framework of thin glass rods ( not shown in the figure ) . A and are cm . apart , and form respectively the anode and cathode of the main , which is maintained by a large battery of storage cells and controlled by a water resistance . and form a system of parallel plates cm . apart , to which a known potential could be applied through the flexible leads and , to determine the deflection of the rays in a known uniform field . As it is almost impossible to maintain a steady current with aluminium electrodes in the presence of mercury vapour , the old method of moving the ctrodes up and down with a float supported on mercury was abandoned in favour of the device indicated in the figure . Into the neck of the bottle is fitted a vertical tube , to the side of which is attached a ground-glass joint ( a good stop-cock does very well ) . The plug of this is elongated as a rod , over which is wound a flexible conducting cable made of a few strands of the hree discs Tixing toint oupportfinest brass wpparatus tovedl 9Electric F of the system , and also of supplying the anode lead , will be easily seen from the figure , the cable runmng under a tension through the copper wire fork This simple arrangement prove quite faultless in , the plates being set at any required point with the eatest ease and accuracy . At the one vindow of the main discharge tube was fixed a glass tube cm . long , carrying a screen of powdered willemite , at the the secondary discharge tube . This in its final form is practically an -ray bulb on a minute scale . The bulb is 1 cm . in diameter , the cathode is a piece of aluminium wire nlll . thick , the end is ground off perfectly flat and just from the thick-walled tube into the bulb . The anode is a brass tube 10 cm . long , 5 mm. wide , plugged at both ends . The the end nearest the cathode is of brass drilled with a mm. hole , at the other is of lead sheet pierced at the centre with the finest possible pinhole . The position of both electrodes must be adjusted with great nicety in order to get rays of sufficient hardness the required pressure . The of the secondary set exactly parallel to the plane of the cathode . The secondary discharge was nlaintained 1 a small mot-d.ivenlVimshurst , the anode being earthed . At first the was intermittent , and the rays far from , a difficulty instlperal)le nntil it was accidentally found . by touching the bulb with the , that an earthed conductor allowed to " " blush\ldquo ; off on to the bulb lendered the quite continuous if its ( Iistance adjusted to suit atmospheric conditions . When the ) aratus working well the of the } ) appeared on the screen over 40 cm . as a sharp and almost perfectly steady circular spot , which could be read after a little practice to bont mm. range of pressure over which suitable thode rays were produced was exceedingly ited , and corresponded to a dark space in the main tube of about 3 of the . By of the dimensions of the secondary tube another be obtained , but the above was used as being most isfactory . The pressure was not actually measured , but could be deduced from the length of the dark space ; it from about mm. in hydrogen to mm. in the other gases . potential between A and read on a Westou , and by means of a double switch the same instrument used for the tion of the standard field between and C. Mr. F. W. Aston . The Distribution of [ Nov. 22 Procedurc . The apparatus was well washed with the gas to be used , and the pressure adjusted by an oil pump and a " " charcoal liquid air\ldquo ; tube until the dark space was of suitable length and showed no ] tendency alter , and the secondary discharge was also steady . The system of electrodes was then wound up until the pencil of cathode rays passed between and C. When these two were both connected to earth a zero was obtained . A known potential was then put on between and , when a deflection of the spot was observed and measured on a scale attached to the screen . The plates were now lowered until the pencil passed through the dark space and the deflections taken corresponding to different distances from the cathode until the negative glow was reached . The plates were now raised and the observations checked on the return journey . Results . A typical set of readings obtained in this way is shown in the accompanying curve , in which detlections of the spot are plotted for different 5 .5 Negattve G Crookes Dark Space positions in the dark space and ative glow . In the latter the deflection was always found to be zero , hence the electric force here is negligibly small ] compared with that in the dark space , a result reeing with that fougd by the author in a previous paper . cit " " that the position of the anode , so long as it is in the glow , has no appreciable effect on the discharge Measurable deflections commence at the boundary of the dark space , 1910 . ] Electric Force in the Crookes Dark and within that the deflection is proportional to the distance from the negative glow , the points practically on a straight line as indicated . ( A critical examination of many sets of results shows a tendency for the curve to be a little steeper towards the ends than in middle . ) This remarkably simple empirical result was obtained with hydrogen , air , oxygen , and , so that for these , and probably for all , gases under the conditions of these expe1iments the electric force the dark space is in limjar proportion to th distance from edgj of glow . Since the total fall of potential across the dark space will be given by integrating the electric forces , it is clear that if we convert the deflections into electric forces this fall of potential will be the area of the curve bounded by the cathode and the edge of the negative glow , i.e. half electric force at surface of cathode multiplied by length of dark space . Before being able to obtain accurate measurements of this potential it will be necessary to find the correction for the curvature of the path of the exploring cathode beam . Assuming the distribution found above , let electric force at unit distance from the negative glow , then , if the length of the dark space is the equation of motion of an electron at distance from the cathode is . If is the diameter of the tube , the velocity of the particles in the athode stream , entering at a point from the cathode and leaving at solving the above equation , we get whence This is the actual displacement in the tube ; to obtain the total deflection at the screen at distance from the tube , we mubt add tiznes the value of at the point of emergence , which is Putting in the values of sinc and , we . obtain the total ction part in square brackets the correcting factor required . . , 532 Mr. F. W. Aston . The Distribution of [ Nov. 22 , Under a uniform field X , the total deflection is , in the same way , Let be the actual deflection when , i.e. for a ray grazing the cathode , and the uniform electric force necessary to give unit deflection , then , putting in the numerical values of and actually used in the experiment , . : But the total fall of potential is , putting in approximate value of . The value of is obtained by plotting the deflections as described above , and finding where the straight line drawn through them cuts the cathode . In the accompanying table are }iven the deflections observed , the fall of potential in the dark space calculated by the above formula , and the voltage actually observed between the electrodes . It will be seen that , although the voltage ( and with it the current in the tube ) was varied over a wide range , . : 1910 . ] Electric in the Crookes Spa ce . the calculated fall of potential , though more often less than oo.reater , never differs from the observed by more than experimental error . From this the author arrives at the conclusion that , under the conditions of the experiment , practically the whole of the potential fall takes place in the Crookes dark space , and is distributed within it in the form of a continuous parabolic field . The so-called " " sprung It will be seen that , considering the close agreement of the fallof potential in the dark space with that between the electrodes , it is difficult to find room for the fall of the order of 20 volts close to the surface of the anode observed by Skinner , and quite impossible to do so for one of 80 volts at the surface of the cathode recently measured an exploring wire by Westphal ( ioc . cit One is therefore driven to the conclusion that the sound does not take up the correct potential when used near the cathode . e ; areful consideration of the conditions under which the experiments performed suggests the following possible explanation . There is little doubt that at the surface of the cathode , when steady ldischarge is taking place , streams of positive ions\mdash ; " " Canalstrahlen represented in the by heavy lines\mdash ; are falling upon the surface of the cathode , and by their impact liberating streams of negative ions\mdash ; cathode . rays , represented in the figure by light lines travelling in the opposite direction . Let be a small material obstacle introduced into such a system , and let it for an instant be at the same potential as the cathode . Such an obstacle , if sufficiently small compared with the of the space , will interfere inappreciably with the supply of ions , the bulk of which are almost certainly generated near or in the negative glow , bnt it will absolutely prevent bombardment of that part , ) of the cathode immediately beneath it , which part will at once cease to liberate \mdash ; ions . is now being bombarbed with ions of only one sign , and its potential must inevitably rise . As this happens it will defiect the passing VOL. LXXXIV.\mdash ; A. 2 . W. Aston . The Distribution of [ Nov. 22 , close to it out of their normal path , making the " " shadow\ldquo ; or inactive part still larger ( fig. 3 ) , until finally its potential will rise so high that it is able to deflect to itself the \mdash ; ions generated at the boundaries of in sufficient numbers to exactly balance the supply of ions in whose direct path it still lies , when equilibrium potential will be established . Since the equilibrium potential between the obstacle and the cathode is . only concerned with the relative intensity of the supplies of \mdash ; ions , it will be practically independent of the gas pressure and the current density , and , in fact , be expected to behave very much as does Westphal 's " " Kathodensprung which seems in all probability non-existent in a normal unobstructed Theoretical Aspects of the Results . A detailed enquiry into the theoretical considerations involved in the somewhat remarkable result of this ation is beyond the scope of the present paper , but a few of the more salient points may be referred to . with Since the rate of change of electric force in the dark space is uniform , the latter must be a region in which the free electrification has a uniform excess positive density , such that if is the potential fall across the dark space and its length , The author has shown ( ioc . cit. ) that if is constant varies very nearly universely as the pressure ; hence for a constant voltage varies directly as the square of the pressure . It , however , bears no simple relation to the voltage or the current density at constant pressure . The assumption made for simplicity by the author in the above paper that the density of the free negative electrification in the dark space be neglected is clearly incorrect , since the excess of positive ions must carry more current in the stronger parts of the field than they do in the weaker ones , so that in the latter ions of both signs must be present to maintain the flow . It appears , indeed , that the actual number of ions of both sigIJs per cubic centimetre increases as we move away from the cathode , their algebraic sum being the constant , which becomes zero with surprising suddenness at the of the negative glow . If we suppose that at the surface of the cathode a constant fraction of the total current is carried by this excess of positive ions , and that their velocity is proportional to the field at . that point , we obtain a value of the mobility , which is the same expression ( with different constants ) as that obtained on other premises in the above paper , and shown to be notably constant for a given gas . 1910 . ] Electric Force in the Croohes Space . 5 35 The fall of potential across the new dark space discovered by the author in helium and hydrogen , *must , from the results of this investigation , be taken as instead of , which works out at 20 volts for hydrogen , 40 volts for helium , but the considerations involved in theory suggested for this phenomenon are not affected . Sn of Results . ( 1 ) The electric force in the negative oolow is ibly small compared with that in the dark space . ( 2 ) The electric force in the dark space very nearly lineal relation to the distance from the negative glow ; and , hence , ( 3 ) The dark space is a of miform positive electrification with great suddenness in the ative glow . ( 4 ) The total fall of potential inside the dark space , calculated from the results obtained , rees within the of experiment ) that obsel'ved across the electrodes . ( 5 ) The method of exploring points is inapplicable to the space , the large falls of potential at the surface of the cathode , observed ) its use , are probably non-existent unobstructed In conclusion , the author wishes to express his indebtedness to Prof. J. J. Thomson , both for the method employed and for his kind hclp and ement during the ation . F. W. Aston , ' Roy . Soc. Proc 1907 , , vol. 80 .

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0950-1207

The density of niton (\#x201C;radium emanation\#x201D;) and the disintegration theory.

536

550

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Dr. R. Whytlaw Gray|Sir William Ramsay, K. C. B., F. R. S.

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6.0.4

http://dx.doi.org/10.1098/rspa.1911.0006

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1911_0006

10.1098/rspa.1911.0006

Thermodynamics

Measurement

Thermodynamics

536 The Density of Niton ( " Radium Emanation " ) and the Disintegration Theory . By Dr. R Whytlaw Gray and Sir William Ramsay , K.C.B. , F.R.S. , University College , London . ( Received December 13 , 1910\#151 ; Read January 12 , 1911 . ) According to the disintegration theory of radioactive change , a definite number of atoms of radium break up per second , each evolving an a-particle which ultimately becomes a helium atom , leaving behind lighter molecules which form the gas known as " radium emanation/ ' or niton . The identity of the a-particle after it has lost its electric charge with the helium atom has been convincingly proved by Rutherford and Geiger ; and measurements of the volume of helium evolved from niton by Ramsay and Soddy , and from radium in equilibrium with its disintegration-products by Dewar , render it exceedingly probable that in each successive change from radium to radium D only one a-particle is expelled per atom . If , then , the view is held that the radium atom on disintegration to niton splits up into two parts only , one of which is the a-particle , then the atomic weight of the resulting niton is 226*4\#151 ; 4 = 222*4 . On the other hand , it may be supposed that the disintegrating radium atom splits up into three or more parts ; helium , and two other bodies of higher atomic weight , if three parts . On account of its greater mass , the heavier particle might be expelled below the critical velocity necessary for the formation of ions in the air , and might itself be non-radioactive ; if this were the case , its presence in a solid state would almost certainly escape detection . There is no direct evidence against such a supposition , for the atomic weights of none of the products of the disintegration of radium have been determined . Experiment alone can settle this question of the true atomic weight of niton ; but on account of the exceedingly small volume of this gas obtainable from a relatively large weight of radium , the experiment is by no means easy . A number of investigators have sought to obtain the atomic or molecular weight by comparing the rates of diffusion of " emanation " and air or nitrogen . Pierre Curie and Danne found ... ... . 176* Bumstead and Wheeler " ... ... ... ... ... 180f * 6 Comptes Rendus/ 1903 , vol. 137 , p. 1314 . t ' Amer . J. Sci./ 1904 , p. 97 . Density of Niton and the Disintegration Theory . 537 Rutherford and Miss Brooks found ... 176* Makower " ... . aloof Chaumont " ... . 70\#151 ; lOOJ Perkins compared the rate of diffusion with that of mercury vapour , also a monatomic gas , and found 235.S Lastly , Debierne made use of Bunsen 's method of causing the gas to issue through a minute perforation in a diaphragm of platinum , and as the result of a very concordant -set of experiments , obtained the number 220 for the molecular weight.|j But none of these methods , however ingenious , can be accepted as conclusive , for the conditions are so different from those usually obtaining in ordinary work that no certain inference can be drawn . In 19091T we attempted the solution of this problem in another way . We found it possible to determine the critical and boiling points of niton with less than one-tenth of a cubic millimetre of gas . Assuming it to belong to the inactive series of gases , we plotted the critical and boiling points of argon , krypton , and xenon against their atomic weights , and found these points to lie almost exactly on a slightly curved line . Extrapolation showed that for the emanation to lie either on the line connecting the boiling points or the critical points , it must possess an atomic weight approximating to 176 . It was quite impossible to bring the value 2224 anywhere near the extrapolated curves ; but it must be observed that , as the curvature is slight , a small error in the constants of argon , krypton , or xenon might alter the curvature in the reverse direction , and so make more probable the higher atomic weight . We realised at the time that the results could not be accepted as certain , and that the only criterion must be the determination of the density of the gas . It is , however , remarkable that all the determinations quoted , with the exception of Makower 's and Chaumont 's , point to an atomic weight either of 176 or of 222 ; these are the tabular atomic weights of the immediate follower of xenon in the periodic table , on the one hand , and of the next member on the other . The members of the series are :\#151 ; Helium . Neon . Argon . Krypton . Xenon . I. II . 4 20 40 83 130 176 222 * ' Trans. E. S. Canada , ' 1901 . t ' Phil. Mag. , ' 1905 . J ' Le Radium , ' 1909 , vol. 6 , p. 106 . S ' Amer . J. Sci. , ' 1908 , p. 461 . || ' Comptes Rendus , ' 1910 , vol. 150 , p. 1740 . IT ' Trans. Chem. Soc. , ' vol. 93 , p. 1073 . 538 Dr. Gray and Sir W. Ramsay . Density of [ Dec. 13 , To determine the density of a gas , four separate measurements are essential\#151 ; the volume , the temperature , the pressure , and the weight of the gas . In the present case , however , the problem was simpler , for the volume of niton at normal temperature and pressure accumulating in a given time from a known weight of radium is a constant and invariable quantity , and has been repeatedly measured . In 1908 Rutherford found this volume to be 0*61 cu . mm. per gramme of radium ; Debierne in 1909 obtained the value 0*58 cu . mm. , and these results were confirmed shortly afterwards by our own work , * which gave 0*601 cu . mm. Rutherford has been able to calculate this constant from the result of his beautiful experiment in which he actually counted the number of a-partieles emitted from a known weight of radium , and the value found was 0*585 cu . mm. It may therefore be taken as certain that the error in this constant does not exceed 5 per cent. For our experiments this figure is unessential , since the actual volume of emanation from the total radium at our disposal had been measured . The problem which we have attacked is the determination of the weight of emanation evolved in a given time from our total quantity of radium . The radium bromide solution from which the niton for these experiments was drawn was contained in three bulbs sealed on to a Topler pump . The maximum measured quantity of emanation which can be extracted with the pump from the solutions in the bulbs is 0*127 cu . mm. By collecting the gas every eight days , the yield was only 76 per cent , of this quantity , so that the total volume . obtainable for weighing scarcely exceeded 0*1 cu . mm. The weight of this volume , on the assumption that the atomic weight is 222 , is less than 1/ 1400 mgrm . It is therefore evident that in order to weigh this minute quantity of gas vrith sufficient exactness , a balance turning with a load not greater than 1/ 100,000 mgrm . was a necessity . This seems an almost inconceivably small weight to attempt to measure , when one considers that the limit of sensibility of a delicate assay balance is about 1/ 200 mgrm . , and that even the Nernst balance will hardly turn with a load smaller than 1/ 2000 mgrm.f The successful construction of a balance capable of weighing these very minute quantities has been* accomplished by Dr. B. D. Steele and Mr. Grant , of the University of Melbourne ; thanks to their skill and ingenuity , they have constructed an instrument 100 times more sensitive than the Nernst micro-balance . Steele and Grant have published an account of their * Loc . cit. , p. 1082 . t As we shall have to deal with very small weights , it is advisable to adopt a new unit ; this is conveniently the millionth of a milligramme . The abbreviation here used for this is fimgrm . 1910 . ] Niton and the Disintegration Theory . 539 Balance , * and they have shown that a sensibility of 1/ 250,000 mgrm . could be attained . After several trials we have been successful in constructing a similar instrument and in determining the density of the radium emanation with its help . It is only fair to state , however , that Dr. Brill , working in the laboratory of University College , improved the Nernst balance , so that it turned with 1/ 10,000 mgrm . The subject was followed up later by Dr. Gwyer , also at University College , who introduced the hydrostatic method of determining small weights , the buoyancy of a small bulb containing a known weight of air being altered by the adjustment of the pressure in the balance case , constructed so that a vacuum could be made . We then corresponded with Dr. Steel , who was so obliging as to inform us cf the principle and construction of his balance , then in an experimental stage . The paper published by Steel and Grant renders a minute description of our balance unnecessary ; but our balances ( for several were constructed ) differ in some small respects from theirs . The beam , for example , was made by placing thin silica rods in grooves carefully ruled on a smooth plane block of graphite , and then fusing the contiguous ends together in an oxygen coal-gas flame ; in this way , a symmetrical beam , lying on a plane surface , was secured . If this condition is not fulfilled , the beam is apt to be deformed by small stresses set up in the quartz at the points of junction , as found by Steel and Grant . It is also necessary that the knife-edge shall be at right angles to the beam in two planes . This was managed by sealing the knife-edge on to the beam with a long guiding rod of silica attached to it , so that adjustment to a right angle is not difficult by trial and error ; this guiding rod , when fused off , left a stem of a few millimetres in length , to which the platinised silica mirror was fused . By this device the mirror revolved without displacement when the balance was deflected . Another improvement was the direct sealing of a fine quartz fibre to the end of the beam , whereby a much freer suspension was attained . Again , while Steel and Grant weighed by displacement of the zero , our weighings were made by a null method , whereby the alteration of pressure brings the spot of light to its original position . In this way , any possible variation in the sensibility of the beam with its deflection from horizontality is avoided . To eliminate as far as possible temperature changes and also vibration , the balance is mounted on a stone pillar in a cellar , and the brass case stands inside a large box of bright tin-plate . The mirror is illuminated by a beam of light from a Nernst lamp , which reflects on to a millimetre scale about 3 metres away . The light is allowed to impinge on the mirror only when a reading is taken . * 4 Roy . Soc. Proc. , ' A , 1909 , vol. 82 , p. 580 . 540 Dr. Gray and Sir W. Ramsay . Density of [ Dec. 13 , The small counterpoise quartz bulb , which contains a known weight of air , serves instead of a set of weights . When the air pressure in the balance case is the same as that in the bulb the apparent weight of the air which it contains is nil . That is to say , the real weight of the air in the bulb is exactly counterpoised by the buoyancy of the air outside . In a vacuum the sealed-up air exerts its full weight , and at any intermediate pressure the arm of the beam carrying the bulb is loaded with a known fraction of this weight . The counterpoise bulb of the balance used by us has a capacity of 22*2 cu . mm. , and the air which it contains weighs 0*027 mgrm . , or 27,000 yu , mgrm . ( millionth milligrammes ) . A pressure change of 1/ 10 mm. can be easily read by a cathetometer , so that any object lighter than 27,000 yamgrm . can be weighed with an accuracy of 3*55 / / , mgrm . By reading the pressure more exactly , say to 1/ 100 mm. , the limit of accuracy could have been increased to one-tenth of the figure above , provided , of course , that the sensibility of the balance is great enough ; to obtain this maximum degree of sensibility two important conditions have to be fulfilled . The centre of gravity of the beam must be most carefully adjusted , and the knife-edge must be perfectly straight and regular , even when viewed through a microscope with a half-inch objective . The final adjustment of the centre of gravity is made by volatilising away from the top of the centre rod , round which the beam is built , minute quantities of quartz in the oxy-coal gas blowpipe ; this is a comparatively simple process . The making of the knife-edge gave a good deal of trouble , but in the end this difficulty was overcome . The edge itself is about 0*3 or 0*4 of a millimetre long , and is ground in the form of a right-angled prism on the end of a quartz rod , which is subsequently fused on to the beam . The grinding and polishing of the edge , which is a very delicate operation , was carried out for us by Messrs. Hilger and Co. Our present balance is sensitive to about 2 yamgrm . ; its zero remains perfectly constant for days together . When the counterpoise bulb is removed , the zero of the balance is not altered by large changes of pressure within the case . The standard of weight , which is , of course , the weight of the air in the counterpoise bulb , has been verified in the following way : A long measured length of very fine aluminium wire was weighed as accurately as possible on an assay balance . A small portion of this wire , about 2 mm. in length , was cut from the longer length in such a way that the cross-sections w*ere as nearly as possible circular ; it was then measured under a reading microscope , and its weight was determined in terms of the counterpoise-bulb on the micro-balance . The weight so determined agreed within 1 per cent. 1910 . ] Niton and the Disintegration Theory . 541 with the weight calculated , on the assumptions that the wire was uniform , and that the weight of the small piece was directly proportional to its length . For the measurement of the density of very small quantities of niton or of other gases , the following procedure was adopted:\#151 ; The gas , of a volume of the order of 0*1 cu . mm. , was forced by means of mercury into a fine capillary tube of about 1 mm. external and 0*2 mm. internal diameter , which wTas sealed on to the apparatus for purifying the gas ( see figure ) . The upper end of this tube was drawn out into a finer very thin-walled tube , the extreme point of which was sealed . When necessary , the volume of the gas was measured at various pressures in the capillary tube , carefully calibrated for this purpose . After measurement , the tip of the tube was surrounded for some minutes with liquid air , in order to condense the gas ; the volume of the gas was then considerably increased , so that any hydrogen still present should expand , and only a minute trace could remain at the top of the tube ; the tube was then sealed at a distance of about 20 mm. below the tip , by aid of a pin-point gas flame . After most carefully cleaning and drying the small tube , it was lifted with platinum-tipped forceps , the tips of which had just been heated to redness , and placed in a little tightly-fitting 44 bucket , " or external tube , of silica , suspended from one arm of the balance by quartz fibre ; the pointed end of the density-tube was downwards , and the lower end of the bucket was slightly curved . A quartz counterweight , suspended to the same arm of the balance , was then adjusted , by fusing on or by volatilising off small pieces of silica , so that the beam was in balance at a pressure in the neighbourhood of 50 mm. After an hour or more the pressure in the case was exactly measured , and the position of the spot of light on the scale was noted . The bucket and tube were then removed with the platinum-tipped forceps ; and , while it was held vertical inside a wider tube , the density tube was pressed down with a glass rod , cup-shaped at the end ; the drawn-out point of the density-tube broke , but no splinters of glass could escape , for they were all retained in the bucket of silica . The bucket and its tube were \lt ; ? then replaced on the balance and the air was exhausted ; air was again admitted , and a second exhaustion was made ; in this way the gas was removed from the interior of the density-tube , and replaced by air . The pressure was then adjusted to bring the zero point back again to its original position . With practice , the whole operation could be carried out in less than five minutes ; this reduced the chance of error from the condensation of moisture on the glass and the settling of dust particles . Before , experimenting with the precious niton , the method was tested with 542 Dr. Gray and Sir W. Ramsay . Density of [ Dec. 13 , the less valuable xenon . Before freezing the gas its volume was measured ; it amounted , at 0 ' and 760 mm. , to 0*0977 cu . mm. It was then frozen , and the density-tube was sealed off and placed in its bucket on the balance ; after breaking the tip , the pressure change was 17*1 mm. ( 70 \#151 ; 52 9 ) , the temperature change was too small to affect the result ; this pressure change corresponds to an apparent loss of weight of 608 / nngrm . But this number 1910 . ] Niton and the Disintegration Theory . 543 does not represent the real weight of the xenon , for in the second weighing the tube is full of air , and therefore to the observed weight the weight of the .air filling the tube at the temperature and pressure of the second weighing has to be added . The volume of the tube being known ( for its length was measured ) , the weight of air under the conditions of weighing ( 52*9 mm. and 16 ' ) proves to be 46 fimgrm . ; hence the total weight is 654 / /mgrm . A further correction has next to be applied to allow for the difference in buoyancy of the glass of the weighing-tube in the two weighings . This correction could , of course , be calculated , provided one knew the weight of the tube , the density of the quartz of the silica counterpoise on the end of the beam opposite to the objects to be weighed , and the density of the sample of glass forming the weighing-tube . It was found , however , to be more accurate and convenient to determine directly on the balance the magnitude of this correction for each experiment . For this purpose the counterpoise bulb containing air was replaced by a piece of quartz of almost exactly the same weight , and under the new conditions the variation of the zero point of the balance for a given change of pressure was determined . Knowing the weight corresponding to each scale-division displacement of the zero point , the variation in buoyancy of the open glass tube between the two weighings was easily and accurately calculated . In general , this correction is a somewhat large one , and amounts in this case to no less than one-seventh of the total weight of the gas . The reason for this is the large difference in weight between the density-tube and the contained gas . The density tube , as a rule , weighed about 30 mgrm . , and the contained gas about 1/ 2000 mgrm . ; hence the weight of the gas is to that of the vessel as 1 to 60,000 , whereas , under ordinary conditions , when weighing 200 c.c. of gas , the ratio is about 1 to 600 . In this experiment , the correction for the buoyancy of the glass proved to be 91 / / , mgrm . ; but there is still a correction to be applied , for there is a change of buoyancy due to the volume occupied by the gas itself . As the volume of the tube was known , this could be calculated with greater accuracy than it could be determined by experiment . In this case , the xenon occupied 0*536 cu . mm. , and the difference in buoyancy of the air between the pressures 70 and 52*9 mm. ( 17*1 mm. ) is 17*1 x 0*536 x 1*29/ 760 x 1000 == 15 / /mgrm . Had the sealed tube been weighed at the lower instead of the higher pressure ( at 52*9 instead of 70 mm. ) , it would have weighed more ; hence this correction is positive . The true weight of the xenon is therefore 654 \#151 ; 91 + 15 = 578 / /mgrm . The calculated weight of 0*0977 cu . mm. of xenon is 577 / migrm . The exact agreement is doubtless a coincidence . 544 Dr. Gray and Sir W. Ramsay . Density of [ Dec. 13 , With niton , two sources of error made their appearance ; in the first place , the density-tube became strongly electrified , and attracted dust particles and adsorbed air , and in the second , the tube was always at a higher temperature than the surrounding atmosphere during weighing , * and convection currents were liable to be set up in the air surrounding one limb of the balance . The first of these effects could not be entirely eliminated , but it was considerably reduced as regards dust by filtering the air through a long column of tightly packed cotton-wool before allowing it to enter the balance-case . In addition , the tube , after suspension from the beam of the balance , was , as a rule , gently heated by passing a non-luminous pin-pointed gas-flame quickly over its surface , thus burning off most of the attracted particles of dust . The same expedient was also adopted , before the second weighing , after the tube had been broken . Blank experiments showed that this procedure did not alter the weight of the tube in the slightest degree , provided it was perfectly clean ; when dust-particles were present , however , there was always a small loss of weight . The effect of convection currents was reduced as much as possible by weighing at a low pressure ; in our five experiments , the final pressure varied from 87 to 13 mm. ; and the concordance of the results precludes the possibility of any serious error from this source . It may also be noted that the density-tube , after removal of the niton , and during the second weighing , contained approximately the equilibrium amount of radium A , B , and C , the heating effect of which is a large fraction of the total heating effect of the emanation in equilibrium with its quick-change products ; hence any error in the first weighing was partially compensated by a similar error in the second weighing . Finally , we would point out that convection currents , on account of the position and shape of the tube , have very little influence on the balance , and their presence should have been revealed by the oscillations of the beam and the position of the zero-point . No irregularity , however , was noticed , and we believe that this source of error produced only negligibly small effects . Before proceeding to cite the experimental results , we have still to explain how the exact volume of niton weighed was ascertained . Taking as a basis our previous measurements , which proved the equilibrium amount of niton yielded by the total amount of radium at our disposal to be 0127 cu . mm. at normal temperature and pressure , we had to determine what fraction of this amount was actually present in our weighing-tube . This was conveniently done by measurement of the 7-ray activity by help of a small aluminium electroscope . The procedure was as follows :\#151 ; * See Ramsay , ' Trans. Chem. Soc. , ' 1907 , vol. 91 , p. 931 . 1910 . ] Niton and the Disintegration Theory . 545 The emanation was drawn off from the radium-bulbs at definite intervals .of time , usually eight or nine days . After explosion of the mixed oxygen and hydrogen gases , it was allowed to stand for several hours , so that the quick-change products should accumulate , and its 7-ray activity was measured in the usual way . It was next introduced into the density-tube , and frozen there , as described for xenon , and the hydrogen was removed by pumping ; about 10 per cent , of the niton was pumped off with the hydrogen , for the niton has some vapour-pressure at \#151 ; 195 ' . The 7-ray activity of the gas removed was compared with that in the sealed-off density-tube , after a suitable interval of time . Other measurements were made to determine the quantity remaining in the purifying apparatus ; but in most cases this was negligible , and , as a rule , the radioactivity of the pumped-off gas , plus .the radioactivity of the gas in the weighing-tube , were together equal , after corrections for the decay had been made , to the initial total radioactivity of the gas before it had been purified . It was found , however , that some niton had entered the walls of the weighing-tube ; this fraction was estimated by determining the radioactivity of the empty tube , immediately after it had been weighed . Obviously , this emanation had not been removed by the pump . In the table which follows , this amount appears in the column " volume left in tube " ; it has been subtracted from the total volume . The operations of drawing and purifying the emanation , measuring its radioactivity , counterpoising and weighing the density-bulb , and measuring the radioactivity of the amount pumped off , as well as that in the weighing tube , required a long day , so that the density-tube could not be broken until 24 hours after the niton was drawn ; the actual volume of niton present at the moment of fracture , however , was easily calculated from its known rate of decay . As the quick-change products A , B , and C are short lived and change rapidly into D , and as D is a solid , it remains in the density-bulb and is not weighed , but the helium resulting from the change of niton into A , A into B , and C into D , escapes for the most part along with the niton ; its weight must be calculated , and that of the escaping gas diminished by its amount , in order to arrive at the true weight of the niton . Five experiments were made in order to determine the total loss of weight on opening the density-tube , and a sixth to obtain an estimate of the weight of the helium produced by the disintegration of the niton as far as radium D. For this purpose a density-tube was filled as described in the middle of the month of July , 1910 ; it remained counterpoised on the balance until October , when the conversion into D was practically complete . As the half-life period of D is about 14 years , it is unnecessary to consider 546 Dr. Gray and Sir W. Ramsay . Density of [ Dec. 13 , any further change . At the end of October the point of the density-tube was broken as usual , and the tube was again weighed , the loss in weight being due to the helium produced . We must here chronicle the fact that during the three months in which the tube hung on the balance a continuous gain in weight was noticed , rapid at first , but attaining an end point ; this amounted to 670 / migrm . On heating the tube , 1280 / imgrm . were lost . The tube had not been heated before it was originally suspended on the balance ; the gain was probably due to condensation of air on the electrified surface , and possibly , but improbably , to the deposition of dust . This gain of weight on standing is , however , not confined to electrified surfaces ; a gold capsule , heated to redness before suspension , gained considerably in weight for two days . The density-tube was heated and re-suspended on the balance , and for three hours there was no alteration of weight . It was then broken and immediately placed on the balance , and weighed within five minutes , during which it might be expected that no change would occur ; the loss of weight was 15 jamgrm . , The volume of the density-tube was 0T96 cu . mm. ; the weight of air filling it at 37'7 mm. pressure and 18'5 ' C. was 12 / xmgrm . ; hence the total weight of helium was 27 / rmgrm . ; no correction for glass displacement of air was necessary , for the pressure did not vary during the readings . The calculated weight of helium obtainable from 0072 cu . mm. of niton , the amount present in the tube , on the assumption that each atom ( or molecule ) of niton loses three a-particles on disintegrating to RaD , should have been 38 / tmgrm . ; of this , only about three-quarters had been removed by the pump . It was necessary to seek for the remainder , which , we believed , had entered the glass of the weighing-tube . Before removing it , however , we thought it worth while to attempt to . dissolve the deposit of radium D from the walls of the weighing-tube , and to estimate its amount by loss . The closed end of the weighing-tube was cut off , and the rest of the tube placed in the bucket along with it , and weighed . The tube itself was then washed out with a mixture of two drops of nitric acid , previously purified by distillation from a silica bulb , and one of water \ the solution was preserved . The tube was then washed with water and dried by aspirating through it a current of dry air ; it was then replaced in the bucket and re-weighed . The loss was 831 yumgrm . Supposing that the emanation , the calculated weight of which , assuming it to have the atomic weight 222-4 , was 713 / nngrm . , had lost three a-particles , the weight should have been 674 / nngrm . The difference , as we have proved by a subsequent experiment on the solubility of glass in dilute nitric acid , is due to the removal of sodium and calcium as nitrates . This must have 1910 . ] Niton and the Disintegration Theory . 547 amounted in the case given to 831 \#151 ; 674 = 157 yamgrm . We identified under the microscope crystals of sodium nitrate . It is obvious that no importance can be attached to the latter half of this experiment , except in as much as it shows a loss of weight of the order required . The weighing-tube still contained presumably occluded helium . It was placed in a silica tube , surrounded by a thicker-walled tube , also of silica , and it was connected with a Topler pump and with an inverted siphon for introducing oxygen . The apparatus was freed from air and washed out several times with oxygen , so as to avoid introducing helium or neon from the air . About one-third of a cubic centimetre of oxygen was then admitted , and the silica tube was heated in a blow-pipe flame until the glass weighing-tube had completely fused ; small bubbles were evolved . The oxygen , together with the gas evolved from the tube , was pumped off and introduced into an apparatus consisting of a calibrated capillary tube in communication with a minute bulb containing charcoal cooled with liquid air . After some hours the oxygen was completely absorbed by the charcoal , and the residual gas was measured . The correction for the unmeasured gas still remaining in the charcoal bulb was found to be 4 per cent. The volume was 0*042 cu . mm. at 0 ' and 760 mm. pressure , and its weight was therefore 8 / /mgrm . The sum of the helium actually weighed ( 27 / /mgrm . ) plus that measured ( 8 / /mgrm . ) gives a total of 35 / /mgrm . , differing from the calculated amount ( 38 / /mgrm . ) by only 3 / /mgrm . That the gas measured was pure helium was proved by surrounding the upper part of the capillary tube with tin-foil , and passing a discharge from a coil through it . The full spectrum of pure helium was seen , and no other lines . This result has astonished us , as , perhaps , it may astonish our readers , , but the conditions under which the last weighing was made were particularly favourable , since the tube was practically non-radioactive . This experiment taught us that about one-quarter of the helium produced by the disintegration of the emanation and its products enters the walls of the weighing-tube , and is not removed by the pump ; we have now all the data for calculating the density of niton . The results are given in the annexed table:\#151 ; Dr. Gray and Sir W. Ramsay . Density of [ Dec. 13 , Table of Results . No. of experiment . Time of accumulation . Total volume of niton . Volume pumped off . Decay of niton . | Volume left in tube . Volume weighed . Apparent weight . Weight of air replacing niton . Correction for displacement due to glass and air . Correction for weight of helium produced from niton . True weight of niton . Micro- Micro- Micro- Micro- Micro- ; Day . Cu . mm. Cu . mm. Cu . mm. Cu . mm. Cu . mm. mgrm . mgrm . mgrm . mgrm . mgrm . 1 8 0 *0969 0 *0052 0 *0182 0 *0007 0 -0728 721 + 31 -29 + 24 - 8 739 2 2 9 0 *1017 0 *0188 0 *0163 0 *0100 0 -0566 477 + 103 -16 + 15 - 7 572 2 3 9 0 *1017 0 *0135 0 *0253 0 *0039 0 -0590 577 + 37 -22+ 9 -10 591 2 4 8 0 *0969 0 *0119 0 *0157 0 *0016 0 -0677 673 + 10 -26 + 12 - 6 663 2 5 8 0 *0969 0 *0082 0 *0152 0 *0005 0 -0730 704 + 29 -33 + 16 - 6 710 2 Mean ... 2 A complete reproduction of Experiment 5 may be given , to show how all the requisite data are obtained and utilised . Volume of niton accumulated in 8 days = equilibrium quantity x fraction surviving ... ... ... ... ... ... ... . . 0*127 x 0*763 = y-ray activity of this sample , divisions per hour ... ... ... . y-ray activity of fraction pumped off ... ... ... ... ... ... ... . . Hence amount pumped off ... ... ... ... ... ... ... ... ... ... ... ... Amount of niton in weighing-tube = 0*0969-0*0082 = ... ... ... The weighing-tube was then counterpoised on the balance . Pressure in balance-case ... ... ... ... ... ... ... ... ... ... ... . . Zero on scale of beam of light reflected from mirror ... ... . Twenty-five hours after drawing , the weighing-tube was broken . The gas pumped out , however , was not the original 0'0887 cu . mm. , but that volume multiplied by the decay-factor for 25 hours , 0*828 , viz ... ... ... ... ... ... ... ... ... ... ... ... . . Pressure in balance-case after breaking the density-tube ... Pressure-change = 54*4 \#151 ; 34*7 ... ... ... ... ... ... ... ... ... ... Zero on scale after breaking ... ... ... ... ... ... ... ... ... ... . Difference of zero =155 \#151 ; 154 = 1 mm. But from measurement , 10 mm. pressure = 77 scale divisions ; hence 1 division = 10/ 77 = ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... This must be added to the pressure\#151 ; 19*7 + 013 = ... ... ... . . The counterpoise-bulb contained 0*0270 mgrm . , or 27,000 / imgrm . of air . Its buoyancy was altered by ( 19*83/ 760 ) x 27,000 = ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... . 0*0969 cu . mm. 3996 divisions . 353 " 0*0082 cu . mm. 0*0887 " 54*4 mm. 155 " 0*07347 cu . mm. 34*7 mm. 19*7 " 154 " 0*13 " 19*83 " 703*8 fimgrm . But air entered the tube when it was broken ; the volume of the density-tube , ascertained by previous calibration , was 0*522 cu . mm. Weight of this air at 34*7 mm. and 17 ' C. = 0*522 x 1290 x 35/ 760 x 273/ 290 = ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... . . 29*2 / xmgrm . The sum of these quantities , 703*8 and 29*2 ... ... ... ... ... ... ... 733 " 1910 . ] Niton and the Disintegration Theory . 549 But the pressure was changed by 19'8 mm. ; this alters the weight of the density-bulb by the weight of air corresponding to the difference in volume between the glass density-bulb and a silica one ; as already described , this quantity was determined directly by replacing the air-bulb by a solid counterpoise of silica , and using the density-bulb as a measure of buoyancy . For 19*8 mm. the " glass displacement " is equivalent to -32*8 / xmgrm . A further correction has to be made , viz. the change of buoyancy due to , the volume occupied by the gas itself . The volume of the density-tube was 0*522 cu . mm. ; the change of pressure was 19*8 mm. ; hence the weight of this air for 19*8 mm. change = 0*522x1290x19*8/ 760x273/ 290 = 16 / xmgrm . , This is a positive correction ; the weight , 733 / migrm . , must be diminished by the difference between 32*8 and 16 , say 17 / xmgrm . The remainder is 7L6 / xmgrm . The last correction to make is the subtraction of the weight of the helium produced by the decay of the emanation during its stay in the weighing-tube . Now 22,400 cu . mm. niton weigh , say , 222*5 mgrm . , and 0*0224 " " weighs " 222*5 / xmgrm . Each atom of niton gives three atoms of helium ; hence , helium from 0*0224 cu . mm. niton weighs 12 / xmgrm . The volume of emanation decayed in the weighing-tube is 0*0887 cu . mm.\#151 ; 0*0735 cu . mm. = 0*0152 cu . mm. , and the weight of three times that volume of helium is 8 / xmgrm . One quarter of this has entered the glass and has not escaped , hence the helium removed weighed 6 / xmgrm . That number deducted from 716 leaves 710 / xmgrm . as the weight of the niton . To return for a moment to its volume . The amount of niton in the weighing-tube was 0*07347 cu . mm. at the moment of pumpiug out . But some niton had penetrated its walls , and was not removed by the pump . That amount was estimated by comparing the y-radio-activity of the weighing-tube after it had been weighed u empty " with that of the gas pumped off , which had , of course , diminished in radioactivity ; this diminution corresponded with the time which elapsed since the last reading , and was measured to verify the constancy of the electroscope . The radioactivity of the residue left in the weighing-tube was , after correction for natural leak , 17 divisions per hour . The original radioactivity of the niton in the weighing-tube was 3996 \#151 ; 353 = 3643 divisions per hour ; its volume in the weighing-tube when decay commenced was 0*0887 cu . mm. ; hence the " volume55 left in the tube by the retention of niton in the walls was ( 17 x 0*0887)/ 3643 = 0*0005 cu . mm. This , subtracted from 0*07347 cu . mm. , the volume of niton in the tube at the moment of pumping out , leaves 0*0730 cu . mm. as the volume actually weighed . All the data are now complete ; 0*0730 cu . mm. of niton at 0 ' and 760 mm. pressure weighed 710 / migrm . A litre weighs 9*727 grm. ; a litre of oxygen weighs l*429grm . ; and the molecular weight of niton is therefore 218 . The nomenclature of Rutherford and Soddy , which has attained the provisional assent of the Brussels Congress , is advantageous as showing the relationship between the degradation-products of the various radioactive elements , but obscures any chemical relationship between the elements themselves . Were it consistently carried out , radium , which undoubtedly belongs to the group of alkaline-earth metals , would have to be named after uranium , a metal with no affinities with that group . The " emanation of radium " is a cumbrous name , and gives no indication of its position in the periodic table , a position which may now be taken as certain . To vol. lxxxiv.\#151 ; a. 2 P 550 Density of Niton and the Disintegration Theory . show its relation to gases of the argon series , it should receive a similar name ; and the spectrum , the freezing-point , the boiling-point , the critical point , the density of the liquid , and the density of the gas , the last establishing , without doubt , the atomic weight of the element , having been determined in this laboratory , it only remains to give it a name . The name " niton , ' " N't , which has been used in this paper , is suggested as sufficiently distinctive . . The research , of which the foregoing is an account , yields a further proof , if such were necessary , of the beautiful theory of the disintegration of the radioactive elements originally advanced by Rutherford and Soddy in 1902 . The determination of the density of a gas , even with approximate exactness , has always been regarded as establishing its molecular weight , the accurate value of which may have been derived from other considerations . In the present case , these considerations are the result of the disintegration theory . Determinations by Madame Curie and by Thorpe of the atomic weight of radium show beyond all doubt that it differs little from 222*4 . That four atoms of helium separate from one atom of radium is rendered almost certain from the work of Dewar , and from experiments by Rutherford , and by Ramsay and Soddy . That three atoms of helium are lost by niton on decay has been shown in the preceding pages . It follows that one helium atom must escape when radium changes into its emanation ; hence the true atomic weight of the emanation must he 222*4 . This number hardly differs from the mean of the atomic weight determinations given in this paper ; and the disintegration theory receives a further confirmation .

rspa_1911_0007

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Obituary notices of fellows deceased.

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xxxviii

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

W. C. U.|J. L.|W. A. T.|J. H. P.|T. E. T.|G. C. F. |P. H. C.|P. H. C.

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http://dx.doi.org/10.1098/rspa.1911.0007

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10.1098/rspa.1911.0007

Biography

Measurement

Biography

OBITUARY NOTICES FELLOWS DECEASED . VOL. LXXXIV.\#151 ; A. b CONTENTS . Page Sir Benjamin Baker ... ... ... ... ... ... ... ... ... ... ... ... . i Edward John Bouth ... ... ... ... ... ... ... ... ... ... ... . . xii Dmitri Ivanovitch Mendel^eff ... ... ... ... ... ... ... . . xvii George Gore ... ... ... ... ... ... ... ... ... ... ... ... ... . . xxi Julius Thomsen ... ... ... ... ... ... ... ... ... ... ... . . xxiii William James Bussell ... ... ... ... ... ... ... ... ... ... . . xxx Simon Newcomb xxxii SIR BENJAMIN BAKER , K.C.M.G. , K.C.B. , 1840\#151 ; 1907 . Sir Benjamin Baker was born on March 31 , 1840 , at Keyford , Erome , Somerset , and he died at Bowden Green , Pangbourne , Berkshire , on May 19 . 1907 . In a career , during the greater part of which he was associated with Sir John Fowler , K.C.M.G. , he achieved the position of an engineer of the highest originality and distinction and was engaged in the design and construction of , or as responsible adviser for , a very great amount of civil engineering work of the most varied character . His connection with the Forth Bridge and the Assuan Dam alone are sufficient to mark him out as an engineer of the highest rank . His parents were Benjamin Baker and Sarah Baker ( nSe Hollis ) . His father appears to have come from Carlow , in Ireland , and was principal assistant at iron works at Tondu , Glamorgan . Sir Benjamin Baker was educated at the Cheltenham Grammar School . At the age of 16 he was articled to Mr. H. H. Price , of the Neath Abbey Iron Works , where some of Trevithick 's pumping engines and some early locomotives and marine engines had been built . In 1860 , he became assistant to Mr. W. Wilson , then in association with Mr. ( afterwards Sir John ) Fowler engaged in the erection of the Pimlico Railway and the Victoria Bridge and station . In 1861 , he passed into the office of Mr. Fowler , where he was engaged in designing roofs , girders , and retaining walls for the Metropolitan Railway , the construction of which was then about to be commenced . He assisted in the preparation of the plans for the extension of the Metropolitan Railway and , in 1870 , became Chief Assistant and junior partner to Mr. Fowler , having general charge of the construction of the Metropolitan and District Railways . His association with Sir John Fowler continued till the death of the latter in 1898 . As soon as he was engaged in Mr. Fowler 's office , Baker set himself with zeal to the investigation of the mechanical problems suggested by the work on which he was engaged and the result of his studies appeared in contributions to ' Engineering , ' in a series of papers on " Long Span Bridges , " 1867 , republished in England and America and translated and printed in Germany , Austria and Holland ; " On the Strength of Beams and Columns , " in 1868 , also republished in 1870 ; " On the Strength of Brickwork , " in 1872 ; and " On Urban Railways , " in 1874 . In the articles on long span bridges , after examining the conditions for securing tire greatest economy of material in the various types of girder then in use , for spans from 300 feet up to the limiting span possible , he arrived at the conclusion that , by a system of cantilevers , supporting an independent girder , an opening might be bridged which could not be spanned by any of the systems previously examined , even With an infinite amount of material . The ii Obituary Notices of Fellows deceased . reasoning is throughout extremely original and instructive , and the conclusion reached was afterwards verified in the construction of the Forth Bridge . The thoroughness of the investigation was shown in the further examination of braced arch , stiffened suspension and suspended girder bridges , types as to which little experience had then been obtained . The advantage of some of these newer types in permitting erection without scaffolding is pointed out . In 1865 , a project for a bridge over the Severn , with a span of 600 feet , was prepared in Mr. Fowler 's office , in which it was proposed to erect successive bays by building out from each side of the main piers , carrying on the process till the two opposing halves met and formed a continuous structure . This was the system subsequently adopted at the Forth Bridge and in many bridges since . In a revision of this treatise in 1873 , a section was added on short span bridges . Baker drew attention to the fact that in short spans the action of the rolling load is the point above all others requiring attention . His experience had forced on him the conviction that the destructive action of a frequently recurring load , not small compared with the dead load , was at that time habitually underrated . This was one of the earliest recognitions in this country by a practical engineer of the law of fatigue which Wohler had discovered . It may also be mentioned in this connection that Baker , in 1887 , contributed to the ' Transactions of the American Society of Mechanical Engineers ' " Some Notes on the Working Stress of Iron and Steel . " He pointed out that while in some bridges in which the ratio of dead to live load was large , stresses of 17,000 to 20,000 lbs. per sq . inch had proved to be safe , yet in small spans such stresses would quickly lead to destruction . Hence in the elevated railway of New York the stresses were limited to 8000 lbs.-per sq . inch in the flanges and to 4500 in members subject to reversals of stress . He gave the results of a series of experiments similar to those of Wohler on soft and hard steel and iron . These showed that the opinion of some engineers , that alternating stresses are destructive only if they exceed the elastic limit , is erroneous . He indicated that the resistance of riveted joints to slipping is due to frictional adherence and stated that in the Forth Bridge the stress on riveted joints was kept within the limit of adherence . He expressed further the opinion that both the old-fashioned Government regulations requiring a fixed working stress for all kinds of loading and modern formulae based on Wohler 's results failed to meet the requirements of engineers . In a further series of articles in ' Engineering , ' in 1868 , " On the Strength of Beams , Columns , and Arches , " republished in 1870 , Baker discussed a problem which troubled many engineers at that time , namely , that the ultimate strength of beams is widely different from the strength calculated on the assumption that the material is elastic up to rupture . He adopted as an explanation Barlow 's theory , which would not now be accepted , the discrepancy being known to be due to plasticity . But Baker used a mass of practical data and derived his coefficients so that his results were approxi- Sir Benjamin iii mately true and useful . He applied his investigation to the then important question of the relative strength and stiffness of different sections of rails . Like all Baker 's papers , these articles contained many experimental observations carefully and accurately made . The first great work on which Baker was engaged in a position of responsibility was the construction of the London Underground Bailways , and his connection with this work continued till the completion , in 1871 , of the sections from Moorgate Street to the Mansion House , a length of 13 miles . He described the works , which were of a specially novel , difficult , and expensive character , in a paper in the ' Proc. Inst. Civil Engineers , ' vol. 81 , 1884\#151 ; 85 , and discussed generally the problem of Urban Bailways in some important papers in ' Engineering ' in 1874 . He pointed out in these articles that at the time of the inception of the system of underground urban railways , none of the engineers concerned , either as promoters or opponents , evinced the dimmest intuition of the fact that the traffic over an urban line might be the heaviest in the world , and of a character to test the capabilities of a locomotive engine to the uttermost . It was even proposed at first to work the trains with locomotives carrying a charge of hot water , and an engine of this type was built , with unsatisfactory results . It was this intention which led to an insufficient provision for ventilation , which afterwards gave much trouble . In portions of the line constructed later , the stations were in open cutting , and a length of open cutting was introduced between the stations . Baker pointed out the great expenditure of power in acceleration required with stations half a mile apart and suggested that an ideal urban railway should undulate , the stations being placed at the summit of the undulations . By this means gravity would assist the engine in starting and supplement the brakes in stopping . He was able to carry out this arrangement subsequently in the construction of the Central London Tube Bailway . He indicated the necessity for great tractive force to ensure a reasonable mean speed and the need of powerful brakes , because the time occupied in accelerating and reducing speed is a large fraction of the whole time of transit when the stations are not far apart . He showed that the laws governing urban traffic were widely different from those obtaining on ordinary railways , and that with weak engines and inefficient brakes the horse-power would vary as the cube of the speed . He calculated that with a level line and moderate speed about 60 per cent , of the energy of the engine is expended in the mischievous wnrk of grinding the brake blocks , and that of 36 lbs. of fuel used per train mile only 15 lbs. would be usefully employed . He checked his calculations by observations on the Metropolitan Bailway , where , with the powerful engines used , the mean speed was only 12 miles an hour . He showed that with an undulating railway with the stations at the summits , 50 per cent , more speed could be obtained with the same fuel consumption as on the existing railway . The building of shallow underground railways through the heart of a great city involved a host of new and unexpected problems in construction and iv Obituary Notices of Fellows deceased . difficulties in dealing with the pipes , sewers , and other obstructions below the street surface , and in supporting , with as little damage as possible , the heavy buildings above the railway . Baker was largely concerned in the introduction of electrically worked tube railways in London . He was Consulting Engineer to the South London , the first tube railway , and the still more important Central London Bailway was constructed under his superintendence . This railway , of 6^ miles in length , consists of two tunnels of circular section , built with a casing of cast-iron segments , 11 feet 6 inches in diameter . At the stations the cylinders are 21 feet 6 inches in diameter . The railway is generally about 60 feet below the street level , and few difficulties or obstructions were met with . In this railway the stations are at the summit of undulations , the gradients falling each way so that the arrangement suggested in the early papers on urban railways was for the first time carried out . The railway was commenced in 1896 and opened by the late King , then Prince of Wales , in 1900 . From the year 1869 , Mr. Fowler was much engaged in Egypt in advising the Khedive Ismail Pasha in regard to various engineering projects for developing the resources of the country , and Baker made more than one visit to Egypt to assist his partner , and later became Consulting Engineer to the Egyptian Government . One result of studies then undertaken was the project for the Soudan Bailway between Wady Haifa and Shendy near Khartoum and a ship incline at Assuan . By means of a railway 3 kiloms . in length , over which boats , floated in a cradle , could be dragged by hydraulic machinery of 400 h.p. , the obstacle to navigation at the first cataract was to be overcome , and continuous navigation without change of boat established between Wady Haifa and Lower Egypt . From Wady Haifa a railway of 550 miles length and of 3 feet 6 inches gauge was to be constructed at a cost of \#163 ; 4,000,000 , to tap the rich southern provinces ; about 60 miles were constructed and then the financial difficulties of Egypt compelled the interruption of the work . Another great project in Egypt in which Fowler and Baker were concerned , in 1875 , was a Ship and Irrigation Canal ( an alternative Suez Canal ) via Cairo and Alexandria . The project embraced a sweet water ship canal , 118 miles in length , from Alexandria to Cairo , and another from Cairo to Suez , a distance of 122 miles . At Cairo , low water is 39 feet above sea level , so that there would be a current down the canals to the Mediterranean and Bed Sea . The rate of the current would be manageable and would depend on the amount of water abstracted for irrigation . Locks were to be provided on both stretches of the canal . For crossing the Kile at Cairo a railway bridge was to be provided , connecting the lines on the two sides of the river , and serving to support a traversing mooring to which ships could be attached when crossing the river . It was estimated that the payments for irrigation water would give a handsome return on the expenditure , independent of .ship dues . In 1883 , when the question of doubling the Suez Canal was mooted , Baker and Fowler , in an article in the 'nineteenth Century Magazine/ recalled attention Sir Benjamin Baker . v to the advantages of this project , not only as providing an alternative ship canal , but as a means of affording high level irrigation and reclaiming a large area of desert . Sir B. Baker was , at various times , consulted about the repairs and additions to the Delta Barrage , erected originally by French engineers , which had proved incapable of sustaining the required head of water in consequence of the unsatisfactory foundation . After various partial repairs by Sir Colin Scott Moncrieff , Sir W. Willcocks , and Colonel J. H. Western , it has finally been rendered completely stable and satisfactory by Major Sir Hanbury Brown . A result of Baker 's visits to Egypt was a paper on the hydrology of the Nile , * dealing with the slope , variation of level and flow , and amount of solids carried , largely based on his own observations . In 1875 , Garibaldi , then at the zenith of his popularity , was urging the Italian Government to undertake the diversion of the Tiber , in order to prevent the flooding of Rome and the Campagna . The Government considered the cost of the project prohibitive , but it had to be treated seriously . Baker and Fowler were called into counsel . Some surveys were made , and finally more moderate plans of rectification and embankment were adopted . In 1878 , Baker designed a vessel to bring Cleopatra 's Needle to this country . Messrs. John and Waynman Dixon first suggested the removal of the obelisk , Mr. Fowler and Lord Vivian obtained the Khedive 's consent , and Mr. Erasmus Wilson offered a contribution of \#163 ; 10,000 for the purpose . While in the case of the Luxor Obelisk , at Paris , the removal occupied seven years , Cleopatra 's Needle was erected on the Embankment 18 months after the order to build the vessel was given . Baker designed a vessel of circular section , in which the needle was rolled into the water and towed to Alexandria . There final arrangements were made , and thence the vessel was towed to England . Unfortunately , in a storm , some rails used as ballast broke loose , and the crew in a panic abandoned the vessel . This accident was due to an oversight , but the vessel was never in real danger . She was found , towed to Ferrol , and then to England . The Needle was fitted with trunnions , lifted in a horizontal position , and then swung to a vertical position , the operation being carried out with the greatest ease . Following some earlier abortive proposals , the Forth Bridge Company was formed in 1873 , to erect a suspension bridge with spans of 1600 feet , designed by Sir T. Bouch . But the failure of the first Tay Bridge , also designed by Sir T. Bouch , led to reconsideration of the plans , the suspension principle was abandoned , and a design for a steel cantilever and central girder bridge , with spans of 1710 feet , submitted by Messrs. Fowler and Baker , was adopted . The construction of this great bridge involved the co-operation of many distinguished engineers and contractors , and its successful completion is an achievement in the honour of which they all share . But , no doubt , the * ' Proc. Inst. Civil Engineers , ' vol. 60 , 1879\#151 ; 80 . vi Obituary Notices of Fellows deceased . general design is due to Baker , who carried out for the first time the previsions of his early treatise on long span bridges . Sir John Fowler and Sir B. Baker also kept a personal and continuous control over the entire operation of building the bridge . The contract was let in December , 1882 , and the opening ceremony took place , under the auspices of the Prince of Wales , on March 4 , 1890 . This is not the place to enter upon a description of this immense work . Baker gave an account of the bridge in a paper at the British Association in 1882 , and at the meeting at Montreal in 1884 ; also in his Presidential Address at the Mechanical Section of the British Association in 1885 , and in papers at the Iron and Steel Institute in 1885 , and at the Boyal Institution in 1887 . Eeference may also be made to the admirable record on the Forth Bridge reprinted from ' Engineering ' in 1890 , and to " Die Forth Briicke , " von G. Barkhausen , 1889 . An exceedingly important and troublesome question in designing the Forth Bridge was the provision to be made for wind pressure . The failure of the first Tay Bridge was due , at any rate to a great extent , to the lateral pressure of the wind , and subsequently , perhaps , excessive values had been assumed for the intensity of wind pressure . In the case of the Forth Bridge , the immense area exposed made the question of wind pressure a governing consideration in design . The maximum wind pressure in accordance with the Board of Trade rule was assumed as 56 lb. per square foot , acting on twice the vertical projection of one side of the bridge . But to remove doubts as to the adequacy of this provision , experiments were made . A wind gauge of 300 square feet area was erected on the island of Inchgarvie , with small comparison gauges . Some account of these experiments was given in the Montreal paper on the Forth Bridge , and in the ' Proc. Inst. Civil Engineers , ' vol. 69 , p. 145 , and vol. 156 , p. 119 . They satisfied Baker that the assumed pressure was in excess of anything likely to be realised . Further experiments were made on the shielding effect of one surface on another surface behind it . A suspended cross bar carried an adjustable flat surface at one end and a model of any structure of more complex form at the other . By oscillating this simple apparatus and adjusting the plane surface , the plane area equivalent in resistance to the more complex model was found . The results were very interesting and valuable . Baker had had great experience in the use of steel , and had made very many experiments on its behaviour under straiidng action . His confidence in it was great , and in designing the Forth Bridge he ventured to use , for the compression members , steel of higher tenacity than had previously been adopted in structures . He thus anticipated the tendency to use high tensile steel , which is now not uncommon in suitable cases . In 1881 , Sir Benjamin Baker contributed a paper to the ' Proceedings of the Institution of Civil Engineers , ' on the " Lateral Pressure of Earthwork . " He pointed out the deficiency of experimental investigation , and criticised adversely the theories of earth pressure on which engineers chiefly relied . The paper contains a mass of instructive observations on the pressure of Sir Benjamin Baker . un earth and the failures of retaining walls . The paper gave rise to a very interesting discussion , and to a communication from the veteran mathematician , Boussinesq . A very characteristic statement from Baker 's reply to the discussion may be quoted:\#151 ; " He protested against the charge implied against him of a contempt for theory . His habit of thought and mode of working were entirely opposed to such a feeling , and indeed , in his opinion , an engineer who did not attempt to classify his practical data , with the ultimate aim of elucidating a satisfactory theory , was wilfully playing the part of a blind man . " Another important practical paper , based on a very large experience , was one on " Railway Springs."* Egypt is a country nearly rainless , and dependent on the Nile for its water supply . Hence , irrigation from the river has been practised from a great antiquity . But the water supply is insufficient in the summer months for perennial irrigation in middle and lower Egypt , and the level of the river is too low to adequately feed the canals . The satisfactory repair of the Delta Barrage made the question of increasing the flow at low Nile a very urgent one . In 1889 , Colonel J. W. Western , R.E. , began an investigation of projects for storing water in the winter months to increase the river flow in summer . On his retirement , Sir W. Willcocks , who was appointed Director of Reservoirs , continued the study and prepared three schemes , one for a reservoir in the Wady Rayyan , two for reservoirs in the Nile Valley , near the Eirst Cataract . Generally , the scheme for a reservoir near Assuan was favoured , the reservoir being formed by constructing a masonry dam across the river . It was shown that if such a scheme were carried out , not only could the supply of the existing irrigation canals be ensured at all times , but a large increased area of land could be brought into profitable cultivation . In flood , * , the River Nile carries so much silt that water then impounded would gradually but certainly fill up a reservoir with deposit . It was necessary , therefore , that a dam should be so constructed as to allow the silt-bearing flood water to pass through , and to impound water only when the river flowred clear . Sir W. Garstin , Secretary to the Public Works Department , generally endorsed the views of Sir W. Willcocks . At his suggestion , an International Commission of distinguished engineers was then appointed by Lord Cromer to report on the plans , consisting of Sir B. Baker ( England ) , Mr. Giacomo Torricelli ( Italy ) , and M. Auguste Boule ( France ) . The two former reported adversely to the other plans , but favourably to the scheme of a reservoir at Assuan , suggested some modifications of the designs of Mr. Willcocks , and selected a site for the dam . M. Boule reported separately , dissenting from the views of his colleagues , not on the ground of any doubt as to the practicability of the scheme proposed from an engineering point of view , but from an objection to any interference with the temples at Phike , which , on the scheme recommended , would be partially submerged . As to the absolute need of a reservoir , no doubt was expressed * ' Proc. T nst . Civil Engineers , ' vol. 66 . viii Obituary Notices of Fellows deceased . by any member of the Commission . It was estimated that its construction would increase the revenue of the State by \#163 ; 750,000 annually , and would result in benefit to cultivators of ten times that amount . Baker suggested that , as a last alternative , the temples at Philse could , if necessary , be raised 40 feet at an expenditure of \#163 ; 200,000 . In the plans of Sir W. Willcocks , the height of the dam was to be 85 feet , and the reservoir capacity 88,300 million cubic feet . To meet objection to the submersion of Philee , the height of the dam was reduced to 65 feet , and the reservoir capacity to 37,612 million cubic feet . In 1898 , Sir Ernest Cassel entered into financial arrangements with the Government , taking bonds repayable in 30 years , and engaging to supply the funds necessary during the progress of the undertaking . A contract was signed with Messrs. John Aird and Company , and Sir B. Baker was appointed Consulting Engineer . The dam consists of two parts , one 4600 feet in length , pierced by 180 sluices at four levels , the other 1800 feet long and solid . A lock and canal makes the passage of the cataract easy to steamers at all times , thus making the Nile continuously navigable up to the Second Cataract at Wady Haifa . The work was carried out successfully , and completed in 1902 , in less than the contract time . The Assuan Reservoir extends to Ibrim , a distance of 140 miles from the dam . On the plan carried out , the water-level , with reservoir full , rose to the floor of the Philse temples , then situated on an island in the reservoir . It was found that parts of the foundations of these temples were on silt and in a bad state , and likely to be further damaged by the action of the water . Underpinning with steel girders surrounded with cement on an extensive scale was carried out with considerable difficulty and at great cost , and the stability of the masonry of the temples was secured . A subsidiary work was simultaneously executed at Asyut , 339 miles below Assuan and 246 miles above Cairo . From this point a large area is irrigated by the Ibrahimia Canal , which was with difficulty supplied during the summer months . By the construction of a dam across the Nile a permanent supply could be ensured , and with the larger flow in the river due to the Assuan Reservoir , a considerably increased area in Middle Egypt could be placed under perennial irrigation . The original plans were prepared by Sir W. Willcocks , Sir B. Baker was appointed Consulting Engineer , and the work was carried out by Messrs. Aird . The river is 2953 feet in width , and the dam is an arched viaduct , founded on a masonry floor , with sluices in the openings . The urgent importance of an early completion of the work being realised by Sir B. Baker , he advised that the contract should be cancelled , the work pushed on regardless of cost , and the question of profit to the contractors left to himself . Lord Cromer and the contractors agreed to these terms , the work was finished a year under the contract time , and the Public Works Department admitted that \#163 ; 600,000 had been saved to the country owing to the extra year 's supply of water . Sir Benjamin Baker . IX In 1902 , Sir Benjamin Baker gave a lecture on the Nile dams at the Royal Institution , at which the Prince and Princess of Wales were present . He contributed an article on the " Nile Reservoirs and Philse " to the ' Nineteenth Century ' magazine in 1894 . ( Reference may also be made to papers by Mr. Maurice Fitzmaurice , C.M.G. , " On the Nile Reservoir , Assuan , " ' Proc. Inst. Civil Engineers , ' vol. 152 , p. 71 ; by Mr. F. W. S. Stokes , " On the Sluices and Lock Gates of the Nile Reservoir , Assuan " ; and by G. H. Stephens , C.M.G. , " On the Barrage at Asyut , " ' Proc. Inst. Civil Engineers , ' vol. 158 , p. 26 . ) The success of an immense work of this kind must depend on the energy , the ability , and the resourcefulness of a great number of persons , and , in speaking of it at the Institution of Civil Engineers , Sir B. Baker gave unstinted praise to his colleagues in Egypt who carried out the operations in a trying climate . But undoubtedly the reliance placed by Lord Cromer and those in authority on Sir Benjamin Baker 's experience and judgment was an important factor in undertaking the work ; he spent time every winter on the works ; he provided beforehand , by careful foresight and consideration , for difficulties which might arise , and his wise direction , resourcefulness , and courage were essential elements in the success achieved . The construction of the Assuan Reservoir proved of immediate and enormous advantage to the prosperity of Egypt , and it very soon became evident that a still larger supply of irrigation water was necessary . By 1905 , the whole of the water stored at Assuan was appropriated , though a vast area of land was still left without water , and the increase in the value and productivity of the irrigated land exceeded expectations . A site for a second reservoir above Assuan was sought , but no suitable position could be found . Finally , it was decided to raise the dam at Assuan 7 metres , or about to the height at first contemplated by Sir W. Willcocks . It is a matter of regret that this will involve the partial submergence of the Philae temples during part of the year . But it can at least be said that this was not decided on till every alternative had been examined and unavoidably rejected . The addition of new to old masonry in a work which has to resist water pressure , and in a country where the temperature changes are great , is a matter of considerable difficulty . Sir Benjamin Baker considered long and anxiously the method of proceeding , and under his direction some very interesting experiments were carried out on model dams to elucidate the distribution of stress . Ultimately he developed a plan for strengthening and raising the dam by constructing an independent mass of masonry free to settle and contract , after which it will be bonded to the older mass by cement grouting . Shortly before his death he went to Egypt , and there the plans were decided on and the contract settled . Before long , the dam will be increased in height so that the storage capacity of the reservoir will be increased two and a-half times . It is not needful in this notice to enumerate Sir Benjamin Baker 's X Obituary Notices of deceased . professional works , but amongst the more important the following may he mentioned : He was , with Sir John Fowler , Chief Engineer for the remarkable Chignecto Ship Bailway , which was commenced , but the works were stopped by the failure of the contractor , and finally abandoned by the Canadian Government . Jointly with Sir John Wolf Barry , he was Consulting Engineer for the Avonmouth Docks ; Engineer for the electrically-operated bascule bridges over the Swale on the South Eastern Bailway and at Walney at Barrow-in-Furness ; Consulting Engineer to the Public Works Department of Cape Colony , and responsible for the bridges erected there ; Consulting Engineer , jointly with Mr. Shelford , for the West African Bailways . He was called into , council when the boring of the Hudson Biver Tunnel at Hew York seemed likely to be a failure , and designed a special form of shield by means of which the work was carried on . Jointly with Dr. Deacon he reported on the schemes for the supply of water to London from Wales . Sir Benjamin Baker was a member of the Light Bailways Commission of the Board of Trade ; and of a Committee which reported to the Board of Trade in 1900 , on the loss of strength in steel rails due to prolonged use , a Committee appointed after the serious accident at St. Neots due to a fractured rail . He was a member of the Standards Committee , instituted at the suggestion of the Institution of Civil Engineers , a Committee which is engaged on the large and important work of establishing standard forms , tests and specifications for all the materials used by engineers and standard types for locomotives and electrical machinery . In 1888 , he was appointed a member of the Ordnance Committee at Woolwich and was senior civil member at the time of his death . This Committee , consisting of military , naval , and civil members , decides on all questions as to design , material , fete . , of the war material manufactured in the Arsenal and small arms factories of the Government , and to his duties on it Baker gave unremitting attention . He was member of a Committee appointed to consider the interference with the work of Greenwich Observatory due to the London County Council generating station on the bank of the river immediately below the Observatory . He was a member of the Executive Committee of the National Physical Observatory . Sir B. Baker was often called in to advise as to the safety of structures which , erected at an earlier period , exhibited signs of decay , and to suggest means of reparation . Thus he reported on the condition of three of Telford 's principal bridges , the Buildwas cast-iron arch bridge , the Over masonry arch bridge over the Severn near Gloucester , and the Menai suspension bridge . He succeeded in restraining the local authorities from pulling down two of these or doing anything which would affect their appearance . In the case of the Menai Bridge , he reported that the main chains were sound and that though the suspending rods had suffered from corrosion they would last till the present timber floor required renewal . When this became necessary he recommended the substitution of a steel floor and the repair of the suspending rods . He reported to the Dean and Chapter on the stability of St. Paul s Sir Benjamin Baker . xi Cathedral . When part of the roof of Charing Cross Station fell , he made an immediate examination at some risk and on his advice the whole roof was reconstructed and the similar roof at Cannon Street Station strengthened . Sir Benjamin Baker was the recipient of many distinctions and took an active part in many scientific societies . At the opening of the Forth Bridge he received the decoration of K.C.M.G. , and for services at Assuan the K.C.B. and the order of Medjidieli of the First Class . He received the honorary degree of I).Sc . at Cambridge , that of LL. I ) . at Edinburgh , and that of M.Eng . at Dublin . The French Academy of Sciences awarded to him and to Sir John Fowler the Poncelet prize . He became Fellow of the Boyal Society in 1890 , member of its Council in 1892\#151 ; 3 , and was one of its Vice-Presidents from 1906 till his death . At the Institution of Civil Engineers he became an associate in 1867 , member in 1877 , member of Council in 1882 , and was President in 1895 . He became member of the Institution of Mechanical Engineers in 1890 , of its Council in 1899 . He was on the Council of the Society of Arts from 1888 and took an active part in its affairs , also member of the Iron and Steel Institute , and hon . A.R.I.B.A. and A.I.N.A. He was made an honorary member of the American Society of Civil Engineers in 1897 , of the American Society of Mechanical Engineers in 1886 , and of the Canadian Society of Civil Engineers in 1888 . Sir Benjamin Baker was always very modest in speaking of his own part in undertakings for which he was responsible , and very generous in acknowledgment of the help he received from colleagues . He was always very ready to discuss with others the difficulties which arose from time to time , and he treated opinions put before him with much consideration , though always forming an independent judgment . He was actively generous in helping younger engineers , and for those who served him he long retained his goodwill , and often continued to correspond with them for years . He attended very closely to the business of numerous councils of which he was a member , and his judgment on the matters which arose was rapid , tolerant , and sagacious , and always carried great weight . w. c. u. Xll Obituary Notices of Fellows deceased . EDWARD JOHN ROUTH , * 1831\#151 ; 1907 . By the death of Dr. Routh on June 7 , after a period of gradually failing health , a commanding figure in the recent history of English mathematics has been removed . Born at Quebec in 1831 , the son of a distinguished British officer , he was educated in London at University College School , and subsequently studied mathematics under de Morgan at University College . He matriculated at Peterhouse in 1850 , but did not drop his London connection , obtaining the gold medal in mathematics with the degree of Master of Arts in 1853 , then a somewhat rare distinction . At Peterhouse he had Clerk Maxwell , who soon after migrated to Trinity , as his rival in the same year ; while Tait and Steel were undergraduates of the College , and Lord Kelvin ( already Prof. W. Thomson , of Glasgow ) was a junior Fellow . Not long after taking his degree\#151 ; in January , 1854 , being Senior Wrangler , and bracketed with Clerk Maxwell for the Smith 's prizes\#151 ; he began the career of tuition of advanced honour men in mathematics , which was soon to lead to a unique reputation as a successful teacher . From 1858 to 1888 he had , in all , between 600 and 650 pupils , of whom the great majority graduated as Wranglers , twenty-seven being Seniors , while forty-one were Smith 's prizemen ; between 1861 and 1885 , when he retired from this strenuous work at the age of 54 , he had all the Senior Wranglers as pupils , with but one exception near the end of the time.f The number of his pupils , which was for many years about 100 , was not at all unprecedented : what was unique was the fact that for all this time he directed , almost without challenge , most of the intellectual activity of the dite of the undergraduate mathematical side of the University . This herculean task naturally demanded methodical arrangements , and the husbanding of his resources to the utmost . What he aimed at was to impart thorough mastery of the main principles of ascertained knowledge over the field of mathematics then cultivated at Cambridge ; it was clearly out of the question to stray very far into the regions of nascent science , in which ordered theory gradually evolves itself in response to concentrated and specialised effort . He was in the habit of claiming that this would follow spontaneously in the case of the mathematician born , once he had learnt mastery of the resources of the science , while even when it did not follow , the record in the legal and other professions of persons who had done well in youth in mathematical studies proved their supreme value as a deductive mental discipline . His plan was to take small classes , each of about ten men selected to run together , and to maintain an average by catechetical methods . Those * Reprinted from ' Nature , ' June 27 , 1907 . t These and other facts have been taken from a valuable notice in the ' Cambridge Review , ' signed W. W. R. B. Edward John xm who could go faster than the average had extra material provided in the form of manuscript digests for study , and especially in the institution of a weekly paper of about a dozen problems , selected from recent examination papers , or abstracted from memoirs in the home and foreign mathematical journals . An element of competition formed a stimulus in answering these papers , while written solutions were afterwards at hand for study in cases of failure to unravel them . Looking back on those times , it might be thought that there was too much problem and too little sustained theory ; but no one ever accused the standard of the problems selected of being lower than it ought to be , while , on the other hand , absence of some such rigid procedure would have rendered quite impossible that focussing of undergraduate mathematical activity and ambition in one place , which was a main feature of the system . Men with further ambitions would struggle with Thomson and Tait 's " Natural Philosophy " or with Maxwell 's " Electricity , " or with brilliant and stimulating courses of lectures given on growing special subjects by the more eminent mathematical physicists , and thus learn that though in youth mastery may be rapid , yet at all times invention must be slow . It was , moreover , thus possible for the abler men to have time to spare , to expand their outlook by taking up some other branch of knowledge as a relaxation from mathematics , or for joining in other activities of the University . Nowadays the field covered by the mathematical instruction offered at Cambridge is vastly wider than would have been conceived as practicable twenty years ago ; but the question is still unsettled how far it is expedient to extend the preliminary undergraduate course into complex special theories . Whatever may be thought as regards Dr. Kouth 's views on postponing special research in favour of thorough preparation , it could not be urged that he did not himself , notwithstanding his other absorbing work , set an example of what research might be . Many of his earlier papers , mainly in the ' Quarterly Journal of Mathematics , ' related to the dynamics of rigid solids , spinning tops , rolling globes , precession and nutation , and such like ; they were distinguished by the development of methods relating to moving systems of co-ordinate axes , and to the differentiation of vectors such as velocity and momentum with regard to them . In another connection he applied the kinematics of special systems of co-ordinate axes , moving along a curve , to problems of curvature and torsion . The advantages of these methods in differential geometry have come again into recognition , as may be seen in such works as Darboux 's " Theory des Surfaces . " Afterwards , arising out of his researches on dynamical stability , which will be referred to presently in more detail , there came a series of papers in the * Proceedings of the London Mathematical Society , ' on the propagation of waves , and the analysis of complex vibrations in networks of interlacing threads , and in other such laminar systems , leading up to a mechanical treatment or illustration of the broad general theory of harmonic analysis , principal periods , and related topics . xiv Obituary Notices of Fellows deceased . In the early 'seventies , the question of the possible explanation of steady , including apparently statical , relations of material systems by the existence of latent steady motions , such as the rotations of concealed fly-wheels or gyrostats attached to the system , was much to the fore . The fundamental problem as regards such representations is their degree of permanence ; for a state of motion which falls away , however slowly , cannot be appealed to in elucidation of secular steadiness of relations . At a later stage the ideas of the subject were crystallised by Lord Kelvin in his British Association address , Montreal , 1884 , entitled " Steps towards a Kinetic Theory of Matter , " and in later addresses on cognate topics , mainly reprinted in vol. i. ( Constitution of Matter ) of his " Popular Lectures and Addresses , " culminating in a way in 1897 in his gyrostatic model of a rotationally elastic optical aether . It is thus not surprising that the Adams prize subject at Cambridge for the period 1875-7 , announced over the signatures of Challis , Clerk Maxwell , and Stokes , should have been the search for " The Criterion of Dynamical Stability . " This subject suited Eouth 's predilections exactly ; and his classical essay , " A Treatise on the Stability of a Given State of Motion , particularly Steady Motion , " composed , as he states in the preface , almost entirely during the year 1876 , was the result . The greater part of the work in the essay is analytical , and is concerned with the discussion of the nature of the roots of the algebraic equation determining the free periods of slight vibration of the dynamical system ; but where it enters upon the discussion of dynamical principles , such as the criteria connected with the Energy and the Action , the essay moves in a high plane . In particular , , the burning question of how adequately to represent latent , and therefore unknown , steady motions , such as those of concealed fly-wheels or gyrostats attached to the system , is solved at a stroke by the famous theorem of the " modified Lagrangian function . " It was established , in fact , that the presence of concealed steady motions does not fundamentally alter the standard mode of analytical specification of dynamical interaction developed originally by Lagrange , except in the one respect that the effective Lagrangian function now involves terms linear in the velocity-components as well as quadratic terms . The procedure of Lagrange , evolved originally from the side of the Principle of Action , constituted the science of general dynamics by eliminating from the problem all variables the values of which are prescribed in terms of the remaining ones by relations of permanent constraint , thus reducing the dynamical analysis to the discussion of just as many quantities as are required to specify the state of the system . It gives cause for some surprise that nearly a century elapsed before the correlative step was taken , namely , the elimination , from the analytical specification of the system , of permanently steady or cyclic motions , as well as the permanent geometrical constraints above mentioned . In the hands of the analysts who treated the subject meanwhile , the requirements of the actual planetary and lunar theories were perhaps the main aim ; it is only recently , and largely Edward John Routh . xv in the hands of the English school , notably Lord Kelvin and Clerk Maxwell\#187 ; in later conjunction with Helmholtz , and building largely on the earlier work of W. Rowan Hamilton , that the subject of general dynamics has been welded into an instrument for the inductive , and in many cases speculative exploration of physical processes in general . Anyhow , it will be evident how fundamental an advance in the principles of the dynamical interpretation of nature was involved in Routh 's formulation of what he called the " modified Lagrangian function . " The problem thus solved by Routh with remarkable simplicity had already been some time in evidence . In the first edition of Thomson and Tait 's " Natural Philosophy " in 1868 , the equations of Lagrange had been applied in most effective manner to problems of motions of solids in fluid media , the energy function involved being determined in terms of the motions of the solids alone , and the fluid thus being ignored in the subsequent work . This procedure was soon challenged by Kirchhoff , as going beyond the existing conditions of validity of general dynamical theory ; a special justification for the case of motion in fluids was given by him , on the basis of a Least Action analysis , and a brief statement of it was included by the author in the German translation of the treatise . Soon afterwards the same difficulty was pressed on Lord Kelvin independently by J. Purser , who also published a justification on more physical lines . This was , not unlikely , the origin of Lord Kelvin 's general theory of . " ignoration of co-ordinates , " first published in 1879 in the second edition of Thomson and Tait 's treatise , but which probably existed in manuscript anterior to Routh 's essay . A report was fence current that most of it was worked out in the harbour of Cherbourg , while his yacht was refitting , and the .carpenters were all the time hammering overhead . This form of the theory , though more expressly suggested by the needs of physical dynamics , was less complete in one respect than Routh 's , in that it did not bring the matter into direct relation with a single characteristic function ( Lagrangian function of Routh , kinetic potential of Helmholtz ) , but simply obtained and illustrated the equations of motion that arose from the elimination of the cyclic co-ordinates that could be thus ignored . Later still , Helmholtz , in his studies on monocyclic and polycyclic kinetic systems , which began in 1884 , and culminated in the important memoir on the physical meaning of the Principle of Least Action in vol. c. ( 1886 ) of Crelle 's Journal , ' developed the same theory more in Routh 's manner , and built round it an extensive discussion of physical phenomena , so that on the \#166 ; Continent the whole subject is usually coupled with his name . Shortly before , the work of Routh and Kelvin had already been co-ordinated with the Principle of Action by more than one \#166 ; writer in England . The most elaborate published result of I)r . Routh 's scientific activity was the " Treatise on the Dynamics of a System of Rigid Bodies , " which began as a thorough , though rather difficult , handbook in one octavo volume , but .expanded in successive editions in a manner of which other classical instances vol. lxxxiv.\#151 ; A. c xvi Obituary Notices of Fellows deceased . readily occur to mind , until it became a sort of cyclopaedia of the dynamical section of theoretical physics . In the course of an inquiry some ten years-ago as to the reason why English mathematical physicists had so much practical command over the application of their knowledge , the mode of teaching in Cambridge came under review ; and in particular this book was discovered by Prof. F. Klein , of Gottingen , who made arrangements for its introduction to the Continental public in a German translation , containing some brief valuable annotations such as the wide analytical outlook at Gottingen suggested . Especially was emphasis given to the great extension of the scope of abstract dynamics above described , with which Routh 's name was associated , it is to be hoped permanently . Somehow the book does not seems to have attracted even yet much sustained attention in France . Until lately , Dr. Routh 's presence was a familiar and welcome one to residents in Cambridge . Though he never sought public positions , his services were in requisition in many ways , as Senator and Fellow of the University of London , as member of the University Council at Cambridge , , member of Council of the Royal Society , and in other activities ; while he declined more prominent offices more than once . In society he was bright and attractive , though somewhat retiring , simple , and entirely free from any suggestion of superiority . The respect and affection which he inspired in a long succession of distinguished pupils found expression on the occasion of his partial withdrawal from work in 1888 , when at a remarkable gathering of judges , engineers , and men of science , his portrait by Herkomer was presented to Mrs. Routh , with many expressions of warm appreciation . His leisure he employed mainly in mathematical research , and in the preparation of a series of treatises on subjects of mathematical physics , of which the only criticism to be made is that his wealth of valuable material tended to convert them into cyclopeedias rather than text-books . His last public action was to-take the lead in opposition to the proposals for change in the system of the Mathematical Tripos at Cambridge . It is possible that he did not fully realise the altered circumstances of the time , and the insistent claims of other studies ; anyhow , it will be matter for congratulation if the new arrangements work as well and as smoothly as did the older Mathematical Tripos during the long period when the practical direction was mainly in his-hands . J. L. -DMITRI IVANOVITCH MENDEL\#163 ; EFF , 1834\#151 ; 1907 . The name of Mendeleeff has long been honoured by the . Royal Society . Though not the first to recognise a relation between the properties of the elements and their atomic weights , he was unquestionably the first to apply the principles embodied in the statement of the " Periodic Law " to the settlement of atomic weights , to the prevision of previously unknown elements , and to the recognition of the true relations of different groups of elements to one another . In recognition of the importance of these generalisations and of the great knowledge and enthusiasm with which he laboured at the subject , the Royal Society awarded to him , in 1882 , the Davy Medal , jointly with Prof. Lothar Meyer , in 1892 the Fellowship of the-Society , and in 1905 the Copley Medal . Dmitri Ivanovitch was the fourteenth child of his father , Ivan Pavlovitch ' Mendeleeff , Director of the Gymnasium at Tobolsk , in Siberia . His mother , Marie Dimitrievna , belonged to the old Russian family of Kornileff , long settled as manufacturers of paper and glass in the neighbourhood of Tobolsk , the glass works being situated at the village of Aremziansk . There can be no doubt that Dmitri Ivanovitch owed much of his intellectual activity to-his mother , who was evidently a woman of considerable mental power and self-instructed beyond the range of ordinary female education of that period . This debt Mendeleeff acknowledges in the introduction to his great work off Solutions , which he dedicated to the memory of his mother in the following interesting lines : " This investigation is dedicated to the memory of a mother by her youngest offspring . She could only educate him by her own work , conducting a factory . She taught by example , corrected with love , and to devote him to science she left Siberia , spending her last resources and strength . When dying she said , ' Refrain from illusions , insist on work and ! not on words , search patiently divine and scientitic truth . ' She knew how often dialectical methods deceive , how much there is still to be learned , but how with the aid of science , without violence , with love but firmness , all superstition , untruth and error are removed , bringing in their stead the safety of discovered truth , freedom for further development , general welfare , and inward happiness . D. Mendeleeff regards as sacred a mother 's dying words . October , 1887 . " How full of energy she was is shown by the fact that at her husband 's death she continued to manage the glass works at Aremziansk . At the age of fifteen , Dmitri Ivanovitch came from his far-off birthplace to Moscow in order to continue his education . A year later he entered the chief Pedagogic Institute in St. Petersburg , where , being associated with the University , he was able to devote himself chiefly to the physical sciences . At the end of this course he was appointed teacher in the Government-school at Simferopol in the Crimea , and later at the gymnasium at Odessa . c 2 xviii Obituary Notices of Fellows deceased . In 1856 he returned to St. Petersburg , and at the early age of twenty-two he was appointed " privat-docent " at the University . At this time , like most young chemists , to judge by the titles of his published papers , he passed rapidly from one subject to another , but he soon found matter for serious thought and experiment in the physical properties of liquids , especially in their expansibility by heat . In 1859 , by permission of the Minister of Public Instruction , Mendel^eff proceeded to Heidelberg , where , in a private laboratory , he devoted himself to further study of the physical constants of chemical compounds , communicating some of his results to ' Liebig 's Annalen ' and to the French Academy . Returning to St. Petersburg in 1861 he secured his doctorate , and was appointed soon afterwards Professor of Chemistry in the Technological Institute . In 1866 he became Professor of General Chemistry in the University , Boutleroff at the same time holding the Chair of Organic Chemistry . He was frequently employed by the Government in connection with the investigation of questions of technical importance , and notably concerning the oil supplies of Baku and the Caspian ; also in the department of weights and measures . The latter service brought him on several occasions to England , where his remarkable and distinguished figure was quite familiar in scientific circles . In 1904 he celebrated his seventieth birthday , on which occasion he received congratulatory addresses from the Chemical Society of London , and from many other scientific associations and academies with which he was connected . Mendeleeff died on February 2 ( N.S. ) , 1907 , followed three days later by his colleague Menschutkin . The chief scientific work of Mendeleeff may be roughly classified under several heads . As already mentioned , some of his earliest labours related to the determination of physical constants , especially the dilatation of liquids , which resulted later in the establishment of a simple general formula for the expansion of liquids between 0 ' and their boiling points . Later , he was led to discuss that theory of solutions which regards them as consisting of definite chemical compounds of the solvent with the solute , existing in a liquid state and more or less completely dissociated . This theory he supported by his own experiments , especially on mixtures of .sulphuric acid and water and of alcohol and water . The densities of the latter have been estimated with very great accuracy , and from them he isolated two out of three assumed compounds represented by the formulae ( 1 ) C2H60 + 12H20 , ( 2 ) C2H60 -f 3H20 , and ( 3 ) 3C2H60 + H20 . In this connection it is interesting to recall the fact that Mendeleeff was a declared -opponent of the doctrine of free ions in solutions of electrolytes . A third subject to which he gave much attention was the nature and the sources of petroleum . After visiting the Caucasus , he went in 1876 to see the oil fields of Pennsylvania , and on his return communicated to the Russian Chemical Society a theory concerning the formation of hydrocarbons in the earth 's crust . Rejecting the hypothesis that these compounds resulted Dmitri Ivanovitch xix from the decomposition of organic remains , he assumed , on various grounds , that the interior of the earth must consist largely of metals , iron predominating . Such a view , in consideration of the relatively high mean density of the earth , was already familiar ; but supposing metals such as iron and manganese saturated with carbon , Mendeffieff explained the production of hydrocarbons from these compounds by contact with water at a high temperature . The resultant hydrocarbons would distil from the lower into the more superficial layers of the earth 's crust , leaving oxides of the metals behind . The subject with which especially the name of Mendeleeff is indissolubly connected is the development of the Periodic Law . The several stages in the history of the recognition of relations between atomic weights and properties of elements extend over more than half a century . So soon as a sufficient number of atomic weights had been estimated with some approach to accuracy , by Berzelius and others , the hypothesis of Prout attracted attention , and down to the time of Stas was regarded with some favour . In 1829 , Doebereiner pointed out the existence of triads of closely related elements , such as chlorine , bromine , iodine\#151 ; lithium , sodium , potassium , in which the atomic weights are so related that the middle term of each series is nearly the arithmetical mean of the two extremes . Thirty years later Dumas drew attention to the close analogy observable in such series with homologous series of carbon compounds . The first step toward the recognition of a periodic relation was taken in 1864\#151 ; 5 by John Newlands , and this was followed , soon afterwards , by a scheme of the known elements , arranged by Odling . But ISTewlands ' attempt was very imperfect , as many of the elements were incorrectly placed , and no room was left for discovery of new elements . Odling , at the end of his article , refers to the probable existence of " some hitherto unrecognised general law . " The question being left in this condition , Mendeleeff communicated to the Russian Chemical Society , in March , 1869 , a paper on " The Delations of the Properties to the Atomic Weights of the Elements . " An abstract published in the ' Zeitschrift fur Chemie ' ( vol. 5 , p. 405 ) contains several obvious misprints ; but , correcting these , the following literal translation serves to show that Mendeleeff had discovered this unrecognised law and perceived most of its important consequences:\#151 ; " When the elements are arranged in vertical columns according to increasing atomic weight , so that the horizontal lines contain analogous elements again according to increasing atomic weight , an arrangement results from which several general conclusions may be drawn . ( Here follows the table of elements . ) " 1 . The elements , arranged according to magnitude of atomic weight , show a periodic change of properties . " 2 . Chemically analogous elements have atomic weights , either in close agreement ( Pt , Ir , Os ) , or increasing by equal amounts ( K , Rb , Cs ) . XX Obituary Notices of Fellows deceased . " 3 . The arrangement according to atomic weights corresponds with the valency of the elements and , to a certain extent , to the difference in chemical behaviour , e.g. , Li , Be , B , C , N , O , F. ~ , " 4 . The elements most widely distributed in nature have small atomic weights , and all such elements are distinguished by their characteristic behaviour . They are thus typical , and the lightest element , hydrogen , is therefore rightly chosen as the typical unit of mass . " 5 . The magnitude of the atomic weight determines the properties of the element , whence , in the study of compounds , regard is to be paid not only to the number and properties of the elements and their mutual action , but to the atomic weights of the elements . Hence the compounds of S and Te , Cl and I , show , beside many analogies , striking differences . " 6 . The discovery of many new elements may be foreseen ; for example , analogues of Si and Al , with atomic weights between 65 and 75 . " 7 . Some atomic weights will presumably suffer correction ; for example , Te cannot have the atomic weight 128 , but 123 to 126 . " 8 . From the table , new analogies become apparent . Thus , U appears as an analogue of Bo and Al , which is in harmony with experience . " Many years later , Mendeleeff found a difficulty in placing the elements of the argon group and radium , these substances having been discovered long subsequently to the formulation of the " periodic " scheme . In an article written for the ' Bussian Encyclopaedia , ' and abstracted into English ( ' Nature , ' November , 1904 ) , he later acknowledges the independent existence of these elements , and places the argon group in a column by themselves . The first place in the same column is assigned to the ether , wdiich he assumed to be molecular in structure with a very small atomic weight . How some of his earlier predictions have been verified by the discovery of gallium , of scandium , and of germanium , which correspond to Mendeleeff 's theoretical elements , ekaluminium , ekaboron , and ekasilicon , is matter of common knowledge , and supplies a complete justification of the scheme . And though there are some outstanding difficulties about individual elements , the construction of this scheme and the enunciation of the periodic law as a principle applicable to the whole of the chemical elements constitute one of the most fertile conceptions in the whole range of modern chemistry , W. A. T. XXI GEORGE GORE , 1826\#151 ; 1908 . George Gore was born in 1826 at Bristol , where his father had a small business as a cooper . Leaving school at thirteen , he began work as an errand boy . At seventeen he was apprenticed to a cooper and worked at that trade till he was twenty-one , meanwhile studying science and making what experiments he could in his small leisure . He was from the first keenly interested in electro-deposition , and probably it was through his desire to pursue this subject that in 1851 he came to Birmingham , already the chief centre of electroplate manufacture , and here he spent the rest of his life . He appears to have supported himself at first by practising medical galvanism , the apparatus for which he had already improved while at Bristol . Meanwhile he held classes on electroplating and on chemistry and thus began his long career as a teacher in Birmingham . Later he was appointed Science Master at King Edward 's School , a post which he held for many years . In 1854 he published the first of a series of papers on the electro-deposition of metals and soon gained a reputation which led manufacturers in Birmingham and elsewhere to bring their difficulties to him for solution , and from this time onwards he held a leading position in the town as a consulting chemist . Perhaps his most important work consisted in the help which he gave in the early days to the art of electroplating by his numerous discoveries , many of them the basis of present day practice . He wrote several text-books on the subject , which have been widely used here and abroad . For a time he was chemist to a phosphorus works , and while in that position he discovered the method of bleaching phosphorus by chlorine , which is still in use . His best known contribution to pure science is his investigation of the properties of anhydrous hydrofluoric acid , which he succeeded in preparing chemically pure . This work occupied him for several years , from 1860 onwards , and was followed by a research on the properties of silver fluoride . Among other researches were investigations on properties of liquid carbonic acid , on ammonia as a solvent of the alkaline metals , and on the thermo-electric action of metals and liquids . An indefatigable and incessant experimenter , he made many minor discoveries . In 1854 he found that antimony deposited under certain conditions in which it contained a small quantity of antimony terchloride was an unstable form , so that when struck or rubbed or touched with a red hot wire it suddenly rose in temperature to over 300 ' C. and changed from a black lustrous body to a greyish powder . This form he termed " Explosive Antimony . " In 1858 he invented " Gore 's Sphere , " an interesting modification of the Trevelyan Bar experiment , in which a sphere is set rolling round a pair of xxii Obituary Notices of Fellows . circular heated rails and continues to roll round . He further found that the sphere would roll round the rails without other heat than that supplied by an electric current passed from rail to rail through the sphere . Another discovery was that if a current is passed through a solution of mercuric cyanide and caustic potash between two pools of mercury , a series of crispations appear on the negative pool and humming sounds are given out . A more important discovery , made in 1868 , was that there is a critical point in iron as it cools from a red heat . He found that as a red hot wire begins to cool it suddenly lengthens and then contracts again . He showed that there was no converse effect on raising the temperature , and that the effect on cooling was accompanied by a change in magnetic permeability . Dr. Gore was an ardent advocate for the endowment of research , writing in its support at a time when its importance was not recognised as it is to-day . Among his publications is a volume on " the Scientific Bases of National Progress , " in which he urged the value of scientific research to the welfare of the nation . His views were to some extent realised in the foundation , about 1880 , of an " Institute of Scientific Besearch " by a few citizens of Birmingham . Here Dr. Gore was installed and here he worked for the remainder of his life . Besides a volume on " the Art of Scientific Discovery , " Dr. Gore occupied his later years , when he was no longer able to experiment so vigorously , in the composition of two works on " the Scientific Basis of Morality " and on " the New Scientific System of Morality . " In these he treated of morals from a materialistic point of view , for which he might have found more sympathy fifty years earlier . Dr. Gore was elected a Fellow of the Boyal Society in 1865 , and in 1877 he received the degree of LL. D. from the University of Edinburgh . In 1891 he was given a Civil List Pension in recognition of his contributions to science . He died on December 20 , 1908 , when nearly eighty-three years of age . By his will his residuary estate was equally divided between the Koyal Society and the Royal Institution for the purpose of assisting original scientific discovery . The share of the Royal Society , amounting to nearly \#163 ; 2,500 , has been invested as " the Gore Fund . " J. H. P. XX111 JULIUS THOMSEN , 1826\#151 ; 1909 . Hans Peter Jurgen Julius Thomsen , distinguished for his tliermocheniical investigations , was born in Copenhagen on February 16 , 1826 . He was . educated at the church school of St. Peter in that city , and subsequently at the von Westens Institute . In 1843 he commenced his studies at the Polytechnic , and in 1846 graduated there in Applied Science , and became an assistant to Prof. E. A. Scharling . Of his earliest years comparatively little is known . Thomsen , always a reserved and taciturn man , talked little about himself even to his intimate friends\#151 ; anS least of all about the days of his youth . It was known to a few that these days had not been smooth . Those who were best informed were conscious that to these early struggles much of that dour and resolute nature which formed a distinguishing trait in his character was due . In 1847 he became assistant to Forchhammer , and fora time supplemented his scanty income by teaching agricultural chemistry at the Polytechnic . In 1853 he obtained a travelling scholarship , and spent a year in visiting German and French laboratories . He probably owed this scholarship in great measure to his first contribution to the literature of chemistry , namely , his memoir , ' Bidrag til en Tliermochemisk System ' ( contributions to a therinochemical system ) , communicated to the Eoyal Society of Sciences of Copenhagen in 1852 , for which he received the silver medal of the Society and a sum of ten guineas to enable him to procure a more accurate apparatus . In this memoir he sought to develop the chemical side of the mechanical theory of heat , doubtless under the influence of Ludwig Augustus Colding , an engineer in the service of the Municipality of Copenhagen , and a pioneer , like Mayer , in the development of that theory . Indeed , the Danes now claim for Colding , who had made experiments on the relation between work and heat as far back as 1842 , but whose labours were practically ignored by his contemporaries , the position which the Germans assign to Mayer ( see Mach 's ' Development of the Theory of Heat ' ; also Tait 's ' Sketch of Thermodynamics , ' 1868 , S 33 ) . In 1861 Thomsen further developed his ideas in a memoir on the " General Nature of Chemical Processes , and on a Theory of Affinity based thereon , " published in the ' Transactions of the Danish Academy of Sciences . ' In this paper he laid the foundations of the chief scientific work of his life . In 1853 Thomsen patented a method of obtaining soda from cryolite , so-called " Greenland , " or ice-spar , a naturally occurring fluoride of sodium and aluminium , Al2F6,6NaF , found largely , indeed , almost exclusively , in Greenland , and particularly at Ivigtut . In 1854 he obtained the exclusive right of mining for cryolite and of working up the mineral in Denmark for soda and alumina . Actual manufacturing operations were begun on a small scale in 1857 , and in the following year Thomsen planned the present large xxiv Obituary Notices of Fellows deceased . factory at Oeresund , near Copenhagen , which was opened on his thirty-fourth birthday . The importance of this industry to Denmark may be seen from the circumstance that during the fifty years of its existence the firm have paid the Danish Government nearly \#163 ; 300,000 for the concession . From the start Thomsen took a large share in the management of the Oeresund works , and by his energy , foresight , and skill placed the undertaking on a sound commercial basis . Although Thomsen died a rich man , mainly as the result of the industry he created , in the outset of his career as a teacher and a technologist his means were very straitened . He came of poor parents , of no social position or influence , and they were unable to further his inclinations towards an academical career . In 1854 he applied unsuccessfully for a position as teacher of chemistry at the Military High School in Copenhagen . During three years\#151 ; from 1856 to 1859\#151 ; while still engaged in developing his cryolite process , he acted as an adjuster of weights and measures to the Municipality of Copenhagen . It was a poorly paid position , but it kept the wolf from the door . At about this period he betook himself to literature , and published a popular book on general subjects connected with physics and chemistry\#151 ; somewhat in the style of Helmholtz 's well-known lectures\#151 ; entitled \#163 ; Travels in Scientific Regions , ' which had a considerable measure of success . He was , however , not altogether unknown even at this time as an author , since in 1853 he had collaborated with his friend Colding in producing a memoir on the causes of the spread of cholera and on the methods of prevention , which attracted much attention at the time of its appearance . In 1859 , whilst engaged in the Oeresund factory , he again applied to the authorities for a position as teacher at the Military High School , and succeeded in obtaining an appointment to a lectureship in physics , which he held until 1866 . During his tenure of this office he devised his polarisation battery , which received many awards at International Exhibitions and was used for a time in the Danish telegraph service . In 1859-60 he was " vicarius " for Scharling at the University , and in 1865 became a teacher , and in the following year Professor of Chemistry and Director of the Chemical Laboratory , a position which he retained\#151 ; active to the last\#151 ; until 1901 , when he retired in the seventy-fifth year of his age . Before his connection with the University , he founded and edited , from 1862 to 1878 , in association with his brother , August Thomsen , ' the Journal of Chemistry and Physics , ' one of the principal organs of scientific literature in Denmark . In 1863 he was elected a member of the Commission of Weights and Measures , and was instrumental in bringing about the adoption of the metric system and the assimilation of the Danish system to that of the Scandinavian Kingdom . In 1883 Thomsen became Chancellor of the Polytechnic High School of Copenhagen\#151 ; a position which he held for about nine years . During this period he entirely changed the character and spirit of the school , and stamped Julius Th xxv it with the impress of his earnestness and industry . Under his direction , new buildings were erected and arranged in accordance with the best Continental and American models . It was while occupying the position of Director of the Chemical Laboratory of the University that Thomsen executed the thermochemical investigations which constitute the experimental development of the ideas he had formulated in his memoir of 1861 . The results of these inquiries were first made known in a series of papers published from 1869 to 1873 in the * Transactions of the Royal Danish Society of Sciences/ and from 1873 onwards by the ' Journal fiir Praktisehe Chemie . ' The papers were republished in collected form in four volumes ( 1882-1886 ) by a Leipzig house under the title of ' Thermochemische Untersuchungen/ A summary of this experimental labour , which extended over a third of a century , was subsequently prepared by Thomsen , and published in 1905 in Danish under the title of ' Thermokemiske Resultater . ' A translation of this volume by Miss Katharine A. Burke , entitled ' Thermochemistry/ renders it readily accessible to English readers . To go through this material in detail is impossible here . It may be stated generally that practically every simple inorganic process has been investigated calorimetrically by Thomsen , or can be calculated by means of the calorimetric data furnished by him . In the case of organic substances , data have been given for estimating the heat of combustion of a large number of compounds . All these estimations were made by Thomsen personally , according to a pre-arranged plan , and in systematic succession during a period of more than thirty years . They comprise more than 3500 calori-metrical estimations . It has been truly said that this work is unique in the chemical history of any country . Among the results of Thomsen 's thermochemical inquiries which have special value for physical chemistry is his investigation of the phenomena of neutralisation , in which he shows that the basicity of acids can be estimated thermochemically , and that it can in this way he proved whether or not a point of neutrality exists . His observation that the heat of neutralisation is the same for a long series of inorganic acids , such as hydrochloric acid , hydrobromic acid , hydriodic acid , chloric acid , nitric acid , etc. , supports the theory of electrical ionisation , inasmuch as this requires that the heat of neutralisation of the strong acids must in all cases be independent of the nature of the acid , because the process of neutralisation for all of them is the combination of the ion of hydrogen in the acid with the ion of hydroxyl of the base to form water . These investigations also led to the important thermochemical result that the heat of neutralisation of acids ( or the heat of their dissociation ) cannot be considered as a measure of the strength of the acids . Another important result is the proof by experiment of the connection which exists between the gradient of the heat-effect with the temperature and the specific heat of the reacting substances . The law of conservation of energy xxvi Obituary Notices of Fellows deceased . requires the relation dU/ dT = Ci\#151 ; C2 , where U is the heat-effect , T the temperature , and Ci and C2 are the heat capacities of the two systems before and after the reaction ; and Thomsen showed by investigation of the heat of neutralisation , the heat of solution , and the heat of dilution , that this relation was satisfied , thus verifying the precision of his determinations . For the purpose of his inquiry , the specific heats of a large number of solutions of salts were estimated by an ingenious method , and with an exactness hitherto unattained . Of no less importance are Thomsen 's thermochemical investigations on the influence of concentration on chemical equilibrium . In the year 1867 Gfuldberg and Waage published their molecular theory of the chemical effect of mass . But they had only verified the theory to a small extent and in particularly simple cases . They had not investigated the complete homogeneous equilibrium , because at that time no method existed for its experimental investigation . Thomsen showed that the estimation could be made thermochemically . By allowing , for instance , an acid to act on a salt of another acid in an aqueous solution , the latter acid will be partly replaced by the first , which will form a salt . By mixing , for instance , a solution of sodium sulphate and nitric acid , there are formed sodium nitrate and sulphuric acid , but the process will not proceed to completion . If we have estimated the heat of neutralisation of the two acids with sodium hydroxide , the difference between these two heat-phenomena will give the amount of heat corresponding to the total decomposition of the sodium sulphate , and the heat found experimentally by mixing the two solutions will therefore show to what degree the transformation has taken place . It would be possible to estimate thermochemically the amount of the four substances in solution , and thereby , by varying the concentration or the proportion between the initial quantities of substances , to calculate whether the Guldberg-Waage theory on the effect of mass was confirmed in this case . Thomsen applied this method to a large number of different acids and bases , and was thus enabled to prove agreement with the law of the influence of mass in all the cases which he examined . He found particularly that the proportion of the one acid which remained combined with the base was constant with mixtures of constant proportion . On this basis he propounded the term avidity for the tendency of the acid to unite with the base , and he verified that the avidity was independent of the concentration , and only to a small extent varied with the temperature . The idea of avidity has since acquired great utility , particularly since other and more exact methods for its estimation have been found . Concurrently with this , its meaning has been made clear by the theory of ionisation . On the basis of these estimations , Thomsen drew up the first table , based on experiments , of the relative strength of the acids , and the numbers in this table have been found to agree with the results obtained by examining the electrical conductivity of the acids . It is worth noting that Thomsen not only produced the experimental proof Julius Thomsen . XXV11 of the correctness of the Guldberg-Waage theory of the effect of concentration soon after the appearance of this theory , but also that he was the first to acknowledge and adopt it . It is remarkable that this work of Thomsen received so little attention , although it appeared in a widely circulated German journal , and it was not until ten years later that the law of the effect of mass was generally recognised , as the result of the work of Ostwald and va n't Hoff . Although Thomsen 's title to scientific fame rests mainly upon his thermochemical work , his interests extended beyond this particular department of physical chemistry . He worked on chloral hydrate , on selenic acid , on ammoniacal platinum compounds , and on glucinum platinum chloride , on iodic acid and periodic acid , on hydrogen peroxide , hypophosphorous acid , and hydrogenium . He early recognised the importance of Mendeleeffs great generalisation , and contributed to the abundant literature it produced . His paper of 1895 , " On the Probability of the Existence of a Group of Inactive Elements , " may be said to have foreshadowed the discovery of the congeners of argon . He pointed out that in a periodic function the change from negative to positive value , or the reverse , can only take place by a passage through zero or through infinity ; in the first case , the change is gradual , and in the second case it is sudden . The first case corresponds with the gradual change in electrical character with rising atomic weight in the separate series of the periodic system , and the second case corresponds with a passage from one series to the next . It therefore appears that the passage from one series to the next in the periodic system should take place through an element which is electrically indifferent . The valency of such an element would be zero , and therefore in this respect also it would represent a transitional stage in the passage from the univalent electronegative elements of the seventh to the univalent electropositive elements of the first group . This indicates the possible existence of a group of inactive elements with the atomic weights 4 , 20 , 36 , 84 , 132 , the first five numbers corresponding fairly closely with ' the atomic weights respectively of helium , neon , argon , krypton , and xenon ( ' Zeitsch . anorg . Chem./ 1895 , vol. 9 , p. 283 ; e Journ. Chem. Soc. , ' 1896 , vol. 70 , II , p. 16 ) . He subsequently made known the existence of helium in the red fluorite from Ivigtut . As evidence of Thomsen 's manipulative ability and his power of accurate work may be mentioned his determination of the atomic weights of oxygen and hydrogen , and incidentally of aluminium . For the atomic weight of hydrogen he obtained the value T00825 when 0 = 16 , which is practically identical with that of Morley and Noyes . He further made most accurate estimations of the relative densities of these gases , and of the volumetric ratios in which they enter into the composition of water . His value for the atomic weight of aluminium is nearly identical with that adopted in the last lieport of the International Committee on Atomic Weights . Thomsen maintained his interest in thermochemical problems up to the end , and was a keen and clear-sighted critic of the work which appeared from time to time during the later years of his life . This interest xxviii Obituary Notices of Fellows deceased . occasionally gave rise to controversy , and some of liis latest papers were wholly polemical . Thomsen was a pronounced atomist , and to him a chemical process was a change in the internal structure of a molecule , and the chief aim of chemistry was to investigate the laws which control the union of atoms and molecules during the chemical process . He considered that chemistry should be treated mathematically as a branch of rational mechanics . But no one insisted more strongly than he how little we really know of these questions . In summarising his theoretical ideas in the ' Thermokemische Resultater , ' he says , " An almost impenetrable darkness hides from us the inner structure of molecules and the true nature of atoms . We know only the relative number of atoms within the molecule , their mass , and the existence of certain groups of atoms or radicals in the molecule , but with regard to the forces acting within the molecules and causing their formation or destruction , our knowledge is still exceedingly limited . " He fully realised that his own work was only the foundation on which the future elucidation of these questions must rest . " He worked , " says Bronsted , " in the conviction that what we somewhat vaguely call the affinity of the atoms\#151 ; their interaction , their attraction , its varying effect , etc.\#151 ; follows the general dynamical laws , and that , as he worded it , the principle that ' might is right ' holds good in chemistry as in mechanics . On this foundation he hoped it might be possible to evolve the laws for the statics and dynamics of chemical phenomena , even although the inner nature of the action is unknown . " Thomsen 's merits as an investigator received formal recognition from nearly every country in the civilised world . As far back as 1860 he was elected one of the thirty-five members of the Danish Royal Society of Sciences of Copenhagen , and from 1888 until his death he was its President . In 1876 he became an Honorary Foreign Member of the Chemical Society of London . On the occasion of the fourth centenary of the foundation of the University of Upsala ( created in 1477 ) he received the degree of Doctor of Philosophy honoris causa . In 1879 he was made an honorary M.D. of the University of Copenhagen . Two years later he was made a Foreign Member of the Physiographical Society of Lund , and in 1888 he was elected a member of the Society of Science and Literature of Gothenburg . In 1885 he became a member of the Koyal Society of Sciences of Upsala , and in 1886 of the Stockholm Academy of Sciences . In 1883 he and Berthelot were together awarded the Davy Medal of the Koyal Society\#151 ; a fitting and impartial recognition on the part of the Society of the manner in which the two investigators , whose work not infrequently brought them into active opposition , had jointly and severally contributed to lay the foundations of thermochemistry . In the same year Thomsen was made a member of the Accademia dei Lincei of Kome , and in the following year he was elected into the American Academy of Arts and Sciences in Boston , and of the Royal Academy of Sciences of Turin . In 1887 he was made a member of the Koyal Belgian Academy . Julius Thomsen . XXIX In 1886-87 , and again in 1891-92 , he was Rector of the University of Copenhagen . In 1888 he became Commander of the Dannebrog , and in 1896 , and on his seventieth birthday , he was made Grand Commander of the same order . On the same occasion the Danish chemists caused a gold medal to be struck in his honour . In 1902 he became a Privy Councillor ( Geheime Konferenz raad ) . In the same year he was elected a Foreign Member of the Royal Society of London . He died on February 13 , 1908 , and was buried on the eighty-third anniversary of his birth and on the jubilee of the opening of the Oeresund factory . His wife , Elmine Hansen\#151 ; the daughter of a farmer on Langeland\#151 ; predeceased him in 1890 . Thomsen played many parts in the intellectual , industrial , and social development of Denmark . To Europe in general he was mainly known as a distinguished man of science . By his fellow citizens he was further recognised as an educationist of high ideals , actuated by a strong common sense and a stern devotion to duty ; as an able and sagacious administrator ; as a successful technologist and the creator of an important and lucrative industry based upon his own discoveries ; and as a man of forceful character , , who brought his authority , skill , and knowledge of men and affairs to the service of the communal life of Copenhagen . Thomsen was a municipal councillor of that city for more than a third of a century . He occupied a commanding position on the Council , and was invariably listened to with respect . The gas , water , and sewage works of Copenhagen are among the monuments to his civic activity . From 1882 up to the time of his death he was a member of the Harbour Board of the port . In these respects Thomsen sought to realise Priestley 's ideal of the perfect-man\#151 ; that he should be a good citizen first and a man of science afterwards . T. E. T. XXX Obituary Notices of Fellows deceased . WILLIAM JAMES BUSSELL , 1830\#151 ; 1909 . William James Bussell was born on May 20 , 1830 , the son of a banker at Gloucester . His grandfather , William Bussell , lived at Birmingham and was an intimate friend of Priestley . He suffered for this friendship by having his house burned to the ground by the Birmingham mob , in the Church and King Biots of 1791 , two days after Priestley 's house had met the same fate . Young Bussell , the subject of this notice , was educated at private schools , at Bristol and Birmingham , and entered University College , London , in 1847 , where he studied chemistry under Thomas Graham ( afterwards Master of the Mint ) and Alexander Williamson . In 1851 he was appointed the first demonstrator of chemistry at the then newly-founded Owens College , and assisted Professor ( afterwards Sir Edward ) Frankland to plan and superintend the building of the original chemical laboratories of the College . In those days , every man who wished to train himself seriously as a chemist spent some time at a foreign University , mostly in Germany . Accordingly , after remaining at Manchester for two years , Bussell went to Heidelberg , where he worked under Bunsen from the autumn of 1853 to that of 1855 and took his degree , Ph. D. After returning to England , he lectured for some time at the Midland Institute , Birmingham , but went back to University College , London , in 1857 , as assistant to his former teacher , Williamson . At this time the methods of gas-analysis were receiving much attention from chemists in consequence of the precision given to them by Bunsen . This precision , however , was attainable only by the application of numerous corrections involving comparatively laborious calculations . It occurred to Williamson that these corrections might , in nearly all cases , be dispensed with if the pressure and temperature of the gas to be measured were made the same as those of a fixed quantity of air caused to occupy always the same volume . Under these conditions it is not necessary , for comparative measurements , to observe the actual temperature and pressure of the gas : the quantity of it is directly proportional to its volume without further correction . Bussell joined Williamson in devising apparatus by means of which this idea could be applied practically with accuracy and convenience , and he continued to occupy himself in improving the details for several years . Among the results of Bussell 's purely chemical work , we may mention his discovery of the precipitation of silver from an aqueous solution of silver nitrate by gaseous hydrogen , and the determination of the atomic weights of cobalt and nickel . By decomposing the oxides with hydrogen he obtained , in 1863 , the values Co = 29*370 and Hi = 29*369 , and six years later , by measuring the hydrogen evolved when the metals are dissolved in hydrochloric acid , he obtained Co = 29*88 and Hi = 29*35 . The corresponding numbers given by the International Table of Atomic Weights for 1908 are Co = 29*5 t William James Russell . xxxi and Ni = 29'35 ( the actual numbers of the International Table are here halved to make them comparable with Eussell 's units ) . Dr. Eussell was among the earliest investigators of the absorption spectra of what are commonly counted colourless liquids . He and Mr. Lapraik , who assisted him in experiments on this subject , remark : " We have been able to find but few liquids which in columns of 6 or 8 feet do not give absorption spectra . " As examples of his acuteness in following up casual observations and his ingenuity and perseverance in varying their conditions , we may mention his experiments " On the action of certain metals and other bodies on a photographic plate in the dark " and " On the formation of definite figures by the deposition of dust . " He traced the effects dealt with in the former of these investigations almost certainly to the formation of traces of peroxide of hydrogen . Those described in the latter paper were successfully explained by Mr. J. Aitken , F.E.S. , who devised an ingenious method of observing the actual process of formation of the figures . Eussell was long engaged in teaching work . From 1860 to 1870 he was Professor of Natural Philosophy at Bedford College ( London ) . From 1868 to 1870 he was lecturer on chemistry in the Medical School of St. Mary 's Hospital and from 1870 to 1897 he held a similar appointment at St. Bartholomew 's Hospital . Both here and at St. Mary 's he succeeded the late Dr. Augustus Matthiessen , F.E.S. He was elected a Fellow of the Chemical Society in 1851 ; he became Secretary of the Society in 1873 , Treasurer in 1875 , retaining the office for fourteen years till , in 1889 , he was elected President . During his presidency , in 1891 , the Society celebrated the fiftieth anniversary of its foundation . He was an original member of the Institute of Chemistry , founded in 1877 , and was President from 1894 to 1897 . Eussell was for twenty-five years , 1878 to 1903 , a member of the Council of Bedford College ( London ) and Chairman from 1887 , and his attention and sound judgment contributed greatly to the prosperity of the College . He was elected Fellow of the Boyal Society in 1872 ; he served twice on the Council and was a Vice-President from 1897 to 1899 . He presided over the Chemical Section of the British Association at the meeting at Bradford in 1873 . ' Personally , Dr. Eussell was quiet but genial in manner , and he was very highly valued by a large circle of friends . He married , in 1862 , a daughter of the late A. Follett Osier , F.E.S. , of Edgbaston . He died , November 12 , 1909 , at his house at Eingwood , leaving one son and one daughter . In the preparation of this notice , use has , by permission , been made of an article published in ' Nature , ' vol. 82 , p. 101 ( Nov. 25 , 1909 ) . G. C. F. VOL. LXXXIV.\#151 ; A. d XXX11 Obituary Notices of Fellows deceased . SIMON NEWCOMB , 1835\#151 ; 1909 . Simon Newcomb was born in Nova Scotia in 1835 , at Wallace , a pretty village-at the mouth of the river of that name . His father was a country school teacher , a nomadic profession in a thinly-populated district . He was the most rational and most dispassionate of men . Newcomb in his autobiography ( which will be freely quoted in this notice ) tells us that his father had learned from careful study " that the age at which a man should marry was twenty-five . A healthy and well-endowed offspring should be one of the main objects in view in entering the marriage state , and this required a mentally-gifted wife . She must be of different temperament from his own , , and an economical housekeeper . So when he found the age of twenty-five approaching he began to look about . There was no one in Wallace who satisfied the requirements . " He therefore set out afoot to discover his ideal . In those days and regions the professional tramp and mendicant were unknown , and every farmhouse dispensed its hospitality with an Arcadian simplicity little known in our times . Wherever he stopped overnight he made a critical investigation of the housekeeping , perhaps rising before the family for this purpose . He searched in vain until his road carried him out of the province . One young woman spoiled any possible chance she might have had by lack of economy in making the bread . She was asked what she did with an unnecessarily large remnant of dough which she left sticking to the sides of the pan . She-replied that she fed it to the horses . Her case received no further consideration . " The search had extended nearly a hundred miles when , early one evening , he reached what was then the small village of Moncton . He was attracted by the strains of music from a church , went into it , and found a religious meeting in progress . His eye was at once arrested by the face and head of a young woman playing on a melodeon , who was leading the singing . He sat in such a position that he could carefully scan her face and movements . As he continued this study , the conviction grew upon him that here was the object of his search . That such should have occurred before there was any opportunity to inspect the dough-pan may lead the reader to conclusions of his own . He inquired her name\#151 ; Emily Prince . He cultivated her acquaintance , paid his addresses , and was accepted . " " My mother was the most profoundly and sincerely religions woman with whom I was ever intimately acquainted , and my father always entertained and expressed the highest admiration for her mental gifts , to which he attributed whatever talents his children might have possessed . The unfitness of her environment to her constitution is the saddest memory of my childhood . More I do not trust myself to say to the public , nor will the reader expect more of me . " His early years were passed amid social conditions of the utmost simplicity . / Simon Newcomb . xxxm 4 ' The women sheared the sheep and made the clothes , but any man who allowed wife or daughter to engage in heavy work outside the house would have lost caste . " As a child , Newcomb was precocious in arithmetic , doing extraordinary calculations for his years with the assistance of a napped counterpane . He was never known to deviate from the truth in one single instance \#166 ; either in infancy or youth . This high praise comes from his father , who adds a little later : " You were uncommonly deficient in that sort of courage necessary to perform bodily labour . Until nine or ten years of age you made a most pitiful attempt at any sort of bodily or , rather , handy work . " He was an omnivorous reader , and a very careful one , never passing a wTord that he did not understand . Among his neighbours he acquired a reputation for learning that he felt was not appreciated , while he was painfully conscious of his inability to drive oxen . And he says : " My boyhood was , on the whole , one of sadness . " At the age of sixteen Newcomb almost decided upon the trade of a carpenter , but at the last moment he was apprenticed for five years to a certain Doctor Eoshay , who turned out to be a quack . While he was with the doctor : " A book peddler going his rounds offered a collection of miscellaneous books at auction . I bought , among others , a Latin and a Greek grammar , and assiduously commenced their study . With the first 1 was as successful as could be expected under the circumstances , but failed with the Greek , owing to the unfamiliarity of the alphabet , which seemed to be an obstacle to memory of the words and forms . " At the end of two years he ran away and worked his passage on board ship to Salem . The year 1854 was spent as teacher in a country school . In 1855 he got a better position of the same character at Sudlersville . The next year he taught in the family of a planter named Bryan , some fifteen or twenty miles from Washington . His first visit to the capital had been in 1854 , but now they became frequent . In 1856 , in the Smithsonian Library he first sawr Laplace 's " Mecanique Celeste . " " About December , 1856 , I received a note from [ Mr. J. E. Hilgard , assistant in charge of the Coast Survey Office ] , stating that he had been talking about me to Prof. Winlock , Superintendent of the * Nautical Almanac , ' and that I might possibly get employment on that work . When I saw him again I told him that I had not yet acquired such a knowledge of physical astronomy as would be necessary for the calculations in question ; but he assured me that this was no drawback , as formulae for all the computations would be supplied me . I was far from satisfied at the prospect of doing nothing more than making routine calculations with formulae prepared by others ; indeed , it was almost a disappointment to find that I was considered qualified for such a place . I could only console myself by the reflection that the ease of the work would not hinder me from working my way up . " The result was that one frosty morning in January , 1857 , he took his seat in the office of the " Nautical xxxiv Obituary Notices of Fellows deceased . Almanac , " at Cambridge , Mass . He was then in his twenty-second year . From this time onwards his career was one of unchequered brilliancy . In 1860 , he went on an eclipse expedition up the Saskatchewan Biver . The weather was cloudy and nothing was seen of the eclipse . In 1861 , he was appointed Professor of Mathematics in the United States Navy , and as such he commenced transit instrument work at Washington Observatory on October 7 . Although he had been on an eclipse expedition in the previous year , he had never been inside an observatory , except on two or three occasions at Cambridge as a visitor . In September , 1863 , he took charge of the mural circle . At this time it was usual at Washington for each observer to reduce his own observations . Newcomb contrived to introduce a uniform system of reduction in imitation of the system already introduced by Airy at Greenwich . In October , 1865 , the new transit circle arrived from Berlin . In the following years Newcomb succeeded in eradicating a vicious practice that obtained not only at his own observatory , but all over the world . He pointed out that clock stars ought only to be kept for place when at least a twelve-hour group has been obtained . For if an error depending on the sine or cosine of the right ascension exists in the clock star list , and observations only extend over six hours , the same error will be reproduced with only an infinitesimal degree of damping ; whereas with twelve-hour groups the error is quickly damped out . In J 869 , he observed an eclipse in Iowa , and in that year he began to turn his earnest attention to the problems presented by the moon 's motion . In 1870 he visited Europe for the first time , partly for an eclipse at Gibraltar that was obscured by cloud , and partly to search through the records of various observatories for seventeenth century observations of the moon . In 1875 Newcomb was offered and declined the directorship of Harvard Observatory . On September 15 , 1877 , he took charge of the Nautical Almanac Office , a post which he held until his retirement in 1897 . The beginning of Newcomb 's astronomical career coincided with the publication of Hansen 's tables of the moon . These tables were an enormous advance on those previously in existence . Hitherto errors in computed coefficients had in many instances exceeded two or even three seconds of arc . Hansen 's tables contain two or three errors in computed coefficients exceeding half a second of arc , but as a rule he attains a far greater accuracy . The chief defect of the tables lies in the determination of the arbitrary constants , and in the omission of a whole group of planetary terms , the existence of which was not then suspected . A passage in Newcomb s autobiography throws much light on the c^use of the former defect . Hansen worked with the assistance of one computer only ; this was no hardship while he was engaged on his theory . It would , in fact , require some management to assign work to a much larger staff simultaneously . Simon Newcomb . XXXV But when he came to compare his theory with observation and to determine his arbitrary constants , he was exceedingly short-handed . Instead , therefore , of making a detailed comparison with all existing observations , he based his comparison on a few years only . The result was utterly unworthy of his great theory . His parallactic coefficient is two seconds in error , his principal elliptic term half a second in error , and so on . He also postulated a mechanical ellipticity in the moon 's figure at least four times too large . With all these defects his tables mark an enormous advance , and his contemporaries believed that " our troublesome satellite has been at length reduced to order . " At the end of Newcomb 's career the theory of E. W. Brown , which is to replace Hansen 's , is complete , and tables based upon it are in the course of preparation . The advance upon Hansen will be greater than Hansen 's advance upon his predecessors , and yet no one believes that the problem of the moon is solved . Newcomb was in touch with all the work done in this period of fifty years , and great portions of this work were done by himself . His first investigation connected with the moon was a redetermination of the elliptic elements of the moon 's orbit . In this paper he brought to light an empirical term that is now known as the Jupiter evection term . It manifested itself as a fluctuation in the moon 's eccentricity and perigee with a period of seventeen years . Some years earlier Airy had analysed eighty years of observations , and had been almost within touch of this term , but had wrongly identified the period as that of the moon 's node , nineteen years . Newcomb at this time did the bulk of his own computing , and to this fact his superior success is plainly due . The explanation of the term was quickly assigned by Nevill to the action of Jupiter . At a time when most astronomers hardly realised that Hansen 's tables needed correction , Nevill was being the pioneer in a new branch of the lunar theory . The question of planetary inequalities was subsequently taken up by G. W. Hill , by Badau , by Newcomb himself and by E. W. Brown . It may now be considered as worked out . At this point we may notice one other contribution of Newcomb 's to the gravitational theory of the moon , viz. : a beautiful theorem for obtaining the secular accelerations resulting from the secular diminution of the eccentricity of the earth 's orbit round the sun . Hansen , like Laplace , had assigned 12 seconds as the secular acceleration of the moon 's mean motion ; Adams had shown that this quantity was twice too large ; but Adams ' accuracy was not immediately admitted . Some years later Newcomb produced his theorem , and again quite recently E. W. Brown , with the help of Newcomb 's theorem , has practically reproduced Adams ' value , which by that time was generally accepted , in a paper so short and simple that one wonders how there could ever have been any controversy on the subject . xxxvi Obituary Notices of Fellows deceased . We turn now to Newcomb 's work of comparison of observations with theory . His great work entitled " Eesearches on the Motion of the Moon " secured for its author the Copley Medal of the Eoyal Society . In the first section he considers the ancient and mediaeval eclipses . He rejects the solar eclipses , he ignores the magnitudes of lunar eclipses ; and he shows the times of the lunar eclipses to be fairly consistent among themselves and with a secular acceleration slightly greater than the theoretical . He assigns the excess to tidal friction . This no doubt is a vera causa , but there is at present no independent measure of its magnitude . In the concluding part of the " Eesearches " he gives the results of occultations observed in the century preceding 1750 . These occultations were not only worked up by Newcomb , but actually extracted by him from the archives of European observatories . He has since extended his series of occultations down to 1898 and the results were published early this year . The older occultations required immense diligence . The observers ' hieroglyphics had to be collected in many cases , in order to decipher their meaning . Clock errors had to be obtained in any way that was possible . Finally taking all the other quantities as known , a somewhat rough determination of the moon 's mean error of longitude is obtained . From that it appears that in the moon 's observed motion there exists a term unknown to theory with a period of about three hundred years . To Newcomb , and to him alone , we owe such knowledge as we have of the moon 's motion in the century preceding 1750 . In his autobiography , Newcomb says : " One curious result of this work is that the longitude of the moon may now be said to be known with greater accuracy through the last quarter of the seventeenth century than during the ninety years from 1750 to 1840 . " The reductions for the latter period leave very much to be desired , but Newcomb 's remark is too drastic . For instance , Newcomb has with his occulations traced an empirical term of sixty years ' period back to 1820 ; before that date it is lost in the accidental error of his material . That term can be traced in the meridian observations back to 1750 . Newcomb 's ' Eesearches ' also contain the first recognition of the error of Hansen 's mean motion of the moon 's node . He deduces his correction by a comparison of an eclipse of 1715 with transit observations in or about 1868 . Although the time interval is large , the position of the node on the first occasion is subject to much uncertainty . The exact measurement of this motion is of great interest in view of the discrepancy from theory exhibited by the perihelion of Mercury . Turning now to planetary theory , Newcomb 's first paper was an investigation on the orbits of minor planets , with the object of ascertaining whether an explosion of a single planet could be assigned as their origin . If such an explosion really took place , and if all secular changes affecting asteroids were already recognised , it would be possible to assign the place and time of the catastrophe ; and the date , if obtained at all , would be obtained with an exactness unparalleled in other speculations as to the past Simon Newcomb . XXXVll history of the universe . Unfortunately , Newcomb 's conclusions were negative . At this time Ueverrier was still working out his theory of the larger planets , going outwards from the sun . He had not yet reached Uranus mid Neptune , so Newcomb took up the orbits of these two planets , and also of their satellites , in order to determine their masses . He also made a series ot observations tor this special purpose , and his work was rewarded with the Gold Medal of the Royal Astronomical Society . Before the close of his life Newcomb had constructed tables for all the larger planets , and in addition for the minor planet Polyhymnia , in order to determine the mass of Jupiter . G. W. Hill relieved him of " about the most difficult [ part ] in the whole work\#151 ; the theory of Jupiter and Saturn . Owing to the great mass of these ' giant planets , ' the inequalities of their motion , especially in the case of Saturn , affected by the attraction of Jupiter , are greater than in the case of the other planets . " Leverrier failed to attain the necessary exactness in his investigation of their motion . . . . [ G. W. Hill ] laboured almost incessantly for about ten years when lie handed in his manuscript of what now forms Volume IV of the ' Astronomical Papers . ' " Newcomb followed Leverrier 's methods in essentials . " Two systems of computing planetary perturbations had been used , one by Leverrier , while the other was invented by Hansen . The former method was , in principle , of great simplicity , while the latter seemed to be very complex and even clumsy . I naturally supposed that the man who computed the direction of the planet Neptune before its existence was known must be a master of the whole subject , and followed the lines he indicated . " I gradually discovered the contrary , and introduced modified methods , but did not entirely break away from the old trammels . " Hill had never been bound by them , and used Hansen 's method from the beginning . Had he given me a few demonstrations of its advantages* I should have been saved a great deal of time and labour . " Possibly in order that his own work , regarded as a verification of Leverrier 's , might be quite independent , Newcomb introduced some changes into the calculations . Leverrier , for instance , used the mean longitudes of the planets . Newcomb used the mean anomalies . Leverrier develops algebraically , according to the mean angles , and then reduces to arithmetical values . Newcomb develops algebraically in eccentric anomalies , reduces to number , and then transforms to mean anomalies arithmetically in each separate case . In a later volume he gives algebraic formulae for the mean anomalies . He has enormously improved Leverrier 's notation by introducing an operator that he terms " I ) . " ' When the final perturbations are compared , we are struck by how little Leverrier left for his successors . When allowance is made for the difference in the assumed masses of the planets , the difference in the perturbations calculated by Leverrier and Newcomb respectively are not such as could ber xxxviii Obituary Notices of Fellows deceased . detected by observation . Newcomb has , however , improved the arbitrary constants , he has used the same planetary masses throughout all the tables , and finally he has enormously reduced the labour required for an ephemeris by following the methods used by Hansen for the moon . Like the lunar theory , the planetary theory is not yet perfect . The principal outstanding problems are :\#151 ; ( i ) A centennial motion of forty seconds in the perihelion of Mercury , and ( ii ) the orbit of Mars . Since Leverrier 's time , the adopted solar parallax has increased by nearly three per cent , and consequently the mass of the earth by eight per cent. Mars is the planet whose tabular orbit is most affected by an erroneous mass of the earth ; but although Newcomb was able to avail himself of the more accurate value of the mass of the earth , his tables of Mars are far less satisfactory than any other of his tables , and the problem has not yet been solved . The discordance from theory in the motion of the perihelion of Mercury had been discovered by Leverrier from a discussion of the transits of Mercury . Newcomb went over the ground again , with a little added material , and asking an additional question , " Are the errors of Mercury so related to those of the moon as to suggest that the earth is not a perfect timekeeper ? " he found that he was not able to assert that such a relation existed . Newcomb 's Fundamental Catalogue and his " Astronomical Constants " must be mentioned , as well as his determination of Precession . These are great works in themselves , but to Newcomb mainly incidents in the thorough discussion of the motion of the moon and of the planets . It was Newcomb also who assigned the lengthened period of latitude-variation to want of rigidity in the earth . Newcomb visited Europe for the last time in 1908 . Soon after his return his friends heard that he was hopelessly ill . He still continued his interest in his work , and passed through the press his last paper on the Moon . He died on July 16 , 1909 , at the age of seventy-four . Twenty-two years had he spent in darkness before he became an astronomer , and subsequently the congenial nature of his work made the world for him one of " sweetness \amp ; nd light . " P. H. C.

rspa_1911_0008

0950-1207

On atmospheric oscillations

551

572

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Horace Lamb, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1911.0008

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1911_0008

10.1098/rspa.1911.0008

Fluid Dynamics

Tables

Fluid Dynamics

]\gt ; 5 51 By AlIB , Received November Read ovember 3 1 . The chief question discussed in this paper ( SS6\mdash ; 13 ) is that of the free oscillations of an atmosphere whose temperature varies with the altitude ; and in particular the case of a uniform vertical temperature-gradient is studied in some detail . For consistenc it is assumed that the expansions and con- tractions follow the adiabatic law . The problem is treated as a twodimensional one , the space co-ordinates olved b horizontal vertical ; and the more definite conclusions arl.ived at relate to the case where the ( horizontal ) is somewhat large in comparison with the height of the atmosphere . The results are most easily interpreted when the -gradient does not much that chal.actel.isbic of a state of convective equilibrium . The normal modes of oscillation then fall into well-defined types . In the most important type , the motion of the air-particles is mainly horizontal , and } ) endent of the altitude , and the aves may thelefole be described as ' : longitndinal The velocity of ation of progressive waves is found to be equal to ) , where denotes what be called the virtual atmosphere , of a " " holnogeneous atmosphere\ldquo ; corresponding to the tenlperature of the . That the result should colle out intermediate in value between the velocity of souud in the lowest stl.atum , iz . , $/ /(r/ H ) , and the zero velocity corresponding to zero temperature which is postulated in the higher regions was to be anticipated ; but that it should be identical in form with that obtained on the hypothesis of an atmosphere whose expansions are subject to Boyle 's the effect of the vard ( lecrease of temperature exactly compensated by the greater elasticity implied in the adiabatic law , is somewhat relnarkab ] When the radiant falls distinctly below the " " convective\ldquo ; value , the character of the oscillation is ] simple . The wave-velocity is somewhat increase must vays r value , which is the velocity of sound in the lowest stratum . 2 . A second type of oscillations depends on the of stability of the atmosphere . * Rayleigh , ' Phil. Mag. ' ( 4 ) , 1890 , vol. 29 , p. 173 ; 'Scientific Papers , ' vol. 3 , p. 33 VOL. LXXXIV.\mdash ; A. 2 Prof. H. Lamb . [ Nov. 14 , The work required to bring unit mass of air from the density to the density under the adiabatic condition is . ( 1 ) Hence if we imagine two thin strata of equal mass , whose densities are and pressures , to be interchanged , the work required to effect this will be , per unit mass , ( 2 ) If we avail ourselves of the notion of " " potential temperature , \ldquo ; *i.e . the temperature which any particular portion of air would assume if adiabatically to some standard density , we have , ( 3 ) where is the constant of the formula $ , ( 4 ) denoting the absolute temperature . Hence ( 2 ) becomes . ( 5 ) Hence if , we must for stability have ; i.e. the temperature must increase upwards . Now , if denote depth below a standard level , we have , in equilibrium , ; ( 6 ) and combining this with ( 3 ) and ( 4 ) , we find . ( 7 ) In convective equilibrium , where , and consequently 3 , is the same at all altitudes , we have . ( 8 ) This equilibrium , though stable for some types of disturbance ( S 8 ) , is in other respects neutral . For complete stability , must be negative , and therefore . ( 9 ) When this condition is fulfilled , we have a series of possible modes of . Bezold , ' Berl . Sitzb 1888 , vol. 46 . 1910 . ] On oscillation whose periods . as they do on the extent which the temperature-gradient differs from the convective value ( S ) , are comparatively . Oscillations of this character , by local conditions , must undoubtedly occur in the atnlosphere , and may conceivably for some of the minor tions of the barometer . There remains a third type of oscillations which , when the wave-length is moderately great , approximate to the chal'acter of waves ated vertically in the atmosphere . These have been discussed in a previous paper by the author . * From a met , eorological standpoint they can hardly be of importance . 3 . The theory of the " " longitudinal\ldquo ; waves is of interest in relation to the large-scale oscillations of the earth 's atmosphere as a whole . This subject was treated by is of some importance in connection with the suggestion put forward by Lord as to the origin of the variation of the baro meter . 's investigation was based on the hypotheses of a uniform equilibrium temperature and an isothermal law of expansion , and on the further the ertical motion of the air-particles may be ected . S Since the circumstances are then practically those of sound-waves } ) ated horizontally , his results naturally involve the " " Newtoniau\ldquo ; velocity of sound , , where is the of the homogeneous atmospbere to the ssunled uniform temperature , viz. , The hypotheses erred to were , of course , adopted only for nlathernatical convenience . As representations of actual conditions they imperfect and there is , moreover , great uncertainty as to the mosb suitable value to be attributed to . It } ) to the writer that firmer for tative conclusions would ) gaiued if it were possible to calculate the wave-velocity ( for ( waves ) , even in the problem , on more natural suppositions as to the constitution of the atmosphere and the law of } ) ansion . In the actual the temperature , as a rule , diminishes } ) although ( as we have seen ) it is necessary for stability that the vradient should nowhere the convective value . The special ] ) of a uniform gradient , which is here adopted as a bnHis uf calculation , is itself an artificial one ; but in spite of fact that it inlplies upper to the atmosphere , it ltay to give , on the whole , a better representation of the ' Lond. Math. Soc. Proc. ' ) , 1908 , vol. p. 122 . ' Mecanique Livre Chap. . See also . cit. 'Roy . Soc. 1882 , vol. 11 ; 'Math . and apers , . p. 341 . S Some such assumption is necessary tu make the prol ) , in the absence of a prescribed condition to ) fullilIed , or to , in the upper ions of the atmosphere . Prof. H. Lamb . true conditions than the isothermal view , on which , indeed , the earth 's atmosphere is merely a local concentration of a medium diffused through space . As ards the law of expansion , since permanent inequalities of temperature are postulated in the equilibrium condition , it is proper to ignore the transfer of heat between adjacent portions of the air during the oscillations . In any case , theory shows that the effect of conduction on such long waves as we have here in view may safely be neglected . * The main conclusion of Laplace was that the free and forced oscillations of an atmosphere a globe , whether this be at rest or in uniform rotation , are identical with those of a liquid ocean of uniform depth ; but . in view of the nature of his premises , and of the uncertainty as to the temperature to be adopted in imating the value of , considerable doubt has been felt as to how far this analogy can be relied upon for quantitative results . The present investigation tends , I think , to show that inferences of this kind will not be very far from the truth , provided the temperature dopted be the mean temperature of the lower strata of the earth 's atmosphere , so far as this can be ascertained . The formal adaptation of the theory of waves to the case of an atmosphere of relatively small depth covering a globe would follow the same course as in Laplace 's investigation . 4 . As regards the semi-diurnal variation of the barometer , the passage of Kelvin 's paper already referred to runs as follows:\mdash ; " " The cause of the semi-diurnal variation of barometric pressure cannot be the gravitational tide-generating influence of the sun , because , if it were , there would be a much larger lunar influence of the same kind , while in reality the lunar barometric tide is insensible or nearly so . It seems , therefore , certain that the semi-diurnal variation of the barometer is due to temperature . Now , the diurnal term , in the harmonic analysis of the variation of temp jrature , is undoubtedly much in all , or nearly all , places than the semi-diurnal . It is then very remarkable that the semidiurnal term of the barometric effect of the variation of temperature should be greater , and so much greater as it is , than the diurnal . The explanation probably is to be found by considering the oscillations of the atmosphere , as a whole , in the light of the very formulae which Laplace gave in his ' Me'canique Ce'leste ' for the ocean , and which he showed to be also applicable to the atmosphere . When thermal influence is substituted for gravitational , in the nerati e force reckoned for , and when the modes of oscillation * This follows from the equations ( due substantially to Kirchhoff and Rayleigh ) given in the ; ' Hydrodynamics , ' 3rd edit . , S343 . Radiation has a different tendency in this respect . 1910 . ] On Atrnospheric corresponding respectively to the diurnal and semi-diurnal terms of the thermal fluence are ated , it will probably be that the period free oscillation of the former rees much less nearly with 24 hours than does that latter with 12 hours ; and that , theref.ore , with comparatively small magnitudes of the tide-generating force , the resulting tide is greater in the semi-diurnal term than in the diurnal The first question which here arises , , whether as a matter of fact the earth 's atmosphere has a mode of oscillation of the requisite type , with a period of about 12 mean solar hours , can at the present time be examined more closely than was possible at the date ( 1882 ) of the above extract . The free oscillations of an ocean of water of uniform depth coveri of the size of the , rotating with the same angular velocity , have been very fully ated by Hough* in the course of his classical work on tidal theory . He finds , in particular , that in the case of the most important free oscillation the same eneral character as a semi-diurnal tide wavs ( i.e. its most salient spherical harmonic constituent is the sectorial harmonic of the second order ) , the depth for which the peried is exactly 12 sidereal hours is given by where is the earth 's radius , and its velocity of rotation . This is evaluated at 29,182 feet . It is to be remarked , however , that the calculation the mutual attraction of the disturbed fluid has been takeu into account , whereas in the rial o this influence must be quite insensible . If the disturbance were accurately of the type of a spherical harmonic of the second order the requisite modification would consist merely in multiplying the previous result by the factor where the decimal fraction in the second meml ) is the ratio of the density of the water to the mean density of the globe , as adopted in 's computation . This would make As the result of a more direct culation , 's algorithm , her with such of bis numerical results as are applicable , I find the last figure being somewhat doubtful . If put , this ivcs feet . 'Phil . Tralls , 1897 , vol. 191 , p. 139 . See pp. 164 , Prof. H. Lamb . [ Nov. 14 , The substitution of a mean solar for a sidereal half-day as the period involves a further slight diminution , which can be estimated pretty closely from another of Hough 's results . He finds that for , the speed of the free oscillation in question is given by . Comparing this with the former result , we infer that for a period of 12 mean solar hours we must have , about . Assuming that when mutual attraction is ignored this rure is to be reduced in the same ratio as the former one , we have , finally , or , with the previous numerical data , feet . It must be remembered , of course , that these numerical results can claim no greater accuracy than the theory on which they rest , in which , in particular , the ellipticity of the earth , which is of the order 1/ 300 , is neglected . On the other hand , the value of for air at C. is about 26,200 feet , with an increase of about 96 feet for every above this temperature . The mean temperature of the air the earth 's surface is usually estimated at C. This would make feet ; but a somewhat lower value for the mean temperature of the lower strata , away from the immediate influence of the ground , would perhaps be more appropriate . Without pressing too far conclusions based on the hypothesis of an atmosphere uniform over the earth , and approximately in convective equilibrium , we may , I think , at least assert the existence of a free oscillation of the earth 's atmosphere , of\ldquo ; semi-diurnal\ldquo ; type , with a period not very different from , but probably somewhat less than , 12 mean solar hours . At the same time , the reason for rejecting the explanation of the semidiurnal barometric oscillation due to a gravitational solar tide seems to call for a little further examination . The amplitude of this variation at places on the equator is given by Kelvin as inch . The amplitude given by the " " equilibrium\ldquo ; theory of the tides is about inch . * Some numerical results given by Hough in illustration of the kinetic theory of oceanic tides indicate that in order that this amplitude should be increased by dy1lamical action some seventy-fold , the free period must suffer from the imposed period of 12 solar hours by not more than 2 or 3 minutes . Since the difference between the lunar and solar semi-diurnal periods amounts to 26 minutes , it * The numerical values given on p. 520 of the author 's 'Hydrodynamics ' relate to the lunar tide , and are , moreover , by an oversight , stated as ' amplitudes instead of as ranges 1910 . ] On Atmospheric Oscillations . is quite conceivable that the solar influence in this way be rendered much more effective than the lunar . The real difficulty , so far as this point is concerned , is the a priori improbability of so very close an }reement between the two periods . The most decisive evidence , however , appears to be furnished by the phase of the observed semi-diurnal equality , which is accelerated instead of retarded ( as it would be by tidal friction ) relatively to the sun 's 5 . The conclu.ding part of the paper ( SS13 , 14 ) is an attempt to examine more closely than has hitherto been done the theory of waves on a surface of discontinuity in the atmosphere . That such waves may play a part in phenomena has been pointed out independently by Helmand Lord Kelvin , but both writers have fined themselves to analogies drawn from the case of superposed homogeneous liquids . It is to be observed that even on this view the disturbance extends , upwards and downwards from the plane of discontinuity , ] a cqpace which is appreciable fraction of the ; hence , apart altogether from the influence of compressibility , the conditions of the question will be modified when the wave-length is such that the ordinary variation of density within this space becomes sensible . It seemed worth while to investigate the matter ; but it must be acknowledged that when there are no currents , the one of temperature antl density only , the analogy proves to be adequate , under such conditions as are likely to occur in the atmosphere , for a considerable range of . For very long waves it would break down , the disturbance to be even approximately concentrated in neighbourhood of the plane of discontinuity . The discontinuity then beconcs , in fact , an unimportant incident in the eneral upward diminution of density . When there is a discontinuity of relocity , the upper fluid in steady horizontal motion relative to the lower , the question , when compressibility is taken into account , is more difficult , and 1 have not been able to arrive at any very simple results . There can be no doubt , , that the aforesaid analogy is sufficient in this case also for wave-lengths less than a certain . In particular , the dynanlical instability pointed out by KelvinS will remain . 'Brit . ' 1908 , p. 606 . The forced tides duc to diurnal and -diulnal wa es of temperature have been studiod by bfargules , 'Wien . Sitzb , vol. 99 , p. 204 . ' Berl . Sitzb ) ; 'Wiss . Abh vol. 3 , p. .300 . . Assoc. Rep ; 'Math . and Phys. Papors , ' vol. 4 , p. ) . S 'Math . and pers , , p. 76 . Prof. H. Lamb . [ Nov. 14 , Theory of Long ospheric Waves . 6 . We consider an atmosphere arranged in horizontal layers of uniform density . The motions contemplated are restricted to two dimensions , , of which is horizontal and vertical , the positive direction of being downwards . The equilibrium values of the pressure , density , and temperature are denoted by ; these are functions of only , and a.re subject to the hydrostatic condition , ( 10 ) as well as to the general relation . ( 11 ) The equations of small motion are , in the usual notation , . ( 12 ) , ( 13 ) where . ( 14 ) The expansions being supposed subject to the adiabatic law , we have also , ( 15 ) where , ( 16 ) i.e. is the velocity of sound corresponding to the equilibrium temperature at the point considered . It is accordingly in general a function of . If we put , ( 17 ) and continue to neglect small terms of the second order , we have ( 18 ) . ( 19 ) Also , from ( 15 ) , ( 13 ) , and , . ( 20 ) Hence , eliminating and , we find* ( 21 ) * It may be noticed , parenthetically , that in the case of an isothermal atmosphere where is constant , these equations are satisfied by 1910 . ] On If we now write , ( 22 ) we deduce from ( 21 ) , by differentiation , , ( 23 ) , ( 24 ) where ( 25 ) The latter equation shows that an irrotational motion is not possible unless , or , ( 26 ) which we have seen to be the case of equilibrium . We note also that , ( 27 ) by ( 20 ) . Eliminating between and ( 24 ) , we obtain . ( 28 ) If we assume that and occur only through a factor , the equations ( 21 ) take the whence ( 30 ) From these , or from ( 28 ) , have 7 . So far , the vertical distribution of } ) is . In the case of temperature diminishing upwards with gradient , to which we now proceed , there is an upper linlit to the . If we take the origin of at this level , W have ( 32 ) Prof. H. Lamb . [ Nov. 14 , where is the gradient in question . It easily follows from ( 10 ) and ( 11 ) that where AIso . Hence and The meaning of the factor , which appears in one of these terms , is to be noticed ; viz. we have where is the temperature-gradient in a state of convective equilif ) rium , as given by ( 8 ) . To solve ( 37 ) we put obtain , ( 40 ) where This is integrable by series , the solution which is finite for being ; or , in the notation of Dr. E. W. Barnes , * . ( 43 ) The remaining solution of ( 40 ) is of the form where stands for the series in ( 42 ) . Tbis is not admissible in the present * See , for example , 'Camb . Trans vol. 20 , p. 253 , where references to other papers are given . If we had assumed place , we should have found . The comparison verifies a well-known identity ; see Barnes , . cit. 1910 . ] On A tmospheric question , since it becomes infinite as for infinitesimal values of whereas the condition to be satisfied at the upper boundary is , or ; see equations ( 27 ) , ( 33 ) . The formulae ( 36 ) now become ( 45 ) the factor being omitted here , as elsewhere , for brevity . The condition that at the lower boundary , where , say , taken in conjunction with ( 41 ) , determines the values of and , the being supposed given . * 8 . In the case of oscillations about convective equilibrium we have . ( 46 ) It follows from ( 24 ) that ; hence either the motion is irrotational , or the period is infinitely The conditions to which the rotational motions thus indicated are subject follow most directly from ( 21 ) . These equations are now equivalent to ( 47 ) by ( 26 ) . Hence const . ( 48 ) The choice of two functions , , to satisfy this equation , together with the two boundary conditions , can be made in an infinite variety of ways . The types of disturbance are periodic in charactel . The formula ( 42 ) and ( 45 ) apply , with ' ( 49 ) in place of ( 41 ) . Since ( 42 ) makes ( 50 ) * The case of apparent failure , where , does not arise . This would require , by ( 36 ) , , or which violates the condition at the upper boundary . Prof. H. Lamb . [ Nov. 14 , the condition that for may be written A complete discussion of the equations ( 49 ) and ( 51 ) is out of the question , but the limiting form to which the results tend as the wave-length increases is easily ascertained . In the first place , it appears that when is small we have , ( 52 ) approximately , since this ensures , by ( 49 ) , that is also small . If denote the virtual height of the atmosphere , as defined above ( S1 ) , we have . ( 63 ) The limiting value of the wave-velocity V is accordingly given by The bearing of this result has been discussed in the introduction . The formulae ( 45 ) , , and ( 39 ) now lead to ( 55 ) the factor being understood . These values fulfil , as they ought , the irrotational condition . ( 56 ) Since the ratio of the amplitude of to that of is of the order , the motion is mainly horizontal , and the present type of waves may accordingly be characterised as " " longitudinal The remaining solutions of ( 49 ) and ( 51 ) , when is small , involve finite as distinguished from infinitely small values of . As will be seen presently ( S11 ) , they approximate to the character of waves propagated vertically in the atmosphere . 9 . In the general case , where ? is not restricted to the precise value , the elation between and is as in ( 41 ) . When is smal ] we have still a longitudinal wave for which is of the order , subject to a certain condition . The equation ( 51 ) leads again to the result expressed by ( 52 ) or ( 54 ) , and substituting in ( 41 ) we find that the implied assumption that is also small will be justified provided be small , i.e. provided the temperature-gradient falls only a little short of the convective value 1910 . ] On Atmospheric 563 . The limiting form of ( 42 ) , when no assumption is made as to the order of magnitude of , is ( 57 ) or in Dr. Barnes ' notation , , ( 58 ) whilst ( 50 ) becomes . It appears from ( 41 ) , without making as yet any special assumption to the smallness of , that when is finite , whilst is small , ratio will be very small or very great . In the former case we have ultimately , and the condition ( 51 ) becoines : . ( 61 ) Since , ( 62 ) in the notatiori of Bessel 's ) tions , this may be written , ( 63 ) provided . ( 64 ) If be a root of ( 63 ) , the corresponding frequency of oscillation is given by and the wave-velocity by , ( 66 ) being defined as before by ) . This result again is accurate a limiting form for increasing wave-length . 10 . The equation ( 63 ) might be discussed , when or ) is , with the help of the tal , les of Bessel 's functions , but it may bc sufficient to consider the case where the ratio is small . It may be noticed that the formula embraces all the modes of the present class , the waves already discussed corresp onding to the of infinitesimal . The roots of ( 63 ) which relate to the remaining modes are now given by , ( 67 ) Prof. H. Lamb . [ Nov. 14 . , approximately ; and in particular the first of these slightly exceeds the first finite root of ( 67 ) . In convective equilibrium we have , if . The first finite root of is , very nearly . Hence for oscillations about a state of very nearly neutral equilibrium we have . In the case of , which makes , a first approximation , given by ( 67 ) , is , and a second is easily found to be This leads to which is about one-fifth the velocity of the longitudinal type of waves . As to the character of these slow rotational* modes , we find from ( 24 ) , ( 68 ) or , by ( 65 ) , . ( 69 ) Having to the kinematical meaning of the functions , as defined by ( 22 ) , we see that the rotational quality in the relative motion of a fluid element predominates over the dilatational . We learn also from ( 45 ) that when the amplitude of is to that of in the ratio , which is small . Since vanishes at the lower boundary , we infer that the vertical component of the velocity is in eneral relatively small . The distribution of horizontal velocity depends ultimately on the function which varies as if be the relevant root of ( 63 ) , or less accurately of ( 67 ) . In the case of the first root , after the small one , this expression changes sign once , and once only , as increases from to . For , the change of sign occurs for , or The general character of the types of disturbance at present under consideration is most easily apprehended in the case of a " " standing\ldquo ; oscillation . If on the preceding expressions we superpose others which The rotational character is , of course , present also in the longitudinal waves , unless exactly , though to relatively slight extent . 1910 . ] On A trnospheric Oscillations . differ only in the of , and reject the imaginary parts , we find , on discarding all but the most important terms , that ( 70 ) The differential equation of the lines of ( oscillatory ) motion , is satisfied by const . , ( 72 ) or . ( 73 ) If we put we get the lines , but the former of these is only an approximation . The annexed figure indicates , without any attempt at minute accuracy , the general arrangement of the lines in the case of the lowest finite root of . In the modes the higher roots there are horizontal nodal planes , in addition to ) oundary . Returning for a ltoment to the more important " " \ldquo ; of motion first considered , we note that the formulae ( 52 ) , ( 54 ) , cease to be accurate , even as limiting , when the ratio diflers appreciably from unity . The and ( 66 ) will , however , still apply , the lowest root of ( 63 ) . As a numerical example , take the case where the temperature-gradient has only one-half the convective value , so that I find that the lowest root of is , approximately , whence . The result must , of course , in any case ] ) less than , or . The of wave-velocity is accompanied by a in the character of oscillation , the variation of .horizontal velocity with altitude now sensible . The preceding formulae also be used to estimate the rapidity of Prof. H. Lamb . falling away from the state of unstable equilibrium which prevails when , the value of given by ( 65 ) being then negative . 11 . The modes for which is large are easily accounted for . We have from ( 41 ) and from ( 45 ) these being approximations which gain indefinitely in accuracy with increase of . On the supposition that is finite , standing the smallness of , ( 75 ) reduces to , as in ( 64 ) . If be a root of this equation , the corresponding frequency is by These nlodes are in the limit identical with the waves of vertical displacement discussed in a paper already cited in S2 . The formulae ( 45 ) show , in fact , that the ratio of amplitude of to that of is for the most part of the order . If we put the equation ( 76 ) takes the , which is identical with equation ( 88 ) of the paper referred to . 12 . It may be worth while , for the sake of the contrast , to give the theory of the oscillations of a heterogeneous but incompressible fluid , whose equilibrium density has a similar distribution . We have now . ( 80 ) If we put as before , we have From ( 80 ) we have 1910 . ] On Oscillations . the stream-function . in ( 82 ) , ( 83 ) , and eliminating and , we find* . ( 85 ) If and occur only in the form , we have . ( 86 ) Also , ( 87 ) and . ( 8S ) If we assulue that , ( S9 ) we have ( 90 ) or Wl'iting , ( 91 ) . ( 92 ) The solution which is finite is , ( 93 ) or , ( 94 ) if . ( 95 ) The second solution becoules infinite as for , and is therefore excluded , in virtue of ( 88 ) , by the condition that ] must vanish at the upper boundary . Since , by ( S7 ) , for , we have This determines , and ) value of follows from ( 95 ) . It is obvious that , when is small , ( 96 ) is not satisfied by linite values of . If be large , but so that remains finite , the equation ( 96 ) rends to the form , ( 97 ) or , ( 98 ) provided If be a root of ) , we have , ( 100 ) *Cf . Love , ' Lond. Math. Soc. Proc. ' ( 1 ) , 1891 , vol. 22 , p. 30 . LXXXIV.\mdash ; A. 2 Prof H. Lamb . [ Nov. 14 , and therefore , for the wave-velocity , . ( 101 ) Thus , if , for the sake of comparison with S7 , we put , we have , whence . ( 102 ) That the frequency should be increased by the incompressibility was to be expected ; that the effect is so considerable is due to the great modification which is caused in the character of the fundamental modes . The modes corresponding to the roots of ( 98 ) have horizontal nodal planes , and the frequencies form , by a descending series , in the case of ( 65 ) . Waves at a Surface of Discontinuity . 13 . When we proceed to examine the case of waves ated along a horizontal plane where the equilibrium temperature is discontinuous , it may be sufficient to suppose the temperature uniform throughout each of the regions , above and below this plane , to which the influence of the waves extends . The plane in question is taken as the plane , and the dependent variables relating to the upper region will be distinguished by accents . The formulae of S6 will therefore apply to the lower region , with the simplification that is a constant ; so that ( 31 ) becomes . ( 103 ) This is satisfied by , ( 104 ) provided . ( 105 ) We are for a type of motion analogous to that of waves on the interface of two liquids of different densities , in which case the values of are . We assume , provisionally , that in our case also the roots of ( 105 ) are real and of opposite signs ; moreover , since the disturbance is to vanish for , the negative sign is to be taken . For the upper region we shall have , ( 106 ) with a similar determination of ; but the positive root is now the appropriate one . *Cf . Rayleigh , ' Lond. Math. Soc. Proc. ' ( 1 ) , 1883 , vol. 14 , p. 170 ; 'Scientific Papers , ' vol. 2 , p. 200 . 1910 . On . 569 If denote the ordinate of the surface of separation , as affected by the waves , we have ( 107 ) for ; and the pressure in either fluid at the point is to be found by putting in the corresponding value of the expression . ( 108 ) Differentiating with respect to , we see that must be continuous at the interface . * This involves , by ( 27 ) , the continuity of , so that the constants in ( 104 ) and ( 106 ) must be equal . Again , it follows from 107 ) that must be continuous , whence , by ( 30 ) , . ( 109 ) This , ether with the two equations of the type ( 105 ) , determines the values of , and To obtain a solution , we denote the equal members in ( 109 ) by ; thus . ( 110 ) Substituting in , we have , ( 111 ) with a similar equation in which is replaced by these two equations in the form , ( 112 ) and eliminating , we have ( P\mdash ; P ' ) . ( 113 ) Now Hence ( 115 ) is of the fourth ttree in , but one root only is relevant to the present question . The common root of ( 112 ) is , ( 116 ) * This might almost have been assumed at once ; but it is to be observed that it would not give the correct condition to be satisfied at ths comulon boundary of two curreis . Prof H. Lamb . [ Nov. 14 , whence ( 117 ) If we now write , ( 118 ) , ( 119 ) the equation ( 115 ) becomes ; ( 120 ) whilst . ( 121 ) It is to be noticed that , ( 122 ) where , are the equilibrium densities at the plane , on the two sides . For sufficiently small wave-lengths , and are very small , and the root of ( 120 ) with which we are concerned is , approximately , whence , ( 123 ) as in the case of superposed incompressible fluids . * To examine the matter further , the simplest procedure is to tabulate the function ( 124 ) for a series of suitable values of . The only case of real interest is where the discontinuity of temperature is very slight , so that is a small fraction . The following table gives a few results calculated on the supposition that , with . The abrupt step in temperature then amounts to of the mean of the temperatures ( absolute ) above and below . * Stokes , 'Camb . Trans 1847 , vol. 8 , p. 441 ; 'Math . and Phys. Papers , ' vol. 1 , p. 197 . 1910 . ] On Atmospheric The fourth column gives the ratio of the frequency to that of waves of the same length on the surface of separation of two homogeneous liquids with the same discontinuity of density , as given by ( 123 ) , , the ratio is on the present suppositions . The seventh column is calculated from , taking metres per second ; and the last from . It is seen that , with increasing wave-length , the wavevelocity tends more and more to exceed the value estimated on the assumption of the eneity and incompressibility of the two fluids . At the same time , the disturbance tends to become , relatively as well as absolutely , less and less concentrated in the neiohbourhoodo of the plane of discontinuity . 14 . In this question , again , it is of some interest to compare the case of waves on the common boundary of two liquids , each of which , though incompressible , has a similar gradation of density . We therefore write , in ( 86 ) , , a constant . If we assume that , ( 126 ) we derive . ( 127 ) These formulae may be supposed to relate to the lower ; for the upper region we write ( for ( 1 , , respectively . The continuity of involves , by ( 87 ) , that of , so that . Also , in virtue of the continuity of ) , we from ( 88 ) where , are the densities just below and just above the plane , If the two fluids had been portions of the same at different temperatures we should have ( 129 ) and therefore Now from ( 127 ) we have . ( 131 ) Hence , if we adopt the elation ( for the sake of the comparison , we must have , or , taking account of the . This leads to and . ( 133 ) On Atrnospheric Oscillations . The positive root of this quadratic in is to be taken , since it is the only one which gives the proper signs to , it being assumed that and therefore . For infinitesimal values of , we reproduce the relations ( 123 ) . In order to make the variations of density follow exactly the same law as in the atmospheric problem of S13 we must give to , the values ( 129 ) . In the notation of ( 118 ) , ( 119 ) , we have then . ( 134 ) The following table , like the former one , refers to the case of . In order that the comparison may be for the same series of wave-lengths , those values of are chosen which were obtained in the previous numerical work . The significance of the column headed the same as on p. 570 . The comparison shows the usual effect of a constraint in increasing the frequency .

rspa_1911_0009

0950-1207

Sturm-liouville series of normal functions in the theory of integral equations

573

575

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

James Mercer, M. A. (Cantab.), D. Sc. (Liverpool)|Prof. A. R. Forsyth, Sc. D., LL. D., F. R. S.

abstract

6.0.4

http://dx.doi.org/10.1098/rspa.1911.0009

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1911_0009

10.1098/rspa.1911.0009

Formulae

Tables

Mathematics

]\gt ; Sturm-Liouville of Normal Functions in the Theory of Integral By JAMES MEXCER , . ( Cantab . ) , D.Sc . ( Liverpool ) , Fellow of Trinity , Cambridge . ( Communicated by Prof. A. R. Forsyth , Sc. D. , .D . , F.R.S. , \mdash ; ( Received January 20 , \mdash ; Read March 3 , 1910 . ) ( Abstract . ) In a memoir read before the Society on last I proved a theorem* which may be stated as follows:\mdash ; liet , be complete stem of fn relating to a is of positive pe in cnul let be tl , e correspon nlar the series converges absoiutel.a has for , the solving function of . I now show that this leads to the following theorem relative to the expansion of an arbitrary function as a series of such normal functions:\mdash ; liet the of the normal functions be such that the values orof magnitudc ; let , ) resprctiv ! and lo10 . lim its of of which function integral in the rval Then ( 1 ) It will be clear that the application of this theorem in any particular case requires the determination of an asymptotic formula for when is negative and numerically great . In the third section I proceed to obtain such a formula for the case in which is the Green 's function of the equation ' Phil. . Roy . Soc Series , vol. 209 , p. 44 574 Dr. J. Mercer . Sturm-Liouville Series of [ Jan. 20 , for an assigned pair of boundary conditions at the end points of . The only restriction placed upon the function of denoted by is that it should be continuous in . By employing this formula I show that , if is any function which has a Lebcsguc integral in , ( 2 ) where are espectivdy the upper and lower bilateral limits of at a point of the open interval . These bilateral limits are defined as follows . Let be any two functions which possess limited second derivatives in an interval , and are such that The upper limit of , ( 3 ) as tends to zero , will , in general , assume different values as the functions , are varied . The lower limit of these values is called the upper bilateral limit of at the point . Similarly , the upper limit of the values assumed by the lower limit of ( 3 ) is defined to be lower bilateral limit of at In the case before us , the normal functions are the solutions of which , for , satisfy the same pair of boundary conditions as . The series is called a canonical -Liouville series corresponding to . It foJlows from ( 1 ) that we have at each point of . This , in conjunction with ( 2 ) , enables us to state general theorems relative to the behaviour of canonical Sturm-Liouville series . Thus , defining the common value of the upper and lower bilateral limits at a point where they are equal to be the bilateral limit at that point , we have : At each point of the open terval where , the bilateral limit of , exists . 1910 . ] in thoe Theory of Integral ations . Again , the case in which , we see that:\mdash ; of acano to at any of the interval eohcrc it concerycs the ? bil ptcrits of at point . In the later portions of this these theorems are extended to the most general type of Sturm-Liouville series ( S In the section I consider the ence of canonical Sturm- Liouville series , a method which is by the proof of the theorem of II , S4 , the asymptotic formula obtained at the commencement of the third section . It is eventually shown that : At any point of . ' oj canonic Sturmcorr]assignc is in 's the same of in In particular we have : If respo to ntcrral conrcr at th , cmd th It is also shown that : If one o.f ' to the l.function , , of its , then all of ] th sct . From the two theorems just quoted sufTicient conditions obtained for the convergence for the uniform euce of series . Finally , the cIre obtained for the Yeneral ille series .

rspa_1911_0010

0950-1207

Conduction of heat through rarefied gases.\#x2014;II.

576

585

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Frederick Soddy, M. A., F. R. S.|Arthur John Berry, B. A.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1911.0010

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1911_0010

10.1098/rspa.1911.0010

Thermodynamics

Tables

Thermodynamics

]\gt ; Conduction through RareJied Gases.\mdash ; II . By FREDERICK SODDY , M.A. , , and ARTHUR JOHN BERRY , B.A. , Physical Chemistry Laboratory , University of Glasgow . ( Received August 25 , \mdash ; Read November 10 , 1910 . ) In a previous paper* measurements were described of the thermal conductivity of twelve different gases in what may be termed a free-path vacuum that is , at pressures so low that the molecules conducting the heat from the hot to the cold surface do not , as a rule , experience mutual encounters . It was that at sufficiently low pressure the conductivity of all the gases was proportional to the pressure , and the conductivity ( defined as the calories dissipated per second , per mm. pressure per square centimetre of hot surface , per 1o difference of temperature between the latter and its surroundings ) was compared with the theoretical conductivity , as calculated approximately from the molecular heat and mean molecular velocity of the gas , by means of the kinetic theory , on the assumption that the heat interchange between the molecule and the surface it impinges upon was perfect . For argon and neon the ratio and respectively ) was in gratifying agreement with this assumption , but for all the other gases the ratio was less than unity . For these the ratio was greater than , except for helium and hydrogen , for which the very low values and respectively were found . The suggestion was hazarded that possibly for these light gases the interchange of heat is imperfect , owing to the greater velocities at which the molecules move . In the present paper some of the earlier measurements have been repeated with the original apparatus , with better provisiou for keeping the temperature of the surrounding water jacket uniform . Then the apparatus was rebuilt to allow of the measurements of the conductivity to be taken over a wide range of temperature , both of the hot and cold surface , and the effect of variation of the temperature on the ratio was examined . Measurements were confined to the three ses\mdash ; hydrogen , helium , and argone Incidentally the effect on the conductivity of hydrogen of using a hot palladium surface instead of one of platinum was examined . The result of these new has been to negative the suggestion already referred to , that the discrepancies between the found and calculated conductivities might be due to imperfect interchange of energy on impact . The ratio appears to diminish as the temperature at which the experiments are 'Roy . Soc. Proc 1910 , , vol. 83 , p. 254 . Conduction of Heat through Rarefied performed decreases and to increase as the temperature is increased , and no anation of this can at present be suggested . eriments with the Original Apparatus.\mdash ; The conductivities of helium , argon , neon , and hydrogen were redetermined by the original method and apparatus . In the whole of the work to be described the water round the apparatus was kept at nearly constant temperature by first circulating through a considerable length of metal tubing immersed in a thermostat , usually at . The values of and of are shown in Table I , ether with the results obtained previously . They agree fairly well with results already given , that of hydrogen slightly Table I.\mdash ; Original Apparatus . Strip at Further experiments then carried out on helium and argon , but the strip was now heated to different temperatures . The electrical arlangements were also somewhat modified . The two ratio arms of the bridge were two 1-ohm coils of stout Eureka wire . The other arm of the bridge was a set of variable resistances of the same , so that the strip could be heated to various known temperatures . In measuring the fall of potential along the strip , an Elliot voltmeter , with an 8-inch dial reading from to volts , was nently connected across the potential leads . To com- pensate for the resista1lce of instrument , an equal resistance ( 389 ohms ) was put in parallel with the corresponding arm . In this series the variable resistance was set so that at the balance point the strip should assume temperatures . with the following :\mdash ; vater at , the points of the following liquids , ether } , water , ethylene dibromide , and aniline This was accomplished with the apparatus filled hydrogen and jacketed at the desired tenlperature , by the variable resistance until balance was obtained with a momentary feeble current . The of the strip at the working temperature was found * This temperature was assumed from esistance of the strip , which was found to be a linear function of the temperature . It if ; probable that the boiliug-point of the aniline had been raised by decomposition . Messrs. F. Soddy and A. J. Berry . [ Aug. 25 , by reading the fall of potential across the potential ] eads when balance was produced with a.known heating current , the walls of the apparatus being cold . The results are included in Table II . They showed that but little change in Table II.\mdash ; Original Apparatus . Temperature of Strip varied . the ratio was produced by changes in the difference of temperature between strip and wall from to , the temperature of the wall being always about . The low conductivity of argon and the comparatively small range over which its conductivity is a linear function of the pressure make the determination of the ratio less accurate than for helium or hydrogen . For helium the ratio remained sensibly constant over the range examined . This was unexpected . On the view suggested tentatively to account for the smallness of the ratio , that perfect interchange of energy is not secured with the faster molecules by a single impact , it is to be expected that the ratio would decrease as the temperature of the strip was increased . Comparison of the Conductivity of drogen with Heated Surfaces of Palladium and Platinum.\mdash ; On the same view it had been deduced , since hydrogen is occluded by heated palladium more than by platinum , that the value of for hydrogen should be greater for a heated palladium surface than for one of platinum . The point was simply tested in the following apparatus employed consisted of two parallel tubes carrying , axially , similar wires of platinum and palladium respectively . The tubes were joined together at their upper extremities and immersed in the thermostat , in order that the same gas might be investigated under identical conditions of temperature and pressure . The two wires formed two arms of a bridge , the rest of the bridge consisting of a stretched wire along which a sliding contact moved . A sensitive galvanometer was inserted between the slider and the two ratio arms of the bridge . Care was taken to avoid 1910 . ] of Heat through Rarefied Gases . heating the wires to such an extent as to cause them to touch the sides of the tubes . Argon and hydrogen were ated by this apparatus . Experiments were performed in water at , and also with the apparatus cooled in a mixture of solid carbon dioxide and ether giving a temperature of about . Both gases were ated over a fairly vide range of pressure , and the behaviour with both was absoluteIy identical , so far as could be seen . The balance point remained at the middle of the wire , only to a very slight extent as the pressure of the gas became reduced , due to a slight difference between temperature coefficients of of the platinum and palladium wires . These experiments , therefore , ative the prediction that hydrogen ) ected to exhibit a higher conductivity when tested with a surface of than with one of inum . new tube , with the platinum strip employed in the appal'atus , was made up in a suitable for work at low temperatures . To allow ansion and contraction of the with change of temperature , a spiral of hard copper wire was employed at the top , instead of a at the bottom as in the original apparatus . But since resistance of this was a considerable fraction of that of the platinum strip , it was no longer possible to work with the strip as of a Wheatstone bl'idge . The diameter of the new tube was very nearly the same as the old one ; it actually cm . , and the potential leads were cm . apart . One of the set of determinations that ] been made with the old apparatus was repeated closely as possible with the new , and the curves obtained were practically identical , showing that the electrical properties of the strip were unchanged . The method of was ollows : strip , with its potential leads connected with the voltnleter , was put in series with a constant esistance of stout Eureka wire ( shunted with the resistance of ohms , equal to that of the voltmeter ) , of such a value as to be equud to the resistance of the portion of the sl , rip between the potential leads at the } temperature , and with a rheostat for the heating current till this equality was obtained . Adjustment was made by the use of a commutator , which exchanged the voltmeter and similar 389 ohrns resistance . The rheostat was then simply adjusted until the volbmeter dings w constant for the two positions of the commutator . With the apparatus sul'rotlnded by liquid air , the strip was worked at two temperatures , ( 1 ) at , and ( 2 ) C. Helinm and hydrogen were ated at both tempelatures . The resistance of the strip between the potential leads was carefully determined at liquid air temperature and in a bath of solid carbon dioxide and ether . This was done by observing with a potentiometer the fall of potexltial Messrs. F. Soddy and A. J. Berry . [ Aug. 25 , across the potential leads of the strip , produced by a known momentary feeble current , when the apparatus was filled with hydrogen and immersed in the cooling bath . It was found that the resistance of the strip was very nearly a linear function of the temperature from to . At low temperatures the linear portion of the curve , expressing the relation between the heat dissipated and the pressure of the gas , is curtailed , and it was not found possible for this reason to work at low temperatures with argon , but experiments were done with hydrogen and helium . The results are given in Table III . Table III.\mdash ; Rebuilt Appal.atus immersed in Liquid Air . From the expression before deduced , in which and are constants , while varies directly as the square root of the absolute temperature and inversely as the absolute temperature , it follows that varies inversely as the square root of the absolute temperature . It had been deduced that the value of for helium at liquid air temperature should approach unity , since at that temperature its molecular velocity is similar to that of neon at room temperature . The ratio for both helium and hydrogen was , however , found to be distinctly smaller at low temperature . As before , variation of ths difference of temperature between the wall and the strip appeared to make little , if any , difference . In these low-temperature measurements the radiation loss was negligible . Further experiments were then performed with the apparatus jacketed with steam and the strip at 19 in one set , and 26 in another , and with the apparatus jacketed with aniline and the strip at In the experiments at higher temperatures , the radiation loss became of considerable importance . It was determined in each case by extrapolating Where is the molecular heat at constant volume , the mean molecular velocity , the number of molecules in 1 . of gas at the temperature of the wall and mm. pressure , and the number in the gram-molecule . 1910 . ] Conduction of through reJied Gases . the curves to zero pressure , except in the experiment with the strip at and the bath at . For this case the separate curves did not give a sufficiently concordant result , and the loss was determined directly in a calcium vacuum . In attempting to push the temperature higher by jacketing with sulphur vapour heated in a quartz tube , the copper wire spring softened , and the apparatus was rendered useless . The results are shown in Table Table \mdash ; Rebuilt Apparatus . High Temperatures . For convenience , the whole of the results are collected for each gas separately in Table . The measurements are } in ascending order of bath temperature , the erent measurements at the same bath temperature being arranged in ascending order of strip temperature . It appears that rise in temperature of both surfaces causes the ratio to increase , while an increase in the difference of temperature between wall and strip causes it to diminish . Helium is perfectly in accord with this view , and so is hydrogen , though here only four measurements have been done . For argon , also , the results , they appear at first sight irregular , are not inconsistent with the view that two opposing influences are at work , and sometimes the one and sometimes the other predominates . It is clear , from the fact that a value as high as for has been obtained for argon , that this conforms to theory hardly better than the others , and that the agreement between the theoretical and experimental values found for it in the last paper was partly fortuitous . The reasons for the discrepancy between the tbeory and the experimental results remain unexplained . Admittedly , the theory , which assumes all the molecules to possess the teml ) erature of the wall , is imperfect , btlG it may be questioned whether this can make any very serious diflerence in the calculated values . It is interesting to note that the conductivity found Messrs. F. Soddy and A. J. Berry . [ Aug. 25 , gases at low pressure val.ies far less with the nature of the gas and with the temperature than is to be expected from kinetic considerations . Thus the extreme values of found in these experiments re and , whereas the extreme values of over the same range are and Table Collected Results . El . Addendum , October 15 , 1910 . Sir Joseph Larmor has called our attention to some recent papers by M. Knudsen on the dynamics of rarefied gases which reveal a source of error 1910 . ] Condnction of Heat through in the oing measurements of the of the gas . First , we may be allowed to state that we had already considered the ents of the pressure to be the least satisfactory , and had decided , if an opportunity of continuin . the work arose , to do away ether with the ange . This could readily be done by having the tube . the hot strip , the volume of which was determined once for all , connected by capillary tubing with a definite volume en.closed between two taps , for definite quantity of any gas to the apparatus . By the apparatus with calcium at the start and ' the heat dissipation after each admission of one such quantity of gas , the experimental work would be much silnplified and the results more definite . For in a previous paper*it has been pointed out that when the free path of the molecule becomes comparable with the diameter of the tube there is , properly , no pressure in the hydrostatic sense , since flow does not operate to equalise the concentlation . It stated that under these conditions " " of pressure in apparatus connected to the gauge by a orifice not , strictly , pressure readi all Knudsen has deduced from the kinetic theory that between two closed sels at difl'erent temperatures containing the same gas , and connected by a tube , of diameter small compared with the mean free path of the gas molecule , there must exist a diffelence of pressure , coiven by where , and , are the pressures and tenlperatures of the two vessels respectively . In fact , Osborne Reynolds , in work on thermal nspiration , had , long previously , alried at the same relation . Knudsell brings in support of this remarkable deduction many striking experiments , and there can be little doubt some common physical measurements , as well as those discussed in the oing pages , are vitiated by this effect . In the measurements , with the tube containing the heated strip jacketed at and low teulperatures , the pressure of the which remained at room temperature , would not represent the pressures in the tube . the tubing was some 3 or 4 mm. wlde , yet this was always compared with the mean free path of the boas lnolecules . As there to be no reason why the above relation cannot be exactly applied to our } ) , we have corrected the ratio , iven in Table , by multiplying it by , where is the lperature F. Soddy and T. D. Mackenzie , ' Roy . Soc. Proc 1908 , , vol. 80 , 1 ) . 102 . " " Eine Revision der ] ihewichtsbdigung der Gase ' Annalen der Physik , ' 1910 , vol. 31 , 205 . Phil. } , p. 727 . VOL. LXXXIV . Conduction of Heat through reJied G of the room , assumed throughout to be C. , and the absolute temperature of the bath . The values so corrected , and multiplied by the factor described below , have been added in italics as another column to Table . It will be seen that the results now have quite a different appearance , not unfavourable to the original hypothesis of incomplete interchange of energy on impact . For helium , the value of is distinctly higher at liquid air temperature than at room temperature , but remains almost constant from room temperature up to . The low value with the bath at and the strip at 26 is exceptional . For , the value of is also highest at the lowest temperature , and falls regularly , so far as can be seen , with increasing temperature . Argon is still somewhat irregular . Over the range investigated , to , temperature appears to have little influence . As already remarked , these results are probably not so accurate as those with the other gases . Finally , reference must be made to a recent paper by M. Smoluchowski , * who , in the last section of his paper , deals with the results obtained by us in our first paper , from the theoretical standpoint . He gives an exact calculation for the conduction of heat in a rarefied gas on Maxwell 's assumption that some of the impinging ecules are reflected with their original velocity , while others are emitted with a new velocity corresponding to the temperature of the surface . He points out that in our roughly calculated formula for , the numerical factor should be instead of 1/ 6 , so that all our values for should be multiplied by the factor In addition , the value of , to correct for imperfect equalisation of the mean energy of the impinging molecules to that of the molecules in the wall , must be multiplied by the factor , where is derived from the formula in which , and denote the temperature of the wall , of the impinging and of the emitted molecules . With only the first correction in the values of , this ratio ranges for the 12 gases examined from for argon , to for , showing that the interchange of energy is always imperfect . Smoluchowski does not discuss the interesting question as to how this coefficient is likely to vary with the velocity " " Contributions to the Theory of Transpiration , Diffusion , and Thermal Conduction in Rarefied Gases 'Bull . International de l'Acad . des Sciences de Cracovie , ' 1910 , No. 7 , p. 295 . Prof. Larmor had sent me the same correction as M. Smoluchowski 's , remarked to him independently by Mr. Sydney Chapman . A slight change has beeu made in the decimal value of the factor . of Potential . or temperature of the molecule . He considers our earlier results to range very much as is to be expected , the of energy with the molecules of the platintlln wall being less perfect for the lighter molecules than for } eavier ones , and also for polyatomic than for nlonatomic , for the reason that intramolecular is less disposed to equalisation by impacts than energy of progressive motion . It is clear that further experimental work must be done in the manner suggested befo the seary data are available . The periment on the conduction of palladium platinum ires tells against the idea of imperfect interchange of en , but it ) no means lsive . Moreover , Prof. remarks that the recent experiments of on electrified water drops in an field , when eted by the of E. make very } , so that , for air on water at any rate , litCle correction of that kind arises . An . for Photo Potential . By GEORGE .C.Sc . , lf . A. , Superintendent of Eskdalemtlir ( Communicated by Dr. . Shaw , F.R.S. October 11 , \mdash ; Road November ) , 1910 . ) The difficulties continuous ation of electrical potential gradient of the atmosphere very great ; but it is not my intention in this paper to discuss these . object is to call attention to the part of an more ) to experiments made with an instrument that pronlises to be of considerable in wolk of this kind . A recording voltmetel ' ought to have a uniform scalc value over the range for which it is intended to be used , it must possess a ) of insulatiou , and it ought to be capable of acting efficiently for periods ) having to be taken to } ) ieces for cleaning . The general excellence of the Dolezalek electrometer and its rlce olnechanical sested to me its use as a , although I do not that it beon The instrunleut designed to measure very small differences of potential Boy . Soc. Proc , 1

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An electrostatic voltmeter for photographic recording of atmospheric potential.

585

588

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

George W. Walker, A. R. C. Sc., M. A.|Dr. W. N. Shaw, F. R. S.

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Electricity

Measurement

Electricity

Photographic Recording of Atmospheric Potential . 585 or temperature of the molecule . He considers our earlier results to range very much as is to be expected , the interchange of energy with the molecules of the platinum wall being less perfect for the lighter gas molecules than for heavier ones , and also for polyatomic than for monatomic , for the reason that intramolecular energy is less disposed to equalisation by impacts than energy of progressive motion . It is clear that further experimental work must be done in the manner suggested before the necessary data are available . The experiment on the conduction of hydrogen with palladium and platinum wires tells against the idea of imperfect interchange of energy , but it is by no means conclusive . Moreover , Prof. Lartnor remarks that the recent experiments of Millikan on electrified water drops in an electric field , when interpreted by the formula of E. Cunningham , * make / 3 very small , so that , for air on water at any rate , little correction of that kind arises . An Electrostatic Voltmeter for Photographic Recording of A t mo spheric Po P\gt ; y George W. Walker , A.R.C.Sc . , M.A. , Superintendent of Eskdalemuir Observatory . ( Communicated by Dr. W. N. Shaw , F.R.S. Received October 11 , \#151 ; Read November 24 , 1910 . ) The difficulties attending continuous registration of electrical potential gradient of the atmosphere are very great ; but it is not my intention in this paper to discuss these . My object is to call attention to the measuring part of an electrograph , and more especially to experiments made with an instrument that promises to be of considerable service in work of this kind . A recording voltmeter ought to have a uniform scale value over the range for which it is intended to be used , it must possess a high degree of insulation , and it ought to be capable of acting efficiently for long periods without having to be taken to pieces for cleaning . The general excellence of the Dolezalek electrometer and its high degree of mechanical symmetry suggested to me its use as a recorder , although I do not know that it has been tried before . The instrument was designed to measure very small differences of potential * ' Roy . Soc. Proc. , ' 1910 , A , vol. 83 , p. 109 . 2 s 2 586 Mr. G. W. Walker . Electrostatic Voltmeter for [ Oct. 11 , between the quadrants with a potential of , say , 100 volts on the needle . The first thing to ascertain was whether , with a fixed difference due to a single Weston cell , the sensitiveness could be reduced so that the movement of the needle would record , on a suitable scale , the potential applied to it . A trial suspension made of phosphor bronze proved successful , and a scale value of about 200 volts per centimetre was obtained on the photographic paper , which is carried on a drum 1 metre from the mirror attached to the needle Up to 500 or 600 volts the behaviour was excellent , but for higher potentials the needle began to tilt , and if a sudden change was made the needle generally discharged to the quadrants . Experience showed that it would have frequently to carry over 1000 volts . The needle was therefore loaded by prolonging the vertical axis to about 3 cms . beneath the needle , and adding at the end a small brass nut of about 1|~ grm. It now carries 1100 volts with perfect safety and stability . The loading reduced the sensitiveness , and I now use three Weston cells and obtain a scale value of about 115 volts per centimetre on the paper . As far as I can test with a high potential Wulf electrometer , the scale value is constant to within 2 or 3 per cent , over the range of the sheet , which is about 900 volts + or \#151 ; . It requires a little care and patience to adjust the instrument to symmetry over this large range of 1800 volts . The present scale value is suitable for ordinary days , but in stormy weather it is too large . We therefore require a second voltmeter working at a lower sensitiveness in order to get a complete record . From what has been said , it is clear that a Dolezalek with one Weston cell would serve admirably . It may be mentioned that although the instrument is not dead-beat at this sensitiveness , the needle comes to rest long before the collecting water-jet responds to change of potential , but discussion of this point is reserved for another occasion . Meanwhile experiments in another direction have been carried on . Some ten years ago Mr. W. G. Pye made for me an experimental voltmeter , in which I proposed to rely on the contact difference of potential between zinc and copper to give a couple on a suspended electrometer needle . Two circular plates were made up of alternate 90 ' sectors of zinc and copper , soldered together at the junctions , and the two plates were set parallel by means of a circular copper ring , thus completing the " box quadrant " arrangement . I was satisfied some years ago that the instrument could be adjusted to give quite reliable readings for a steady potential on the needle . When the question of having a second recorder for high potentials arose , it occurred to me to ascertain if the zinc-copper voltmeter would do . The old plates 1910 . ] Photographic Recording Atmospheric Potential . 58 were accordingly looked out , and , although they had been damaged and repaired some years ago , an instrument was made up in the observatory workshop , closely resembling the Dolezalek in general features , although equal mechanical accuracy was impossible in the circumstances . When connected to the Dolezalek and collecting system , the photographic records from the two instruments were perfectly similar . Fig. 1 is a reproduction of a specimen record . Eskdalemuir Dolezalek Electrogram , 1910 , July 25\#151 ; 26 . Eskdalemuir Zn-Cu Voltmeter Electrogram , 1910 , July 25\#151 ; 26 . It proved fairly easy to adjust the new instrument to uniform scale value ( about 290 volts per centimetre ) over a range of 400 or 500 volts + or \#151 ; ; but for greater potentials I found considerable difficulty . This arose simply from the lack of perfect mechanical symmetry in the instrument , but with patience I finally succeeded in getting practical uniformity up to 1100 volts + or \#151 ; . I think these results , obtained with a " home-made " instrument , warrant the making of a new one , which shall equal in mechanical precision the Dolezalek electrometer , and so admit of easier adjustment . At present the needle is not sufficiently damped for very rapid changes , but this can be overcome by using a Dolezalek needle or by electromagnetic damping . The instrument possesses an obvious advantage for recording work , as insulation of the quadrants is unnecessary . The only part requiring good insulation is the head for carrying the needle . This may be done with amber , but we avoided the expense and got quite as good a result by moulding a sulphur bush . The question of a cheap and efficient insulator is strictly beyond the scope of this paper ; but as we have obtained most satisfactory results by using sulphur , I have been advised to refer to the matter . It is practically impossible to work sulphur in the ordinary mechanical way , and resort must be had to moulding . For this purpose a carefully cleaned glass tube or test-tube of the required diameter is used . Ordinary 588 Photographic Recording of Atmospheric Potential . roll sulphur is then melted in a clean porcelain dish , and it is essential that the temperature should be just sufficient to melt the sulphur and no more . The slightest darkening of the liquid is fatal to a good result . The molten sulphur is run into the glass tube and allowed to set for 24 hours . It may then be taken out , and usually the test-tube has to be sacrificed in the process . Initially the rod insulates magnificently , but in the course of a few days it gets defective . If , however , the glossy surface is then removed by light rubbing with fine sand-paper , the insulating power is recovered and maintained . I cannot yet say how long this will last , but I have some pieces in use that have not been touched for over six months , and they insulate now as well as they did originally and quite as well as amber . I have made special tests in very damp weather without finding any failure of the sulphur . If the support has to stand any strain it may be fitted into a brass socket with a piece of . thin paper . Five such supports , 1-inch diameter , carry our copper tank , which is 3 feet in diameter and 6 inches deep and filled with water . An idea of the insulation may be obtained from the fact that when electrified the tank falls to l/ \lt ; ? of its original potential in from 50 to 60 minutes normally . I have found that sulphur moulded directly into brass or copper tube gradually deteriorates , and on breaking the sulphur it is found to contain dark streaks of what I presume is copper sulphide . If , however , the brass is first lined with thin paper the sulphur maintains its insulating power for \lt ; * months without any sign of deteriorating . It is important not to touch the sulphur with fingers at all greasy . If occasion arises to remove a spider 's thread , it is best to do so with a piece of fine sand-paper or even a piece of fine tissue paper . Mr. Black , the observatory mechanic , has greatly assisted me in ascertaining what precautions are necessary to make sulphur a serviceable insulator in laboratory work . [ Note added December8.\#151 ; Zinc-copper couples have been used before by Lord Kelvin and by Prof. C. V. Boys.* Sulphur insulation , with the remarkable efficiency of which this paper is concerned , has also been advocated by Mr. C. T. R. Wilson , by Dr. Threlfall , and by Prof. Le Cadet.f ] * ' Electrician , ' 1896 . t ' Annals de l'Universit6 de Lyon , ' 1898 , vol. 35 , p. 32 .

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The measurement of end-standards of length.

589

595

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

P. E. Shaw, B. A., D. Sc.|Prof. Poynting, F. R. S.

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10.1098/rspa.1911.0012

Measurement

Tables

Measurement

589 The Measurement of End-Standards oj Length . By P. E. Shaw , B.A. , D.Sc . ( Communicated by Prof. Pointing , F.R.S. Received November 18 , 1910 , \#151 ; Read January 12 , 1911 . ) During the last few years there have been improvements in this branch of metrology . In 1905 , as pointed out by the writer , * the best gauges were greatly defective as to their end faces and the machines for their measurement were faulty in principle . Since then Jolianson has , by a secret process , produced gauges incomparably superior to anything previously on the market , with the result that other gauge-makers have been stimulated to improve their standards . The ordinary bar gauge has flat ends . This paper deals with this form only . The ideal gauge would satisfy two conditions : ( 1 ) The ends to he absolutely plane and parallel , though they need not be truly normal to the length of the bar ; ( 2 ) the distance between the planes to be exactly the length for which the gauge stands . In this paper only condition ( 1 ) is considered . Testing work too extensive for full publication has been performed , but the following brief account shows some improvements effected both in gauges and in measuring machines . The method of measuring is fully described in the above paper . In brief , the machine consists of a massive bed carrying two measuring head-stocks and a table for carrying and adjusting the gauge . The headstocks each carry a horizontal micrometer screw , working parallel to the bed , and a nut with a graduated head . These measure the bar , which rests on and is clamped to the table . In taking a measurement the left screw , say , is brought into electric contact with the gauge , then the right screw is brought into electric contact with the gauge , and wiien the current passes through the gauge from one measuring point to the other , the two divided heads are read . The difference in the readings is a measure of the distance through the gauge from one measuring point to the other . In addition to the usual precautions against temperature changes provision is made to avoid shaking by arranging that the graduated heads are not actually touched by hand , but are worked by a hand pulley and string . There are two novelties in this method of measuring : ( 1 ) the measurement is made electrically between point and point instead of between rough plane * See ' Roy . Soc. Proc. , ' A , 1906 , vol. 77 . Dr. P. E. Shaw . [ Nov. 18 , and rough plane ; ( 2 ) the gauge can be moved , after a measurement in one position , into another parallel position at a known distance away and a new measurement taken . Thus the two gauge faces are simultaneously explored and errors become manifest . Improvements Gauges . Suppose the face of the gauge is circular . Take 13 places equi-spaced as shown on the face . The first measure is taken from the centre of the face along a line normal to the face to the other face . The second measure is taken from point 2 along a parallel line , and so on for 13 measurements . 11 3 fi 2 13 Since the gauge face generally slopes away from the centre in all directions , the centre is a place corresponding to maximum length through the gauge , and we should expect to find the greatest irregularities for the larger numbers , 10 , 11 , 12 , 13 , approaching the edge of the face . Such , in general , is the case . The accompanying curves ( fig. 1 ) show at a glance that the measures taken are very unequal for curves A , B , C , D , and less so for E , F , G- . One curve is produced from the measurements as above explained ; the gauge is then reversed , and the twin curve produced . This is the procedure for curves A , B , C , E , F. The small vertical divisions on the paper imply 0'5 yu , ( = 1/ 2000 mm. ) ; the horizontal divisions are arbitrary , but the whole length of curve represent generally about 6 mm. Thus the irregularities of the pair of gauge faces are exaggerated 400 times . Let A = the arithmetic mean of the differences for all the readings at one time . Let 3 = the arithmetic meail of the differences in the readings for any one place . Thus A and 3 give respectively measures of the accuracy of the gauge and of the machine . During the experimental work temperature changes may effect the length of the gauge . This would increase 3 and , to a less extent , A. 1910 . ] The Measurement of End-Standards of Length . 591 } 3-inch commercial . ) 6-inch commercial . ) 9-inch commercial . 150 mm. commercial . 150 mm. M.A. } M.A. M.A. Fig. 1 . If both gauges and machine were perfect the curves in fig. 1 would be horizontal straight lines , whereas if the gauge alone were perfect the curves would be sinuous on account of the uncertain action of the machine . The lower curves in the figure approximate to the conditions of perfection , whereas the upper ones are very sinuous . A. This represents readings on a 3-inch commercial gauge , measured direct and reverse . A = 3'6 ytt , 0'4 B. A 6-inch commercial gauge , direct and reverse . A = 3'2 ju , S = 0*8 ju . C. A 9-inch commercial gauge . This shows an advance in accuracy , the machine is much more true than the gauge . A = 2-6 fu , S = 0'4 D. A comparison between a 150 mm. commercial gauge which has A = 3*5 / jl and a much better one , marked M.A. , for which A = TO / u. ( This gauge and those used for curves E , . F , G- , were kindly made for the writer by Messrs. Manlove , Alliott , Ltd. , Nottingham , who took much trouble during these experiments to perfect a lapping method of their own . ) E. This is a good gauge marked M.A. A = TO / u,8 = 0-5/ u. Dr. P. E. Shaw . [ Nov. 18 , F. Another special gauge marked M.A. After taking a set of readings giving one curve , the gauge was re-lapped , measurements repeated , and the second curve produced . A = 0*6/ 4 , S \#151 ; 0*4 fi . ( 4 . A mild-steel gauge . This is the.best curve produced so far . The commercial gauges mentioned are made by various well-known firms , whose names cannot , of course , be given ; the gauges had been in sound keeping since they came from the makers , and were in a state of good preservation , so that the tests are fair . From the above experimental curves and figures it is obvious that ( 1 ) it is possible to make far better gauges than those commonly issued as standards ; ( 21 the best gauges so made are so nearly perfect in form that such errors as are found may be due to the imperfect working of the measuring machine and not to the gauge itself . Improvement in the Measuring Machine . At this juncture it seemed advisable to improve the machine . The table carrying the gauge was the chief source of error . It is very difficult to provide a reliable mechanism for translating the gauge parallel to itself . Any looseness or rotation occurring during this translation will introduce errors in the measurements . The table , as described in the former paper , was discarded . In its place is one involving a different principle . There is a plane surface plate set perpendicular to the bed . The plate on which the gauge rests is pressed by springs so as to rest against the surface plate , touching it at three points . If the surface plate is true and rigid , and the three feet remain always pressed against it , the movements of the gauge resting firmly on .the plate must be strictly parallel . The surface plate is set perpendicular to the run of the bed by an optical arrangement . The Jolianson gauges are made in slabs , the cross-section in all cases being 35 mm. x 10 mm. They are used singly or composite ; in the latter case two or more are wrung together with pressure so as to adhere , and form a rigid composite gauge equal to the sum of the component parts . Whether .single or composite these gauges were known to be very accurate , but it was hoped that with the improved measuring machine as described , any irregularities could be detected . The following tables are typical of results found:\#151 ; 1910 . ] The Measurement of End-Sta Length . 593 Johan son Gauges . 2-inch single . r 0-850 inch . 2-inch composite .\lt ; 0 " 450 " [ 0 -700 " A. B. B-A . A. ! b- B-A . 487 -2 487 -2 0-0 487 -4 487 -3 -0-1 487 -1 487 -1 o-o 487 -2 487 -1 -o-i 487 -2 487 -0 -0-2 487 -1 487-1 -o-o 487 -0 487 -2 0-2 487-1 487 -0 -o-i 487 -0 487 -2 0-2 487 -1 486 -8 -0-3 487-1 487 -2 o-i 487 -2 486 -8 -0-4 487 -0 487 -2 0-2 487 -1 486 -8 -0-3 487 -0 487 -3 0-3 487-0 486 -8 -0-2 A = 0 -2 fx . A = 0 '3 | A = 0 '5 / a. A = 0 *4 , u. A = 0 " 5 , u. ! A = 0 -4 The first number in Column A gives the result for one place on the gauge as 487'2 / x. This is the difference in readings of the two headstocks . It is not the actual length of the gauge , which for present purposes is immaterial . On moving the gauge parallel to itself , the number obtained is 487'1 fi , and so on . After an interval of time , Column B is obtained and Column B\#151 ; A results . Thus , consistency in The Columns A and B taken vertically shows accuracy in the gauge , and consistency when they are taken horizontally shows accuracy in the machine . Inspection of these results shows ( 1 ) that the 2-inch single is ( naturally ) more .consistent than the 2-inch composite , the mean values of A being 025 and 045 / a respectively ; ( 2 ) that the inconsistencies of the machine , as shown by the B \#151 ; A column , are of the same order as the irregularities of the gauges . So the apparent errors in the gauges may be attributable to the defects in the machine . In order to see how ordinary gauges stand tests with the new machine , two 2-inch specially good standards were tested and came out as shown . Two 2-inch Ordinary Gauges . G-auge A. 1 Gauge B. 655 *4 654 -2 655 *0 653 -8 655 *1 654 -5 655 *2 653 -9 655 -2 654 -2 A = 0 -4 A = 0 -7 594 The Measurement of End-Standards of Length . These gauges are thus less satisfactory than the Johanson gauges of the same length . But the superiority of the latter is much greater than appears , for the test was made over about three-fourths of the end faces in all cases . In the ordinary gauge this area is about 20 sq . mm. , whereas in the Johanson gauge it is 350 sq . mm. , or 17 times the area . Any one who has attempted to make accurate plane surfaces in metal will allow that it is a wonderful achievement to make two planes of this size , plane and parallel to within 0*3 micron . 2-inch single Johanson . 2-inch composite Johanson ? In the accompanying curves ( fig. 2 ) , the small divisions vertically represent 0*5 micron . The length of the ordinary gauge curves is about one-sixth of that of the Johanson gauges , corresponding to the diameter of the faces . Until recently the gauge maker has insisted that the measuring machine is more accurate than the gauges it is used to measure ; and that the gauges are themselves more accurate than is required for practical engineering purposes . But we here see that the best machine is powerless to detect errors in these wonderful Johanson gauges , and an advance in accuracy of the former is demanded . The writer is now designing a machine which he hopes will give consistent readings to OT micron , under the trying conditions that the gauge shall be moved parallel to itself between the readings . In recent years the work of Michelson and of Fabry and Perot has placed the measurement of line standards of length on a high level of accuracy . An even further advance is promised by the use of Grayson 's rulings by Dr. Tutton.* If a much improved measuring machine on scientific principles can be produced , the measurement of end standards should exceed in refinement that now obtaining in the parallel branch of metrology , since the latter suffers from the optical limitation of the microscope . 2-inch ordinary . Fig. 2 . * See ' Phil. Trans. , ' A , 1909 , vol. 210 . On the Absolute Expansion of Mercury . 595 The writer wishes to tender his thanks to Mr. J. M. C. Paton , of the firm of Manlove , Alliott , Ltd. , for much assistance , freely given , in the making of gauges ; also to Dr. E. T. Glazebrook , for giving him every facility in tests made on his machine at the National Physical Laboratory ; also to the Eoyal Society for a grant which defrayed some of the cost of ' this work . On the Absolute Expansion of Mercury . By H. L. Callendar , M.A. , LL. D. , E.E.S. , and H. Moss , B.Sc. , A.E.C.S. , Demonstrator of Physics , Imperial College of Science and Technology , S.W. ( Eeceived November 19 , 1910 , \#151 ; Eead January 12 , 1911 . ) ( Abstract . ) Kegnault 's experiments on the absolute expansion of mercury were reduced by Wullner , and subsequently by Brooch . Their reductions differed by nearly 1 per cent , at 300 ' C. Begnault 's own reductions differed by nearly 1 per cent , from either at 40 ' C. Chappuis ' later determinations by the weight thermometer method , which were not absolute , agreed , fairly well with Wiillner 's reduction of Begnault at low temperatures , but differed from Wullner in the opposite direction to Brooch by more than 2 per cent , when extrapolated to 300 ' C. The object of the present investigation was to repeat Eegnault 's method on a larger scale with modern appliances , and the apparatus was designed to secure an order of accuracy of 1 in 10,000 , or 0'01 ' C. , which , it is believed , has been substantially attained . The principal modifications made in Eegnault 's apparatus were as follows : \#151 ; ( 1 ) In place of the single pair of hot and cold columns , each 1*5 metres long , employed by Begnault , six pairs of hot and cold columns , each nearly 2 metres long , were connected in series as a multiple manometer , giving nearly eight times the expansion obtainable with Eegnault 's apparatus . ( 2 ) The difference of level to be measured was directly referred to a standard Invar scale divided in millimetres with divisions 4 microns wide , by means of a pair of telescopes with micrometer eyepieces reading to .O'OOl cm . The difference of level corresponding to the fundamental interval 0 ' to 100 ' C. was 20'5 cm . , so that the limit of accuracy of reading was 1 in 20,000 of this interval , or 0'005o C. The lengths of the hot and cold columns , each nearly 2 metres , could be read to 0'01 cm . , giving the same order of accuracy . ( 3 ) The mean temperatures of the hot and cold

rspa_1911_0013

0950-1207

On the absolute expansion of mercury.

595

597

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

H. L. Callendar, M. A., LL. D., F. R. S.|H. Moss, B. Sc., A. R. C. S.

abstract

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Tables

Thermodynamics

Tables

]\gt ; On of Mercury . The writer wishes to tender his thanks to Mr. J. M. C. Paton , of the firm of NIanlove , Alliott , Ltd. , for much assistance , freely riven , in the making of also to Dr. R. T. Glazebrook , for giving hinl every facilit in tests made on his machine at the LaborRtor ; to the Royal Society for rant which defrayed some of the of this vork . On Absolnte of By H. L. LLENI ) , LL. D. , , and H. llfoss , Demonstrator of Physics , College of Science and ( Received November 19 , 1910 , \mdash ; Read January 11911 . ) act . 's experiments on the absolute expansion of mercury were reduced by Wiillner , and uently b ] . Their reductions differed by nearly 1 per cent. at C. 's own leductions differed by nearly 1 per cent. from either C. } ) ' later determinations by the thellnometer metbod , which were not absolute , reed fairly well with Wullner 's reduction of egnault at low temperatures , but differed from Wiillner in the opposite direction to Brooch by more per cent. when extrapolated to C. The ject of the present ation to repeat 's method on a scale with model.n appliances , and the apparatus was designed to secure an order of ccuracy of 1 in 10,000 , or C. , which , it is believed , has been substantially attained . The principal modifications made in Regnault 's apparatus were as : In place of the single pair of hot and cold colunlls , each metres , employed by Reguault , six airs of hot and cold colunns . each nearly 2 metres long , were connected in series as a multiple manometer , giving nearly eight times the ) ansion oinable with ) ( 2 ) The difference of level to be nleasnred directly referred to a standard Invar scale divided in millimetres divisions 4 lnicrons wide , by means of a telescopes with lliclometer to cm . clilference of level . to the fundamental to . was cm . , the limit of accuracy of reading was 1 in 20,000 of this interval , or C. } of the hot and cold columns , each nearly 2 metres , could be read to cm . , the same order of accuracy . The mean temperatures of the hot an cold On the of Mercury . columns were observed by means of a pair of platinum thermometers equal in length to the columns , and reading to C. The possible error of this reading would not amount to more than C. at C. , and would be much less at lower temperatures . ( 4 ) Uniformity ) constancy of temperature were secured by a continuous circulation of oil , heated by means of resistance coils traversed by an electric current . The method of electric heating permitted the most delicate regulation of the temperature , even at 30 C. , with the least possible disturbance of the surrounding conditions . ( 5 ) 's were taken with the cold column at the atmospheric temperature of to C. , which left the reduction to C. somewhat uncertain , and was the chief cause of the discrepancy in the reduction of his obseryations at low temperatures . In the present investithis uncertainty was avoided by taking a special series of observations with the cold column at C. and at C. ( 6 ) The chief cause of the discrepancy between the reductions of Wullner and Brooch at temperatures appears to be that Brooch applied a correction for the conduction of heat along the cross-tubes connecting the hot and cold columns in Regnault 's apparatus . These cross-tubes were not quite horizontal , and introduced some uncertainty in the effective of the columns . In the present investigation , the cross-tubes were made of steel tube 1 mm. in bore , to diminish conduction of heat at the point where they emerged from the hot bath , and were held rigidly horizontal , by means of a specially desi , bracket , for the short in which the temperature changed from hot to cold . The effective height of the hot column was thus rendered definite and accurately measurable . With the apparatus above described , 94 complete sets of observations were taken on 33 days in the course of 1908 , 1909 , and 1910 , for 16 different ranges of temperature covering the interval from C. to C. The mean results at each temperature agree to 1 in 10,000 above 10 C. , or to C. below 10 C. , with the following formula for the mean coefficient from C. to C. The results cannot be represented satisfactorily by a linear formula for the mean coefficient over the whole range ; but for approximate work the following simple formula may be sufficiently exact to be of This formula gives results which are practically correct at 10 and 20 C. , with a maximum error of C. between C. and 20 C. , but the value of the mean coefficient is more than 1 in 400 too small at 30 C. Proof of the Theorem of Double Six of Straight . 597 The results of Eumorfopoulos*for the boiling-point of sulphur on the scale of the constant pressure air thermometer were about 1o C. lower than the previously accepted value C. , when reduced by the BrochRegnault formula for the expansion of mercury ; but are brought into practically perfect agreement with the old value , when reduced by reference to the results of the present investigation . A Proof of the } of a Double Six of By H. , Sc. D. , ( Received Noyember 21 , \mdash ; Read November 24 , 1910 . ) * We assume that if two quadric surfaces have common two intersecting generators , their remaining common points lie upon a plane . This is capable of sirnple geometrical proof . Further , we prove a subsidiary theorem regarding eight lines , which we , 2 , 4 , , which satisfy certain conditions . These conditions } first that in the schelne 1 2 o ) 4 1 ' 2 ' each line intersects the three which are not in the same or column of the as itself ( so that the lines can be arranged as two skew quadrilaterals , with the property each side of either intersects a particular side of the other and second that one of the two lines which call be drawn to meet 1 ' , 2 ' , 3 ' , 4'\mdash ; say ( \mdash ; intersects one of the lines which can ) drawn to meet 1 , 2 , 4\mdash ; say . The conditions for the eight lines are then briefly expressible as the existence of a schelne 1 ' 2 ' 3 ' 4 ' 'Roy . Soc. Proc , 1908 , vol. 81 , p. 339 . If and be the common gene1atol s , intersecting in , a variable plane through will touch the quad1 respectively , say , in and , on , and the nges will be projective with the pellcil ; these have the ummon point , and will thus have another commou ) , say , lying 011 , let be the ) of ? ? other than , at the qnad1ics touch . If now be any point of the two quadrics not lying on or the plano A cuts the surfaces ely in conies having comlilon and , at A and B. These comics thus coincide in one , which } c.onstitute the remaining of intersection of the quadrics .

rspa_1911_0014

0950-1207

A geometrical proof of the theorem of a double six of straight lines.

597

602

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

H. F. Baker, Sc. D., F. R. S.

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6.0.4

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10.1098/rspa.1911.0014

Formulae

Tables

Mathematics

]\gt ; Proof of the Theorem of Double Six of Straight Lines . 597 The results of Eumorfopoulos*for the boiling-point of sulphur on the scale of the constant pressure air thermometer were about 1o C. lower than the previously accepted value C. , when reduced by the BrochRegnault formula for the expansion of nlercury ; but are brought into practically perfect agreement with the old value , when reduced by reference to the results of the present investigation . A Geometrical Proof of the Theor.em of a Double Six of Straight Lines . By H. , Sc. D. , ( Received Noyember 21 , \mdash ; Read November 24 , 1910 . ) * We assume that if two quadric surfaces have common two intersecting generators , their remaining common points lie upon a plane . This is capable of simple geometrical proof . Further , we prove a subsidiary theorem regarding eight straight which we name 1 , 2 , 3 , 4 , 1 ' , 2 ' , 3 ' , , which satisfy certain conditions . These conditions first that in the ] elne 1 ' 2 ' 3 ' 4 ' , each line intersects the three which are not in the same row or column of the as itself ( so that the lines call be arranged as two skew quadrilaterals , with the property that each side of either intersects a particulal ' side of the other and second that one of the two lines which can be drawn to , 4'\mdash ; say \mdash ; intersects one of the two lines which can be drawn to meet 1 , 2 , , 4\mdash ; say . The collditions for the eight lines are then briefly expressible as the existence of a scheme 1 ' 2 ' 'Roy . Soc. Proc , 1908 , vol. 81 , p. 339 . If and be the common generators , intersecting in ariable plane through will touch the respectively , say , in and , on , and the ranges } , will be projective with the pencil ; these ranges have the cummon point , and will thus have auother c.ommon point , say , lying on . Similarly , let be the point of other than , at which the quadrics touch . If now be any common point of the two quadrics not on or , the plane A cuts the surfaces respectively in conics having H comnlon and touching at A and B. These conics thus coincide in one , which ) constitutes the curve of intersection of ) quadrics . Dr. H. F. Baker . Geometrical Proof of the [ Nov. 21 , where as before each of the ten lines of this scheme meets every line not in the same row or column of the scheme as itself . Then , denoting the point where the line meets the plane containing the three points , 1 , 4 by ; 23 ' , 2'3 , 14 and so on , the subsidiary theorem is that the three points ; 31 ' , 3'1,24 , 1'2,34 are collinear , and the line 4 passes through these three points . To prove this subsidiary theorem , consider the quadric surface constructed to have the three skew lines 1 , 2 , , as generators , say the quadric ; and with it consider the quadric These quadrics have common the two intersecting generators , . Their common points not lying on these common generators are therefore coplanar . Two such common points are 1 , and . But in fact the lines 3 ' and 4 ' are generators of the quadric , because they meet each of the lines 1 , 2 , ; and similarly the lines : and 4 are generators of the quadric Thus , two further points of the two quadrics , not lying.on the lines or , are and Hence , the four points are coplanar . Similarly , the four points are coplanar , and so are the four points ( 3 , 1 , . This proves that the line 4 passes the three points ; 31 ' , 3'1 , 24 ; 12 ' , 1'2 , 34 which is the subsidiary theorem . We can now proceed to the theorem of a double six of lines . This theorem is that if 11 lines be in relations expressible by the scheme 1 2 3 4 o 1 ' 2 ' 3 ' 4 ' 5 ' 6 wherein each line intersects those not lying in the same row or column of the scheme as itself , then there exists a line intersecting 1 ' , 2 ' , 3 ' , . ' ( a ) The given scheme includes as part of itself the scheme 1 ' 2 ' 3 ' 5 ' 6 ' Let the line , other than 4 , which meets 1 ' , 2 ' , 3 ' , 5 ' be called , so that we have a scheme of conditions 1 ' 2 ' 3 ' 5 ' 6 ' The eight lines 1 , 2 , 3 , , are thus in relations such as those considered in the subsidiary theorem . Hence the three points ; 23 ' , 2'3 , 16 ; 31 ' , 3'1 , 26 are collinear , and the line may be defined as the line containing these : 1910 . ] Theorem of Double Six of Lines . ( b ) The given scheme of 11 lines contains also as part of itself the scheme 1 ' 2 ' 3 ' Let the line , other than 5 , which meets 1 ' , 2 ' , 3 ' , 4 ' , be called , so that we have the scheme of conditions 1 ' 2 ' 3 ' The eight lines 1 , , 3 , are therefore in relations such as those considered in the subsidiar.y , theorem . Thus the three points all lie on the line Thus , which meets 1 ' , 2 ' , 3 ' , coincides with which meets 1 ' , 2 ' , 3 ' , 4 ' ; namely , there exists a line meeting 1 ' , 2 ' , , as was to be shown . If this line be c.alled 6 , and the line joining the points , be called [ 1 , 2 ] , we have incidentally shown that the line [ 1 , 2 ] meets the six lines [ 3 , 4 ] , [ 3 , 5 ] , [ 3 , 6 ] , [ 4 , 5 ] , [ 4 , 6 ] , [ 5 , 6 ] . If be the line of intersection of the plane of the lines 1 , 2 ' with the plane of the lines 1 ' , 2 , the argument equally shows that intersects . It is only necessary to put plane for point , and point for plane throughout ; in particular two quadrics with a pair of intersecting generators common , have a common enveloping quadric cone . We have considered in the subsidiary theorem a set of lines satisfying conditions of the type and further subject to the unsymmetrical condition that one of the two lines which meet 1 , 2 , 3 , 4 , intersects one of the two lines which meet 1 ' , 2 ' , 3 ' , 4 ' . It appears now that in such case the other hne which meets 1 , 2 , 4 , intersects the other live which meets 1 ' , ) ) , and that this deduction is another form of the theorem of a double six of lines . [ Added December 12 . ] Conversely consider eight lines satisfying ihed by the scheme with the further condition that the four points 12 ' , 1'2 , 34 ' , are coplanar ; such a set of lines depends on 19 constants . Then it can be shown : ( a ) That either of the lines meeting 1 , 2 , 3 , 4 , meets one of the meeting 1 ' , 2 ' , 3 ' , 4 ' , ( b ) that the points 31 ' , 3'1 , 24 ' , 2'4 , are coplanar , ( c ) that the points 23 ' , , are coplanar , ( d ) that , if VOL. LXXXlV . Dr. H. F. Baker . Geometrical Proof of the [ Nov. 21 , denote the line joining the points . and so on , the four lines are concurrent , say , in ; the four lines are concurrent , say , in ; and the four lines are concurrent , say , in , ( e ) that if denote the line of intersection of the planes 12 ' and 1'2 , and so on , the lines , meet in , the lines , meet in 02 , the lines , meet in . The demonstrations of these results are as follows:\mdash ; Draw one of the two lines which meet 1 , 2 , 3 , 4 , say , 5 ' , and then draw the unique line , other than 1 , which meets , calling this line 6 ; consider then the two quadric surfaces ( 643 ) and ; these will have the common generators 6 and 5 ' ; of the quadric two generators are 1 and 2 ; of the quadric ( 643 ) one generator is 2 ' . As the common points of these quadrics which do not lie on 5 ' or 6 are coplanar , their plane is that determined by the points 34 ' , 3'4 , 12 ' ; the generator 2 of ) , which already meets on 5 ' , meets ( 643 ) in one other point lying on this plane . Now the plane of 34 ' , 3'4 , 12 ' , meets 2 in the point 1'2 ; this point is therefore on ( 643 ) . The points 1'3 and 1'4 are , however , also on ( 643 ) ; hence the line 1 ' is a generator of ( 643 ) and meets 6 ; as was to be proved . ( b ) The line lies plane hence meets ; it lies in the plane 3'2 , and hence meets ; thus it passes through the intersection of with . Again , the line lies in the plane 32 ' , and hence meets ; it lies in the plane 1'4 , and hence meets ; thus it passes also through the intersection of with . So that the points , are coplanar . ( c ) The line lies in the plane 24 ' and hence meets ; it lies in the plane 3'1 and hence meets ; thus it passes through the intersection of with line lies in the plane 31 ' and hence meets and lies in the plane 2'4 , and hence meets ; thus it also passes through the intersection of with So that the points 23 ' , 2'3 , 14 ' , 1'4 are coplanar . ( d ) The line lies in the plane 21 ' and hence meets ; it lies in the plane 3'4 and hence meets and thus passes through the intersection of with Again line lies in the plane 2'1 and hence meets ; it lies in the plane 34 ' and hence 1910 . ] Theorem of Double of Straight Lines meets thus also passes through intersection with This establishes the existence of the points ( e ) The plane 12 ' , as containing the points 13 ' , 2'4 , contains the line ; this same plane 12 ' , as containing the points 14 ' , 2'3 , contains the line through 03 . Again the plane 1'2 , as the points 1'3 , 24 ' , contains the line through 03 , and , as containing the points 1'4 , 23 ' , contains the line through . The line , in which the planes 12 ' , 1'2 intersect , thus passes through . So the line C34 passes . The point has thus a correspondence with the plane of 12 ' , 1'2 , 34 ' , 3'4 , which contains the lines [ 1 , 2 ] , [ 3 , 4 ] , respectively defined as and . Similarly for the points and It from the above that if we regard the planes of , as rectangular , meeting in , and the plane as lying at infinity , the four intersections , of the pairs of the eight lines 1 , 2 , , 3 ' , 4 ' , which lie in any one of the three rectangular planes , form a rectangle , with sides parallel to two of the axes such a rectangle is constituted for exalnple by the points 23 ' , 1'4 , 2'3 , 14 ' , lying in . It is proved above that the line [ 56 ] , joining the points meets each of [ 23 ] , , which are the diagonals of the rectangle in the plane ; thus the centres of the three rectangles lie in one straight line [ 56 ] . It is easy now to see that the points , , , in which the lines 1 , 2 , , 4 ' meet the plane at infinity , are the projections from of the corners a rectangular parallelopiped whose edges parallel to the rectangular axes . Hence the four lines , are concurrent . It can be shown that their point of concurrence lies on [ 56 ] . Dually , if the line , defined as the intersection of the planes 56 ' , which is also the line of tersection of the three planes , , , be joined to the point by a plane , this plane cuts the of lines ( 1 , 1 ( 2 , 2 ( 3 , 3 ( 4 , 4 in four pairs of points , each pair being collinear with As the tetrahedron ives rise to these relations , I have formed the equation of the cubic surface containing the lines , and find that it may be put into the form , when / 7 , , are the co-ordinates referred to this tetrahedron , where ) . And with this , when the co-ordinates of a line are defined by the equations , the line 4 is , the line 4 ' is obtained 602 Proof of the Theorem of a Double Six of Straight Lines . from this by replacing , by , the line 1 by replacing by , the line 1 ' by replacing , by , and similarly for 2 , 2 ' , and 3 , 3 ' . The line is then , and the line [ 56 ] is . The whole figure reciprocates itself in regard to the quadric . Of this cubic surface fifteen lines are determined rationally , namely , 1 , 2 , 3 ' , 4 ' , , the remaining twelve , , which form a double six , depend upon a single square root .

rspa_1911_0015

0950-1207

The chemical physics involved in the precipitation of free carbon from the alloys of the iron-carbon system.

1

13

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

W. H. Hatfield, B. Met. (Sheffield University)|Prof. W. M. Hicks, F. R. S.

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6.0.4

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10.1098/rspa.1911.0015

Measurement

Chemistry 2

Measurement

PROCEEDINGS OF THE ROYAL SOCIETY . Section A.\#151 ; Mathematical and Physical Sciences . The Chemical Physics involved in the Precipitation of Free Carbon from the Alloys of the Iron-Carbon System . By W. H. Hatfield , B. Met . ( Sheffield University ) . ( Communicated by Prof. W. M. Hicks , F.R.S. Received October 7 , \#151 ; Read November 10 , 1910 . ) [ Plates 1\#151 ; 5 . ] As a result of recent research* it is held that the iron-carbon alloys must be considered as an iron-iron carbide system as indicated in the accompanying diagram ; the author is satisfied that the double diagram based on the assumption of a metastable and a stable equilibrium is inaccurate , since , in the liquid or the solid state , that carbon which is in solution is contained in solution as carbide . The experiments to be described afford evidence that the carbide must separate out from the solution before free carbon can appear , and that it is only the structurally free carbide that can dissociate ; free carbon will not separate from the solid solution . The influence of silicon , sulphur , and manganese upon the precipitation are investigated , with the following results :\#151 ; 1 . The silicon ( if it be the only foreign element present ) is not uniformly distributed through the material . The carbide , whilst not containing so much as the matrix , has present a percentage increasing with the silicon content of the alloy . 2 . The manganese is largely found in the carbide to the exclusion of the silicon . * Goerens , ' Metallurgies 1906 , vol. iii ; 1907 , vol. iv . ! VOL. LXXXV.\#151 ; A. 1\gt ; 2 Mr. W. H. Hatfield . Precipitation of Free Carbon [ Oct. 7 , 3 . The sulphur appears to cause the exclusion of the silicon from the carbide , but the methods employed failed to reveal the presence of any quantity of sulphur in that constituent . OF EUTE :tic FREEZING RESO LUTION OF HAR DENITE INTO PE 0 0*50 10 1-5 2-0 2-5 30 3 5 4-0 45 % OF CARBON , \#151 ; = accepted lines . . . . . = readings obtained by Carpenter and Keeling which suggest other lines . 4 . The heat treatment experiments indicate that the presence of these elements , by modifying the composition of the carbide , renders it more or less difficult to dissociate at a given temperate . Further , by altering the composition of the alloy , the solubility of the carbide in the austenite was modified and therefore more or less free carbide was subjected to the conditions of dissociation . It is also shown that the space occupied by , and the structure of , the free " annealing " carbon nodules are determined by the size and structure of the free carbide from which they are produced . The precipitation of free carbon during cementation is discussed and the phenomenon of " black " steel is considered in the light of the observations made during the research . The Free Carbon as Found in the Iron-Carbon Alloys . The free carbon observed in the alloys of iron and carbon is always one of the two varieties , graphite or annealing carbon . 1910 . ] from the Alloys of the Iron-Carbon System . Graphite is formed immediately after the solidification of the eutectic , and its distinctive form is most probably due to the influence of the primary crystallization . Obviously upon an examination of the iron-carbon freezing diagram it will be seen that the graphite could not be produced previous to the freezing of the eutectic , otherwise it would not be found evenly distributed through the mass , but would have risen by its own specific gravity to the surface . Further , as the eutectic is proved to consist of 4*3 per cent , of carbon in combination , it will be necessary for the eutectic to separate into carbide and austenite , before the carbide can dissociate and thus give birth to the free carbon . At the point of solidification , the solubility of the iron for the carbon is that of the eutectic composition , 4*3 per cent. , but the change from the liquid to solid state reduces the solubility to such an extent that the separation of the superfluous carbide causes , the distinct evolution of heat which is known to take place at about 1137 ' C. In irons such as the highly siliceous ones , it is difficult to conceive* how the carbide in the finely divided state , in which it exists immediately after this separation , can live through the immediately subsequent conditions . The following corroborative evidence should be considered : Two bars { 2 " x 1 " x 12 " ) were cast of the following composition :\#151 ; C ... ... ... ... ... . 3*20 per cent. S ... ... ... ... ... ... . : ... 0*02 per cent. Si ... ... ... ... . . 1T0 " P ... ... ... ... ... . 0*20 " Mn ... ... ... ... ... . 0'41 per cent. The first , cast with the metal at about 180 ' C. higher temperature than the other , in fracture was mottled , and the second was perfectly grey . The unetched microstructure of the grey bar is shown in fig. 1 , Plate 1 , and to .one accustomed to white iron structures it shows that the primary cementite has decomposed in situ . Fig. 2 , Plate 1 , shows the structure when etched , and indicates that it is only the structurally free carbide that has dissociated . The microstructure of the mottled bar , fig. 3 , Plate 1 , indicates that the precipitation commences at several centres , and if continued spreads through the mass . In fig. 4 , Plate 1 , the unetched structures of the free carbon areas are illustrated . It will be seen that the free carbon exactly conforms in structural position with that held by the cementite . As previously shown by the author)- the initial casting temperature materially influences the dissociation of the carbide . In these instances the free carbon would unquestionably be classed as graphite , and the microstructures throw light upon the manner of the birth * Heyn and Bauer , ' Stahl und Eisen , ' vol. 27 , 1565\#151 ; 71 and 1621\#151 ; 25 . t Hatfield , 'Iron and Steel Institute Journal,5 1906 , vol. i. B 2 4 Mr. W. H. Hatfield . Precipitation of Free Carbon [ Oct. 7 , of graphite . Fig. 26 , Plate 4 , shows the typical graphitic iron , which results from prolonged cooling of these bars . Annealing carbon differs little from graphite except in that the temperature at which it is precipitated being low the amorphous form is retained . The composition of the iron , the size and structure of the cementite or free carbide , and the temperature at which the carbide dissociates , are , as will be shown , the determining factors of the size and character of the annealing carbon . As an instance of the influence of the size of the free carbide upon the size of annealing carbon the results of the following experiment are given . Two test bars of white cast iron of the . following composition were made:\#151 ; Si ... ... ... ... ... . 0*70 per cent. S ... ... ... ... ... . . 004 per cent. Mn ... ... ... ... ... . . 0*80 " P ... ... ... ... ... . . 0-11 " C ... ... ... ... ... ... 3*40 per cent. One bar A was allowed to cool normally , its microstructure is shown in fig. 5 , Plate 1 . The other bar B was quenched when it had cooled to 1000 ' C. , and the structure of this one will be seen in fig. 7 , Plate 1 . It will be noticed that whereas in the naturally cooled bar the cementite is in large thick membranes , in the quenched one the structure is very different . The matrix seen in the micrograph of B actually contains considerably more carbon in solution than is present in the pearlite of A. In fig. 25 , Plate 4 , is seen the microstructure of a globule of this iron when poured molten into a mass of cold water ; it illustrates the comparative structure of iron approximating to the eutectic composition shortly after solidification . Samples A and B were heated to a temperature of 1050 ' C. , maintained there for three-quarters of an hour , and quenched at a temperature of 1030 ' C. Fig. 6 , Plate 1 , illustrates the microstructure of the bar A , and if the structure is compared with its condition before this heat treatment it would appear that the annealing carbon results from the dissociation of the cementite membranes of carbide observed before the treatment . The heat treated bar B presented a 'structure shown in fig. 8 , Plate 1 . The whole of the small cementite had decomposed , with the result that this bar contains no cementite , but only small annealing carbon nodules in martensitic austenite , as seen when examined under a high power . This experiment indicates that the size of the original cementite is certainly an influence in determining the size of annealing carbon , and it might be well at this point to refer to a very interesting paper by Mr. Levy.* * Levy , 4 Journal Iron and Steel Institute , ' 1908 , vol. 2 . from the Alloys of the Iron-Carbon System . His theory that it is necessary for the carbide to ball up before it can dissociate would appear to be disproved . The author has made the statement that the " annealing carbon " sometimes appears to be merely dissociated carbide , i.c. a mixture of finely divided iron and carbon occupying the position of the original cementite . He would refer to two of his micrographs illustrating this phase , fig. 27 , Plate 4 . Here it will be seen that in a sample of white cast iron , which was undergoing heat treatment at the comparatively low temperature of 835 ' to 840 ' C. , the cementite of a whole area of the section decomposed in situ . The micrograph of the drastically heat-treated blister-steel , fig. 34 , Plate 5 , is an example of the annealing carbon occupying a similar position and of a similar size to the original cementite . On further heat treatment such mixtures of free carbon and iron undergo a change , the carbon segregating , and the precipitated iron entering structurally into the mass . As an instance of this , fig. 11 , Plate 2 , represents the microstructure of a bar of heat treated white iron quenched at about 860 ' O If this temperature be maintained for a considerable time after the precipitation of the annealing carbon the structure is as shown in fig. 12 , Plate 2 . Influence of Varying Composition upon the of the Structurally Free Carbide . The presence of silicon , sulphur , and manganese is well known to influence the precipitation of annealing carbon , and the author therefore decided to determine the manner in wdiicli this influence was brought to bear . Four irons of varying composition were chosen for experiment and were of the following analysis :\#151 ; C. Cr . Si . Mn . S. P. A 3*62 nil 1 *20 0*18 o-oii 0-041 B 3 2 ? f 0-81 0*14 o-oio 0*04 C 3 4 n 0*85 2-66 0-012 0*041 D 3*16 V 0-97 0*04 0-45 0-04 The micrographs of these four materials are shown in Plate 3 , figs. 13 , 14 , 15 , and 16 , and are seen to consist as usual of cementite carbide ( FegC ) and pearlite . From bars hardened at 740 ' C. quantities of the respective carbides were obtained . On analysis , they were found to be of the following composition :\#151 ; 6 Mr. W. H. Hatfield . Precipitation of Free Carbon [ Oct. 79 Bar . Si . Mn . C. A per cent. 1-09 0-6L 0*15 0*37 per cent. 0*19 0*16 3*74 traces per cent. 6*79 6*40 7-20 6*60 B C D The method , though crude , gave interesting results . It may be mentioned that the whole of the silicon , apart from that found in the carbide , was found in the solution , it having perfectly entered into solution in the cold dilute hydrochloric acid . The exposure of the material to the acid was of 48 hours ' duration in each case- . When the bars in the unhardened condition were decomposed in the same manner the analysis of the residues gave vastly different results , which were as follows :\#151 ; Bar . Si . Mn . A per cent. 2*15 101 1 *45 0*49 per cent. 0*28 0*19 3-62 traces B C I ) The silicon was therefore not dissolved by the HC1 as in the former instances . This may be explained after careful consideration of the physical condition under which the " silicide " exists in such samples . Since , however , the pearlite exists as hardenite at the temperatures now being discussed , the problem may , for the present , be dismissed . The author would claim the following deductions from these experiments :\#151 ; 1 . That the silicon is not uniformly distributed through the material , but that the carbide , whilst not containing as much silicon as the matrix , contains an appreciable quantity , corresponding to some extent to the total percentage . 2 . That in the case of sample C the manganese is found largely in combination in the carbide , to the exclusion of the silicon . 3 . In the case of the high sulphur iron the silicon is abnormally low in the carbide , and although the sulphur is not found in it , it would be deduced that it is responsible for the comparative absence of the silicon . The ease with which sulphur compounds are decomposed by even dilute hydrochloric acid would lead one to believe that though it is not found in the carbide it from the Alloys of the Iron-Carbon System . does not follow that some of it was not there originally . The author is aware , however , that the sulphur prints give contrary evidence . Influence of Composition upon Precipitation of Annealing Carbon White Iron . Charpy and Grenet publish some interesting figures upon the influence of silicon on the precipitation of annealing carbon in their paper on " The Equilibrium of the Iron and Carbon System."* Irons of varying composition were poured into water , thus obtaining irons up to very high silicon content in the white state . Although Charpy and Grenet state that the samples all had the normal white iron structure , the free carbide in their samples would be smaller and in less quantity than in a normal casting and the matrix much higher in carbon , facts which must be taken into account in comparing the two series of results . The author 's micrographs , figs. 5 and 7 , Plate 1 , and fig. 25 , Plate 4 , illustrate the condition and quantity of carbide likely to have been present in these samples , representing as they do the structures of normal white iron , white iron quenched from 1000 ' C. and from the molten state respectively . With abnormal silicon , however , this would be the only way to entrap the carbon in the combined state . The author 's heat treatments were made in a Clinch-Jones muffle , and this ensured that the material , by being heated in a reducing atmosphere of unignited gas , was not decarburized . Pars A , B , C , and I ) , Plate 2 , figs. 13 , 14 , 15 , and 16 , recently described , were placed in the muffle standing at 920 ' C. , and were maintained at this temperature for one hour and then carefully quenched in iced brine . After quenching , microsections were taken from these bars and etched . The results are to be found in Plate 3 , figs. 17 , 18 , 19 , and 20 . In each case it will be seen that the cementite is beginning to disappear . This is explained by the increasing solvent action of the matrix for carbide , owing to the rise in temperature to 920 ' C. In the case of A it is clear that the cementite had to an extent redissolved in the matrix , but that some of the remaining cementite had decomposed . In the case of B considerable areas of cementite have redissolved in the matrix , whilst several nodules of annealing carbon are seen . In the case of C no annealing carbon is observed , and further the cementite seems much corroded , having obviously been to a considerable extent dissolved in the matrix . In the case of D similar changes have taken place in the structure . * 'Bulletin de la Societe d'Encouragement pour l'lndustrie Nationale/ vol. 10 pp. 399\#151 ; 407 . 8 Mr. W. H. Hatfield . Precipitation of Free Carbon [ Oct. 7 , In the second series samples of the same composition were maintained for one hour at 1050 ' C. and quenched from that temperature . Plate 3 , figs. 21 , 22 , 23 , and 24 , illustrates the structures obtained . In the case of A all the cementite has disappeared . Some is in solution in the austenite and the remainder is dissociated into iron and carbon . Micrograph fig. 21 illustrates the structure . In the case of B all the cementite has disappeared . It is either in solution in the austenite or dissociated into iron and carbon . Micrograph fig. 22 illustrates this . The carbon wTould appear to be further segregated , but since both samples were treated alike the author is unable to explain this . This variation , however , may be traced to the form and size of the original cementite . In the case of C the cementite is partly in solution , partly decomposed , and the annealing carbon occurs in a matrix of austenite in which the martensitic structure is well developed . Only traces of undissociated carbide remain . Considering the high percentage of manganese in this sample C , the precipitation is interesting . In the case of D , much undissociated cementite and some peculiarly well-rounded nodules of annealing carbon appear in the matrix . The following table gives the amount of free carbon found in these samples after quenching from 1050 ' C.:\#151 ; Sample . After treatment . Combined carbon . Free carbon . Carbon in austenite . per cent. per cent. per cent. A 1 *55 2*07 1 '55 B 1 71 1 *49 1 71 C 2 *26 1 -12 2*26 1 ) 2 *46 0 70 ? These experiments prove that the presence of the silicon in the carbide * renders it less stable ; that manganese and sulphur render the carbide more stable , but that at 1050 ' C. even 3*00 per cent , of manganese , or 045 per cent , of sulphur , fail to render the carbide stable . The Precipitation of Annealing Carbon in Blister Steel . The introduction of carbon into iron by cementation is of great interest . It will be found that Percy , in his book , discusses the subject to date , and the subsequent microscopical researches of Sorby and Arnold developed considerably our knowledge of the process . 1910 . ] from the Alloys of the Iron-Carbon System . It is proposed , before discussing the precipitation of free carbon , first to consider the chemical physics of the process . With regard to the percentage of carbon it is possible to introduce , Saniter introduced 2*9 per cent. , whilst Charpy , confirming Marguerite 's observations , introduced 6*72 per cent , by this process , Charpy using KCN and a temperature 650 ' C. In cementing bars of commercial sizes , it is impossible by means of charcoal to introduce more than an average percentage of 1*8 to 1*9 of carbon at the temperatures employed . It would seem from present experimental data to hand that iron carbide ( Fe3C ) is synthetically produced at low temperatures when iron and carbon or some of its compounds are in contact , and it will be found , on examining the experimental data of the recorded instances of high percentages of carburizing , that they have all been performed on finely-divided iron , very fine wire , or drillings . If attempt is made to cement bar iron , say 3 " x a very different set of conditions will be found ; the iron and carbon in contact produce the carbide , but it is not until the temperatures at which diffusion* takes place are reached that the carburization can penetrate to the interior . Before the carbon can diffuse , the carbide must be in solution in the iron , and hence the degree to which the interior can be carburized is controlled by the solubility of the carbide . This solubility rises with the temperature , but at the temperatures normally employed , it seems , does not exceed 1*60 per cent , of carbon , even if Benedick 's theory , elaborated by Iiowe , f is taken into consideration . Such being the chemical physics involved in the cementation process , it is interesting to consider their bearing upon the precipitation of " annealing carbon " during such heat treatments . Materials of the following composition were put through a somewhat drastic heat treatment . No. 1 is " washed iron , " and contains 3*30 per cent , of carbon ; the other four are high-class crucible steels of gradually increasing carbon content . The complete analyses were as follows :\#151 ; No. 1 Carbon . Manganese . Silicon . Sulphur . Phosphorus . 1 3 *30 Trace 0*074 0*01 0*01 2 0*85 0*26 0*093 0*01 0*01 3 1 -05 , 0*31 0*084 0*01 0*01 4 1 -10 0*27 0*102 0*01 0*01 5 1 *20 0*31 0*084 0*01 0*01 The bars were cemented with charcoal , seven days being required to attain the necessary heat of 950 ' to 1000 ' C. ; they were then maintained between * Arnold and McWilliam , ' J. Iron and Steel Institute , ' 1899 , vol. i. t ' American Institution of Mining Engineers ' Journal , ' 1908 . 10 Mr. W. H. Hatfield . Precipitation of Free Carbon [ Oct. 7 y these temperatures for a period of five days , after which they slowly cooled during a further period of five days . Before the heat treatment , all the carbon in each of the bars was in the combined state ; the analyses after the treatment are of considerable interest , and are given in the next table :\#151 ; No. Total carbon . Annealing carbon . Combined carbon . Gain in carbon . 1 3*30 3 75 0*15 Nil 2 1 *54 0*10 1 *44 0 69 3 1 *46 0*26 1 *20 0*41 4 1 *50 0*88 0*62 0*40 5 1*60 1 *00 0*60 0*40 It will thus be seen that in this instance a precipitation of free carbon was obtained , and it will be observed that the higher the initial carbon percentage the higher the free carbon . Before discussing further this set of results , the author considers it better to present another set of experiments which were made in collaboration with Mr. Albert Senior . Bars of pure Swedish wrought iron , were normally cemented five times at a temperature of 1050 ' to 1100 ' 0 . , at which maximum temperature *they were maintained in each case for about 12 days . The carbon percentages thus introduced are recorded in the following table:\#151 ; Total carbon . Combined carbon . Annealing carbon . After first cementation 1 *28 1 *28 Nil , , second , , 1 *43 1-43 " third " 1 *50 1 *16 0*34 . , fourth . , 1 *49 0*53 0*96 " fifth " 1 *68 0*71 0*95 It will be seen that it was ' not until the third drastic heating that any free carbon in this instance appeared , but that the fourth heat treatment precipitated 0*96 per cent , of it . In the earlier experiment , however , a precipitation was obtained in a single cementation at 950 ' to 1000 ' C. in bars having after exposure to the temperature 1*50 to 1*60 per cent , carbon . In Plate 4 , fig. 28 , will be seen the microstructure of No. 1 of the first series ; it will be seen to consist of a matrix of laminated pearlite in which are embedded the annealing carbon nodules in ferrite envelopes . In figs. 29 to 32 , Plate 4 , will be seen the structures of the other four bars . Bar 2 showed a typical cemented bar structure of cementite and pearlite , in Bar 3 here and there the cementite had decomposed with resulting 1910 . ] from the Alloys of the Iron-Carbon System . annealing carbon as seen in the micrograph , whilst in Bars 4 and 5 all the carbon of supersaturation , i.e. all the free massive carbide , has been dissociated into free carbon and iron . Turning now to the second series of experiments , on Plate 5 , fig. 33 , will be found an illustration of their microstructure after the first cementation ; in this instance the cementite of the pearlite has been balled up ; after the second cementation the structure was much the same . On examination of the bars after the third heat treatment the massive cementite had broken down apparently in situ , see fig. 34 . After the fifth cementation , it was found that all the carbon of supersaturation had been precipitated and that the structure , as shown in fig. 35 , Plate 5 , merely presented a pearlite matrix in which the annealing carbon appeared in the usual manner enveloped in ferrite . In the first set of experiments free carbon was precipitated , and roughly in proportion to the carbon of supersaturation present in the original bar . It would therefore appear that the original cementite was in some manner the cause of the action ; as to what this action was is not clear , as , each bar having absorbed more carbon , it would appear that this free cementite must for the most part have been redissolved in the " austenite . " Owing to the comparatively low temperature , however , it is most ' likely that some outstanding islands of carbide would be subjected to the temperature of the treatment . As shown earlier , the carbide of iron is very unstable when temperatures approximating to 1000 ' C. are reached , and hence it is likely would thus dissociate . The second series support this theory , because , on heating up to 1050 ' to 1100 ' C. , a further 100 ' C. , no precipitation was obtained until the third heating , and then it would only appear to consist of a local breaking down of the massive cementite , as shown in fig. 34 , Plate 5 . The increase in temperature would tend to prevent the cementite remaining undissolved in the " austenite , " owing to the increased solubility of the carbide with this rising temperature . The Precipitation of Annealing Carbon in Ordinary Steels . It is now proposed to discuss the problem of the black steels of commerce in the light of experiments previously recorded . Dr. Arnold and Prof. McWilliam , in their paper on the " Thermal Transformations of Carbon Steel , " record some interesting data and also an equally interesting explanation . They point out that it is only in steels which are supersaturated that the precipitation is likely to be observed . This the author confirms , as he has never met the phenomenon except in steels which normally present a microstructure in which free cementite occurs . 12 Mr. W. H. Hatfield . Precipitation of Free Carbon [ Oct. 7 , The author found that when the annealing carbon was produced by simple heat treatment a formation of microstructure similar to fig. 35 , Plate 5 , was obtained , and such is the general appearance of annealing carbon when produced in this manner . If free carbon be produced by working and rolling at low temperatures the .author finds that a very different microstructure is presented . In figs. 9 and 10 , Plate 2 , will be seen the microstructures of such a bar ; fig. 9 represents the structure of the normal portion of the bar ; fig. 10 illustrates the form which the free carbon takes. . The author 's theory is , that in such an instance the cementite membranes as such have decomposed and then drawn in and decomposed the cementite produced by resolution of the pearlite . Intense pressure and friction reasonably might be expected to .commence such an action , which , once commenced , might run some distance through the material , thus accounting for this dissociation of the carbide . With regard to the hypothesis put forth by Arnold and McWilliam* as to the chemical physics involved in the precipitation during the annealing * process , the author with deference to those workers would presume to take some exception . They state that " during the slow cooling from 1000 ' C. the dissolved cementite completely fell out at about 900 ' C. , and from this temperature downwards gradually segregated into nodular masses . Afte the A.R. 12 3 change point , the pearlite gradually became laminated . Then , acting over a certain radius of molecular attraction , the A or cementite carbide drew in about half the B or pearlite carbide , thus augmenting its own mass , and leaving round it a large mass of crystalline ferrite , the outer boundaries of which mark the radius of action through which the nodules of cementite asserted their attraction on the striae of B carbide in the laminated pearlite . Then , for some reasons which the authors cannot specify , the whole of the segregated masses of FesC decomposed into amorphous carbon and iron , the latter augmenting the crystalline ferrite surrounding the free carbon masses . " In the light of the author 's work already recorded , he would suggest that , in the instance to which reference has just been made , the whole of the cementite would possibly not be in solution at the high temperatures . As previously suggested , any structurally free carbide , on exposure to the temperature of 1000 ' C. for such a period , would tend to dissociate , and , as during the slow cooling the cementite gradually precipitated , it would by nucleus action be drawn into the regions of chemical activity , and be progressively decomposed . The fact that the size , shape and position of the subsequent " annealing " carbon bear no relation to the similar features of * ' Journal Iron and Steel Institute , ' 1905 . w ^-\gt ; 1 % . . * $ ? \#166 ; ^ *v , * ? ; X*'\ Vv\gt ; \lt ; *X % \amp ; S m ss v~4 ; ^k*S . ? t# S*\#171 ; S 0\amp ; T-5S *.*\lt ; *\lt ; HN'3- X52 dias . Etched HNO3 . HNQ3- X52 dias . Etched HNO3 . 1910 . ] from the Alloys of the Iron-Carbon System . the cementite in such a steel in the normal cementite-pearlite condition supports this view . That the whole of the carbide decomposes in the region of A.R. 1 2 3 , as suggested by Arnold and McWilliam , the author considers to be unlikely , since , unless the action has begun at high temperatures , his experiments prove the stability of iron carbide ( Fe3C ) at such a low temperature under a simple heat treatment . It would thus seem that there is always a possibility of the production of black steel when free cementite is present , and that only by the addition to the steels of elements which will produce a stable carbide can the difficulty be overcome . In the normal iron-carbon steels of commerce if the annealing or working is not conducted at a temperature at which the cementite is dissolved in the austenite there is always a danger of this phenomenon . The author would like before closing to thank Dr. W. M. Hicks for the very kind interest he has taken in the research , and also to associate with it the names of Mr. J. F. Crowley and Prof. A. McWilliam , who have also wherever possible rendered valuable assistance to him in the prosecution of his research .

rspa_1911_0016

0950-1207

On the Fourier constants of a function.

14

24

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

W. H. Young, Sc. D., F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1911.0016

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1911_0016

10.1098/rspa.1911.0016

Formulae

Tables

Mathematics

]\gt ; On the Fourier of a Function . By W. H. YOUNG , Sc. D. , F.R.S. ( Received December 10 , 1910 , \mdash ; Read January 26 , 1911 . ) S1 . Considerable ress has been made lately in the study of the properties of the constants in a Fourier series , using this term in the most general sense possible consistent with the extended definition of integration due to Lebesgue . Thus we now know that these coefficients necessarily under all circumstances have the unique limit zero , the integer denoting their place in the series increases indefinitely , and that the same is true if we substitute for that integer any other quantity which increases without limit . Further , we know that the series whose general term is where is the typical coefficient of the sine terms , always converges , and we are able to write its suln . That the series whose general term is , where is the typical coefficient of the cosine } , converges when the origin is an internal point of an interval throughout hich the function has bounded variation , and that accordingly the series whose general term is , ConV , is an immediate consequence of known results . Should the function have its square we knowS that the series eneral term is converges , and we can write down its sum . We can also sum the series of the products of the Fourier coefficients of two such functions . From the property that converges , we can that the series and ) , necessarily converge absolutely . Again , making use of a theorem recently proved we integrate the Fourier series of any summable function , after multiplying it term term by any function of bounded variation , with . certainty that we shall obtain the same as if the Fourier series converged to the function to which it corresponds , and such term-by-term integration were allowable . Choosing for the function of bounded variation in question various simple B. Riemann , " " Ueber die Darstellbarkeit einer Function durch eine trigonometrische Reihe S 10 , 'Ges . Werke , ' 2nd edition , 1854 , p. 254 ; H. Lebesgue , ' Lecons sir les series triques 1906 , p. 61 . H. Lebesgue , , S53 , p. 102 . function is , in accordance with the usage now accepted , said to be summable when it possesses a Lebesgue proper or improper . This has superseded the nomenclature in Hobson 's ' Treatise on the Theory of Functions of a Rsal Variable . ' S P. Faton , ' Series trigonometriques et ries de Taylor ' Acta . Matb 1905 , vol. 30 , pp. W. H. Young , " " On the Integration of Fourier Series 1910 , presented to the L.M.S. On the Fourier Constants of Function . functions we shall obtain the sums of a number of series involving the Fourier coefficients of any summable function . By using the other theorems . in the paper last cited we obtain other results of a less general character . In the present note I propose to employ the theorems of that paper to prove the following properties of the coefficients:\mdash ; ( 1 ) WhatevetI be the nature of umnlable function , provided only that in the neighbourhood of the origin it is of bounded variation , then not only as is obvious the series of the , but also the series of the , is convergent when the individual terms of the series are divided by any the same positive power , however small , of the integer denoting the place of the coefficient in the Fourier series ; further , the sums of the series are expressible as simple integrals . * ( 2 ) Whatever be the ature of the summable ction f , proyided only that in the hbourhood of the origin its square is summable , the same property holds , so long as the in dex of the power of the is greater than ; the sums of the series are of the same form as in ( 1 ) . ( 3 ) If in the neighbourhood of the origin we can only assert that the function is bounded , the statement remains true if we interpret the terms " " convergence\ldquo ; and " " sum\ldquo ; both in the Cesaro sense . ( 4 ) If in the hbourhood of the one of the three conditions holds , while in the rest of the interval possesses a Harnack-Lebesgue integral , the corresponding statement is true , if we interpret the terms " " convergence\ldquo ; and " " sum\ldquo ; in the Cesaro sense . The Fourier series is then a generalised one . Closely associated with the first of these four statements is the following which is also proved below:\mdash ; ( 1 bis ) Whatever be the nature of the sumlnable function , provided that in some interval containing the origin the function is summable , the series whose general term is , is convergent ; if , on the other hand , for some value of the constant , the function is summable in some interval containing the origin , the series whose general term is , is convergent ; in both cases it is to be supposed that in the rest of the the function is summable . Moreover , the formulae for the sums have ) same form as in ( 1 ) . The first part of the statement ( 1 bis ) just made contains a , sult which seems to have a special interest of its own . As is well known , the series See below S3 , formulae I and II ; S6 , formula III ; S6 , formula ; SS7 and 8 . Dr. W. H. Young . [ Dec. 10 , whose general term is converges , and has for its sum when is a function of bounded variation . The result in question is what may accordingly be called the companion result , namely , ) the series whose general term is converges , and has for its sum , provided only that this integral exists . Here it must be ] ected that has been made periodic in the usual way , so that the integral in question certainly exists between any limits of integration which do not contain the origin between them ; thus the only limitation of the nature of the function rolates to the neighbourhood of the origin . The results have all been stated with reference to the coefficients and not to the Fourier series itself . It should , however , be hardly necessary to remark that , by transforming the origin , we obtain corresponding results relating to the Fourier series itself , and to very important , up to the present almost entirely ecGed , companion series , from it by interchanging the coefficientis of the sine and cosine terms , and the sign of the latter . In particular we have in this way the sum of the companion series , when a certain function is summable ; we cau also find the function of which this series is the Fourier series in an important class of cases , in which we know it to be a Fourier series . I reserve for subsequent publication the further development of this remark . In conclusion I would add that the formulae obtained may be generalised in a variety of ways by means of the theorems here utilised . The present paper , however , contains the complete solution , within the limits proposed , of the problep with which we started , thus illustrating the usefulness of the theorems in the paper so frequently quoted . S2 . Denote by the function which is zero at the extremities of the interval , and which , inside this interval , is equal to the expression while , outside this interval , such values are to be assigned to as to make it periodic , with period Denote by the function from by changing into . evidently and are summable , have their squares summable , are bounded , or of bounded variation , in a neighbourhood containing the origin , if possesses these respective properties . urther , since and are both zero , it is clear that the *S9 , formula 1910 . ] On the Fourier Constants of a Function . indefinite integrals of will all be periodic , and accordingly oscillate finitely as the upper limit of integration approaches infinity . Again , as we have just seen , the Fourier series corresponding to and will be deficient of constant term . Moreover , where is a constant . Also ] Similarly , S3 . We first consider the case where has bounded variation in the neighbourhood of the origin , and the index of the power to which the integer is raised lies between zero and unity , the extreme values not included . Put , where , and consider the integral Except in the neighbourhood of the origin , is a function of bounded variation in the whole infinite interval , and has , as increases indefinitely , the unique limit zero . Moreover , ) is such that is a periodic function of which oscillates finitely in the whole infinite interval Hence , by the extension to infinity of the theorem cited in S1 , is the sum of the series of integrals got by integrating , between the limits and infinity , the successive terms of the Fourier series of , after having previously multiplied them by . Next consider . In the interval of integration is summable , while has bounded variation , provided our choice of has been a suitable one , which we may suppose to be the case . To this integral we may apply the theorem already cited in its simple form , so that we see that it is equal to the sum of the series of integrals got by integrating between the limits and the successive terms of the Fourier series of , after having previously multiplied them by Adding the two results so obtained , and bearing in mind that the Fourier iseries of has no sine terms , we have VOL LXXXY . Dr. W. H. Young . [ Dec. 10 , Similarly Hence , since we know that , when and Sq , we get cos Similarly S4 . Before going on to obtain the corresponding formulae when is not internal to the interval , we remark that the results above obtained are obviously true , mutatis , when near the origin is respectively bounded , or has its square summable . In the former case the above argument is unaffected , provided only we interpret the words\ldquo ; sum\ldquo ; and\ldquo ; convergence\ldquo ; of a series in the Cesaro manner . In fact , the reasoning for the interval applies , as before , as all that was required of in that intelval was that it should be summable in every finite portion of it . As regards the interval , the theorem used is still applicable , as is shown in the paper quoted , with the proviso in question . If , on the other hand , all we know of , and therefore of and in the neighbourhood of the origin , is that its square is summable , we need the summability of the square of in the interval . This requires to be greater than . With this understanding , therefore , our results are . still true . If , finally , we only know of near or that it possesses a Harnack-Lebesgue integral , the corresponding portion of the integrals will in general only conyerge in the Cesaro way . * Hence in this case , even if is of bounded variation near the origin , the final series can only be summed in general in the Cesaro way . S5 . Let us now make the hypothesis that is unity . By the theory of the integration of Fourier series , we have , if , , denote any definite integrals of , const . const . " " On the Integration of Fourier Series S7 . 1910 . ] On the Fourier Constants of Function . The first equation gives us no information , the second equation tells us that . const . . Here the summation must be supposed performed in the Cesaro manner , when the Fourier series is a generalised one . * This result is due to Lebesgue , in the case when the Fourier series is an ordinary one . S6 . To obtain the sum of the series whose general term is , we must adopt a different method . require to use the fact that , in the neighbourhood of the origin , has , under all the circumstances supposed , its square summable . On the other hand.the function has , except in the neighbourhood of the origin , bounded variation throughout the interval . In the neighbourhood of ths origin it has its square summable\mdash ; in fact , Therefore , Hence , also , the square of the function in question , . , is less than a summable function . Thus the interval can be broken up into two parts , in one of which one of the two functions and is of bounded variation and the other is summable , while in the remaining part both the functions have their squares summable . Applying , therefore , the theorems already referred to , to these separate portions , and adding the results , we get , ( IV ) since the generic Fourier constant of the is Here we have assumed to be summable . If , in any portion of the interval , it have only a Harnack-Lebesgue integral , the argument still applies , provided we sum the series in the Cesaro way . S7 . Since the function corresponding to an integrated Fourier series is an integral , it is , of course , a continuous function , and belongs also , a fortiori , to the class of functions whose square is summable . Accordingly , * W. H. Young , " " On the Conditions that a Trigonometrical Series should have the Fourier Form 1910 . Supplementary Note . Presented to the London Mathematical D. Bernoulli , ' Petrop . N. Comm 1772 . See Hobson 's ' Theory of Functions of a Beal Variable , ' p. 639 . Dr. W. H. Young . [ Dec. 10 , the method of S6 enables us to sum the series , whose general terms are respectively where and are the Fourier constants of any summable function whatever . The formulae , of course , closely resemble that obtained at the conclusion of that article . On the other hand , the series whose general terms are where , and are the Fourier constants of any summable function whatever , are obtained by mere repetition of the process employed in S5 , their sums having a form which closely resembles that of the series summed in that article . S8 . The case in which is greater than unity , and not an integer , alone remains to be considered . The method to be adopted is obvious . We have only to apply to the integrated series the reasoning of S3 , with this simplffication , that the function to which the Fourier series corresponds , being now an integral of , or of , as the case may be , is certainly of bounded variation in the case of an ordinary Fourier series , and at least continuous in the case of a generalised Fourier series in every finite interval , so that no special hypothesis is needed . The formulae are easily obtained . S9 . To write down ( by request ) the formula referred to in SS7 and 8 , it is convenient to use the following notation:\mdash ; so on . We then have the following formulae , which are those given in S5 and the analogous formulae referred to at the end of S7:\mdash ; nx , 1910 . ] On the of Function . , thus , thus , thus , thus and so on . The formula obtained in S6 , S may evidently be written Similarly , without any restriction on , with the notation just ] ained , bearing in mind that , we have the analogous formulae referred to at the beginning of S7:\mdash ; and so on . Dr. W. H. Young . tDec . The formula referred to in S8 , in which , are then as follows:\mdash ; ' and so on . S10 . We now assume that is summable in an interval containing the origin , and proceed to prove the results ( 1 bis ) of the introduction . Since is , by a summable function , so is , Also is a function of bounded variation in any finite interval . Hence , using the theorem so often quoted , and denoting the integral ] nx\amp ; , we have ; 1 so that , in particular , the series on the right-hand side converges . Now the summation on the right-hand side of the preceding equation is the unique limit when increases indefinitely of the following:\mdash ; 1910 . ] On the Fourier of Function . But Hence ( 1 ) becomes for in ( 2 ) the second and third terms on the right vanish when we proceed to the limit , since and the Fourier coefficients of a summable function , have zero as unique limit when increases indefinitely , while the integrals by which they are multiplied are always numerically less than But , by the usual argument , S . ( 4 ) Hence , adding ( 3 ) and ( 4 ) , and using the fact that , we have which may , if is summable , be written in the form ( V ) S11 . A slight modification of the argument used in the preceding article enables us to show that our formulae ( 1 ) and hold on the new hypothesis of the introduction , lying , as before , in the open interval . In formula ( 2 ) we require to be summable in the neighbourhood of the origin , while in formula ( I ) the condition is that should for some value of the constant be summable in the neighbourhood of the origin . To prove this we work with the factor , instead of , and arrive , by the same reasoning as in S10 , at the equation corresponding to ( 3 ) , viz. :\mdash ; Adding to this the equation corresponding to ( 4 ) , we get , as before , nx . ( II ) Again in like manner , , ( 1 ) On the Fourier Function . where and therefore Hence the summation on the right-hand side of the equation ( 1 ) , just written down , is the unique limit when increases indefinitely of one half of the following expression:\mdash ; . ( 3 ) Hence , using ( 2 ) , we get from ( 1 ) the following equation:\mdash ; since the second and third terms on the right-hand side of ( 3 ) have , as increases indefinitely , the unique limit zero , and being the Fourier coefficients of a summable function . But , by the usual argument , Adding the last two equations , we get , as in S3 , the required result:\mdash ; S

rspa_1911_0017

0950-1207

The charges on ions in gases, and some effects that influence the motion of negative ions.

25

29

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Prof. John S. Townsend, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1911.0017

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1911_0017

10.1098/rspa.1911.0017

Thermodynamics

Fluid Dynamics

Thermodynamics

]\gt ; The on Ions in Gases , Some Bffects that Influence the Motion of Ions . By Prof. JOHN S. TOWNSEND , F.B.S. ( Received December 12 , 1910 , \mdash ; Read January 12 , 1911 . ) 1 . In two previous papers published in the 'Proceedings of the Royal Societ method was described of finding directly the charges on positive and negative ions produced by secondary Bontgen rays in gases , in terms of the charge on a monovalent ion in a liquid electrolyte ; and the results of some experiments made with air were given . A number of investigations have since been made with oxygen , hydrogen , and carbonic acid , which have taken a considerable time to complete , for although a determination of the charge can be made very accurately from a few simple observations , it requires a long time to investigate the effect produced by complete drying on the motion of the negative ions . This effect can be observed by means of the same kind of experiments as are necessary for determining the charges on the ions , and it is of considerable interest to find at what forces and pressures the negative ions in dry gases assume the corpuscular state and move under an electric force according to laws that are quite different from those which govern the motions of the positive ions . In all these experiments exactly similar results were obtained with the three gases that have been examined , as were previously obtained with air . With regard to the charges on the negative ions , the values obtained for the product No being the number of molecules per cubic ceirtimetre in a gas at 760 mm. pressure and C. , and the charge on an ion in electrostatic units ) with different forces , pressures , and strengths of radiation were all practically the same and arly equal to , which is the value of No for monovalent ions in liquid electrolytes . The mean values of No obtained in a set of experiments were for oxygen , hydrogen , and carbonic acid respectively . The values of No for positive ions , under different conditions of force and pressure , were nearly the same as for negative ions when the secondary rays ionising the gas proceed from a bright metallic surface , the corresponding numbers being , and . Higher values of No were obtained for positive ions in all when the rays proceeded from a surface covered with a thin layer of vaseline , showing that some of the positive ions produced by the more penetrating radiation have double * 1908 , , vols . 80 and 81 . Prof. J. S. Townsend . The Charges on Ions in [ Dec. 12 , charges . The mean values obtained for the three gases under these conditions are , and 2 . The principle that was used in these investigations was to allow a stream of ions to pass through a circular aperture in a thin plate , and after passing along a certain distance under the action of a known electric force X , to receive the ions on a disc of the same diameter as the aperture and on a flat surrounding the disc . The stream opens out as the ions move under the electric force , and according to the ordinary laws of diffusion the ratio of the charge received by the disc to that received by the surrounding ring depends only on the product . There is therefore a definite relation between and X which is independent of the pressure when the motion of the ions obeys the simple laws of diffusion , as is always the case with the positive ions with the pressures and forces used in these experiments ; so that the value of Ne can easily be obtained . In finding the values of Ne for negative ions it is convenient to a slight amount of water vapour in the gas of a millimetre pressure is sufficient when dealing with oxygen at 10 mm. pressure , or with hydrogen at 30 mm. pressure ) , as the negative ions then obey the simple laws of diffusion under which their kinetic energy of agitation ( or the partial pressure of the ions ) is equal to that of an equal number of moJecules of the gas in which they move . The determinations of Ne may also be made in perfectly dry gases at somewhat higher pressures when forces not exceeding 1 volt per centimetre are used . 3 . When a gas has been dried for several days and the pressure is below a certain value , depending on , a large increase in the lateral diffusion of the stream of negative ions is obtained , and only a small proportion of the ions is received on the disc on which the centre of the stream impinges . With a given force , the pressure at which this effect can be observed is greater in hydrogen than in oxygen , and is much smaller in carbonic acid than in the other gases . When this stage is arrived at the ratio no longer follows the ordinary laws of diffusion . If the force is kept constant the opening out of the stream increases rapidly diminishes ) as the pressure of the gas is diminished , which is in marked contrast to the effects obtained when a little water vapour is present , as the value of is then independent of the pressure of the gas P. Thus , in dry oxygen , with a force of 2 volts per centimetre , the ratio of the charges was found to be when the pressure was 10 mm. , and when the pressure was mm. ; whereas , if a small amount of water vapour were present , both these ratios would be about As has already been mentioned in one of the previous papers , the motion 1910 . ] Gases , and the Motion of Negative Ions . of the negative ions in a dry gas at low pressure can be explained on the supposition that the negative ions have assumed the corpuscular state when the value of is sufficiently great , and the relative velocity in directions perpendicular to direction of the electric force is due to an increase of the velocity of agitation above the value this velocity would assume if the ions were in thermal equilibrium with the molecules of the gas . From the experiments which have been made , it is easy to deduce the ratio of the partial pressure of the ions when diffusing in this way to the partial pressure of an equal number of molecules in thermal equilibrium with the gas , and the curves obtained for air show that when volt per centimetre and mm. , the partial pressure of the ions is twice that of an equal number of molecules . * Since the partial pressure is proportional to , this result shows that the velocity of agitation of the ions is greater by the factor than the velocity of agitation of particles of the same mass in thermal equilibrium with the molecules of the gas . The conclusion to which these experiments lead indicates that the velocities due to electric forces of negative ions in dry gases should be very large when the values of are of the same order as those used in the above experiments . 4 . Mr. R. T. Lattey has recently investigated the velocities under these conditions , and he has found that in dry air large increases in the velocity of negative ions are obtained by making comparatively small increases in the electric force . Thus , in air at 10 mm. pressure , the velocity due to a force of volt per centimetre is 173 cm . per second , and when the force is increased to volt per centimetre , the velocity is 1845 cm . per second . It is interesting to apply the theory of diffusion to calculate the coefficient of diffusion of negative ions into air under the above conditions , as the investigation shows how the group of molecules associated with each diminishes as the force increases . This method was used some time agoI to find the masses of negative ions in gases at atmospheric pressure when acted on by small forces . When is small , then , the apparent mass of an ion in air is constant over a large range of values of . The rate of diffusion of the ions is slow in this case , and , by comparing the rate of diffusion of ions into air with that of into air , it may be seen that the apparent mass of the ion is about 11 times as great as that of a molecule of carbonic acid . In applying the theory of diffusion to the cases in which is large , it is * J. S. Townsend , ' Roy . Proc 1908 , vol. 81 , p. 468 . R. T. Lattey , ' Roy . Soc. ' 1910 , , vol. 84 . . S. Townsend , ' Phil. Trans 1899 , The Charges on Ions in , etc. necessary to give the correct value to the partial pressure of the ions , the velocity under the electric force and the rate of diffusion both depend on the velocity of agitation of the ions . The equations of motion of the ions are of the form so that the velocity under the force X is given by the equation being the coefficient of diffusion while the force is Usually , as when is small , the partial pressure of the ions is connected with the number of ions per , by the equation being the number of molecules per cubic centimetre of agas at atmospheric pressure and temperature C. , which is the temperature of the gas the velocity was determined . When volt per centimetre and mm. , the partial pressure is larger than the above value by the factor , so that on substituting for its value in terms of the equation for becomes since and No The high value thus obtained for is due partly to the fact that the velocity of ag tation of the ions exceeds that of particles of equal mass in thermal equilibrium with the gas by the factor . Hence particles equal mass would , unde ordinary conditions , diffuse into air at 10 cm . pressure at a rate corresponding to the value of . The coefficient of diffusion of into air is , the sum of the pressures of the gases being 760 mm. , so that at 10 cm . pressure the coefficient of interdiffusion would be . Experiments on diffusion show that the coefficients of interdiffusion are inversely proportional to and being the masses of the molecules of the two gases . Hence the ratio of the mass of the negative ion to the mass of a molecule of is . The quantity is the average value of the mass of the group of molecules associated with the ion , which is continually changing , and the above investigation shows that the average value must be less than the mass . of a molecule of air when . This shows that ( luring part of Since the rates of diffusion of different gases into a slandard gas are approximately proportional to the velocities of agitation of the molecuIes of the different gases , it ia assumed here that the rates of diffusion of the ions are also proportional to their velocities of agitation . Energy Distribution Scattered R. 29 time the negative electron must be free from molecules of the gas . When increases , becomes smaller still , but as the velocities have not yet been determined accurately higher values of , further investigation on these lines must be postponed . In order that the equations of diffusion should hold in these cases , it is necessary that the velocity of the ion in the direction of the electromotive force should be small compared with the velocity of agitation . It is easy show that this condition holds . Since the velocity of agitation of a molecule of at centigrade is centimetres per second , the velocity of particles of an average mass 1/ 43 of that of the molecules of would be , and while under the electric force their velocity of agltation would be , which is large compared with the velocity , 1845 centimetres per second , in the direction of the lelectric force . On the Energy and Distribution of Scattered Rontgen Radiation . By J. A. , Fellow of St. John 's College , Cambridge . Communicated by Prof. Sir J. J. Thomson , F.R.S. Received December 13 , 1910 , \mdash ; Read January 26 , 1911 . ) Introduction . It has been shown by Prof. Sir J. J. Thomson that it is possible , on certain assumptions , to calculate the number of electrons in an atom of any element from considerations of the scattering undergone by a rapidly moving electl'ified particle in the substance . In a paper recently read before this Society*I was able , by means of experiments there described , to show that the scattering of homogeneous -rays by thin sheets of different substances did follow very closely the laws predicted by the theory , and to calculate the number of electrons contained in the atoms of some half dozen different elements . It was found that , in every case , the number of electrons per atom was equal to about three times the atomic weight . Although the agreement between theory and experiment was very close , it seemed desirable to collect as much independent evidence as possible upon such a point . Some years ago Prof. Sir J. J. Thomson showed that in the phenomenon of the scattering of a beam of Rontgen rays we have another possible method of attacking the problem . * Roy . Soc. Proc 1910 , , vol. 84 , p. 226 . 'Conduction through Gases , ' 1906 , p. 321 .

rspa_1911_0018

0950-1207

On the energy and distribution of scattered r\#xF6;ntgen radiation.

29

43

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

J. A. Crowther, M. A.|Prof. Sir J. J. Thomson, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1911.0018

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1911_0018

10.1098/rspa.1911.0018

Atomic Physics

Tables

Atomic Physics

]\gt ; Energy Distribution Scattered R. 29 time the negative electron must be free from molecules of the gas . When increases , becomes smaller still , but as the velocities have not yet been determined accurately higher values of , further investigation on these lines must be postponed . In order that the equations of diffusion should hold in these cases , it is necessary that the velocity of the ion in the direction of the electromotive force should be small compared with the velocity of agitation . It is easy show that this condition holds . Since the velocity of agitation of a molecule of at centigrade is centimetres per second , the velocity of particles of an average mass 1/ 43 of that of the molecules of would be , and while under the electric force their velocity of agltation would be , which is large compared with the velocity , 1845 centimetres per second , in the direction of the lelectric force . On the Energy and Distribution of Scattered Rontgen Radiation . By J. A. , Fellow of St. John 's College , Cambridge . Communicated by Prof. Sir J. J. Thomson , F.R.S. Received December 13 , 1910 , \mdash ; Read January 26 , 1911 . ) Introduction . It has been shown by Prof. Sir J. J. Thomson that it is possible , on certain assumptions , to calculate the number of electrons in an atom of any element from considerations of the scattering undergone by a rapidly moving electl'ified particle in the substance . In a paper recently read before this Society*I was able , by means of experiments there described , to show that the scattering of homogeneous -rays by thin sheets of different substances did follow very closely the laws predicted by the theory , and to calculate the number of electrons contained in the atoms of some half dozen different elements . It was found that , in every case , the number of electrons per atom was equal to about three times the atomic weight . Although the agreement between theory and experiment was very close , it seemed desirable to collect as much independent evidence as possible upon such a point . Some years ago Prof. Sir J. J. Thomson showed that in the phenomenon of the scattering of a beam of Rontgen rays we have another possible method of attacking the problem . * Roy . Soc. Proc 1910 , , vol. 84 , p. 226 . 'Conduction through Gases , ' 1906 , p. 321 . Mr. J. A. Crowther . On the Energy and [ Dec. 13 , Assuming that the scattered Rontgen radiation is emitted by the electrons in the atoms traversed by the primary rays executing forced vibrations in the period of the incident rays , it can easily be shown that the energy radiated per electron is equal to where is the energy in the primary pulse , and and the charge and mass of the electron . The total energy radiated by a given mass of substance is therefore equal to where is the total number of electrons in the given mass . This equation gives us an independent method of arriving at the number of electrons in the atom . So far as I am aware , no determinations of the energy of scattered Rontgen radiation have been made since the early experiments of Barkla*on the secondary radiation from gases . He compared the ionisation in two similar electroscopes , one placed in the path of the primary rays , the other in a direction at right angles to it . He thus compared the energy of the secondary rays in a given fixed direction with that of the incident beam . To deduce the total secondary radiation he assumed a law of distribution deduced from the simple theory described above . As no experimental proof of this law of distribution had been iven , and in view of the new which has been thrown upon the whole subject since these early experiments were performed , it was thought . desirable that a fresh determination of the energy of the scattered Rontgen radiation should be made . It was not found feasible to measure immediately the whole of the rays . scattered by a given radiator . The experiment therefore resolved itself into . two parts : ( 1 ) The comparison of the intensity of the scattered radiation from a given radiator in a fixed plane ( namely , that at right angles to the primary beam ) . ( 2 ) The determination of the distribution of the scattered radiation around the radiator . The following sections of this paper describe the methods employed and the results obtained . * Barkla , ' Phil. Mag 1904 , [ 6 ] , vol. 7 , p. 643 . 1910 . ] Distnbution of Scattered Rontgen On the Energy of the Rontgen Radiation Scattered in a Plane at Right Angles to the Primary Beam . The direct mechanical measurement of the energy of Rontgen radiation is practically impossible . In order to compare the intensities of two given streams of Bontgen radiation , we must rely on their power either to affect a photographic plate or to ionise a gas . Of the two methods , the latter is the more definite , and the less open to objection . In fact , if the two beams have the same penetrating power , and pass through the ionisation chambers without striking any solid object , it seems reasonably certain that the amount of ionisation produced per unit length of path in the chamber will be simply ortional to the energy of beams . If , however , the rays fall upon the electrodes and walls of the ionisation chamber , the bulk of the ionisation produced is due to the emission of corpuscular radiation from the substances struck . The amount of this will depend upon the shape and material of the chamber , and the way in which the rays strike it . Results with two different chambers will therefore not in general be strictly comparable . This objection , however , does not apply if the same ionisation chamber is used to measure successively different quantities of radiation , providing all pass through the chamber in the same way . As it was desirable , on account of possible variations in the -ray tube , to make simultaneous measurements of the primary and scattered radiations , and to eliminate as many sources of uncertainty as possible , it was decided to arrange matters so that neither the nor the secondary rays should impinge on any solid object in the vicinity of the ionisation chambers . The effect to be measured was thus greatly reduced , but it was that this was more than compensated for by the increased certainty that the measurements of the two beams were really comparable . The methods employed will be readily understood from fig. 1 , which represents a section of the apparatus . The -ray tube supplying the rays is completely enclosed in a thick lead box , to eliminate any fear of stray radiations ; the leads from the coil were introduced through thick porcelain tubes . A narrow pencil of rays , limited by a series of circular apertures passes.upwards through the lead tubes , so that no radiation can emerge into the secondary ionisation chamber except at the point , where a gap cm . in length is left for the radiator . On its way , the beam passes through the small primary ionisation chamber , fitted with two parallel aluminium electrodes , well out of the path of the rays . The measuring electrode is provided with a guard ring in order to ensure a uniform field across the chamber . 32 Mr. J. A. Crowther . On the and [ Dec. 13 , FIG. 1 . The rest of the apparatus is symmetrical about the line of the primary beam , which it completely surrounds like a belt . MM and are two lead cylinders , 24 cm . in diameter and cm . apart , and serve to limit the secondary rays from to a fairly narrow sheet . The secondary ionisation chamber is fitted with two parallel plate electrodes ; the measuring electrode being surrounded by guard lings , as in the case of the primary chamber P. Wires passing through earthed tubes , not shown in the diagram , connect the electrodes and to two Wilson electroscopes ; and are charged to saturation potentials from a cabinet of accumulators . The radiator took the form of a hollow cone of aluminium foil , with a vertical angle of . The primary rays thus met it everywhere at an angle of , and the secondary rays emerged at the same angle . The scattered radiation from the air was not sufficient to measure with any accuracy . As the chamber was large , there was a very appreciable spontaneous ionisation current across it . To eliminate this , a cylindrical ionisation chamber , charged to the opposite potential , was connected to the same .electroscope . The effective volume of this compensator could be varied by 1910 . ] ibution of ttered Rontgen Ra , means of an earthed tube sliding over the inner electrode . By varying the length of the electrode exposed , the two cm.rents could be made to each other . In making the measurements , readings were taken wibh the rays passing , but with no radiator at , and then with the radiator in position . The difference gave the effect due to the radiator alone . The effect in the absence of the radiator was always very small . By means of a key , not shown in the , the electrode could be directly connected to the electrode of the chamber . In this way the capacities of the two systems could be directly compared . To compare the relative amounts of energy in the primary and secondary beams , we may proceed as follows:\mdash ; Let be the energy per unit volume in the primary beam , its cross-section , and the effective length of path in the ionisation chamber ; that is to say , the length of path in that portion of the gas of which the ionisation is measured . The volume of gas ionised is thus , , and the rate of ion isation is therefore , where is a constant endino on . the nature of the gas and the hardness of the rays . Similarly , for the secondary beam , we have the rate of ionisation equal to , where . is the same factor as before , since the secondary rays are of the same hardness as the primary . If is the number of ions of one sign produced in a time , the charge conveyed to the electrode in that time is equal to , where is the on an electron . If the capacity of the electrode is , and the potential acquired in the time is equal to , we have , thus the rate of production of OIlS Equating these expressions , we have so that Since for a limited beam energy crossing any cross-section of the beam in a given time is constant , is constant for a given beam of The following are the experimental values:\mdash ; cm . , cm . , VOL. LXXXV.\mdash ; A. Mr. J. A. Crowther . On the Energy [ Dec. 13 , Rate of charging up of the two systems in volts per minute:\mdash ; 0.074 0.070 11.O Mean . . . Thus The thickness of the aluminium.radiator measured the path of the primary rays was mm. The angle of emergence of the secondary beam was on each side of a plane through the radiator perpendicular to the primary beam . The value given above has still to be corrected for the absorption of the primary and secondary rays in the radiator itself . Although conical radiator was quite symmetrical about the primary beam , the equations obtained for the absorption in the radiator were not capable of explicit evaluation . The radiator was purposely made as thin as possible , in order to make the correction as small as possible . The following method was adopted for its determination : Consider the cross-section of the cone made by any plane perpendicular to its axis , and therefore to the primary beam . This cross-section will take the form of a ring , bounded by two concentric circles , whose distance apart is equal to , where is the thickness of the foil of which the cone is made . Consider any point in this ring whose distance from the outer circle is . Then the distance traversed by the primary rays in the cone in reaching is also , since the cone is inclined to both primary and secondary ra at an angle of . The intensity of the primary rays at is therefore , where is the coefficient of absorption of the rays . For the rays used in these experiments , was equal to cm . Consider now the secondary rays from in the plane of cross-section . When is very small compared to the radius of either bounding circle , the ordinate through at angles to the radius becomes infinitely great compared to . In ths limit , therefore , the absorption is the same as if the radiator consisted of two parallel plates perpendiou ] are to the radius through P. In practice the absorption must always be less thau this limiting value . If is the depth of the point below the surface of one of the plates , the path of a ray inclined at an angle to the normal is 1910 . ] Distribution of Scattered Rontge Radiation . If the initial intensity of radiation from between the directions and is I , the emergent intensity is I . The total emergent radiation is therefore I for the rays emerging on the side nearest For those which pass through both plates the path is , and the emergent radiation is therefore . I have not been able to evaluate these rals explicitly . They lend themselves , however , quite readily to evaluation by graphical methods . By actually plotting the graphs of against for different values of from to cm , , and the areas of the curves so obtained , a series of values were found for the absorption of the secondary rays , different depths in plate . It has been shown that the absorption of the primary rays re[ching a point at a depth in the radiator is Multiplying each of the values for the absorption of the secondary rays by the corresponding values of , we obtain , by a final raphical integration , the whole absorption of the rays in the material . It was foumd to be by the equation This represents the maximum absorption when theadius of the cross section is compared with the thickness of the foil . Turning now to the apex of the cone , where the cross-section is a circle of radius , we can , by pursuing a similar course of operations , find the absorption for the cross- section of this shape . In this way it was found that the absorption for case was given by This represents the minimum absorption . The actual value mtlst lie between these two . The values are not very far . We shall not commit any serious error if we take the true absorption in the radiator as iven by I is the radiation as measured by the secondary chamber . To obtain the true value , in the absence of any sorPtion in the radiator , we must multiply our result by , that is by . Making this correction , we get finally Considel.ing the beams at the point where their cross-section is unity , we have Mr. J. A. Crowther . the Energy [ Dec. 13 , On the of the Scattered Radiation rov , nd the Radiator . In order to measure the distribution of the rays round the radiator it was necessary to design an ionisation chamber which could rapidly and accurately be brought to any desired position with respect to the primary beam and the ladiator . At the same time , as a Wilson electroscope is very sensitive to slight changes of level , and other variations in external conditions , it was necessary , if accurate measurements were to be made , that the electroscope itself should remain fixed on a firm basis . The apparatus finally designed for the experiment is shown in FIG. 2 . The ionisation chamber used to measure the emergent scattered radiation is mounted upon the circumfelence of a large wheel , which can be rotated about a fixed vertical axle A. The ionisation chamber is cylindrical in shape , the cylinder being placed with its axis passing normally through the axis of rotation of the wheel . A window , closed with thin aluminium foil , serves to admit a cone of the secondary rays of fixed angle into the ionisation chamber . A lead plate , pierced with a suitable aperture to allow of the passacre of the primary beam , is fixed to , and serves to support the radiator B. In this way , by simpJy turning the wheel , the secondary chamber can be made to take up any position with respect to the radiator . position of can be read off on a circular scale fixed to , and read by a pointer attached to the fixed axle A. As the amount of scattered radiation is very small , the ionisation 1910 . ] of chamber was made fairly , and in order to obtain saturation with a reasonably small voltage a system of plane parallel electrodes of aluminium leaf mounted on wire rings was introduced , as shown in the figure , instead of the more usual , but unsatisfactory , tral wire electrode . In order to make connection between the moving electrode and the fixed electroscope , the key was mounted so that the brass rod came directly above the axis of rotation of the wheel D. The distance from to thus remains constant when wheel is rotated , and the two can be joined together by a thin copper wire , shielded in an earthed metal tube in the usual way . The focus tube X is enclosed as before in a lead ) . A system of lead stops , limits the emergent ra . is so that the cross-section of the beam at is 3 cm . in diameter . This was verified by placing a fluorescent screen at , when it was found that the beam passed the aperture and was quite well defined . The primary beaul passes between two ] electrodes , the ionisation between which can be measured in usual way and serves to standardise the primary beam . In the measurements readings were made , as before , with and without the radiator in position . The difference gay the true effect due to the radiator alone . Owing to the scattering of the rays in the there was always a small appreciable effect even when the radiator was not present ; but this was eliminated by the method of measurement described . The radiator took the form of a sheet of the substance under experiment , the thickness being kept as small as possible , in order that the absorption of the rays in the radiator should be small . The absorption of the rays used by the substance was , however , measured , and a correction calculated for position of the ionisation chamber . The following table contains a typical set of ions for an aluminium radiator . The first column of figures gives the angle made by the axis of with the direction of the primary beam . R.H. and L.H. nify that the nber is to the right or left hand , looking along the direction of the primary beam : " " returned\ldquo ; denotes that the radiation is measured on the side of the radiator facing the incident " " transmitted\ldquo ; that it is measured on the further side . The second and third columns the ionisation with and without the radiator , in arbitrary units , corrected for variations in the of the primary beam . fourth column is the differexlce of the second and third and gives the effect due to the radiator alone . The fifth column gives bhe correcting factor for the absorption of primary and secondary rays in the radiator . This has been calculated as follows :Consider a small volume of Mr. J. A. Crowther . On the Energy and [ Dec. 13 , unit area and thickness situated at a distance from the front face of the radiator , which is struck normally by the primary beam . If is the initial intensity of the primary beam , the intensity on reaching the small volume is equal to , where is the coefficient of absorption of the rays . Suppose now that the fraction of this ensrgy is scattered in a cone of small angle about the angle with thenormal . The path of these rays before emerging from the face of the radiator for the returned radiation is and for the forward radiation , where is the thickness of the radiator . The energy of radiation from a small volume at depth is thus in a return direction , and in a forward direction:\mdash ; The whole intensity in the direction is thus given by and The intensity in the same directions in the absence of any absorption is simply and respectively . Evaluating the integrals , we find if represent the rected and the measured values of the intensity in the direction for the returned radiation , and for the transmitted radiation . For the rays used was cm . 1910 . ] Distribution of Scattered ntgen The values of these expressions for the different values of are the correction factors given in the table in column 5 . The sixth column gives the values of , the intensity of the scattered radiation in the direction ; that is to , the energy of the scattered radiation per unit area at an with the primary beam . According to the simple theory of scattering outlined above , the distribution of the scattered radiation should be symmetrical both about the direction of the primary beam , and about a plane perpendicular to this direction . The intensity should be a minimum in this plane , and rise to a maximum 011 both sides of the radiator in the direction of incident beam . The ratio of the maximum to the minimum intensities , assuming that the electrons are displaced in the plane of the wave-front , should be 2 to 1 . The actual distribution obtained differed considerably from this . Fig. 3 shows , raphically the actual distribution around a small radiator , the primary rays falling upon in the direction of the arrow . Radii are drawn from ] , showing the angle of inclination of the scattered rays with the normal , and lengths are marked off along them proportional to the intensity of radiation at that inclination . In this way we get a picture of the distribution of the rays about . The same results are also shown as an ordinary graph in fig. 4 . will be seen from fig. 3 that the scattered radiation is symmetrical about the incident beam , but not about the plane perpendicu ] to it , through the radiator . It will be seen at once from both figures that ] the intensity of the scatterea1 radiations is a maximum both forward and backward along the line of the primary beam , and falls to a minimum in the plane perpendicular to this direction , the distribution about this plane is by no means symmetrical . At any given inclination to the primary beam the In these experiments the bulb was placed so that the path of the cathode rays in the bulb was perpendicular to the plane of rotation of the ioniaation chamber . If the path of the cathode rays is in the plane of rotation , there is always a slight reponderance of the scattered radiation on that side of the primary beam to which the cathode rays are directed . This effect , which has been pointed out by several observers , is due to the partial polarisation of the primary rays . It was in order to eliminate any error to thiS effect that the secondary chamber in the energy experiments already described was made to surround completely the primary beam . 40 . J. A. Crowther . On the Energy [ Dec. 13 , in the forward direction is always greater than that in the reverse direction , and this inequality becomes greater as the direction approaches more and more nearly to that of the primary beam . The distribution of the retulned radiation agrees fairly well with that given by the le theory . It was impossible to measure the returned radiation actually in the line of the primary beam . By interpolation , however , it was found that the intensity in this ection was about . The intensity at right angles to this was lound to be ; the ratio being . It seems , therefore , that while the maximum in the forward direction is greater than is required by the theory , the maximum in the reverse direction is somewhat less . The form of curve suggested that the preponderance in the forward direction might be due to some other form of radiation superposed upon the true scattering . A considerable number of experiments have been made with a view to testin this point , but I have so far failed to obtain any evideuce that such is the case . The distribution of the radiation does not seem to depend upon the thickness of the radiator , though it does to some extent upon the material , the eccentricity being rather less for paper than for aluminium . There was no ) difference in the hardness of the 1910 . ] Distribution of Radiation . rays returned , and those transmitted , the relative intensities in the two directions being unaltered when sufficient aluminium was placed in front of to cut down the radiation entering the ionisation chamber by more than one-half . The effects cannot be due to a " " characteristic\ldquo ; radiation from the aluminium , as measurements on characteristic secondary have shown that it is distributed equally at all angles round the radiator . * At present , therefore , we 1nust regard the whole of the radiation as purely scattered . To obtain the whole energy of scattered radiation we may proceed as follows . Let be the intensity of the radiation at any angle with the primary beam , so that the energy included in a hollow cone of and increment round the primary beam is equal to . The area vept out by this hollow cone on a sphere of radius passing the window of the ionisation chamber is . Now , if is the area of the window , supposed to be sufficiently small to be included in this belt , the intensity of the rays entering the ionisation chamber is equal to But is constant , being the area of the window , and . is constant . } can write therefore constant The values of are iven in the last column of the previous table . The whole of the scattered radiation is equal to , that is to Similarly , the energy measured in the first part of the experiment is that included between angles of with the plane perpendicuIar to the primary beam , i.e. , , where We can integrate these quantities by a raphical method . A curve is plotted between and . The area of the whole curve gives the ) of , that is , of the whole scattered radiation . The area included between the gives in a similar way the energy the angles . Drawing the curve we find that the whole area is 2292 in arbitrary units ; the area between ordinates is 138 on the same scale . * J. A. Crowther , ' Camb . Phil. Soc. Proc November , 1910 . Mr. J. A. Crowther . the Energy [ Dec. 13 , The energy measured in the first experiment is thus 138/ 2292 , or of the whole scattered radiation . On the Energy of Scattered Radiation the Number of Electrons in the Atom . We are now in a position to form an estimate of the fraction of the energy of the primary Rontgen radiation scattered per unit mass of the radiator . We have found that of the energy of the primary beam is radiated between the angles with the plane perpendicular to the primary beam by an aluminium radiator mm. or cm . thick . We have also seen that this energy represents of the whole scattered radiation . The total energy of scattered radiation must therefore be or of the energy in the primary beam . The density of aluminium is ; the mass per unit area of the radiator is therefore grammes per square centimetre . For a radiator of unit mass square centimetre we should therefore have\mdash ; It must be remembered that as we have corrected our results for the absorption of the primary rays this number represents the rate at which the primary radiation is scattered . Representing the scattering by the equation where and I are the intensities of the scattered and primary rays , and is the mass per unit area , the number represents the factor , which we may term the mass coefficient of scattering . We have seen that the elementary theory of scattering does not entirely represent the actual distribution of the scattered radiation round the radiator . It seems probable , however , that the theor*v is sufficiently near the truth to give us a fairly reliable estimate of the energy scattered . Assuming that this is the case , we have per . per sq . cm . , where is the total number of . electrons . Taking as e.m.u. ( Rutherford and Geiger ) and as e.m.u. ( Bucherer ) we have psr 1910 . ] Distribution of Scattered . 43 Now the mass of a hydrogen atom is utherford and Geiger ) ; the mass of an atom of aluminium is therefore or the number of atoms of aluminium per gramme is The number of electrons in this mass of aluminium as given by the is . The number of electrons per atom of aluminium is therefore found to be \mdash ; or 85 . The number of electrons per atom of aluminium obtained from the measurements on the scattering of homogeneous -rays is 83.* The agreement between the two results arrived at from entirely different points of view is very satisfactory . It seems therefore that the estimate of the number of electrons in the atom as being three times the atomic weight is probably not far from the truth . The distribution of the scattered Rontgen radiation round a radiator has been measuled . The intensity of the scattered radiation reaches a maximum on sides of the radiator in the line of the primary beam , and falls to a minimum at right angles to this direction . At any given inclination to the primary beam there is a preponderance of radiation in the forward direction , the ratio increasing as the direction of the beam is approilched . The energy of the radiation scattered in a given direction has been compared with that in the primary beam . From the result so obtained , and the known distribution of the radiation , the total radiation scattered by an aluminium radiator has been determined . It has been shown that the value obtained leads to the same result for the number of electrons in the atom as that previously calculated by the author from his experiments on the scattering of homogeneous -rays . In conclusion I once more to express my thanks to Prof. Sir J. J. Thomson for his inspiration and advice during the course of these experiments . * J. A. Crowt fier , ' Roy . Soc. Proc 1910 , , vol. 84 , p. 239 .

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The origin of magnetic storms.

44

50

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Arthur Schuster, F. R. S.

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10.1098/rspa.1911.0019

Fluid Dynamics

Tables

Fluid Dynamics

]\gt ; The Origin of gnetic S By ARTHUR , F.R.S ' . ( Received January 9 , \mdash ; Read January 26 , 1911 . ) 1 . Lord Kelvi discussing the origin of magnetic storms , came to the collclusion that they could not be due to a direct solar action on account of the enormous which would have to be supplied by the sun . This verdict was generally accepted until recently , wheri the theory of a direct solar action has been in ) form , which is assumed to be free from the ection raised , the magnetic action being supposed to be due to a swarm of electrified corpuscles ejected by the sun . The question of energy has not , so far as I know , been discussed in this case , and it seems to be taken for granted that the total energy of the magnetic field due to a swarm of corpuscles is equal to the sum of the energies of each , calculated as if the others were not present . If the corpuscles are sufficiently far apart , this is approximately correct ; but in that case the magnetic field itself would to be negligible , except within molecular distance from each particle . How far we may go wrong by treatin the energy as if it could be obtained by a process of addition oecomes apparent when we consider that such treatment would lead to coefficients of self-induction which are proportional to the length of a circuit and independent of its shape . 2 . If represent the components of electro-kinetic potential and , the current components at any point , the total electro-magnetic energy is given by In a previous paper I have shown that in evaluating the integral the displacement currents need not be taken into account so hr as the components of current , while they become important , however , in calculation of A. If we take the axis of to be the.direction of motion , the expression for the energy reduces to where stands for the convection ourrent per unit wi\amp ; in the swarm of electrons and A is the component in the direction at ot the eleotrokinetic momentum due to the -current 'Roy . ' 1892 , vol. W. and the energy per unit length becomes As the swarm increases in length , the energy increases in a greater proportion than the length . 3 . Before discussing the results obtained , we write down the corresponding expressions for a swarm of electrons uniformly filling a sphere and moving with speed in the direction of the axis of . If be the total quantity of electricity in the sphere , the magnetic energy outside the sphere is The magnetic force inside the sphere is , where stands for the quantity of electricity contained in a sphere of radius , which is equal to . Introducing this and integrating through the volume of the sphere , we find for the total electro-kinetic eneJgy of the moving sphere 2 magnetic force at the surface in the plane being . If denote this magnetic force , the energy is if the volume of the sphere . Comparing the expressions for the cylinder with those for the sphere , it appears that in writing for the energy contained in volume V we shall underrate its value in both cases . As rf is the magnetic force at the point where it reaches its greatest value , we may take the above expression to represent the smallest amount of energy which a swarm of electrified particles can contain if it occupies a volume and causes a magnetic force H. 4 . Sir Oliver Lodge*has calculated the numerical values of dimensions of a swarm of electrons , producing a magnetic field as great as that of the storm of September 25 , 1909 . If the velocity of the particles be estimated at , he finds , taking into account the duration of the , that the square of the cross-section has the value , so that the total energy transmitted in unit time would be 4 , or , -a6 ohange in the magnetic force on this occasion was , we obtain lie per second for the rate at which the sun would have neaey . The number obtained by Lord Kelvin was torm hi\amp ; 'caused a magnetic force than the tenth th*-caeder9d by ' Natur 1892 , vol. difficulty might to some extent be overcome if it were possible to reduoe th6 cross-section of the swarm , but this was fixed to suit the atidn of the storm , and could not materially be diminished . It will also appear that tho electrostatic repulsion between the particles puts a small cross-section out of the range of possibility . We may pause for a to consider whether more favourable results might not be obtained by assuming the projected particles to have comparable with those of ordinary atoms of matier . It seems , however , impossible that the high velocity required could be imparted to such heavy calriers , except by a radioactive process , and examination shows that inadmissibly large quantities of radium would have to be involved , if appreciable magnetic effects are to be produced . 6 . We proceed to examine the electrostatic effects , which must show themselves in the gradual . expansion of the beam and in the redistributiom of the icity on the surface of the . The magnetic force . at a point due to a charge moving with velocity is eu , if be the angle which the line between and the charge forms wiffi the direction of motion . On the other hand the electric force at resolved in a plane right angles to the direction of motion is , where is the velocity of light . Hence if be the component of electric force at right angles to the direction of motion , H. This relation must hold for the total effect of all current elements , provided they are all parallel . The acceleration at of the charge having mass is H. We found from energy consideration that must be greater than but leaving this out of account altogether , and putting for . its possible value , which is , we may assert that 50 Dr. A. Schuster . [ Jan. energy and from electrostatic considerations alike , hafnow been shown to bo fatal to the theory in any form . If , therefore , we wish to adhere to the hypothesis that the oonnexion between solar outbursts and terrestrial magnetism is due to a projection of particles by the sun , we are driven to accept the view , which I have advocated for a long time , that the particles act by increasing the ionisation of the outer regions of the atmosphere and allow the electromotive forces which are always present locally to increase the intensity of the electric circulation . The rotation of the earth , which is the primary cause of the electromotive forces which come into play , then becomes responsible fo energy . The view that the impact of the projected particles causes luminosity remains allowable , so that Prof. Birkeland 's theory of the aurora borealis is still tenable . On the Periodicity of Sun-spots . By ARTHUR SCHUSTER , F.RS . ( Received January 19 , \mdash ; Read January 26 , 1911 . ) In the year 1906 I presented to the ' Royal Society an investigation*in which it was shown that the frequency of sun-spots was subject to recurrent variations , not only in the well-known 11 years ' cycle , but also in other periods , which were determined . As we now ossess additional material extending over 10 years , it is interesting to examine how far the minor maxima of the subsidiary periods can be traced in the more recent records . The accompanying figure gives diagrammatically the sun-spot areas measured at Greenwich between 1898 and 1909 . The numbers plotted represent the sum of the mean areas during four successive rotations , beginning with the four rotations 593/ 596 of Carrington 's series . There is a period of years , which in the previous communication was shown to be persistent during the whole time by sun-spot reoor more persistent , in fact , than that of 11 years . I have marked on the diagram the predicted times of maxima of the period wffih en arrow pointing upwards . The first maximum , towards the snd of ear , which

rspa_1911_0020

0950-1207

On the periodicity of sun-spots.

50

53

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Arthur Schuster, F. R. S.

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10.1098/rspa.1911.0020

Meteorology

Tables

Meteorology

Dr. A. Schuster . [ Jan. 19 , energy and from electrostatic considerations alike , has now been shown to be fatal to the theory in any form . If , therefore , we wish to adhere to the hypothesis that the connexion between solar outbursts and terrestrial magnetism is due to a projection of particles by the sun , we are driven to accept the view , which I have advocated for a long time , that the particles act by increasing the ionisation of the outer regions of the atmosphere and allow the electromotive forces which are always present locally to increase the intensity of the electric circulation . The rotation of the earth , which is the primary cause of the electromotive forces which come into play , then becomes responsible for the energy . The view that the impact of the projected particles causes luminosity remains allowable , so that Prof. Birkeland 's theory of the aurora borealis is still tenable . On the Periodicity of Sun-spots . By Arthur Schuster , F.R.S. ( Received January 19 , \#151 ; Read January 26 , 1911 . ) In the year 1906 I presented to the Royal Society an investigation* in which it was shown that the frequency of sun-spots was subject to recurrent variations , not only in the well-known 11 years ' cycle , but also in other periods , which were determined . As we now possess additional material extending over 10 years , it is interesting to examine how far the minor maxima of the subsidiary periods can be traced in the more recent records . The accompanying figure gives diagrammatically the sun-spot areas measured at Greenwich between 1898 and 1909 . The numbers plotted represent the sum of the mean areas during four successive rotations , beginning with the four rotations 593/ 596 of Carrington 's series . There is a period of 4'79 years , which in the previous communication wTas shown to be persistent during the whole time covered by sun-spot records , more persistent , in fact , than that of 11 years . I have marked on the diagram the predicted times of maxima of the period with an arrow pointing upwards . The first maximum , towards the end of the year 1898 , which was timed to arrive during the rotation 604 , actually took place three rotations , or about months , earlier . The second maximum ( September , 1903 ) was * ' Phil. Trans. , ' 1906 , vol. 206 , p. 69 . 1911 . ] On the Periodicity of Sun-spots . predicted to take place during rotation 668 . It actually took place during the rotation 671 , though an almost equally strong maximum was observed during rotation 667 . We may therefore say that there is here an almost absolute coincidence in the predicted and observed times . The maximum of July , 1908 , was delayed by about two months , but the activity had already risen considerably at the predicted time . In all three cases the coincidences of the predicted and actual times are very satisfactory , if it be remembered how variable is the observed maximum of the 11 years ' period . This periodicity of 479 years seems characterised by one or two sharp outbreaks near the time of the maximum , and throughout the time that accurate records are available it nearly always shows itself in each cycle as a separate peak in the curve representing sun-spot frequencies . The outbreaks of sun-spots connected with this period can be traced also in the magnetic records . There were several disturbances during September and October , 1898 , notably one on September 9 . In 1903 there was a magnetic storm on October 12 , and more violent ones at the end of the month . Finally , in 1908 , we had strong distxirbances on September 11 and 29 . Dr. A. Schuster . [ Jan. 19 , We must conclude that the previous evidence establishing this period has been further confirmed . In the meantime the same period has been discovered quite independently in the records of magnetic declination by Mr. Oppenheim.* Taking the average daily ranges for two successive years , as observed by Lamont in Munich during the years 1836\#151 ; 1886 , Mr. Oppenheim , using a method differing essentially from that adopted by myself and others , comes to the conclusion that it is subject to a period of 4*92 years with an amplitude of about 12 seconds of arc . The difference between 4*92 and 4*79 , as found by myself , is not important , considering that Mr. Oppenheim bases his calculation on a two-year mean and only 12 complete periods . This work being apparently undertaken in ignorance of the previous discovery of this period in the sun-spot records , the moral value of the confirmation it affords , is increased . At the foot of the diagram I have represented the average rise and fall of this period as obtained from the mean of all observations extending over a range of 16 periods . The scale is that of the larger diagram , showing that the efficiency of this outbreak has been well above the average . A period of 4*38 years , indicated as doubtful in my previous communication , receives no support by the additional material , though the evidence is not perhaps decisively adverse . The times at which this period should have reached its maxima are marked in the diagram by arrows pointing downwards . A further periodicity of about 8*36 years , which appeared with considerable regularity between the years 1836 and 1887 , has not since then shown itself . There should have been a maximum during the summer of 1904 at a time when there actually was a considerable diminution of activity . A few words may be said on the apparently delayed maximum of the dominant periodicity of 11 years . The date of the maximum , as deduced from Fourier 's analysis , differs from that found by observation , because the analysis picks out the simple period , while the observations include the harmonics . It is known that the sun-spot curve rises much more quickly before the maximum than it falls after it . The resulting curve , when analysed , gives the simple periodicity of 11 years , with a maximum later than the observed one , and it is the first harmonic which has its maximum coinciding with the observed maximum of solar activity . The true maximum of the 11 years ' Fourier period should have taken place in 1905*35 , but the greatest outbreak of spots which coincide with the maximum of the 5*56 year period was to be expected already in 1903*75 . The times of these maxima are indicated in the diagram by lines drawn without arrow-heads . * ' Met . Zeits . , ' 1910 , vol. 27 , p. 270 . On the Periodicity of Sun-spots . 191.1 . ] The first of them coincides with the maximum of the 4-79 period , and it is therefore open to us to ascribe this maximum to the 11 years ' cycle rather than to the minor period . But in that case the subsequent behaviour of the activity becomes anomalous , as the spots ought to have diminished in number immediately afterwards . To judge from the appearance of the curve , it looks as if the two peaks in 1905 represent the true maximum of the 11 years ' period , and that we must ascribe the outbreak in 1909 to some unknown cause . It was pointed out in my previous communication that the three well-established periods have periodic times which are sub-multiples of 33'375 years . It has often been remarked that the 11-year period shows particularly pronounced maxima during the first , third , and seventh decades , suggesting a periodicity of 33 years , and it is remarkable that this period can be traced in the Chinese records , reaching back to the beginning of our era.* Though the last maximum was exceptional , in so far as it was rather below the average in intensity , the coincidence between the period of 33 years and the time of revolution of the Leonides meteorites is remarkable , and deserves careful attention . The delayed and disappointing display of Leonides at the end of last century is perhaps connected with the delayed and disappointing appearance of the last sun-spot maximum , while the exceptional brilliance of both phenomena 33 years previously is suggestive . In the diagram the vertical scale represents sun-spot areas . Along the upper margin shorter lines are marked at intervals of 10 rotation periods , while the longer lines represent the divisions between successive years . * 'Observatory , ' 1906 , vol. 29 , p. 205 .

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The absorption spectra of lithium and c\#xE6;sium.

54

58

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Prof. P. V. Bevan, M. A.|Sir J. J. Thomson, F. R. S.

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10.1098/rspa.1911.0021

Atomic Physics

Tables

Atomic Physics

]\gt ; The Absorption of Lithium and Coesium . By Prof. P. . BEVAN , M.A. , Royal Holloway College . ( Communicated by Sir J. J. Thomson , F.R.S. Received January 20 , \mdash ; Read March 9 , 1911 . ) In a paper*communicated to the Royal Society in February , 1910 , I gave the results of measurements of absorption lines for the three alkali metals , potassium , rubidium , and caesium . Up to that time I had not been able to obtain the spectrum for lithium vapour . This was owing to the fact that lithium vaporises at a considerably higher temperature than the other alkali metals , and at the high temperatures required for a sufficient density of vapour the lithium attacks the material of all tubes which I was able to use . SCeel , brass , platinum , glass , silica , carbon are all attacked , and no satisfactory could be obtained . Recently , however , by using a relatively large quantity of lithium in a steel tube sufficient vapour was obtained to give an absorption spectrum showing 27 lines of the principal series . The method was the same as that described in the paper referred to , with the exception that a second steel tube was placed in the outer steel absorption tube . This was simply for the protection of the outer tube , which would probably collapse after being acted on by lithium vapour at the bright red heat to which it was raised . The source of light used was the cadmium spark , as the limit of the series is so much further in the ultraviolet than in the case of the other alkali metals . The following table ives the -lengths and oscillation requencies for the complete series of lithium lines . ( See Table I opposite . ) The lines 1 to 9 are given by Kayser , 10 to 27 are new . In addition to the absorption spectrum consisting of these lines of the principal series , there is a fluted region corresponding to the similar region in the cases of sodium and potassium vapours . This extends over the wavelengths between about 4500 and 5500 , and corresponds fairly closely in position with the sodium fluted region . The fluted is , in appearance , like those in the cases of sodium and potassium , and appears under similar circumstances\mdash ; when the vapour is fairly dense , giving a broadened line for the first member of the principal series . It consists of a number of fine lines , grouped so as to show under small dispersion bands with fairly definite edges the central position of the spectrum\mdash ; at the two ends the appearance of sharp edges is lost . ' Roy . Soc. Proc , vol. 83 , p. 421 . The Absorption Spectra of Lithiurn and xjsium . Table I. The table contains in the second column the estimated possible errors in the determinations of the wave-lengths . Hicks* has emphasised the importance of recording the possible errors in determinations , and , although these determinations do not make any pretence at great accuracy , the possible errors for each wave-length have been estimated . They vary through the series owing to the differences in the situation of lines ; for example , the two lines 1od and 20 of the series have possible errors of given to them owing to the fact that they occur close to the cadmium line of -length 2313 , and where we have absorption lines close to an emission line of the source of \mdash ; in this case the cadmium spark\mdash ; the exact position of the centre of the line is difficult to determine . An attempt was made to obtain the absorption spectrum with another source than the cadmium spark , but without success\mdash ; the cadmium spark seems to give the best intensity of light so far in the ultra-violet as the lines under discussion . The lines 8 and 9 were measured . The values given by Kayser are due to Living and Dewar , and no estimate of error is given . The values obtained by me are the same as those of Living and Dewar . ' Phil. Trans vol. 210 , p. 58 . Prof. P. V. Bevan . [ Jan. ) Various formulae have been suggested for series lines . Those of Rydberg and Kayser and } have been shown to be not sufficiently accurate for representing observed values , and several modifications of these have been brought forward . The most promising of these is perhaps that of Hicks , * which is a modified formula . This formula gives , the oscillation frequency , the number of waves per centimetre , in the following form\mdash ; where is the universal Rydberg constant , 10967 , and takes the values 1 , 2 , 3 , etc. , for the different lines of the series , the other quantities being constants the particular substance . With the values of these constants found by Hicks for lithium , we find very agreement for the calculated and observed values of the wave-lengths ; in the last column of Table I there are given the differences between the observed and calculated wave- lengths under the heading . The agreement is seen to be the estimate of the possible error , but there is an indication that the observed values are all smaller than the calculated values . This would be accounted for by a value of the constant , which is too smalL The possible error in this constant , , is according to Hicks . The maximum amount allowable would make in the wave-lengths a difference of or to the nearest tenth of an ngstrom unit . This would still leave over a small negative error in the values , which may fairly be accounted for by the nature of the lines measured ; they are faint absorption lines , and so not so sharp as good emission lines . This series for lithium is interesting , as on the lines of work of Hicks , already referred to , the series is of a different type from the principal series of the other alkali metals . This difference is discussed by Hicks in the paper already cited . From the physical point of view , however , the series seems to behave just like the series in the cases of the other alkali metals . The set of lines appears under very similar conditions as absorption lines , taking account of the higher temperature required for volatilisation of the lithium , and the series is accompanied by the channelled space spectrum as is the case with sodium and potassium . The earlier members of the series are easily reversed in the arc , and anomalous dispersion effects appear in transmitted for wave-lengths in the hbourhood of the series lines . In these respects the physical characteristics of these hnes are exactly like those exhibited by the corresponding lines in the cases of the other metals . 1911 . ] The Absorption Spectra of Lithium Coesium . It is difficult then to see what the of the difference in type as discovered by Hicks can be . It may be remarked in this connection that the values for the constants of the Hicks formula , that is the wave numbers of the heads of the series , viz. , Li 43482 , Na 41446 , 35006 , Bb 33687 , Cs 31400 , continually decrease as the atomic weights increase , so that we cannot attach too much importance to the fact that the first members of these series do not fall into such regular order , the number for lithium apparently out of place . It may also be mentioned that the order into which the wave numbers of the first members of the series fall for the elements other than lithium does not show any close relation to the atomic weights . In a note from Prof. Hicks he has pointed out that in the for the caesium principal series lin es published in a paper I communicated to the Royal Society in January , 1910 , there re probably some errors in determinations , some of the later lines of the series show departures from values which seem probable as calculated from his formula . I have made a re-determination of these lines from raphs of the absorption spectra for caesium vapour set free by the action of sodium and potassium on the chloride of caesium . I have not been able to obtain metallic ciesium , and the presence of the vapour of the other metals-rather obscures the absorption lines due to the metal . With some better a few more lines been measured , extending the list to 24 for the principal series . With the vapour of caesium itself there is not much doubt that a considerably largel number of the lines could be The following table gives the re-determinations of wave-lengths for the lines from No. 8 of the series ; 22 , 23 , and 24 are new lines . With regard to the accuracy of determination of those measurements , it is not so good as for the lithium lines , as there is considerably more dispersion in the occupied by these latter , so that we can estimate the possible error as of an tYstrom unit . In the third column is given the difference between the observed and calculated values of the wave-length , the calculated being obtained from the Hicks formula , . The comparison spectrum for this purpose was that of the iron arc . It will be noticed that all the differences iu the third column are of the same sign ; a change in the constant A of the Hicks formula , sufficient to make a change of in the limiting wave-length , would bring all these observed wave-lengths into agreement with the formula . The possible error , however , Prof. P. V. Bevan . [ Jan. 20 , Table II . in A of the formula cannot be determined , for the observations used in its calculation have not their possible errors ascribed to them . Dispersion in Vapours of the Alkali Metals . By Prof. P. . BEVAN , M.A. , Holloway ( Communicated by Sir J. J. Thomson , F.R.S. Received January 20 , \mdash ; Read March 9 , 1911 . ) [ PLATES 6 AND 7 . ] In the 'Proceedings ' of the Royal Society , , vol. 84 , p. 209 , I gave an account of experiments with Potassium vapour , which had for their object the determination of the dispersion curve for the vapour . The effect of the first three pairs of lines of the principal series was quantitatively estimated , and it appeared that certain conclusions could be drawn as to the numbers of systems taking part in the absorption of light . The present communication deals with further experiments of the same kind with vapours of Sodium and nbidium , and again with the vapour of potassium , as far as regards a temperature effect , which will be discussed later . The experiments were made possible by a grant from the Royal Society , which enabled me to obtain metallic rubidium , and I am glad to take this opportuniby of thanking the Government Grant nttee .

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0950-1207

Dispersion in vapours of the alkali metals.

58

76

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Prof. P. V. Bevan, M. A.|Sir J. J. Thomson, F. R. S.

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10.1098/rspa.1911.0022

Atomic Physics

Tables

Atomic Physics

]\gt ; Prof. P. V. Bevan . [ Jan. 20 , Table II . in A of the formula cannot be determined , for the observations used in its calculation have not their possible errors ascribed to them . Dispersion in Vapours of the Alkali Metals . By Prof. P. . BEVAN , M.A. , Holloway ( Communicated by Sir J. J. Thomson , F.R.S. Received January 20 , \mdash ; Read March 9 , 1911 . ) [ PLATES 6 AND 7 . ] In the 'Proceedings ' of the Royal Society , , vol. 84 , p. 209 , I gave an account of experiments with Potassium vapour , which had for their object the determination of the dispersion curve for the vapour . The effect of the first three pairs of lines of the principal series was quantitatively estimated , and it appeared that certain conclusions could be drawn as to the numbers of systems taking part in the absorption of light . The present communication deals with further experiments of the same kind with vapours of Sodium and nbidium , and again with the vapour of potassium , as far as regards a temperature effect , which will be discussed later . The experiments were made possible by a grant from the Royal Society , which enabled me to obtain metallic rubidium , and I am glad to take this opportuniby of thanking the Government Grant nttee . 1911 . ] Disper.sion in Vapours of the Alkali Metals . In a former paper*I gave results of the measurements of wave-length of the principal series lines for rubidium obtained in the absorption spectrum . This spectrum was obtained by heating rubidium chloride with metallic potassium ; enough vapour was formed to give an absorption spectrum showing 25 lines of the series . With metallic rubidium it is easier to get the absorption spectrum , and the list of lines has been extended to include 30 members . A better reading microscope has been available since the original measurements , so that the complete series of lines has been remeasured . The method adopted was the same as that described in the paper referred to , so that there is no need for further description . The following table gives the measurements of the of the lines of the principal series . The first four members ve been measured by Kayser , and the fifth by Ramage . The sixth member appears in some photographs as a pair , but the two lines are close together , and generally broadened somewhat , so that the readings cannot be made so accurately as for later members of the series . Wave-lengths of Lines of the ) Series for ubidium . With the measuring instrument used , the lines 10-30 should not have any error as great as Ltrom unit . The measurements were made to unit , and are expressed here to that order , but the last figure is not reliable . The lines 8 and 9 could not be determined accurately , but should be within of the correct value . In 6 and 7 the accuracy is still less , but there should not be a greater error than tenth-metre . [ Note.\mdash ; It is interesting to compare the values of the wave-lengbhs for the principal series lines of rubidium with the values as given by the formula proposed by Hicks . For rubidium this formula is 'Eoy . Soc. Proc , p. 421 . W. M. Hicks , ' Phil. Trans , vol. 210 , Prof. P. V. Bevan . [ Jan. 20 , where is the universal Rydberg constant 109675 , A is 336875 , is for the more refrangible of the pairs of lines and for the less ible member , and is and for the pairs of lines . For lines as high as the sixth of the series account of the difference in the values of need not be taken . In the observed values the difference between the two members of each pair is not to be detected after the sixth member , and it is therefore a little difficult to decide what exactly to take as the calculated values . The more refrangible component of a pair is the more intense where the members are separable , and therefore the observed value of the centre of the line , where the two appear as one , is probably rather nearer the more ible component . In the following list the differences Observed -Calculated ) are given for the one observe and two calculated values after the sixth of the series . The formula Doiyes very good reement with the observed values for the pair 6 ; for 7 , 8 , and 9 the observed value is between the two calculated values ; 10 is not in such good yreement , the observed value being outside the two calculated values , but by very little . The other lines are in good reement , on the whole , the observed values lying a little to the side of lower wave-length , but in all cases the departnre is not more than the estimated possible error . A slight alteration of the constant A such as is possible to Prof. Hicks ' calculations could adjust this . The difference between the wave-lengths of the pairs of lines is considerable up to about the 13th pair in the series , and it ought to be possible to measure the separate members . I hope to be able to do this in the future ; measurements of such a character would have considerable interest . ] Fig. 1 , Plate 6 , is a photograph of a series of the absorption spectra 1911 . ] Dispersion in Vapours of the Alkali Metals . of Rubidium vapour . The vapour was of increasing density for the spectra 1 to 6 , after this at density . The principal series lines are the most evident feature . The continuous absorption for less than the limit of the series is noticeable in 1 , 2 , 3 , especially . This phenomenon is similar to that observed by Wood in the case of sodium . The broadening of the lines is also very evident in the spectra of the denser vapour . Some of the potassium lines appear in these raphs owing to the presence of this metal as impurity . Rubidium also possesses a channelled-space spectrum , very similar to the spectra of sodium and potassium . This consists of a very number of lines , with strong absorption at certain intervals , giving the appearance of bands with sharp edges . This spectrum was photographed with a small diffraction grating and laboratory spectrometer , the telescope being replaced by a camera . The aperture and beino small , detailed examination of the spectrum was impossible , but the wave-lengths to the heads of the bands were determined . For comparison , the neon red spectrum used . Three lines were found in this which not to be discovered iu the list of neon lines by Baly . The wave-lengths of these lines are ) , and . I have not been able to identify these lines with any belonging to other elements , aItd assume that they are new lines . The wave-lengths of the edges of the rubidium bands are as follows : The ratios of these numbers to , the wave-length of the line of the first pair of the principal series with greatest wave-length , from to . The corresponding ratios for sodium range from to , and for potassium , from to Carter has measured the lines of the potassium spectrum , and has given a table with lines marked " " very strong\ldquo ; and " " strong These are similaY to the lines obtained from Wood 's work on sodium , and so may be taken as the of the bands . These give numbers for the ratios ranging from to . It is an interesting fact that these numbers all fall within the same . With more light available , more of this type of line would appear for rubidium , and the correspondence be closer still . It is curious that the ratios agree for the more refrangible of the first pair of the principal series\mdash ; if the less refrangible line be taken , we have no obvious correspondence . Lithium also 'Phil . Mag January , 1910 , p. 199 . 'Physical Review , ' , 1908 . Prof P. V. Bevan . [ Jan. 20 , shows a similar spectrum . situated in the same region , relative to the red lithium line . There are other points of interest in the rubidium absorption spectrum notably , in the way in which the lines broaden with denser vapour , and in the appearance of lines which seem associated with the principal series lines . These points are , however , still under investigation . For the dispersion of light due to rubidium vapour , the same method was adopted as was described in the paper already referred to . The vapour prism was in a tube with quartz plates for its ends , and the crossed prism system adopted . The achromatic lens described in the former paper was used . This lens proves very satisfactory with a small aperture\mdash ; a larger aperture allows a considerable amount of spherical aberration to spoil the definition . With this lens , an of a horizontal slit , , illuminated an arc light , is thrown on the slit of the spectrograph . This , without the metallic vapour , gives a linear spectrum . On placing the tube , with metallic vapour in it , in the beam of light , vertical dispersion takes place , and the dispersion curve is seen in the spectrograph . With the quartz spectroraph used there is very little dispersion at the red end of the visible spectrum , but sufficient for photographs to be taken , which showed the complete dispersion curve over a range including all the lines of the principal series except the first pair . The main features of the phenomena to be observed are very similar to those described in the case of the similar experiments with potassium vapour . In the case of rubidium , the pairs of lines are more widely separated than with potassium , so that it is easier to observe the region between the lines of a particular pair . The dispersion effects can be detected on at the first members of the series . Measurements could be made at the first four members , which were fairly reliable . At the next two members measurements could be made , but these could only be regarded as giving the order of the effect . As before , the quantities measured were the displacements of the spectrum from its undeviated position at various -lengths . These quantities when reduced\mdash ; to allow for the " " tilt\ldquo ; of the plate in the \mdash ; are proportional to the deviation of the rays by the vapoul prism , and so are proportional to when is the efractive index ; being very nearly 1 , this is again proportional to , and so to the well-known expression of the Sellmeier dispersion formula . For rubidium , the early lines of the series being pairs separated by a considerable amount , it was found impossible to treat the pair of lines as a single line at a mean position . The case is thus more complicated than 1911 . ] Dispersion in Vapours of the Alkali Ietals . that of potassium , as two constants are required for each pair of the series . It appeared that the ratio of these constants for a pair of lines was approximately constant throughout the series . This conclusion is only tentative , as the determination of the ratio of these constants is a matter of considerable difficulty . A very small error in a wave-length used for the determ.ination makes a considerable change in the value of the constant . However , it was assumed that lihe ratio was the same and this was determined from observations at the pair of lines . No reliable measurements could be made at the first pair , as the dispersion available was small . This constant then being determined , its value was assumed for the other pairs , and the values of the separate constants deduced from the observations . The dispersion formula of Sellmeier for this case can be written , when , are the wave-lengths of the pair of lines , and , the corresponding constants . The effect due to the first pair of absorption lines is far larger than that due to succeeding pairs , so that , as was done in the case of potassium , the main part of the dispersion that not in the immediate neighboUl.hood of the second , third , etc. , pairs of lines\mdash ; was determined first and then detailed observations were made in the regions of the pairs of lines . Several different photographs were used , as those suitable for one region might not be suitable for other parts . The deviations were reduced so as to all be measured on the same scale . With vapour of sufficient density to show the effect at the second and later pairs of lines the red end of the visible spectrum is almost completely absorbed down a wave-length of about 6400 . The following tables give the measurements of deviations ( corrected reduced to the same scale ) for the oorresponding wave-lengths . I.\mdash ; Deviation for Main Portion . 1911 . ] Dispersion in Vapours of the Metals . By plotting the main curve and deducting the values of deviation corresponding to the first of lines from the observations near pairs , we obtain the deviation at various wave-lengths as far as they depend on any particular pair of the series , for the influence of any pair after the first is confined to the immediate neighbourhood of the lines . In this way we obtain the observed deviations , which are proportional to the ntity and the corresponding quantities for fher metlbers of the series . From these quantities we can find the values of the constants , etc. With the large number of observations made it was a little difficult to decide how to obtain the best values of the constants . The method of least squares would have been laborious , and , as the observations are of very varying weights , it was thought that no great advantage would be obtained by applying it . Near the absorption lines slight errors in wave-length determination would involve large errors in the calculated constants , and VOL. LXXXV.\mdash ; A. Prof. P. V. Bevan . [ Jan. 20 , these errors would be small , at some distance from the absorption lines , the small deviations become uncertain in measurement . It is difficult to balance these two sources of error ' . so the method adopted was to plot all the observa and find values of the constants which gave a curve fitting the observations as well as possible . The two constants and , as has already been remarked , seemed to have about the same ratio for each pair of lines , so that this ratio was determined once for all from the observations in Table II for the second pair of lines and was assumed to be the same for the other pairs . The values of the constants obtained are as follows:\mdash ; The values for 5 and 6 are very doubtful , as the deviations are so small except very close to the absorption lines . For example , the observations for gave three values , , and , multiplied by . These values , therefore , can only be regarded as giving an estimate of the order of the effect . In text-fig . 1 the dispersion curve is plotted for the range from 6300 to 3200 . The region of wave-length is not shown , as the curve would not show the effects at the second , third , and fourth lines if on a small enough scale to show the curve at the red lines . Also , with the apparatus at my disposal , sufficient accuracy could not be obtained in the determination of wavelengths in the red to the small dispersion available . The curve represents the quantity with the values of the constants above . The observed values of deviations are indicated by points which lie very fairly closely about the curve . In fig. 2 ( p. 68 ) the ordinates represent the quantity Prof. P. V. Bevan . [ Jan. 20 , the second two terms of which we can regard as the deviation due to the second pair of the lines of the principal series . The scale is much larger than that of fig. 1 . The observed deviations are represented by points and crosses . The points refer to the observations of Table II , the crosses to those of in the same table . The observations were from a photograph with the iron arc as source of light , so that the wave-lengths are accurately lxnown ; the deviations are , however , not so good as for the observations Figs. and 4 ( p. 69 ) represent the quantities and so that the ordinates may be taken to represent the deviations due to the third and fourth pairs of the principal series of lines . The points represent the observations recorded in Tables III and In this series of curves the points representing observed deviations are found to lie very fairly closely about the curves . Better agreement could perhaps be found if a more elaborate method of determining the constants ] were employed , bnt there seemed no reason at present for the enormously increased arithmetic necessary for an application of the method of least . squares to the observations . Fig. 2 of Plate 6 is a photograph of the dispersion effect in the neighbourProf . P. V. Bevan . [ Jan. 20 , two potassium lines 7699 and 7665 have effect as only one line . In fig. 2 , just to the left of 7806 , the slight effect of potassium as impurity in the rubidium is visible . In Plate 7 , , two photographs of the effect at the rubidium lines 4215 , 4202 , are shown ; and are enlargements of is with denser vapour than . To the left of the photographs the effect at the next pair of lines also appears\mdash ; 3591 , 3587 . In these photographs the potassium impurity also shows itself by the slight break at the lines 4047 , 4044 . Fig. 5 shows the at the third and succeeding pairs of lines ; is again an enlargement of . The position of the undeviated spectrum was also photographed on this plate . This raph shows also a good number of the absorption lines nearer the limit of . the series . The potassium line at 3447 also appears . Fig. 6 gives examples of the dispersion curves with the undeviated spectrum at the lines 4215 , 4202 , the pair at 3590 . Sodium . For the case of sodium the dispersion corresponding to the lines has been investigated by Wood . * He , however , has not made measurements of the dispersion corresponding to the other lines of the principal series , and it seemed worth while to obtain values of the constants for sodium to see if there be a general relation to be found in the values of these constants for the alkah metals . Wood has investigated the dispersion between and near to the lines , but his numbers do not enable us to obtain any reliable value of the ratio of the two separate constants for the lines . ] that can be said is that the constant for the line of smaller wave-length is greater than the other , in accordance with the observed results for rubidium and potassium , and with the fact that the line of shorter wave-length of all the pairs of these series for the alkali metals is more intense than the other . Sodium is , for dispersion near lines other than the ] ines , more difficult for investigation than the other metals of the group except lithium . This is owing to the fact that a higher temperature is necessary to obtain the vapour in sufficient density . With sodium , however , the first pair of the principal series is in a more suitable part of the spectrum for visual observation and also for photographic methods , the red end , where the potassium , rubidium , and caesium lines occur , being more difficult to see and photograph than the yellow . The dispersion effects could only be measured with any accuracy at the lines 3304 and 2853 . The effect could be observed * Phil. Mag [ 6 ] , 1904 , vol. 8 , p. 293 . 1911 . ] Dispersion in yapours of the at the two next pairs of lines , but no reliable measurements could be made . For the sodium measurements , instead of a slit as source of , the naked arc was used , with a grating of fine wires wound on a wooden frame in front of this . The plane of the wires being nearly horizontal , the . different distances from the lens used to focus them on the slit of the spectroscope , so that with a rough adjustment of focus some of the images of the wires would be in good focus on the spectroscope slit after the heated tube was introduced . This device saved a good deal of trouble in focussing . The following table gives the results or deviations and wave-lengths:\mdash ; The deviations in the second two colnmns are from the mean position of the curve , not the whole deviations ; they represent , therefore , the quantities , being the mean wave-lengths of the second and third pair of lines for the sodium series . The deviations in the first column give the data for the main part of the dispersion curve , being Using the measured deviations instead of we obtain for ? for this set of observations . From the other deviations we obtain and . In fig. 5 , I , the curve is traced with these values of the constants , and the observed values of deviations marked by crosses . These points , near the lines 3303 , 2853 , were obtained by adding the observed deviations of the above table to the calculated value , taking only the first term of the Sellmeier formula . In other words , the observed deviations are only observed partly\mdash ; their values measured from the position 1911 . ] in Vapours of the Alkali Question of the Effect , Temperaturc Rdative Values of the Constants of the Dispersion If attention be confined to the effects of dispersion near single pair of lines , the constant of the dispersion formula appropriate to this line increases with the temperature of the vapour used . It is not quite clear whether it is the density gradient or the prismatic form of the vapour in tube which the dispersion effect , or whether both of these causes co-operate . I am inclined to think that the second effect is of most importance , but in any case , if the tube is heated more strongly , we get a vapour of greater average density and so greater dispersion effects . The question naturally occurs as to whether the different constants change proportionally with this change of average temperature in the vapour . On the view that was put forward in my earlier paper , which reference already been made , that different specialised atoms are in the ption of the different lines , it seems that the relative numbers of these special atoms should depend on the temperature of the vapour . If more complex systems are required for the absorption corresponding to higher members of the series of lines , seems likely that the relative number of atoms correto the her members should decrease with incre . as of temperature . We sbould expect , therefore , a in the relative values of the constants , etc. , which would appear as an increase in the ratios , etc. , with increase in temperature . An effect of this kind was therefore sought in the case of potassium and sodium . As will appear , there is evidence for an increase in these ratios which is fairly conclusive . The actual determination of the constants has , of course , a considerable amount of certainty , but a number of measurements were made , and there does seem to be a definite increase in the ratios indicated . For the case of sodium photographs were used with different densities of vapour . For the most dense vapour the absorption was complete in the region 5000 to 4600 . This photograph was the one used for the measurements for the sodium dispersion curve already described . Ths next of the series of gave dispersion in the region uear the lines of rather less than one-half that occurring in the first . On this photograph measurements could be made giving fairly good values of the constants corresponding to the first three lines of the series . The third photograph was with vapour of considerably less density , and the effect at the third line was too small for any reliable measurements . Measurements of deviations were made a nulnber o points near the absorption lines , so that several of the values of the constants could be obtained . ' Roy . Soc. Proc , vol. 84 , p. 209 . Disperrion in Vapours of the Alkali Metals . Potassium ( 3 ) . 2 . 2.47 Mean , 242 2.44 . 7.2 8.7 9.8 6.64 Mean , 9.3 Mean , 92 9.6 Tbese numbers give us the table for the ratios The values of tlJe constants in ( 1 ) are the best ; in this case the measurenlents of deviation were largest , and so admit of fair accuracy . For the measurements ( 2 ) the accuracy is good for and is , however , uncertain , wide differences occurring in the four values obtained . For ( 3 ) and are fairly good values , but again shows wide variations in the individual numbers . Still , allowing for the uncertainty in the observations , the diminution in the numbers for and the greater value of for ( 1 ) indicates pretty clearly that there is a real change in the relative values of the constants . The values and 7 for from ( 2 ) and ( 3 ) are so near together , and the individual differences in the values of for ( 2 ) and ( 3 ) are so great , that the apparent increase from to 7 is of no significance . These numbers for potassium with those of a similar character for sodium seem to indicate a real change dependent on the temperature of the vapour . This being so , we cannot expect any relation between the constants of the different metals , as before any such relation should appear we must have the vapours of the metals at corresponding temperatures , and as yet there is no evidence to show at what temperatures we should expect correspondence to exist .

rspa_1911_0023

0950-1207

Report on the separation of ionium and actinium from certain residues and on the production of helium by ionium.

77

81

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

B. B. Boltwood, Ph. D.|Prof. E. Rutherford, F. R. S.

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6.0.4

http://dx.doi.org/10.1098/rspa.1911.0023

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1911_0023

10.1098/rspa.1911.0023

Chemistry 2

Atomic Physics

Chemistry

77 Report on the Separation of Ionium and Actinium from Certain Residues and on the Production of Helium by Ionium A By B. B. Boltwood , Ph. D. , John Harling Fellow , University of Manchester . ( Communicated by Prof. E. Rutherford , F.R.S. Received February 4 , \#151 ; Read February 23 , 1911 . ) The material consisted of certain substances separated from 500 kilos , of ' pitchblende residues purchased by the Royal Society from the Vienna Academy of Sciences , and treated at the works of the Armet de Lisle at . Nogent-sur-Marne , in France , for the removal of the radium contained in them . The operations to be described were carried out with that portion of the residual material returned to the Royal Society as " actinium residues . " The material consisted of a wet paste , and was a heterogeneous mixture containing considerable proportions of lead chloride and gelatinous silica and small proportions of copper , zinc , iron , tin , and other elements . * Note by Prof. E. Rutherford , F.R.S.\#151 ; In 1907 the Royal Society kindly allowed me to test the actinium residues in their possession . Preliminary observations on a small fraction of the dried residue showed that it gave off the actinium emanation freely , and contained a small quantity of radium . Observations on the rate of growth of radium in the part of the residue obtained in solution showed that the amount of ionium present was less than 1/ 10 of the amount to be expected if all the ionium in the uranium residues had been separated with the actinium . This is borne out by the result of the chemical separation of the ionium , which is described in the paper . This result was disappointing , and indicates that the greater part of the ionium was lost in some part of the process to which the main pitchblende residues had been subjected . As there was no definite published information as to the best method of separation of actinium and ionium from such residues , it was necessary to devise suitable methods . Preliminary observations in this direction were made by Dr. Ritzel , a research student in the laboratory . These were continued by Mr. Greenwood , who carefully examined the activity in the form of thin films of definite small fractions of the material obtained at each stage of the chemical treatment . Working on a small scale , a satisfactory method was found of separating the greater part of actinium and ionium from the residues . As the laboratory had no provision for chemical work on the comparatively large scale required , it was arranged , that the initial work of concentration should be done by Messrs. Tyrer and Co. at their works , \mder the direction of Mr. Greenwood . It will be seen that the method applied on the large scale was successful in the separation of the ionium , but did not effect a separation of the actinium at the right point . As activity measurements had been made at each stage of the chemical process it was finally not difficult to locate the position of the actinium , and to affect its partial concentration . My thanks are due to Mr. Greenwood for his assistance in the initial work of separation , and particularly to Dr. Boltwood for the great trouble he has taken in separating and concentrating the ionium and actinium in the residues . 78 Dr. B. B. Boltwood . Report on the Separation oj [ Feb. 4 , The preliminary treatment was carried out at the works of Thomas Tyrer and Co. , at Stratford , London , under the direction of Mr. H. C. Greenwood , M.Sc . , of this laboratory , and consisted of the following operations :_ The weight of the wet paste was 21-2 kilos . The ignition of a small sample indicated that the proportion of volatile material present was equal to 68 per cent , of the total . The paste was heated with 35 litres of commercial hydrochloric acid , the mixture was boiled down to remove the excess of hydrochloric acid , and the residue was boiled with 100 litres of water . The undissolved materials were allowed to subside , the clear solution was decanted , and the remaining solids were repeatedly treated with hot water until all soluble substances had been removed . The insoluble portion was again treated with hydrochloric acid and with water . The solutions obtained were combined and allowed to cool , when a considerable quantity of lead chloride separated . This was removed , and the solution was treated with an excess of hydrogen sulphide . The precipitated sulphides were filtered ofF , and the solution , after the addition of about 8 litres of strong nitric acid , was heated to boiling . An excess of ammonia was added to this solution , and the mixture was boiled with steam . After standing over night the precipitated hydroxides were removed by filtration , and the filtrate was evaporated down until a considerable residue of ammonium salts was obtained . This residue will be referred to later as residue B. The precipitate of hydroxides was dissolved by warming with dilute hydrochloric acid , and the solution was diluted with water . To this solution was added a solution of 3 kilos , of oxalic acid . Ammonia was also added to neutralise the excess of hydrochloric acid . The mixture was allowed to stand for 17 hours , and the precipitated oxalates were filtered off , dried , and ignited at a low red heat . The oxides obtained in this manner were digested with hydrochloric acid , in which they were almost completely dissolved , and the insoluble material was removed from the solution by filtration . This filtrate , after diluting with water to a total volume of about 20 litres , was nearly neutralised with ammonia , and was then mixed with about 20 litres of a 6-per-cent , solution of hydrogen peroxide . The mixture was allowed to stand over night , and the precipitate which formed was filtered off and dried at 120 ' . The weight of the dried material was 160 grammes . All of the materials separated in the course of these operations were carefully preserved . The various solutions obtained were concentrated by evaporation . The activities of the different products were measured immediately after they had been separated , and were further observed at frequent intervals over a period of about nine months . The various operations described up to this point were all carried out either by , or under the direction of , Prof. Iiutherford and Mr. Greenwood . The first material placed at my disposal consisted of the precipitate obtained with hydrogen peroxide . As already stated , this precipitate , when dried , weighed 160 grm. Its activity was about 20 per cent , of the total activity of all the substances which had been separated from the original material . An examination of the records of the different measurements which had been made of the activity of this material from the time of its separation showed that the activity had at first risen by about 20 per cent , and had then fallen to about 65 per cent , of its initial value , after which it had remained approximately constant . 1911 . ] Ionium and Actinium from Certain Residues , etc. 79 A preliminary chemical examination of the precipitate indicated that it contained a considerable proportion of rare earths and calcium , but the somewhat surprising observation was made that very considerable amounts of fluorine were also present . It was at first difficult to account for the presence of this element , but from inquiries it was learned that the hydrogen peroxide solution used for the precipitation had been prepared by a process which resulted in its being largely contaminated with hydrofluosilicic acid . Owing to the presence of the fluorine , the decomposition of the precipitate was extremely difficult , but was finally accomplished by heating the material with concentrated sulphuric acid . The product obtained in this way was extracted with cold water , and the insoluble portions were again heated with sulphuric acid . After this operation had been repeated several times , a solution containing the rare earths , and an inactive residue consisting of calcium sulphate and silica , were obtained . The solution was heated to boiling and an excess of ammonium oxalate was added . The mixture was allowed to stand for 24 hours and the precipitate formed was removed by filtration . This precipitate was dried and converted into the oxides by gentle ignition . The weight of the oxides , which consisted chiefly of cerium and didymium oxides , was about 95 grm. The oxides were dissolved by hydrochloric acid and the rare earths present were precipitated as hydroxides by adding an excess of ammonia . The hydroxides were dissolved in a slight excess of hydrochloric acid . The solution was diluted , heated to boiling , and an excess of sodium thiosulphate was added . The mixture was boiled for some time , and the precipitate which formed was finally filtered off . This precipitate was decomposed by warming with a slight excess of hydrochloric acid , and the precipitation with sodium thiosulphate was repeated . This operation was carried out in all four times , and the precipitate obtained in the last operation was dried and strongly ignited . The final material obtained in this manner consisted of pure white thorium oxide and weighed T8 grm. It was highly radioactive , because of the ionium which it contained , and had an activity about 3000 times that of an equal weight of uranium oxide . Two thin films of this material , one weighing T27 mgrm . and the other weighing 0-65 mgrm . , were prepared and the number of a-particles emitted by these films were kindly counted for me by Dr. Geiger . According to his measurements , the average number of a-particles emitted by the total quantity of T8 grm. of material was 18T x 107 a-particles per second . It has been shown by Butherford and Geiger* that the number of a-particles emitted by 1 grm. of radium is 3'4 x 1010 per second . The * 'Roy . Soc. Proc. , ' A , 1908 , vol. 81 , p. 162 . 80 Dr. B. B. Boltwood . Report on the Separation of [ Feb. 4 , amount of ionium present with the thorium was therefore equal to the amount in equilibrium with 5'3 mgrm . of radium . A sample of the original " actinium residues " had been tested and found to contain a considerable proportion of actinium , but very little actinium , if any , had been separated with the " hydrogen peroxide " precipitate which contained the ionium . An effort was therefore made to discover what had become of the actinium . It has been noticed by several observers* that the precipitation of actinium by ammonia is very uncertain and is often quite incomplete . It therefore appeared highly probable that the actinium present in the original " actinium residues " had remained in solution after the treatment with ammonia described on p. 78 . The residue of ammonium salts ( denoted on p. 78 and below as " residue B " ) obtained by concentrating the filtrate from the hydroxides precipitated with ammonia was carefully examined . It was found from the records kept that the activity of these salts had at first fallen to about 70 per cent , of its initial value , and had then risen until it was 20 per cent , greater than when the salt was first prepared . This rise in the activity during a period of about six months indicated the presence of some permanent radioactive constituent having chemical properties similar to those of actinium . The total weight of " residue B " was about eighteen kilogrammes , and , as already stated , it consisted chiefly of chloride and nitrate of ammonium . By fractional recrystallisation the greater proportion of the ammonium salts were separated and were found to be practically free from radioactive constituents . The ammonium salts remaining in the mother liquor were destroyed by continued boiling with a mixture of hydrochloric and nitric acids . The excess of acid was largely removed by evaporation and the residue , consisting chiefly of calcium salts , was dissolved in water and diluted to a volume of about ten litres . This solution was heated to boiling , and a very slight excess of pure ammonium hydroxide was added . A slight precipitate formed and , when the solution had cooled , this was filtered off . It was finally ignited , and weighed about ten grammes . The material obtained in this manner was only slightly radioactive when first prepared , but its activity increased rapidly and at a rate corresponding to the recovery of activity by an actinium preparation from which the radio-actinium and actinium X have been separated . After about four months its activity was over 20,000 times that of an equal weight of uranium oxide , and it gave off relatively large quantities of actinium emanation . The relative amount of actinium present in this material was * Halm , 'Phil . Mag. , ' 1907 , vol. 13 , p. 165 ; Levin , 'Phys . Zeit . , ' 1907 , vol. 8 , p. 129 ; Boltwood , 'Am . Journ. Sci. , ' 1908 , vol. 25 , p. 292 . 1911 . ] Ionium and Actinium from Certain Residues , etc. 81 not accurately determined , but it was roughly estimated to be equivalent to the amount of actinium in equilibrium with 30 mgrm . of radium in a radioactive mineral . A further concentration of the actinium of this material was not attempted . Production of Helium by Ionium . A portion of the thorium oxide containing ionium , which was obtained in the chemical operations previously described , was used for determining these production of helium by ionium . The amount of material taken weighed^ 1*5 grin . This was sealed up with a small quantity of pure oxygen in a tube of Jena " combustion " glass . After a period of 125 days the ionium : preparation was heated to a bright red heat , and the gases were pumped out . of the tube and collected . The amount of helium present in the gases was then accurately measured , and was found to be 0'031 cu.mm.* The identity of the helium was readily demonstrated by spectroscopic tests . The number of a-particles emitted by T5 grm. of the ionium preparation was 15T x 107 per second . This corresponds to the number of a-particle 's emitted by 00045 grm. of radium . Since the production of helium per gramme of radium is 0T07 cu . mm. per day , the amount of helium produced per day by the ionium should be 4 75 x 10-4 cu . mm. In 125 days the amount would therefore be CH)595 cu . mm. This is about twice the amount that was actually found , but as no other means than heating was-employed for displacing the helium from the solid thorium oxide , the fact , that the quantity obtained was smaller than the quantity to be theoretically expected is not in itself significant . The main result of this investigation was to demonstrate clearly that helium is produced by ionium as well as by other products which emit an a-radiation . ' * The method employed and the apparatus used for the determination of the helium will be described elsewhere . j : : VOL. LXXXV.--A . G

rspa_1911_0024

0950-1207

The relative atomic weights of nitrogen and sulphur.

82

98

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

F. P. Burt|F. L. Usher|Sir William Ramsay, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1911.0024

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1911_0024

10.1098/rspa.1911.0024

Thermodynamics

Chemistry 2

Thermodynamics

82 The Relative Atomic Weights of Nitrogen and Sulphur . By F. P. Burt and F. L. Usher . ( Communicated by Sir William Bamsay , F.R.S. Received May 26 , \#151 ; Read June 30 , 1910 . ) ( From the Chemical Laboratory , University College , London . ) In 1905 , nitrogen sulphide was being prepared and used in large quantities at University College , Bristol , and it was due to a suggestion of Prof. Francis that it might prove a suitable substance for determining the relative atomic weights of its constituent elements , that the present research was undertaken . Ho direct measurement of the ratio N : S has previously been made , and since the atomic weight of sulphur is still uncertain , a useful step is gained in acquiring an accurate knowledge of that ratio . The compound U4S4 has the advantage of containing no other element . Preparation and Purification of Nitrogen Sulphide . All the nitrogen sulphide employed in this research was made in Bristol by Prof. Francis and Mr. 0 . C. M. Davis , by passing dry ammonia into a benzene solution of sulphur chloride . The main products of the reaction are nitrogen sulphide , nitrogen , and hydrogen chloride . The sulphide which was deposited on concentrating the benzene solution contained traces of sulphur . We used as our raw material some sulphide which had stood for many months in the air , and which contained a large proportion of free sulphur as well as ammonium salts . The mixture was extracted with pure dry benzene in a Soxhlet apparatus , and the resulting solution contained all the nitrogen sulphide and relatively little sulphur ; on cooling , large needles of nitrogen sulphide were deposited , together with a little finely divided sulphur . The crystals , after being twice washed with cold carbon disulphide , and then with benzene , were powdered on a porous the and placed in a desiccator containing calcium chloride and cocoanut charcoal . Prof. Travers suggested that an attempt should be made to analyse the sulphide in such a way as to obtain free nitrogen , which could be measured in a constant volume gas thermometer , and with this end in view it was sought to decompose the substance by heating it vacuo . It was found that at about 80 ' the sulphide began to volatilise without decomposition , being deposited again as a crystalline sublimate on the cool parts of the vessel . If the sulphide was sublimed in vacuo over a roll of silver gauze , tightly packed in a vertical glass tube , decomposition was complete when The Relative Atomic Weights of Nitrogen and Sulphur . 83 the temperature of the silver was above 200 ' , though at temperatures between 100 ' and 120 ' the vapour was not decomposed to any appreciable extent . This fact at once suggested a satisfactory method of freeing the sulphide from any traces of sulphur . Blank experiments showed that if free sulphur was similarly sublimed in vacuo below silver gauze , the silver blackened evenly from below upwards , and no trace of sulphur could be detected on the clean glass above the gauze . The powdered nitrogen sulphide , obtained as described above , was placed in quantities of about 1 gramme in a series of vertical glass tubes which could be exhausted by means of a mercury pump . Above the sulphide in each tube a roll of silver gauze about 5 cm . long was fitted . A steam jacket surrounded each tube up to the level of the top of the silver gauze.* The nitrogen sulphide was then sublimed in vacuo , when it was deposited in crystals on the upper cool portions of the tube . From 12 to 24 hours ' heating was necessary to sublime 1 grm. of the sulphide . It was noticed that a deep blue transparent film gradually made its appearance on the walls of the sublimation tube some way above the yellow sulphide , and finally crept down to meet the latter if the heating was continued long enough . The probable explanation of this curious phenomenon is discussed by one of us elsewhere.f The blue substance has been shown by analysis to be a sulphide of nitrogen , having the same percentage composition as the ordinary sulphide , but under these conditions it is formed in practically unweighable quantities . During the process of sublimation the silver gauze was superficially coated with sulphide , and a small quantity of nitrogen was pumped off , amounting to a fraction of a cubic centimetre after 12 hours ' heating . The traces of gas evolved had an odour of benzene , carbon disulphide , and sulphur dioxide ; the last was possibly due to traces of oxygen in the silver , while the others must have been derived from the solvents used . We never succeeded in obtaining nitrogen sulphide that did not yield traces of benzene ( or other solvent ) on sublimation in vacuo unless that nitrogen sulphide had already been sublimed in vacuo . At the end of the experiment the sublimation tubes contained a small white residue , consisting of fragments of filter paper and porous the . The product obtained by sublimation over silver in vacuo consisted of large , orange-coloured crystals , which must necessarily have been free from liquid or gaseous inclusions . When struck , or rapidly heated in air , they detonated violently . Dr. Herbert Smith has kindly examined their crystalline form , * This was previously heated red-hot in the outer cone of a blow-pipe flame in order to remove oxidisable impurities . t 'Trans . Chem. Soc. , ' 1910 , vol. 97 , p. 1171 . G 2 Messrs. F. P. Burt and F. L. Usher . [ May 26 , and finds that they belong to the monoelinic system . They are therefore of the same type as the crystals deposited from solution , examined by Artini.* The specific gravity of the sublimed sulphide , which was required in subsequent calculations , w*as determined by weighing in air and water at 20 ' in a small specific gravity bottle . We obtained as the result of two determinations the values 2*248 and 2*235 , giving a mean of 2*24 , sufficiently accurate for a vacuum correction . The specific gravity of the unsublimed sulphide was also determined ; we obtained the values 2*21 and 2*19 , giving a mean of 2*20 , which is in agreement with the results of other observers . Nitrogen sulphide is so slowly hydrolysed by water that it is perfectly safe to use this liquid . A large number of analyses were carried out by subliming nitrogen sulphide in vacuo over silver gauze heated to about 360 ' . The silver gauze ( which was supplied by Messrs. Johnson and Matthey ) was freed from oxygen by heating to redness in a stream of hydrogen , and the occluded hydrogen was got rid of by prolonged exhaustion at the same temperature . The gauze was finally exhausted from nitrogen at 360 ' . As the results obtained were unsatisfactory , the apparatus is not described . There was every reason to believe that the nitrogen sulphide was completely decomposed by the silver ; the line of demarcation between the silver sulphide and the unattacked silver was perfectly sharp and definite at the end of a determination ; moreover , the cool part of the reaction tube above the silver gauze would have shown the presence of unweighable traces of nitrogen sulphide or sulphur , and the glass was found to be always perfectly clean . We are inclined to attribute the discrepant results to the occlusion of nitrogen by silver sulphide at the moment of its formation . A similar phenomenon has been observed by Dr. R. W. Gray in the reduction of nitric oxide by metallic nickel.f If this is the correct explanation , it would have been necessary to fuse the silver sulphide , which would have involved manipulative difficulties of so serious a nature that we decided to devise some other method of analysis which should dispense with the employment of a metal . Our first attempt was to replace the silver by tightly packed quartz wool , but we found that at 360 ' the quartz only partially decomposed the nitrogen sulphide . We finally succeeded by using a quartz reaction tube , in which quartz wool was heated to bright redness by a naked flame . * * Zeitschr . fur Kryst . , ' 1906 , vol. 42 , p. 68 . t " tiber das Atomgewicht des Stickstoffs , " Inaug . Dissert . , Bonn , 1907 . 1910 . ] Relative Atomic Weights of Nitrogen and Sulphur . 85 Description of Apparatus and Details of Procedure . The figure represents the apparatus in which our final analyses were carried out . A weighed quantity of nitrogen sulphide in the small quartz bucket A was placed in the quartz reaction tube B ; a plug of quartz wool C , which had been treated in a manner to be subsequently described , was then pushed into the centre of the reaction tube , and the latter was attached to the greased push-join D. The Topler pump E could be put in communication c SCALE x 0 0925 either with the reaction tube or with the manometer head F by means of the three-way tap G. The capillary fall tube of the pump was turned up and sealed as an inserted join into the gas collector H. A capillary tube sealed to the upper end of H carried another three-way tap J leading on the one hand to the measuring cylinder K and on the other to the potash tube L , which could also be opened to the air through the third three-way tap M. The measuring cylinder K was connected by means of capillary tubing with the dead space N and manometer F. Before a determination was started Messrs. F. P. Burt and F. L. Usher . [ May 26 , the dead-space , measuring cylinder , and connecting capillaries , after exhaustion by the pump , were filled with mercury from the reservoir 0 . The reaction tube was then exhausted , the air being expelled through the collector and potash tube ; after exhaustion was complete , any traces of gas sticking at the end of the capillary fall tube or on the walls of H were collected by lowering the reservoir P with the tap J closed , until the mercury in the collector fell to the level of the inserted capillary ; the reservoir was then raised again , and any gas collected was expelled into the potash tube L and thence into the air . The apparatus was now ready for a determination to be started . A D-shaped roof of asbestos B was placed over the reaction tube so as to cover the quartz wool , and the last 8 cm . of the reaction tube passed through a closely fitting circular aperture into a cubical asbestos oven S , which could be heated by an ordinary Bunsen burner . The oven carried a thermometer , of which the bulb was in close proximity to the nitrogen sulphide in the tube . A stream of cold water was arranged to drip on the junction D throughout the determination . A large , roaring Bunsen flame was placed under the quartz wool in the reaction tube , and after an interval of about ten minutes the flame was lit under the asbestos oven . The nitrogen sulphide was volatilised at a temperature which rose throughout the determination from 100 ' to 170 ' , and the pump was worked so as to keep the average pressure of nitrogen at a few millimetres of mercury . The sulphur was deposited as a lemon-yellow crust in the neighbourhood of the push-join . As soon as the collector H was full of gas , the latter was at once transferred to the measuring cylinder , and , at the end of the determination , the last traces of gas were collected in the way already described , and added to the main quantity in the measuring cylinder . Mercury was finally taken through the tap J and set to a mark T on the capillary . Measurement of the Nitrogen . The volume of the measuring cylinder between two marks T , U , on the capillary stem was determined on two occasions with an interval of four years . The earlier calibration was made with water , and the later with mercury ; the following are the values obtained\#151 ; Calibration with water ^ ^flo ' CTMean = 105,372 c.c. L(n ) 105-373 " J , , f ( i ) 105-367 c.c.T in Calibration with mercury i05-'70 J*Mean = 10o-369 c.c. The agreement obtained was very satisfactory , and since the small difference after a period of four years was within the limits of experimental 1910 . ] Relative Atomic Weights of Nitrogen and Sulphur . 87 error , the more recent value was adopted . The capillary volume between the marks U and Y was calibrated with mercury , and amounted to 0T52 c.c. The lead-glass dead-space , manometer tube , millimetre scale , and the water-bath in which they were set up had already been used by Dr. Gray and one of us in a research on the compressibility of hydrogen chloride.* The volume of the dead-space was 1-275 c.c. To carry out a measurement of nitrogen , the measuring cylinder K was surrounded by a bath containing powdered ice and water , and the mercury was set exactly to a glass point in the dead-space . The distance between the upper mercury meniscus in the manometer tube and the dead-space point was then determined by means of the scale suspended in the bath , fractions of a millimetre being measured by a telescope provided with a Hilger micrometer eyepiece . For a fuller description of this part of the apparatus , the paper already referred to may be consulted . The temperature of the mercury column was kept constant by a stream of water circulating through the bath , and was registered by two thermometers , one at the level of the dead-space and the other at the level of the upper meniscus . In this way the pressure exerted by a known volume of nitrogen at a known temperature was obtained , and in order to - calculate its mass a knowledge of the density of the gas was all that was required . We have taken the value 1'2514 grm. as the weight of a litre of nitrogen at 0 ' and 760 mm. in London . The question of the density of nitrogen is considered at the end of the paper . The nitrogen sulphide was weighed in a small quartz bucket , provided with a handle so that it could be lifted with a glass hook without contact with the fingers . The weight of the bucket was about half a gramme . It was carefully cleaned by treatment with hot chromic acid and subsequently heating to redness on a platinum wire , and was first weighed empty . A suitable quantity of nitrogen sulphide was then introduced by means of a glass spatula and the bucket was weighed again , and then immediately lowered into the reaction tube . While the weighings were in progress the reaction tube was cleaned with chromic acid , washed , dried , and finally heated red-hot . Preparation of the Quartz Wool . The quartz wool employed was obtained from the Silica Syndicate in the form of a hank of fibres with a mean diameter of about 0 01 mm. It was first of all necessary to " felt " this by hand so as to form a compact plug , * 'Trans . Chem. Soc. , ' 1909 , vol. 95 , p. 1659 . 88 Messrs. F. P. Burt and F. L. Usher . [ May 26 , and i , t was found that 3 grm. when so treated occupied a length of about 6 cm . when tightly pressed into the reaction tube . Such a plug was .calculated to contain 10f miles of fibre with a surface of over 5,000 sq . cm . It was realised that so large a surface might involve an appreciable correction for occluded air , and a series of measurements was made to elucidate the question . After the process of " felting , " the wool was packed into an open-ended quartz tube\#151 ; of the same internal diameter as the reaction tube\#151 ; and heated for several hours to bright redness in a stream of dry air , freed from dust and carbon dioxide , and finally allowed to cool in the air-stream . In this way any carbonaceous matter was oxidised and the wool was never again touched with the fingers . From the open quartz tube it was pushed into the reaction tube by means of a glass rod . The reaction tube was attached to the pump , exhausted in the cold , and then heated as in an actual analysis . The small quantity of gas evolved was collected and measured in the calibrated capillary at the top of the collector H. When no more gas could be pumped off the tube was allowed to cool and air was admitted through a soda lime tube at the capillary W. The reaction tube was removed and most of the grease in the mouth was wiped off with a clean rag . The tube was then held horizontally and the last traces of grease were burnt out of the neck by heating red-hot with a naked flame in a current of dust-free air . In order to prevent backward diffusion of the products of combustion on to the quartz wool , a piece of quill tubing of silica , which conducted the air current , was pushed well inside the mouth of the tube beyond the heated zone.* As soon as the tube was cold the wool was transferred by the aid of a glass rod bent into the form of a corkscrew to the open-ended quartz tube and the latter was at once put into a desiccator containing potash . In this way the wool underwent precisely the same manipulation and short exposure to the air of the laboratory that were inevitable between two actual analyses . Two more blank experiments were made with the same wool in exactly the same manner as just described . The volumes of air obtained in the three cases were:\#151 ; ( i ) 0-0173 c.c. ( ii ) 0-0099 c.c. ( iii ) 0-0056 c.c. The diminution in the volume of occluded air was due partly to a small mechanical loss of wool , occasioned in transference , and partly , perhaps , to a decrease in its occluding power , owing to the prolonged heating . * After an analysis of nitrogen sulphide the mouth of the reaction tube contained not .only grease but sulphur , and this was burnt out with the grease in the manner described . In order to keep the conditions as similar as possible , a piece of sulphur was placed in the neck of the reaction tube and burnt out with the grease in " occlusion " experiments , .on occasions when a sublimate was not already present . 1910 . ] Relative Atomic Weights of Nitrogen and Sulphur . 89 If the volumes of air obtained are plotted against the ordinal numbers of the experiment , the three points lie very nearly on a straight line . In any series of analyses , therefore , it was only necessary to make two occlusion measurements , one at either end of the series , and to use a straight line interpolation for fixing the correction to be applied to the intermediate determinations . It was found inconvenient in practice to start any series of experiments with a plug of quart/ wool occupying a greater length than 6 to 7 cm . of the reaction tube , and this quantity only sufficed for about six experiments ( whether occlusion measurements or analyses ) partly because of the small constant loss , and partly because the continued heating and manipulation rendered the wool inelastic and powdery , when it would no longer form a tight plug in the reaction tube . It will probably be conceded that no more air , that is , oxygen and nitrogen , would be washed out of the hot wool when nitrogen sulphide was being sublimed over it than would be pumped off by exhaustion in vacuo at the same temperature , though this would not be true for any denser gases which might find access to the wool . Of such gases , the only two which could possibly have reached a significant concentration in the room in which we worked were carbon dioxide and sulphur dioxide , * and since it was impossible to avoid exposing the wool to the laboratory air for a short period between each experiment , it was essential to investigate the possibility of quantitative error from this source . We may state at once that , so long as the wool was exposed to the laboratory air for indeterminate periods , we failed to obtain constant results for the N : S ratios , even when the necessary correction was made for occluded air , but it was subsequently discovered that if the nitrogen volumes in a series of determinations were treated with moist potash and then dried , a contraction occurred , which at once brought the ratio to a constant value . The results of a large number of our earlier determinations might have been corrected , had we at that time suspected the presence of traces of gas absorbable by potash . A point still to be considered was whether the air pumped off the hot wool in vacuo contained any gas absorbable by potash . Since two separate corrections were made on the nitrogen , namely , that for air , which was fixed by the occlusion experiments , and that for carbon dioxide or sulphur dioxide , which was determined by measuring the contraction of the nitrogen on treatment with potash , the total correction would have been too large if any carbon dioxide had been measured as occluded air . By exposing the * Neither ammonia nor water vapour need be considered , as both would be removed by the phosphorus pentoxide between the reaction tube and the pump . Messrs. F. P. Burt and F. L. Usher . [ May 20 , minute quantities of gas obtained in the occlusion experiments to potash , and then remeasuring them , a very small contraction of the order of 1 cu . mm. was observed . This could be neglected without appreciable error . At an early stage in our experiments with a quartz reaction tube , it was discovered that a small quantity of hydrogen from the flame passed through the hot quartz ; moreover , when a similar flame was used , the quantities of hydrogen that entered the tube in unit time were remarkably constant . This conclusion was arrived at in two different ways , and was repeatedly confirmed . In the first place , it was noticed that it was impossible to pump the heated tube " tight , " gas continuing to collect in the pump at the rate of about 3*5 cu . mm. per hour . In order to apply a direct test for hydrogen , the gas obtained in a particular occlusion experiment was mixed with a little additional air , and transferred to a small gas burette provided with , platinum electrodes . On passing a spark a contraction occurred :\#151 ; Volume before sparking = 0*065 c.c. Volume after sparking = 0*046 " Contraction = 0*019 " Therefore Volume of hydrogen = 0*019 x S = ( K)13 c.c. in 3f hours = 0*0036 c.c. per hour . Values obtained by direct measurement of the eorfstant quantity of gas , , collected when the empty tube was heated , varied from ( M)033 to 0*0040 c.c. per hour . For correcting our nitrogen volumes , we assumed the hydrogen to enter at the rate of 0*0036 c.c. per hour . Treatment of Nitrogen with Potash . After the initial measurement of nitrogen , the gas was taken , vid the collector , into the tube L. This tube had been prepared before it was set up , by melting a stick of caustic potash in it , and rotating it so as to cover the walls with a film of the fused alkali . Before letting in the nitrogen , the mercury in L was taken down to the bottom of the tube , with the tap M closed , by lowering the reservoir Q ; any bubbles of gas caught in the potash film escaped into the vacuum so produced , and were collected and expelled into the air , when the mercury was taken up again . This operation was always carried out twice . A thread of water ( 30 or 40 cu . mm. ) was now introduced through the capillary tube X , so as to moisten the potash , and the nitrogen was then transferred to U After standing over-night , the nitrogen was returned to the measuring cylinder , again with the same precaution of lowering the mercury , so as to obtain the last traces , and the 1910 . ] Relative Atomic Weights of Nitrogen and Sulphur . 91 mercury in the dead-space was taken below the level of the side-tube Y. By an alternate manipulation of the taps Z and Z ' , the gas was cautiously taken into the pump until the pressure in the measuring cylinder was reduced to a few centimetres of mercury . Keeping the taps Z and Z ' open , a stroke of the pump was taken , so as to fill the collector H ; the tap J was then opened , so that gas flowed from the collector to the measuring cylinder , and thence over the phosphorus pentoxide hack into the pump chamber . About 30 strokes were taken , so as to dry thoroughly not only the gas , but also the glass walls of the collector , measuring cylinder , and dead-space . When this was accomplished mercury was allowed to rise in the dead-space , and seal the tap Z , which was then turned off . The rest of the nitrogen was then returned to the measuring cylinder , by working the pump till exhaustion was complete ; the last traces were collected by lowering the reservoir P , and the mercury was set again to the mark T on the capillary . A second measurement of the nitrogen was then made . We found that the operation of circulating the gas through the system could be carried out without gain or loss ; on repeating the whole process with a quantity of nitrogen which had already been treated with potash and dried , we recovered the original volume to within 1 part in 50,000 . In the two series of experiments of which the results are given in the following table , the quartz wool was treated in a precisely similar way . The addition of the potash tube to the apparatus was made between the two series , so that the actual contraction of the nitrogen on treatment with potash was only measured in the second series . Since , however , the ratios from Experiments 2b and 3b were in good agreement respectively before and after the gas had been treated with potash , and since , further , the uncorrected results of Experiments 2a , 3a , and 4a agreed with each other , and with the uncorrected results of 2b and 3b , we applied the correction determined in these two cases to the corresponding experiments in series A. Again , since the corrected result of Experiment 1b agreed with the corrected results of 2b and 3b , the same contraction correction actually determined in the case of 1b was applied to 1a . In every series of analyses with a given specimen of quartz wool , the value from the first experiment was always higher than the values from the succeeding ones . This was apparently due to the presence of a larger proportion of gas absorbable by potash , as indicated by the contraction measured in Experiment 1b . When the history of the wool and the time of its exposure to laboratory air had also been the same , as in the two series given , the values from the first experiments also agreed very closely . The values obtained from the second , third , and sometimes the fourth to Table of Eesults . No. of experiment . Nitrogen sulphide . Yacuum correction . Pressure of gas . Yolume at N.T.P. Correction for hydrogen . Occluded air . Gas removed potash . Corrected volume . Density at observed pressure . Weight of nitrogen . Weight of sulphur by difference . Eatio , N/ S. lA grin- 0 -469455 mgrm . 0-258 mm. 812 -73 c.c. 114 -162 c.c. 0-013 c.c. 0-019 c.c. 0-084 c.c. 114 -046 1 -25148 grm. 0 -142726 grm. 0 -326729 0 -43685 2a 0 -442787 0-243 766 -18 107 -624 0-012 0-017 0-018 107 -578 1 -25144 0 -134627 0 -308160 0 -43688 3a 0 -456326 0-249 789 -50 110 -902 o-oii 0-014 0-018 110 -859 1 -25146 0 -138736 0 -317590 0 -43684 4a 0 -470072 0-258 813 -29 114 -240 o-oio 0-012 0-018 114 -200 1 -25148 0 -142919 0 -327153 0-43686 1b 0 -466918 0-252 808 -41 113 -550 o-oio 0-014 0-084 113 -442 1 -25147 0 -141969 0 -324949 0--43690 2b 0 -491307 0-261 850 -07 119 -404 0-012 0-013 0-018 119 -361 1 -25150 0 -149380 0 -341927 0-43688 3b 0 -484307 0-265 837 -97 117 -704 0-011 o-oii 0-018 117-664 1 -25150 0 -147257 0 -337050 0 -43690 Mean N/ S 0 -43687 ' PvnhnKlp error \#177 ; 0-000006 1 * S Messrs. F. P. Burt and F. L. Usher . [ May 26 , 1910 . ] Relative Atomic Weights of Nitrogen and Sulphur . 93 experiment in a series , were nearly constant . Following these constant results came a much lower value , suggesting that some of the nitrogen sulphide had escaped decomposition , because of the diminution in quantity and efficiency of the quartz wool . As a matter of fact , a low value could always be foretold , before the nitrogen was measured , by the appearance of the sulphur sublimate . As long as decomposition was complete , the sulphur solidified at once on cooling , and the colour of the sublimate was a pale lemon-yellow ; if , on the other hand , complete resolution of the nitrogen sulphide into its elements had not been . effected , the sulphur did not solidify quickly on cooling , and eventually exhibited darker patches of a red or brown colour . A glance at the table on p. 92 will show that the three separate corrections made on the volumes are very small compared with the total nitrogen volumes ; moreover , the probable error on the correction itself is in each case very small . In the case of the hydrogen , the experiments already cited indicate the order of this error to be less than a cubic millimetre for three hours heating , which was the average time occupied by a determination . The largest correction for occluded air is less than 1/ 6000 of the total nitrogen volume , and the probable error on the correction itself is not greater than 5 per cent. Finally , the validity of applying a similar contraction correction in cases where it was not actually measured , is supported by many preliminary experiments which showed that quartz wool will take up from the air condensible gases in amount depending almost entirely on the time of exposure , and also by the very good agreement of the ratios among each other before this correction was made . The agreement already referred to between the constant values on the one hand and the high initial values on the other is evident from the following list of ratios uncorrected for gases absorbed by potash:\#151 ; Experiment ... . 1a . 1b . 2a . 3a . 4a . 2b . 3b . Ratio N/ S ... . . 0-43735 0-43740 0-43698 0-43695 0-43696 0-43699 0-43701 The following is a full calculation from the data in Experiment 1b :\#151 ; Weight of bucket + nitrogen sulphide Weight of bucket ... ... ... ... ... Weight of nitrogen sulphide ... ... ... ... ... ... ... ... ... ... ... ... ... . 0"466666 " Vacuum correction ( 17 ' and 758 mm. ) ... ... ... ... ... ... ... ... ... ... ... +0*000252 " 1-032683 grm. 0-566017 " Corrected weight of nitrogen sulphide 0-466918 Messrs. F. P. Burt and F. L. Usher . [ May 26 , Nitrogen reading:\#151 ; Volume of measuring cylinder at 0 ' ... ... ... ... ... ... . . Volume of dead-space , 1'275 c.c. Temperature of gas in dead-space , 8''83 Volume of gas in dead-space at 0 ' = \#151 ; ... ... . . Volume of intermediate capillary , 0T52 c.c. Volume of gas in intermediate capillary at 0 ' = ^ ^28 105'369 c.c. 1-235 " 0-142 " Total volume at 0 ' and at observed pressure ... ... . Pressure measurement:\#151 ; Micrometer readings . Millimetres . Distance from meniscus set 84 , 84 , 84 , 84 , 85 , 0'654 to point in dead-space to 85 : mean 84-33 scale-line 1 above it Distance of upper meniscus 636 , 634 , 636 , 635 : 4'924 below scale-line 815 mean 635'25 Uncorrected manometric height , 810-076 \#151 ; 0-346 = ... ... ... ... ... ... Correction for scale errors ... ... ... ... ... ... ... ... ... ... ... ... ... . Contraction of scale from 16 ' to 8''9 ( = 7'1 x 0-000009 x 810 ) ... . Correction of observed manometric height from 8 ' " 88 to 0 ' ... ... . . Corrected pressure ... Volume of nitrogen at N.T.P. = U6'751 x 8Q8'405 = 8 760 Correction for hydrogen ... ... ... ... ... ... ... ... ... . . Correction for occluded air ... ... ... ... ... ... ... ... . Contraction on treatment with potash ... ... ... ... ... . 106-751 " Scale readings 0"346 mm. 810-076 " 809-730 " + 0-034 " - 0-052 " - 1-307 " 808-405 " 113"550 c.c. - 0-010 " - 0-014 " - 0-084 " Corrected volume of nitrogen at N.T.P ... ... ... ... 113-442 " Density at observed pressure = 1-25144 x 1-000027 = 1*25147 . . . Weight of nitrogen = 113-442x0-00125147 = 0T41969 grm. Weight of nitrogen sulphide taken ... ... = 0-466918 " Weight of sulphur by difference ... ... ..= 0-324949 " Ratio N/ S = 0-436897 " Discussion of Errors.\#151 ; The question of the purity of the nitrogen sulphide has already been considered . With regard to its stability in dry air we may remark that no change in weight in a specimen was detectable after several days ' standing in a desiccator ; moreover , it was found to be immaterial as regards the resulting ratio , whether we used nitrogen sulphide just removed from a sublimation tube , or crystals that had been kept for several days in dry air . In order to ascertain whether there was any danger of losing nitrogen sulphide by volatilisation during the preliminary exhaustion of the reaction tube at the room temperature , a weighed quantity of the finely divided substance contained in a quartz bucket was sealed up in a glass tube , which was then exhausted and left for an hour . No loss in weight 1910 . ] Relative Atomic Weights and Sulphur . 95 .could be detected , and was certainly less than 0'000005 grm. ; any loss , therefore , during the half hour required for the preliminary exhaustion must have been quite negligible . Weighings.\#151 ; The weighings were made on an Oertling 's assay balance carrying a maximum load of 2 grm. Each arm of the beam was divided into 50 parts , and fractions of a milligramme were estimated with a milligramme aluminium rider . The sensibility of the balance for the loads used was about six pointer-scale divisions per 01 mgrm . , and an accuracy of five in the sixth place ( 1 in 80,000 on the nitrogen sulphide ) was probably attained . The pointer oscillations were read with a lens , tenths of a division being .estimated by eye . In weighing nitrogen sulphide we used the platinum weights alone of the same set with which the measuring cylinder was \#166 ; calibrated . By using weights of the same set for both operations , any small error due to deviation of the weights from their absolute face values was , of course , eliminated . The weights were calibrated against each other in air , using another set as counterpoises , according to the method of Richards . Vacuum corrections were applied to the apparent weights of nitrogen sulphide , and of water or mercury used to calibrate the measuring cylinder , but not to the brass and platinum weights themselves , since absolute values were not required . Accuracy of Nitrogen Measurement.\#151 ; The calibration of the constant volume has been discussed already . In order to see whether there was an appreciable change of volume of the measuring cylinder as the internal pressure changed , the exhausted cylinder was filled with mercury to a mark on the capillary . Air was then admitted into the dead-space , and the movement of the capillary meniscus observed as the internal pressure rose . It was found that the cylinder expanded by 0-002 c.c. for a rise of pressure of 300 mm. Since in our experiments the pressure of the nitrogen never differed from the atmospheric pressure by more than 100 mm. , this source of error could be neglected . That the volume of the measuring cylinder was not altered by distortion when filled with mercury was proved by observing the behaviour of the meniscus in the capillary when the whole cylinder was immersed in mercury ; the change , if any , was not greater than 0 0002 c.c. The two thermometers in the manometer bath were previously compared with a standard thermometer at 0 ' , and at 8'*8 , which was about the usual temperature of the water . In correcting the volume of gas in the dead-space to 0 ' we used the coefficient 1/ 273 ; this was quite accurate enough , as the volume to be corrected was only 1-275 c.c. It was only necessary to know the temperature of the gas in the intermediate capillary to within 5 ' . Messrs. F. P. Burt and F. L. Usher . [ May 26 , Accuracy of Pressure Measurement.\#151 ; Since the accuracy of the pressure measurements made in this particular apparatus has already been fully discussed , * it is unnecessary to examine it again here . We believe that the corrected pressure of the gas was known to within 0-02 mm. , which corresponds with an error of 1 in 28,000 on the N/ S ratio . The Tensity of Nitrogen.\#151 ; Guye , f discussing the results obtained by Rayleigh and Ramsay , Leduc , and Gray , arrived at the value 1-2507 grm. for the weight of a " normal litre " of nitrogen . On correction to the latitude of London this becomes 1*2507 x 1-000588 = 1-25144 . Using the value obtained by Chappuis for the compressibility coefficient between 1 and 2 atmospheres , namely , \#151 ; 0 00043 , we have applied a small correction where the observed pressure differed appreciably from 1 atmosphere . Atomic Weight Discussion.-\#151 ; The long debated question as to whether the atomic weight of nitrogen was more accurately represented by the number 14-04 or 14-01 has now been generally agreed upon , and the lower value , 14-01 , which has been adopted by the International Commission , may be taken as a very close approximation to the true atomic weight . The subject has been exhaustively discussed by Guye , } by Gray , S and by Brauner , j| and the balance of evidence seems in favour of a value very slightly lower than 14*01 . As regards the atomic weight of sulphur , later researches have yielded results not very different from Stas 's value 32*06 . From the results obtained by Richards and Jonesll on converting silver sulphate into silver chloride , an atomic weight of sulphur can be calculated , but it depends on the value of chlorine , and , unfortunately , a small variation in the value adopted for chlorine involves a large difference in the resulting value for sulphur . Thus , if Cl = 35-457 , S = 32-070 ; whereas if Cl = 35-460 , S = 32-078 . The values arrived at by physical methods vary from 32-050 to 32"070 . Guye , ** by reducing the critical constants of sulphur dioxide , obtained the value 32-065 , taking the density as 2*9266 grm. per " normal litre , " and Baume and Perrot , -j**j* adopting the same procedure with hydrogen sulphide , obtained the value 32-070 , taking the density of this gas as 1*5392 * * * S ** * Gray and Burt , loc. cit. t ' Journ. Chim . Phys./ 1907 , [ 5 ] , p. 217 . I 'Bull . Soc. Chim . , ' 1905 , [ iii ] , pp. 33\#151 ; 34 , 44 . S " Uber das Atomgewicht des Stickstoffs , " Inaug . Dissert . , Bonn , 1905 . || ' Abegg 's Handbuch der anorganischen Chemie , ' vol. 3 , [ iii ] , p. 34 . IT ' Journ. Amer . Chem. Soc. , ' vol. 29 , p. 826 . ** 'Comptes Bendus , ' 1905 , vol. 140 , p. 1241 . ++ 'Journ . de Chim . Phys. , ' 1908 , vol. 6 , p. 610 . 1910 . ] Relative Atomic Weights of Nitrogen and Sulphur . 97 and the atomic weight of hydrogen as 1-00775 . D. Berthelot , * calculating the limiting density of sulphur dioxide from the compressibility measurements of Leduc , and of Goye and his colleagues , deduced from the results of the former an atomic weight S = 32-050 , and from those of the latter , S = 32-064 . There is reason to believe that the form of the isothermal of a readily condensible gas , such as sulphur dioxide , can be accurately determined only by making a large number of different pressure and corresponding volume measurements , and that attempts to extrapolate from two or three points by means of a parabolic formula or by the application of Van der Waal 's equation are not entirely satisfactory We were unable to find any direct check on our N/ S ratio in atomic weight literature , but an instructive comparison was obtained by examining some of the results of Bichards and his colleagues . From the equations:\#151 ; AgCl/ Ag = 1-32867 , t AgN03/ Ag = 1-57479 , S and 2AgCl/ Ag2S04 = 0-91933 , || we obtained by eliminating silver and chlorine the simple relationship ( S + 64)/ ( 2N + 96 ) = 0-774648 . By assigning a definite value to either nitrogen or sulphur , the ratio N/ S can be calculated , and this ratio is scarcely affected* by any probable alteration of the atomic weight of nitrogen . For example , if N= 14-010 , N/ S becomes 0-43683 , whereas if N = 14'009 , the ratio becomes 0"43682 . The agreement between these numbers and our own ( 0*43687 ) is all the more surprising when one considers the very indirect process by which the former was calculated . From Bichards ' results sulphur becomes 32-070 if N = 14-009 , whilst our ratio makes S = 32-067 to the same standard . We suggest that some indirect evidence for an atomic weight of sulphur slightly lower than 32*070 is afforded in the recent paper by Thorpe and Francish on the atomic weight of strontium . From a determination of the ratios SrCl2/ 2Ag , SrCl2/ 2AgCl , SrBr2/ 2Ag , SrBr2/ 2AgBr , SrCl2/ SrS04 , and SrBr2/ SrS04 , the authors obtain six values for the atomic weight of strontium , namely , 87"638 , 87"646 , 87'645 , 87"653 , 87'661 , and 87"629 , when Ag = 107-880 , Cl = 35-460 , Br = 79-916 , O = 16 , and S = 32-07 . Now the excellent agreement in the first four values is apparently not quite so well maintained in the last two . Out of curiosity , the mean atomic weight of * ' Comptes Rendus , ' 1907 , vol. 144 , p. 269 . t Gray and Burt , loc. cit. , p. 1660 . + ' J. Amer . Chem. Soc. , ' 1905 , vol. 27 , p. 525 . S Ibid. , 1907 , vol. 29 , p. 826 . || Ibid. , 1907 , vol. 29 , p. 844 . IT ' Boy . Soc. Proc. , ' A , vol. 83 , p. 287 . VOL. LXXXV.\#151 ; A. H 98 The Relative Atomic Weights of Nitrogen and Sulphur . strontium obtained from the first four ratios , namely 87*646 , was inserted in the last two equations , and the corresponding values for sulphur were calculated . These proved to be 32*068 and 32*066 respectively . Then , starting with the mean of these two , namely , 32*067 , and keeping the same values as before for the other elements , the atomic weight of strontium was recalculated from the last two equations . The values obtained were 87*641 and 87*640 , which show an excellent agreement with each other as well as with the mean from the first four ratios , 87*646 . On the assumption that our ratio N/ S = 0*43687 is correct , we may conclude that if 14*009+ 0*001 be the number assigned to nitrogen the atomic weight of sulphur may be taken as 32*067 + 0*002 . All the preliminary work in this investigation was carried out at University College , Bristol , and we desire to express our thanks to Dr. Morris W. Travers for his invaluable help and suggestions , and for the continued interest which he took in the research ; to Prof. Francis , who not only was personally responsible for much of the earlier experimental work , but who also afforded us every facility in the prosecution of the research during this period ; and to Mr. O. C. M. Davis , for preparing most of the nitrogen sulphide . We have also to acknowledge a grant from the Chemical Society , which defrayed the expenses of the earlier part of the work . The later part , including the analyses with quartz wool , was carried out at University College , London , and we wish to thank Sir William Eamsay for his interest and encouragement . Finally , we are indebted to Dr. E. W. Gray for his courtesy in placing at our disposal much of the apparatus used .

rspa_1911_0025

0950-1207

The production and properties of soft R\#xF6;ntgen radiation.

99

118

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

R. Whiddington, B. A.|Sir J. J. Thomson, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1911.0025

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1911_0025

10.1098/rspa.1911.0025

Atomic Physics

Electricity

Atomic Physics

99 The Production and Properties of Soft Radiation . By R. Whiddington , B.A. , St. John 's College , Allen Scholar of the University of Cambridge . ( Communicated by Sir J. J. Thomson , F.R.S. Received January 20 , \#151 ; Read February 16 , 1911 . ) There is a class of problem of the greatest interest in connection with primary Rontgen rays , which as yet has received but little attention from experimental investigators . The kind of problem referred to is indicated by the following two leading questions :\#151 ; ( 1 ) How do the properties of Rontgen radiation depend on the velocity of the parent cathode rays ? ( 2 ) How do the properties of Rontgen radiation depend on the nature of the anticathode used to arrest the motion of the parent cathode rays ? The present communication has to do with soft Rontgen radiation such as is produced in a discharge tube working at only a few thousand volts . The only investigator who appears to have worked with such rays is W. Seitz , and his experiments are referred to later . As a preliminary it will be convenient to present a general view of the ground which will be covered , and to indicate broadly the method employed . In the present experiments slow cathode rays of known velocity were directed on to one of a series of metallic anticathodes , the Rontgen rays so produced being led out into the open air through an aluminium window , and there tested . The tests applied to the rays were quantitative measurements of:\#151 ; ( 1 ) Their energy , as indicated by the ionisation produced in a definite thickness of air ; ( 2 ) their penetrating powers , as indicated by the values of their absorption coefficients in different materials ; and qualitative observations on ( 3 ) their power of producing corpuscular emission when incident on metal surfaces . These three properties of Rontgen rays were chosen as being the most important , and the most easily observed . The first two are especially important , since a pulse radiation is sufficiently defined for some purposes by a knowledge of its energy and absorption coefficients . A preliminary account of the work was given in August of last year to the Cambridge Philosophical Society.* * Whiddington , ' Proc. Camb . Phil. Soc. , ' vol. 15 , Part VI , p. 574 . H 2 Mr. R. Whiddington . The Production and [ Jan. 20 , This paper is divided into the following sections:\#151 ; S 1 . A description of the apparatus . S 2 . A theory of the influence of the aluminium window on the constitution of the emerging Rontgen radiation . S 3 . The dependence of the energy of Rontgen radiation\#151 ; ( a ) On the nature of the anticathode . ( 6 ) On the velocity of the parent cathode rays . S 4 . The dependence of the absorption coefficients of Rontgen radiation\#151 ; ( a ) On the nature of the anticathode . ( b ) On the velocity of the parent cathode rays . S 5 . The corpuscular radiation excited by the incidence of Rontgen radiation on metallic surfaces . S 6 . Summary and conclusions . S 2 occupies the place it does because the theory there advanced makes it much easier to remember the somewhat complicated and otherwise dis- % connected results of SS 3 and 4 . S 1 . The Apparatus . The apparatus can be described conveniently under two main headings : ( 1 ) That part of it which generated the radiation , i.e. the discharge tube ; ( 2 ) That part which tested the rays , the ionisation chamber and its connections . ( 1 ) The Discharge Tube . ( Fig. 1.)\#151 ; The discharge tube consisted of a tube 65 cm . long and 4 cm . in diameter ( its length being at right angles to the E\amp ; rbh wire 1911 . ] Properties of Soft Rontgen Radiation . 101 plane of the figure ) , along the bottom of which aluminium rails were laid down . This tube was fused to two slightly narrower and much shorter side tubes in the manner indicated in the figure . The horizontal one was 5 cm long , terminating with a thin aluminium window ; the vertical one was about 30 cm . long , ending in a ground-glass joint . The plane containing these two tubes was at right angles to the length of the long tube . An aluminium carriage T ran on wheels along the track already referred to . This carriage carried a row of anticathodes of various materials , all inclined at about 45 ' to the horizontal . The materials used were Ag , Al , Sb , Cu , Fe , Hi , Pb , Pt , Sn , Zn . Their surfaces were ground smooth and finally polished with jeweller 's rouge . The carriage T was magnetically controlled from outside by means of an electro-magnet and a bar of soft iron mounted under the carriage . The upper flange of the ground-glass joint J carried a tube B , enclosing a concave cathode C mounted at a convenient distance from the carriage . The joints at J were made tight with sealing wax . The tube B , which fitted very tightly round the cathode C , served two 'purposes : firstly , it prevented the cathode from sputtering on the walls of the outer tube , and secondly , it helped to concentrate the cathode stream down the centre of the tube . It was found to be extremely important for quantitative work to prevent sputtering on the outer tube , since when it becomes conducting the beam of cathode rays is irregularly attracted to the walls owing to spasmodic induction effects . The parallel beam of cathode rays striking an anticathode A produce Bontgen rays , * some of which pass down the horizontal tube and emerge through the window W. The window consisted of a thin sheet of aluminium foil ( 0'002 cm . thick ) supported on a coarse brass-wire grid . The grid was mounted on a heavy brass flange which was waxed on to the end of the horizontal tube . A brass annulus could be screwed down tightly on this flange , thus gripping the foil and making all air-tight . The tube was in direct communication with a Topler mercury pump and a charcoal liquid-air tube . In all experiments the anticathode system , consisting of rails and carriage , was connected to earth and made the anode . The window could either be earthed or charged to a potential , as occasion required . The experiments described below were carried out with potentials between the cathode and anode of the tubef up to 3600 volts . The potential up to this point was * If the potential generating the cathode rays is say 2000 volts , and the anticathode is Pb , then the emerging radiation will for convenience be termed the 2000 volt radiation from Pb . + Hereafter referred to as " the generating potential . " Mr. R. Whiddington . The Production and [ Jan. 20 , obtained from a battery of small accumulators . The high potential was connected to the tube in series with a high voltage key , a milliampere meter and a variable liquid rheostat ( copper sulphate in water ) . The milliampere meter was a Weston instrument , each division being equivalent to 1/ 10 milliampere . The variable liquid rheostat was operated from a distance by a cord passing over pulleys , and gave a control of about 200 volts on the tube . The potential across the tube ( i.e. between the anode and the cathode ) was measured by a Braun electrometer , with a scale which could be read to 20 volts between 500 and 3500 volts . Now it is well known that the cathode rays produced by a steady discharge from cells are homogeneous as regards their velocity , which is approximately given by the relation where 2 e/ m. V = ejm = the universal charge to mass ratio ( E.M. units ) , v = the velocity of the cathode rays , V = the potential in E.M. units applied to the terminals of the tube , i.e. the reading of the voltmeter x 108 . Thus the reading of the voltmeter , multiplied by 2\lt ; ?/ m x 108 , gives approximately the square of the velocity of the cathode rays within the tube . The vacuum in the tube was initially adjusted by use of the Topler to give a current of 0'2 milliampere at approximately the required potential , the final adjustment being made with the liquid resistance . During the course of a long run the potential across the tube would gradually fall , indicated rather by a diminution in the intensity of the emergent Rontgen rays than by the reading of the electrometer . This was due to the liberation of electrode-gas , which could be absorbed by turning on the charcoal-tube tap for a few moments . After a few months ' use , however , this effect became extremely small . ( 2 ) The Ionisation Chamber and its Connections.\#151 ; The ionisation chamber I ( fig. 1 ) was a cylinder of brass , fitted with a detachable gauze front N. Both the gauze and the case of the chamber were usually charged to a saturating potential . To obviate the leakage of charge from the case to the insulated electrode A ' , the wire support was encased in and insulated from a brass sheath tube S kept permanently connected to earth . This arrangement somewhat increased the electric capacity of the measuring system , but not to any serious amount . This sheath tube had the additional and very great advantage of completely protecting the insulation which really mattered , 1911 . ] Properties of Soft Ro Radiation . 103 and this insulation once put in and enclosed in this way remained good almost indefinitely . The electrode A ' was connected to a mercury key K , enclosed in an earthed box containing a capacity C which could he added to the insulated system in connection with the gold leaf and thus diminish the sensibility . It was necessary in some experiments to adjust rapidly the distance of the gauze N from the window W. For this reason the whole measuring system\#151 ; chamber , key , and electroscope\#151 ; were mounted together on a rigid movable platform . It was then easy to move the whole system relative to the X-ray tube . Ebonite insulation was used throughout , and except in very damp weather proved very satisfactory . The absorbing screens had of necessity to be extremely thin , on account of the very low penetrating power of the rays dealt with . The thinnest obtainable leaf was used . The thicknesses were obtained by weighing . The screens were mounted on metal frames fixed to a geometrical slide , the whole being earthed . The geometrical slide enabled any required screen to be inserted with a minimum of delay . This time-saving device was found to be necessary , since it was not often that the tube would run steadily for long at a time . S 2 . A Theory of the Influence of the Aluminium Window on the Constitution of the Emerging Rontgen Rays . The experiments described in SS 3 and 4 are so diverse in their nature and apparently so disconnected that it seems advisable to precede the experimental results by a theory which welds them together , and so aids the memory . This is the only excuse for presenting the following theory here instead of later , and it is to be regarded as tentative , since its simplicity must needs suffer should factors like selective transmission and so on be taken into consideration . It is well known that many metals can be made to give out characteristic secondary radiation when stimulated by a suitable primary beam . The distinguishing feature of a characteristic radiation , according to Barkla , is its individuality . The quantity may depend on circumstances , but never the quality . It is , however , only when the primary beam contains a constituent more penetrating than the characteristic to be excited that the stimulation can be effected . This law governing the emission of characteristic radiations , in fact , is closely analogous to that law f^und by Stokes to be true in cases of light fluorescence . The recent researches of Prof. R. W. Wood , however , have shown that there are cases of light fluorescence in which Stokes 's law is^flagrantly disobeyed . 104 Mr. R. Whiddington . The Production and [ Jan. 20 , The possibility of similar exceptions to the parallel law of characteristic radiation or Rontgen ray fluorescence is indicated by the easy explanation on such an hypothesis of the otherwise hardly explicable results in connection with aluminium described in this paper . The basal assumption is this , that aluminium is capable of emitting a characteristic radiation which may be more penetrating than the exciting primary . Put in other words , it is assumed that Al is an exception to Stokes 's law as applied to Rontgen ray fluorescence . We will now consider what , on such an hypothesis , will be the state of affairs on the emergent side of a plate of aluminium ( such as the window of the discharge tube ) on which a beam of Rontgen rays is incident . If the rays are excessively soft , their intensity on the emergent side will be very small\#151 ; let us suppose inappreciable . Now imagine the incident primary beam to become gradually more penetrating while keeping its energy constant . Then , if the Al emit no secondary rays , there will come a stage ( a ) , corresponding to a penetrating power Pc of the primary rays , when the emergent radiation becomes just strong enough to be detected . But it is conceivable that if the Al were to emit a secondary radiation of greater penetrating power than Pc , radiation might escape from the emergent side of the plate even if the incident primary rays possessed a penetrating power less than Pc . This would happen if PAL \gt ; Pc , where PAl is the penetrating power of the characteristic Al radiation , Pc is the penetrating power corresponding to that quality of incident beam , which , in the absence of secondary effects , would just emerge in measurable quantity . The condition PAL\gt ; PC involves the violation of the " Rontgen ray fluorescence " law referred to above . In the apparatus shown in fig. 1 it will be seen that the Rontgen radiation produced by the incidence of the cathode stream on the target A must pass through the Al window W before reaching the testing vessel I. The above considerations show that it is not impossible , with certain assumptions , for radiation to be detected by the vessel I even if the primary radiation from A is too absorbable to penetrate the window . As a sort of corollary it would follow that up to a certain limit of generating potential the quality of the emerging radiation would be constant ; that is , the penetrating power of the emergent Rontgen radiation would remain apparently constant and independent of the velocity of the cathode rays striking the target ( see fig. 7 ) . It is now necessary to consider some other and more complicated consequences of a violation of the " fluorescence law . " There will be no further assumptions made , but it will be necessary to anticipate some of the simpler experimental results of SS 3 and 4 . 1911 . ] Properties of Soft R Radiation . ( 1 ) The materials experimented with can be assigned positions in one of two classes according to their power or inability of emitting secondary Rontgen radiations . Group A , which includes Al , contains those anticathodes which emit secondary radiations , while Group B\#151 ; the larger class\#151 ; contains those which do not . This is a purely experimental classification . Metals of Group A when subjected to a beam of cathode rays , and so to a beam of primary Rontgen rays , are imagined to be capable of emitting characteristic radiations of the type conceived above ; whereas metals falling into Group B are supposed to emit no secondary radiation when placed under similar conditions . ( 2 ) Experimental analysis of the radiations from members of Group B shows that they are all of the same quality at the same generating potential , but that their penetrating powers increase with the generating potential . So much for the experimental results which it is necessary to anticipate for the purposes of the following considerations . Consider , first , the constitution of the radiation from a representative anticathode of Group B. Since the rays have to pass through the Al window they must contain a certain amount of the Al characteristic radiation . If the generating potential is low enough , the radiation will consist wholly of this Al characteristic . But with increasing generating potential* the primary rays from the anticathode will become hard enough [ stage ( a ) ] to penetrate the window and so form a constituent of the emergent radiation . Further increase of the generating potential will have no influence on the quality of the secondary radiation from the window , but it will have the effect of increasing the penetrating power of the primary radiation from the anticathode . A stage will be reached when this primary radiation will possess a penetrating power greater than that from the window . A representative member of Group A can be regarded as emitting a radiation which is the same as that from a typical member of Group B with the addition of a strong secondary radiation from the anticathode itself . This strong secondary radiation can be regarded as the partial return in the direction of observation of the forward directed hemisphere of radiation spreading down into the anticathode . In the case of anticathodes of Group B it is supposed that this forward hemisphere is absorbed and lost in the anticathode , although of course it may be partially scattered . Fig. 2 will now be readily understood . It is intended to represent in a quantitative sort of way possible analyses of the radiations from members of Groups A and B at two different cathode ray velocities corresponding to generating potentials V and Vi . The figure , for simplicity , takes Al as typical of Group A. PQ represents , in section , the plane of the window Mr. R. Whiddington . The Production and [ Jan. 20 , Al.characberisbic radiabion ( from anbicabhode ) Window radiation ( characberisbic ) Primary radiation ( due bo the cabhode rays ) Generating Potential = V ( 2,000 volts ) j AL.characberisbic radiabion ( from anbicabhode ) Window radiabion ( characberisbic ) Primary radiabion ( due bo bhe cathode rays ) Generating- Potential =V , ( 3,000volts ) Fig. 2 . distances measured at right angles to PQ representing actual distances at right angles from the window . Take the top curve aa'e , which represents 1911 . ] Properties of Soft RRadiation . the characteristic radiation from an A1 anticathode at V volts . The radiation represented by this curve can penetrate no further than the distance be , or , rather , beyond e it produces no measurable ionisation . Further , the area included between aa'e and be represents the energy of the emerging radiation as measured by the ionisation produced on its total absorption . If , however , only the radiation to the right of a'b ' be absorbed , then the observed energy ( ionisation ) will be given by the area included between a'e and b'e . These explanatory remarks apply equally to the other five curves . It may be here pointed out that of the six curves in fig. 2 , four possess the same penetrating power , and , in fact , are representatives of the same type of radiation produced under different circumstances . These four curves are shaded in the diagram . In fig. 2 , V\lt ; Vi , indicating that the variable primary constitutent cc'f is less penetrating at Y volts than the corresponding constituent c\cff\ at Vi volts . Consider ( i ) of fig. 2 first of all . The two bracketed curves and cc'f represent the constitution of the radiation from some member of Group B. The invariable window radiation is represented by while the primary component ( at this potential supposed to be softer ) is represented by cc'f . The total ionisation produced by this radiation = [ area pqr + area cc'f\ The total ionisation which would be produced by any other member of Group B would be = s [ area ^r+area cc'/ ] , where s is the appropriate constant.* Now the constitution of the radiation from an A1 anticathode can be represented by the three curves aa'e , pqr , and cc'f , the latter two curves requiring a suitable factor when their areas are taken into account . The curve aa'e represents the secondary characteristic radiation spreading out from the anticathode . The total ionisation produced by this radiation = area aa'e + a [ area pqr -f- area cc'f\ The area aa'e is here much the more important , since a is a factor much less than unity . This factor is introduced because , apart from the secondary radiation represented by the area aa'e , the A1 radiation is the same as that from members of Group B , only on a smaller scale . * This involves the assumption that a linear connection exists between the energy of the primary and that of the window radiation . 108 Mr. R. Whiddington . The Production and [ Jan. 20 , Turning to ( ii ) of fig. 2 , representing the constitution of the radiations at Vi volts , we notice the main differences . The variable primary constituent CiCi/ i is here shown to be more intense and somewhat penetrating , while the aluminium characteristic radiation from the anticathode has considerably increased in ionising value . We are now in a position to write down in terms of the areas of these curves expressions for the radiation values* of A1 and of members of Group B. It is clear from the definition that in the case of a member of Group B , the relative radiation value is equal to s , the constant already introduced . It is shown below that the radiation value of a member of Group A cannot be so simply expressed , but depends on the method of measuring the ionisation . Expressions are obtained for the radiation value of Al , firstly taking account of the areas of the complete curves to the right of PQ , and , secondly , only taking account of the areas to the right of AB . The first method involves the measurement of " total ionisation , ' ' while the second involves the measurement of what may be termed " end ionisation . " 1 . Method of " Total . ' The relative radiation value VRT at V volts of the Al anticathode is given by I ? _ / area ae + a [ area pr+area c/ ] \ 7 T V area pr + area cf Not much error will be introduced by neglecting the effect of the window ; in which case yliT = Similarly v , Rt \#151 ; / area ae + u area \ area cf f 100 oo . \ area j / area a\C\ 4-\#171 ; area cp'f \ area C\f\ area area 100 . * The relative radiation value of an anticathode A is given by the defining relation EA=h/ *SXl00\#187 ; where RA = the relative radiation value of an anticathode A , iA = the energy of the Rontgen rays emitted by A , is = the energy of the rays emitted under the same experimental conditions , by a standard anticathode S , 100 = the standard radiation value at all generating potentials of the standard anticathode . 1911.]- Properties of Soft R Radiation . 2 . Method of " End If R and Rr are the relative radiation values , using this method at Y V E Vi E volts and Yi volts respectively , then ^ ^area a'e + a area c'f ^ -^qq Vikb = fsea ai , ei+a area c'\amp ; \ 100 \ area c'f / gi + \#171 ; a area ^_area a'e\ area c'f j 100 , +area a\i\ wo . area c1 From the diagrams in fig. 2 we see at once from these expressions that tRt \lt ; ur \#187 ; and VjEt \gt ; v^e\gt ; while between Y and Vi there must be some potential Yx where V , RT = v^Re-* We see that , on the views suggested , the relative radiation value of an A1 anticathode should depend entirely on the fraction of energy absorbed by the measuring apparatus . That this is experimentally the case is shown in Table I , where it is seen that the potentials corresponding to Y and Yi are 2000 and 3000 volts respectively . The same theory applies to the case of a Pt anticathode , which emits a strong secondary radiation of much the same penetrating power as that from aluminium . S 3 . The Dependence of the Energy of ROntgen Radiation\#151 ; ( a ) On the Nature of the Anticathode . ( b ) On the Velocity of the Parent Cathode Bays . It is well known that all metals do not make equally efficient anticathodes . Kaye , f for example , found that , using cathode rays of rather high velocity , they could be arranged in descending order of efficiency , uranium being at the head of the list and titanium at the foot . His experiments were carried out in the following general way:\#151 ; An ionisation chamber was subjected to the action of Rontgen radiation from various anticathodes and the ionisation currents measured . From the value of these ionisations the relative radiation values of the anticathodes ( a standard anticathode having been chosen ) were calculated from the defining relation already given Ra = i^ik x 100 , where Ra = the relative radiation value of an anticathode A , ix = the ionisation current produced by an anticathode A , is = " " " the standard , 100 = the value assigned to the radiation value of the standard . * In this case/ and A would fall on the dotted line of fig. 2 . t G. W. C. Kaye , 'Phil . Trans. , ' A , vol. 209 , p. 137 . 110 Mr. R Whiddington . The Production and [ Jan. 20 , A list drawn up in this way cannot be satisfactorily interpreted unless the absorption coefficients in air of the radiations are known . For an anticathode occupying a high place in the relative radiation scale may owe its position to the emission of very absorbable rays , which will , of course , produce great ionisation in the chamber\#151 ; which in Kaye 's experiments only partially absorbed the rays dealt with . In the present experiments the radiations* are totally absorbed , and therefore the results are not open to objections of this nature . The ? experimental results of the first part of this section show how the relative radiation values of a number of anticathodes depend on the velocity of the cathode rays incident on them . The experiments were carried out using cathode rays generated at steady potentials ranging from 1600 to 3600 volts , corresponding to velocities between 2-4 x 109 and 3*7 x 109 cm./ sec. . The results are shown in fig. 3 , and may be verbally stated as follows :\#151 ; 1 . The relative radiation values of the anticathodes Ag , Pb , Sn , Sb , Ni , Cu , . Fe , Zn , * are independent of the velocity of the parent cathode rays . 2 . The relative radiation values of A1 and of Pt rise rapidly as the velocity of the parent cathode rays increases . Before these relative radiation values can be regarded as quantitatively reliable it will be necessary to be quite certain that the finish of the anticathode surface has no effect . This is a matter requiring experimental investigation . It is quite conceivable that such a surface effect might exist ( more especially with slow cathode rays ) , but even if its existence were proved it would not affect the validity of conclusions based on the variation of the radiation values with the generating potential . The radiation values found under the experimental conditions of this investigation in no way agree with those found by Kaye ( cit. ) . These discrepancies are perhaps due to secondary emissions at the high potentials which he used . The graph shows very clearly how it is possible for A1\#151 ; in spite of its low atomic weight and density\#151 ; to be the most efficient anticathode between certain limits of cathode ray velocity . These results were obtained using the particular ionisation chamber arrangement of fig. 4 , in which the window of the discharge tube is connected , to the case of the chamber and charged to a saturating potential . By this means the total ionisation ( see S 2 ) was measured , since the chamber was long enough to totally absorb the radiation involved . Now the ionising radiation has had to pass through 0002 cm . of aluminium window\#151 ; a thickness which at this stage of the experiments was as small as could be conveniently manipulated . It was thought that interesting results-* Hereafter ( and in S 2 ) referred to as members of Group B. 1911 . ] Properties of Soft Rontgen Radiation . Ill Al Sn 2,000 2,5 OO Generating robenbial . Fig. 3 . Fig. 4 . 112 Mr. R. Whiddington . The Production and [ Jan. 20 , might be obtained by repeating the experiments just described , using a thicker window or an effectively thicker one . In this way , it was thought , light might be thrown on the constitution of the different radiations . This end was attained experimentally by means of the arrangement of fig. 1 , in which the gauze front N " is a centimetre or so from the window W. The total ionisation is thus not measured , since the ionisation between W and N is not included . We may use the term " end ionisation " to denote what is measured . The relative radiation values found in this way at generating potentials of 2000 and 3000 volts are given in the following table , which includes , for the sake of comparison , the radiation values from fig. 3* at these two potentials . Table I. Cu 100 100 100 100 Pt 227 302 400 100 Sn 229 243 236 240 A1 226 298 515 220 Ag 262 251 266 281 Fe 132 138 128 122 Cd 112 112 127 136 Ni 152 150 148 144 Zn 93 97 Total ionisation . End ionisation . Total ionisation . End ionisation . Fig. 4 . Fig. 1 . Fig. 4 . Fig. 1 . 2000 volt radiation . 3000 volt radiation . It will be observed that again A1 and Pt , as representative members of Group A , are differentiated from members of Group B , but in this case by the dependence of their relative radiation values on the amount of energy absorbed by the ionisation chamber . These results follow from the theory given in S 2 and are easily remembered by its aid . We have now seen how the relative intensity of Rontgen radiation from some anticathodes varies with the velocity of the parent cathode stream . It yet remains to see how this velocity determines the actual energy radiated . The results for a nickel anticathode are shown in fig. 5 , the arrangement of fig. 4 being used . This experiment is but barely alluded to , as I am making it the basis of a separate research . From the graph it will be seen that very little radiation emerges from the window below 1200 volts , at which potential a quite sudden coming-in of ionisation is followed by a linear * Making use of " total ionisation " by use of fig. 4 . 1911 . ] Properties of Soft R Radiation . connection between energy of radiation and generating potential ( the current passing through the tube being kept constant ) . The generating potential , 1200 volts , at which the issuing radiation begins to become appreciable does not depend to any large extent on the thickness \#166 ; 6 300 1,200 1,400 1,600 - Generating- Potential ( Ni.anbicathode ) Fig. 5 . of the window . This is shown by the points \#169 ; and x on the graph obtained with two different thicknesses of window 0-002 and 0'0004 cm . Preliminary experiments have indicated that the curve of fig. 5 , so far as shape is concerned , is the same for all anticathodes as for Ni . The generating potential 1200 volts , corresponding to a cathode ray velocity of 2T x 109 cm./ sec. , will , on the view put forward in this paper , furnish a value lor the minimum cathode ray energy capable of stimulating the A1 characteristic radiation . S 4 . The Dependence of the Absorption Coefficients of the Eon then Eadiation on\#151 ; ( a ) The Nature of the Anticathode . ( b ) The Velocity of the Parent Cathode Rays . Absorption curves in Cu of the 3000 volt radiation from all the anticathodes are plotted in fig. 6 , where the logarithm of the radiation intensity is plotted along the y axis and the thickness of the screen in arbitrary units along the x axis . The ionisation produced after absorption of the VOL. LXXXV.\#151 ; A. T Mr. R. Whiddington . The Production and [ Jan. 20 , rays in a thickness of copper equal to 5 in fig. 6 is put equal to 100 units . The arrangement of fig. 1 was used , the distance between W and 1ST being about 1 cm . , so as to admit the slide carrying the absorbing screens . It follows from the graph that once again A1 and Pt stand apart from the remaining anticathodes . In this experiment their absorption curves have an early steep part , whereas the similar curves for members of Group B are coincident straight lines with just a very slight initial steepening . These experimental results can receive only one interpretation , and that is that the 3000 volt radiation from members of the B group of anticathodes is very nearly homogeneous and independent of the nature of the anticathode , * whereas that from A1 and Pt contains not only a radiation of the same penetrating power as that from Group B , but also one of a considerably softer character . I have plotted absorption curves similar to those of fig. 6 at different generating potentials , and it seems that ( using an A1 anticathode ) the part CB of the absorption curve DCB becomes steeper as the generating potential diminishes . At 2600 Volts , or thereabouts , CB disappears , and the complex curve DCB degenerates to practically a straight line , f corresponding to the earlier steep part DC . At potentials less than 2600 volts the slope of DC remains much the same , although the intensity of the radiation itself is * J. J. Thomson , " On the Electrical Origin of the Radiation from Hot Bodies , " 'Phil . Mag. , ' Aug. , 1907 , p. 230 . This paper anticipates theoretically this experimental result . t The radiation is not quite homogeneous . 1911 . ] Properties of Soft R Radiation . continually diminishing . When an anticathode of Group B is used instead of Al , much the same sequence occurs , only in this case the energy escaping from the tube is much less . The variation in absorption coefficient \/ p with the generating potentials in volts is shown in fig. 7 . In these experiments a Ni anticathode , as representative of Group B , was used . The absorption coefficients plotted in fig. 7 correspond to the early part of the curves of fig. 6 , taken of course at different potentials . The graphs show how the slight initial steepening observable at 3000 volts becomes very important at lower generating potentials , when , on the theory of | 2 , the variable primary constituent of the examined radiation is becoming of less importance . These absorption coefficient variations have been observed for screens of gold , copper , tin , air , * and aluminium . With the exception of the latter the general results are independent of the material of the screen . Brom fig. 7 it is clear that , taking the air curve as typical , the absorption coefficient of the radiation issuing from the tube is up to 2600 volts independent of the generating potential.f At generating potentials above * The dotted curve of fig. 7 is the air curve with its ordinates quadrupled . t This remarkable result has already been obtained with Al screens for a similar range of generating potentials by W. Seitz , ' Phys. Zeitschr . , ' 6 Jahr . , No. 23 , p. 757 . Mr. R. Whiddington . The Production and [ Jan. 20 , 2600 volts the graph shows a sudden diminution in and the value of Y at which this drop takes place is independent of the screen . The potential at which this diminution in X/ pappears must depend on the thickness of window used , because drawing the ionisation chamber further away from the window has the effect of shifting the bend in the curve towards a higher value of V. It will be clear that up to 2600 volts or thereabouts the radiation emerging from the window or , rather , entering an ionisation chamber a centimetre away , is mainly ( to within a few per cent. ) the aluminium characteristic radiation . The absorption coefficients of this radiation ( using the 2700 volt radiation from Al ) in various absorbing screens are shown in the following table . The very high values for Cu and Ag screens are noteworthy . The last column shows the parallel coefficients for the softest characteristic radiation studied by Barkla , namely , that from chromium :\#151 ; Table II . Screen . X/ p. X/ p ( Cr radiation).* pt 2010 516 -8 Au 1760 507 Cu 3900 143 Ag 2020 580 -5 Sn 1030 713 -7 Al 580 136 Air 1150 \#151 ; * Barkla and Sadler , ' Phil. Mag. , ' 1909 , vol. 17 , p. 749 . It has been mentioned that the curves of fig. 7 are of the same general shape for the screens Au , Cu , Sn , and air , but this does not quite hold in the case of Al screens . The horizontal part of the curve persists for a rather greater distance , and shows in fact a very slight tendency to rise before finally falling towards the Y axis . S 5 . The Corpuscular Radiation excited by the Impact of Soft ROntgen Rays on Metallic Surfaces . For the purposes of the experiments described in this section the ionisation chamber was cemented on to the discharge tube in the manner shown in fig. 4 . By means of liquid air and a charcoal tube the chamber could be evacuated . The Rontgen rays from the aluminium anticathode passed through the window W and fell on the plate I. When the plate I was Cu , Pb , Ni , Ag , 1911 . ] Properties of Soft Ro Radiation . or Zn the same effects were always observed , viz. , that that plate received a negative charge . This was proved to be due to the emission of negative particles from the window by applying a strong magnetic field across it . When the magnet was " on " no deflection could be observed in the electroscope in two minutes . When the magnet was " off " the rate of negative charging up of the electroscope was about two divisions a minute , the current through the discharge tube being 1/ 5 milliampere at 3400 volts . When the plate A was either aluminium or platinum , the incidence of the rays caused the electroscope to charge up positively , the rate being increased considerably when the magnetic field was switched on . The conclusion is , therefore , that the emission by aluminium and platinum of a strong secondary Eontgen radiation is accompanied by an emission of corpuscles . S 6 . Summary and Conclusions . 1 . The variations with the generating potential ( which is proportional to the ( velocity)2 of the primary cathode rays ) of the relative radiation values of 10 anticathodes have been studied . The potential limits were 1500 to 3600 volts . Eight of these anticathodes ( members of Group B ) were found to have definite radiation values not depending on the generating potential , while the remaining two ( A1 and Pt ) rapidly increased their radiation values with rising potentials . At any definite generating potential the actual radiation values of A1 and Pt depend enormously on the amount of energy absorbed by the ionisation chamber , whereas the radiation values attached to the members of Group B are not so influenced . If a particular view of the constitutions of the radiations be taken ( see S 2 ) these results are easily explained , and , moreover , fall into line with other results of an entirely different kind . Briefly this view is as follows:\#151 ; The behaviour of the 10 anticathodes studied under the particular experimental conditions of this research leads to their classification under two headings , termed for convenience Groups A and B. At a definite generating potential the radiations from members of Group B are regarded as differing amongst themselves only in quantity ( ionising power ) ( fig. 3 ) and not in quality ( absorption coefficient ) ( fig. 6 ) . The quality , however , does depend on the generating potential ( fig. 7 ) . The radiations from anticathodes of Group A ( A1 and Pt ) also are regarded as containing a component whose quality depends on the generating potential . But they are also imagined to contain relatively strong constituents of the characteristic type , which are peculiar in their possible possession of absorption coefficients less than those of the exciting primary rays . In other words 118 The Production and Properties of Soft Radiation . it is supposed that these characteristic radiations can be stimulated by less penetrating exciting rays . Such an hypothesis is not glaringly absurd , since the law to which it does not conform is after all only a restatement of Stokes 's law of light fluorescence , and Prof. E. W. Wood has shown its limited applicability . 2 . Below a generating potential of 1200 volts only a very weak Bontgen radiation can be detected . This is regarded as a secondary effect of the window . The sudden coming in of relatively strong radiation at 1200 volts is very striking ( fig. 5 ) . Above 1200 volts there is a linear connection between the energy of the Bontgen rays emerging from the tube and the energy absorbed by the discharge , the current through the tube being kept constant . 3 . Over a certain range of generating potentials the speeding-up of the parent cathode rays produces no effect on the absorbability of the emerging radiation ( fig. 7 ) . This also is regarded as an effect due to secondary radiation from the window . In fact with the measuring chamber 1 cm . from the A1 window the view held is that the only radiation which is measured below 2600 volts is , with any anticathode , the aluminium characteristic radiation . At 3000 volts the radiations from A1 and Pt and members of Group B have been analysed , and the results show conclusively the emission of secondary radiation from the former two , and its almost complete absence in the rays emitted by the latter eight . 4 . It has been shown that A1 and Pt under the impact of these soft rays emit corpuscular radiation in addition to the above-mentioned secondary Bontgen radiation . In this respect again A1 and Pt are differentiated from members of Group B , which do not emit under similar circumstances any measurable quantity of charged particles . It gives me pleasure to thank Prof. Sir J. J. Thomson for his interest in this investigation , which was carried out at the Cavendish Laboratory .

rspa_1911_0026

0950-1207

Experiments on stream-line motion in curved pipes.

119

131

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

John Eustice, B. Sc.|Sir Joseph Larmor, Sec. R. S.

experiment

6.0.4

http://dx.doi.org/10.1098/rspa.1911.0026

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1911_0026

10.1098/rspa.1911.0026

Fluid Dynamics

Thermodynamics

Fluid Dynamics

119 Experiments on Stream-line Motion in Curved Pipes . By John Eustice , B.Sc. , Professor of Engineering , Hartley University College , Southampton . ( Communicated by Sir Joseph Larmor , Sec. R.S. Received January 26 , \#151 ; Read February 16 , 1911 . ) Authors previous Experiments.\#151 ; In the paper read by the author on the " Flow of Water in Curved Pipes , " before the Royal Society on June 2 , 1910 , it was shown that even a small curvature in the length of a cylindrical pipe affected the quantity of flow of water through the pipe . The effect at velocities below the critical velocity for a straight pipe was most remarkable , inasmuch as the experiments showed that in coiled pipes there was apparently no critical velocity region , whilst in less pronounced curves , where the critical velocity is not entirely absent , a very slight sinuosity of the pipe lessened the flow . This was shown by the increase in the value of the index n in the formula , s = Krn/ m from n \#151 ; 1 , for perfectly straight pipes , to n = IT to 1*2 for pipes slightly curved or sinuous . Here or is the hydraulic gradient , v is the velocity of flow , mis the hydraulic mean radius , and K is a constant . In an attempt to discover the cause of this departure from the law of flow in straight pipes , the author had tried Prof. Osborne Reynolds ' colour-band test in a coiled glass tube , but the arrangements were of a primitive character and the results obtained were not decisive . At the suggestion of Sir Joseph Larmor the colour tests have been repeated with specially made glass tubes , in which the stream motion could be traced by the introduction of coloured water through capillary nozzles . Arrangements for Coloured Filaments.\#151 ; The following arrangement was adopted:\#151 ; A brass tube A ( fig. 1 ) of about 2 cm . internal diameter was fitted internally with a piece of brass B of boat-shaped section , into which six separate supplies of dyed water could be introduced through the nipples shown in fig. 1 . The dye was supplied from the open tubes T , the height of each of which could be adjusted so as to allow the dye to flow in a gentle stream from the nozzles N , U , which were 1'25 mm. external and 0'3 mm. internal diameter . The supply of water came from a tank through a cock at C ; to this was connected the pipe which contained the nozzles . The water from the tank in its passage past the nozzles carried the dyes with it . The direction of flow is shown by the arrows , the velocity of flow was regulated by a pinch-cock PC placed on a flexible tube at the outlet end of the tube under 120 Prof. J. Eustice . Experiments on [ Jan. 26 , observation . Glass tubes of various shapes could be connected at the joints J , J , and the stream-line motion made visible by the dyes could be observed and photographed or sketched . In older to trace the paths of the streams of dye from each nozzle separately , six different colours were used , the nozzles and supplies of colour being so arranged that the stream from each could be observed separately ; by an adjustment of the tube which contained the nozzles , every part of the tube could be investigated . In fig. 1 , six streams of dye are shown passing through the conical glass connecting tube JJ ; the paths of two only of the filaments are traced in the U-tube . In fig. 2 the complete paths of six such colour bands are traced . The first tubes experimented on were U-shaped , as shown in figs. 1 and 2 ; the experiments in these tubes are described in detail , since they illustrate the methods adopted for other curved tubes . For the purpose of observing and photographing the stream-lines , the U-tube , with its central plane horizontal , was placed in a tank ; mirrors with their planes at an angle of 45 ' with the plane of the U-tube were arranged in positions for obtaining the side and end elevations . In order to lessen the effect of refraction , the tube was completely covered with water ; photo Stream-line Motion in Curved Pipes . 1911 . ] graphs were taken of the tube and the reflections , and sketches were made from which fig. 2 has been drawn . The photographs and drawing show the character of the stream-lines , but it is impossible to reproduce the extremely beautiful effects due to the interlacing of the colour bauds . Although each band kept distinct from the others it was necessary when tracing out the stream-lines to shut off all the colour bands except the one under observation . Results obtained inU -tubes.\#151 ; A stream filament a ( figs. 1 and 2 ) if it is in the central plane of the tube and close to the outer wall of the bend , breaks up into two parts immediately it reaches the curve of the bend , each of which leaving the central plane in opposite directions and following the wall of the tube crosses to the inner wall , and coming towards the central plane the divided filament forms the loop shown in the end elevation of the bend ( fig. 2 ) ; the filament is now spread out into a narrow band and passes ' through the outlet limb , the path taken being shown by the lines a , a. Stream filaments which are near the outer wall of the tube and just above ( or below ) the central plane will cross the bend as shown by the line b ( fig. 2 ) , and follow the surface of the tube , keeping above ( or below ) the central plane . The behaviour of other filaments which are not in the central plane of the tube may be seen from the paths of c and d. Both these lines strike the outer wall of the bend and cross over near the surface of the tube , c to the inner wall of the bend and d to the inner wall of the outlet limb . The filaments e and / pass around the bend and do not strike the walls . Several U-shaped tubes , right angled bends , and other tubes bent in curves of large radius were experimented on ; some of these are illustrated in the diagram ( figs. 3 to 7 ) . The tubes are drawn accurately to scale . The radius in centimetres of the centre line of the curve is in each case given by the number printed at one end of each tube . The drawings of the stream-lines in fig. 2 are from sketches and photographs of some of the experiments . In fig. 3 ( 2 ) the filament a strikes the outer wall at A ( which is near the central plane of the tube bend ) , where it spreads out into a flat band and after following the wall of the tube it strikes the inner wall at A ' and then takes the form of path shown ; a section of such a colour band after leaving A ' is usually curved . In fig. 3 ( 4 ) the colour bands \amp ; BB ' and eCC ' illustrate the effect of increasing the velocity , cCC ' being at a mean velocity of flow of 3'7 cm . per sec. , whilst \amp ; BB ' is at a velocity of 11 cm . per sec. In fig. 3 ( 6 ) the band dDD ' after leaving D ' breaks into branches , the main portion D flowing near the centre of the outlet limb whilst T\gt ; 'd " flows near the inner wall of the tube . Stream-line Motion Curved Pipes . 1911 . ] In fig. 3 ( 8 ) the line/ FF ' , taken at a velocity of 4'6 cm . per second , is of the same character as the lines previously described ; after striking at F , it spreads out into a wide band , collects at F# and leaves the tube in a fairly regular band of colour . The line rEE ' shows the effect of increasing the velocity to 18 cm . per second . In fig. 3 ( 10 ) the line gGQ ' is at a velocity of 17'5 cm . per second and the line / iHH/ is at a velocity of 5'5 cm . per second , just sufficient for the colour band to strike the outer wall of the curve at H " , the band then spreads as shown in the sketch . The effect of increasing the velocity in a curved tube is to increase the curvature of the filaments ; for example the band H'H " which is shown touching the tube at H " would pass down the outer straight part of the tube without touching it if the velocity of flow is increased ; other examples of this are given in the right-angled bend fig. 4 ( 2 ) and in fig. 1 , Results in Tubes of large Radius.\#151 ; The same general results are obtained in tubes in which the radius of curvature of the tube length is large ; fig. 3 ( 25 ) illustrates the effect of doubling the velocity of flow in a tube 1 cm . diameter bent to a curve of 25 cm . radius ; the line/ J ( velocity 5-5 cm . per second ) shows the repeated crossing of the colour band ; il is at double the velocity of flow ( 11 cm . per second ) . The increased curvature of the band at the higher velocity is again apparent . The filament h in fig. 3 ( 50 ) and l in fig. 3 ( 100 ) show that , even when the curvature is very small , if the curve is sufficiently long the stream-lines will all strike the outer wall and follow the surface of the tube to the inner wall . The filament m in fig. 3 ( 100 ) enters the straight part of the tube in the central plane close to the outer wall ; it spreads out into wide bands both above and below the central plane , and after crossing the tube opens out into two bands which remain uncombined for the whole remaining length of the tube , the inner radius of the bend being quite free from colour . In a longer tube these bands would cross over again to the outer radius , as is shown in the coiled tube , fig. 5 , where all the stream-lines repeatedly cross from the inner wall to the outer wall and back . In a straight tube the colour bands remain distinct and the surrounding water is not tinted ; in curved tubes after the colour bands strike the walls of the tube , although the bands can be distinctly traced , some of the colouring matter is dispersed into the surrounding water , the outlet water being tinted . In a coiled tube of several convolutions the distinctive character of the colour filament is gradually lost and after passing through several coils can scarcely be traced . Results in right-angled Bends.\#151 ; In the series of right-angled bends illustrated Prof. J. Eustice . Experiments on [ Jan. 26 , in fig. 4 , the lines a , b , c , in ( 2 ) were taken at a velocity of 105 cm . per second ; when the velocity was increased to 15*2 cm . per second the positions of all the lines changed slightly , the line a , which at the lower velocity was in the position of the regular curve shown , broke up at the higher velocity into two branches , one of which formed a spiral vortex near the central plane of the tube and interlaced with the line c. The position of the filament b was arranged so that it struck the extreme part of the outer curve , where it scattered as shown ; at the increased velocity the line b passed through the outer straight tube without scattering . In ( 4 ) the velocity is 7*3 cm . per sec. , the line / strikes the bend below the central plane and crosses over close to the surface of the tube ; other lines , such as e , which are above the central plane , follow paths shown at eE , whilst the lines represented by d nearer the central plane and the inner surface of the tube pass around the bend in an unbroken curve . In ( 6 ) the velocity is 12'5 cm . per sec. , the line g crosses under the other line , which passes through in an unbroken curve . In ( 8 ) the velocity is 8 cm . per sec. , the line h is close to the side of the tube near the central plane , it spreads immediately on entering the curved part , crosses the tube , and collects inside the bend , then leaves the bend in separate filaments ; the other stream-line passes freely through the tube . In ( 10 ) the velocity is 10 cm . per sec. ; the results are very similar to that shown in ( 4 ) . The results obtained in sharp right-angled elbows are shown in figs. 6 and 7 . The curious looping of the lines in fig. 7 will be understood from the somewhat similar loop shown in fig. 6 . The table on p. 125 is given to indicate the range of velocities employed , but the experiments were of a qualitative rather than of a quantitative character . The U-tube , fig. 2 , is 1*7 cm . internal diameter , all the others are 1 cm . diameter . The lengths of the curved part and the total lengths of each tube are given in Column 2 . In each case the straight parts of the tube at both ends are of equal length . Except in fig. 2 a connecting tube , 20 cm . long , was used in the position JJ , fig. 1 ; this tube tapered from 2 cm . to 1 cm . diameter for 10 cm . of its length , and was 1 cm . diameter for the remaining 10 cm . For fig. 2 the connector was only 4 cm . long , and tapered from 2 cm . to 1'75 cm . diameter . The head in the tank varied from 20 to 30 cm . Precautions taken in the Experiments : ( ) To ensure the equal velocities of flow of the colour filaments and the surrounding water.\#151 ; Before using 1911 . ] Stream-line Motion in Curved Pipes . 1 . Fig. 2 . Length of tube , cm . 3 . Radius of curve , cm . 4 . Temp. 'C . 5 . Mean velocity of flow in diagram , cm . per sec. 6 . Turbulent motion , cm . per sec. 7 . Critical velocity by Reynolds ' formula . Curved part . Total length . Fig. 2 7-8 34 -8 2-5 17 -0 3 5 7\#151 ; 8 12 *8 Fig. 3 ( 2 ) ... 6-3 50 -0 2*0 18 -0 a 10-0 r x o .^7 1 17\#151 ; 27 21 5 Fig. 3(4 ) ... 12 -6 50 -0 4-0 18-0 { c 11-0 } 17\#151 ; 21 21 -5 Fig. 3 ( 6 ) ... 18 -8 50 -0 6 -0 18 -5 d 7-8 18\#151 ; 20 21 -3 Fig. 3 ( 8 ) ... 24 -1 50-0 8 -0 18-0 f e 18 *0 \ If 4-6 J 18\#151 ; 23 21 -5 Fig. 3 ( 10 ) ... 31 4 50 *0 10 -o 18-0 J \lt ; 7 17 *5 1 1 h 5-5 J 20\#151 ; 26 21 -5 Fig. 3 ( 25 ) ... 50-0 60-0 25 0 19-0 fi 11-0 \ \j 5-5 / 19\#151 ; 21 21 -0 Fig. 3 ( 50 ) ... 50 -0 60 -0 50 -0 18 0 k 10-0 20\#151 ; 21 21 -5 Fig. 3(100 ) ... 50 -0 60-0 100 -o 18 -0 J l 12-6 \ \ m 6 '4 J 20\#151 ; 21 21 *5 Straight tube \#151 ; 60-0 CO 16 -0 \#151 ; 19\#151 ; 21 22 -5 Fig. 4(2 ) ... 3-1 13 -1 2-0 19 -0 10 -5\#151 ; 15 -2 18\#151 ; 20 22-5 Fig. 4(4 ) ... 6-3 16 -3 4-0 19 -0 7-3 19\#151 ; 21 22 -5 Fig. 4 ( 6 ) ... 9-4 19 -4 6-0 19 -0 12-5 18\#151 ; 20 22 5 Fig. 4(8 ) ... 12 -6 22 -6 8-0 19 -0 8-0 19\#151 ; 21 22 -5 Fig. 4 ( 10 ) ... 15 7 25 7 10 -o 19 -0 10 -o 19\#151 ; 21 22 5 the arrangement of nozzles and colour supply sketched in fig. 1 , the author designed an apparatus for a single filament of colour which acted automatically so as to give equal pressures on the colouring liquid and the flowing water ; it could be so arranged that at any pressure the coloured liquid would ooze very gently into the flowing stream . In other tests the colour was allowed to accumulate in the tube BC , fig. 1 , when no water was flowing ; the colour was then shut off and water allowed to flow through the tube , the paths of the stream-lines could be distinctly traced , following the same general directions as in the case of the regular filaments . The motion of the solid particles referred to on p. 129 is an additional proof of the effect produced not being due to the filaments having a higher velocity than the surrounding water . The arrangement described above for single filaments was used for high pressure experiments in metal pipes , which were 150 cm . long and 1 cm . diameter . Between these pipes and the colour distributing nozzles was interposed a converging tube which was connected to the metal pipe by a glass tube , 15 cm . long , of the same diameter as the metal pipe ; a similar glass tube was connected to the outlet end of the metal pipe . When the metal pipe was kept straight the colour filament showed distinctly in the 126 Prof. J. Eustice . Experiments on [ Jan. 26 , glass tube at the outlet end ; when the metal pipe was bent into a slightly curved form the colour filament no longer appeared in the glass tube at the outlet end as a thread of colour , but , if visible , it was as a flat band of colour , or it was more or less dispersed into the surrounding water . Long , straight , glass tubes of from 1 to 2 metres long were substituted for the metal pipe , and when curved tubes were connected at the outlet end the same effect was produced as when the intervening connection was only a few centimetres long . ( b ) Establishment of a steady regime.\#151 ; From the preceding section it will be seen that in some of the experiments the tubes were sufficiently long to ensure that the filaments and water had settled down to a steady In all the experiments the brass tube A , fig. 1 , containing the nozzles for colour filaments was close to the tank , but between A and the tube experimented on there was interposed a converging tube , the dimensions of which are given on p. 124 . This tube was of sufficient length to establish steady flow , as will be seen by comparing Columns 6 and 7 of the table . Column ( 6 ) gives the commencement of the turbulent flow , Column ( 7 ) the critical velocity as calculated by Reynolds ' formula . The same general results were obtained at low velocities when a steady regime is produced in a fairly short pipe at velocities far below the critical . In the U-tube , fig. 2 , the connecting tube was short , and unsteady motion commenced at a much lower velocity than is given by Reynolds ' formula . The turbulent motion given in Column ( 6 ) and the calculations in Column ( 7 ) are for the straight part of the pipe . Comparison between the Flow of Water in Bends of Open Channels and of Closed Pipes.\#151 ; Prof. James Thomson , * in his theory of the transfer of solid particles along the bed of a river from the outer to the inner bank , has shown that the centrifugal force of the more rapidly moving water near the surface overcomes that of the water close to the bottom , which is retarded by the friction of the bed of the river . Prof. 0 . Reynoldsf has adopted this theory in his work " On Certain Laws relating to Rivers and Estuaries . " Thomson 's experiments were carried out in open channels , and he has suggested that the theory of flow in curved channels is applicable to pipe bends . In introducing the theory he states that " a stream flowing along a straight channel , and thence into a curve , must flow with a diminished velocity along the outer bank and an increased velocity along the inner bank . " The author 's experiments show that the motion at the commence* \#163 ; Roy . Soc. Proc. , ' May 4 , 1876 , vol. 25 , and June 21 , 1877 , vol. 26 . t 'Report Brit. Assoc. , ' 1887 , and 'Sci . Papers , ' vol. 2 , p. 329 . Stream-line Motion in Curved Pipes . 1911 . ] meant of the curve of a pipe bend is not that of a " free " vortex , for the velocity is greater near the outside than it is near the inside of a curve . There is another difference between the two cases . In an open channel there is freedom in a vertical direction , and , as Thomson has pointed out , the difference of pressure between the inner and the outer banks causes the surface of the water to be inclined from the inner to the outer bank of the curve . No such freedom is possible in a pipe which is running full , hence it is probable that the curvature of the stream-lines is greater and the effect of pressure on the transfer of water from the outer to the inner curve is more pronounced in a pipe than in a channel . In experiments on U-shaped open channels of semicircular section , about 1 cm . radius , the author has noticed that the flow of water near the surface is retarded , for if a filament enters the bend just below the surface MN in the position of 2 , fig. 9 , it divides so that a part goes under the stream , as in fig. 9 ; another part of the filament follows a somewhat similar course near the surface of the water and flows towards the centre of the stream , where it is carried around near the central curve of the bend . Filaments entering close to 1 behave in the same way , except that some of the colour is in this case carried slowly around the bend quite close to the outer radius . With these differences between open channels and pipes the following explanation may be looked upon as an experimental confirmation of Prof. J. Thomson 's theory w'hen applied to curved pipes . AB D . _h . J Motion in a Plane Sheet Perpendicular to Central Plane of Bend.\#151 ; Consider a set of stream-lines flowing through the straight part of a pipe in a plane sheet which is at right angles to the central plane of the U-tube as shown Prof. J. Eustice . Experiments on [ Jan. 26 , at B and at b"W ( fig. 8 ) where the circles at I , II , III , and IY represent sections of the tube taken along the radial lines 01 , Oil , OIII , and OIY respectively . Since the stream-lines near the centre of the sheet are flowing at a higher velocity than those nearer V and it follows that when the sheet enters the bend , the force required to make the stream-lines in the centre of the sheet ( at b in section I ) tend to follow the curve of the bend will be greater than the force required nearer V and b " , that is to say , the pressure between* b and the outer wall of the bend will be greater than the pressure nearer b ' and b " , and a flow of water will take place along the path of least resistance , i.e. from the region of greater to the region of less pressure , in the directions shown by the arrows in II , III , and IY . The centre portion of the sheet will gradually approach the outer wall , whilst some portion of the water near b ' and b " will be carried round the inner wall of the tube . Motion in a Sheet in the Central Plane of the Bend.\#151 ; Consider the streamlines flowing in the central plane MN of the tube ( fig. 8 ) . Changes in pressure above and below the central plane will have no effect in disturbing the position of the lines , since the tube is symmetrical on both sides of the plane MN . In any other sheet M'N ' which was parallel to the central plane before it entered the curved part , since there are less stream-lines , and the velocities are less than in the plane MN , the pressure at M ' will be less than the pressure at M , and the pressure at NT ' will be greater than the pressure at NT ; hence there will be a flow of water from M to M ' , that is to say , the water close to the surface of the tube , which in a straight tube is at rest , will even in a slightly bent tube be set in motion . As the flow of water from between a stream-line and the tube wall takes place , the stream-line will gradually approach the outer wall of the bend , the displaced water flowing around the walls of the tube from the outer to the inner wall of the bend . After entering the bend the sheet M'N ' becomes inclined in the direction of a normal to the curves ( fig. 8 ) , as is shown by the deviation of the filaments from the central plane in the left-hand view of fig. 2 . Motion of the Filaments near the Walls of the Tube.\#151 ; The order in which the stream-lines flow around the walls is shown in fig. 9 . A filament which approaches the curve at the outer radius of the bend strikes the tube and divides into two parts , each of which crosses a half circumference of the tube to the inside , as shown at 1 . A filament at 2 which approaches farther from the central plane MN flows inside the filament 1 . A filament 3 flows inside 2 , and so on ; this is represented in the lower section of the tube in fig. 9 . Stream-line Motion in Curved Pipes . 1911 . ] It was often noticed that the colour filaments in the position of 2 and 3 crossed the tube in small waves or ripples , showing the approach of unstable motion , which ultimately leads to the mixing of the colour filaments with the surrounding water . After reaching the inside of the tube the re-crossing always occurred in the half of the tube in which the filament entered , or in a tube of regular bore , the stream-lines are reflected back so as not to cross the central plane MIST . This reflection is shown in some of the diagrams as in fig. 3 ( 10 ) and ( 25 ) , and in the coiled tube fig. 5 . Turbulent Motion.\#151 ; The experiments described above were carried out at velocities sufficiently low to give unbroken motion , but in all cases the effect of increasing the velocity was observed , and , although it was naturally impossible to trace the colour filaments for turbulent motion in the same way as has been done for steady motion , by increasing the quantity of dye or by placing finely divided solid matter in the tubes and carefully increasing the velocity until turbulent motion was reached , it was observed that the same general features hold good for turbulent motion . For example a layer of sand placed along the inside of the tube at aa ' in fig. 1 , in which the central plane of the tube is vertical , will not go around the outer radius of the U-tube but will follow the path a'a " . The author has*shown that , when water is flowing at high velocity in a metal pipe bend , if a tube communicates from a ' to a " outside the tube a continuous stream of water is carried through the external tube from a ! to Summary and Deductions.\#151 ; The experiments show that when water is flowing at low velocities in a straight tube of uniform bore , filaments of colour maintain their form and relative positions , but when entering upon a curved portion of a tube some of the filaments spread out into bands of colour and cross to the inner part of the tube , travelling round its section close to the walls . If the curvature is sufficiently large or the curve sufficiently long , all the filaments would be affected . Other experiments in U-tubes seem to suggest that slipping may take place concomitant with the surface flow at the walls of the curved part of the tube . A quantity of dye having been spread over the whole of the surface of the tube , when water was allowed to flow through the tube , even at extremely low velocities , the colour disappeared immediately from the outer wall of the bend , more slowly from the inner wall , and very slowly indeed from the straight part of the tube . In the experiments it was observed that as the velocity of flow increased there was an increase in curvature of the stream-lines . It is inferred that the resistance to flow along the tube walls from the outer to the inner wall does not vary as the velocity directly , as in the ordinary viscosity equation , VOL. LXXXV.\#151 ; A. K 130 Experiments on Stream-line Motion in Carved Pipes . but it varies as the velocity raised to a power n , where n is greater than 1 , and probably greater than 2 . Except for the stream-lines near the walls of the tube the flow in a curved tube at low velocities appears to be in accordance with the viscosity law . The increased resistance referred to above applies to the water which has impinged upon the walls and is in its circuit along the walls of the pipe . If a pipe is not perfectly straight , the flow for the whole section of the pipe cannot be wholly viscous flow , since associated with viscous flow there is always some surface flow , that is to say , there is " skin friction , " the effect of which is to increase the resistance of the pipe and to lessen the total discharge ; or , for a bent pipe , n is greater than unity in the formula S = ~K . un / m. In the author 's previous experiments referred to on p. 119 , it was shown that the increased resistance due to curvature of a pipe was relatively greater at velocities below the critical velocity than at velocities which give turbulent motion in a straight pipe . This relatively greater resistance at low velocities is probably due to the generation of " skin friction , " which would not exist in a straight pipe of the same area at the same velocity , whereas the " skin friction " already existing is merely augmented at velocities which would cause turbulent motion in a straight pipe . Although surface flow and viscous flow may exist together in a curved pipe , it was observed that in U-tubes and in angle pipes whilst the filaments in the straight pipe before reaching the walls of the bend continued unbroken up to the usual critical velocity in a straight pipe , the filaments flowing through the straight pipe after leaving the bend usually broke up at velocities much below the critical velocity . The surface flow which commenced in the bend generated vortices which persisted in the water flowing through the outlet straight part of the pipe . This shows that the effect of a pipe bend or of an angle is not only to increase the resistance to flow in the bend itself , but also to increase the resistance in the contiguous straight pipe after the water has left the bend . This agrees with the results obtained by investigators who have experimented on the loss of pressure in the pipe bends used by engineers . The foregoing experiments indicate that , where it is beneficial to break up the regular lines of flow in a pipe , a curved pipe is more effective than a straight one . They show , for example , that in a tubular boiler or in a condenser of a steam engine , curved pipes would be more efficient than straight pipes , for when water is flowing at low velocity in a straight pipe , the water near the centre of the pipe section does not approach the sides during its passage through the pipe , but in a curved pipe the water is continually Secondary y-Rays produced by / 3-Rays . 131 changing its position with respect to the sides of the pipe , and the water which is flowing near the centre at one part approaches the sides as it moves through the pipe , and flowing near the sides it exerts a " scouring " action on the pipe walls , thus increasing the effectiveness of the pipe surface in transferring heat . Secondary y-Rays produced By J. A. Gray , B.Sc. , 1851 Exhibition Scholar , University of Melbourne , ( Communicated by Prof. E. Rutherford , F.R.S. Received February 4 , \#151 ; Read February 23 , 1911 . ) When the cathode rays of a vacuum tube impinge on any material they produce the X-rays , which are not deviated by a magnetic field , and are much more penetrating than the cathode rays which produce them . We might , therefore , expect that when the / 3-rays from radioactive substances impinge on a plate , similar penetrating rays would be emitted from the-plate . Such a penetrating type of rays , the 7-rays , is almost invariably associated with the / 3-rays , but it has generally been thought that these-7-rays are due to the expulsion of the / 8-ray from the radioactive atom . In-some cases they are certainly not due to the impact of / 3-rays on external ! objects , the 7-rays of radium C being an instance of this . Here the 7-rays come ; from the radioactive atoms , and in such amount that they effectually mask the possible production of 7-rays by / 3-rays as the experiments of H. Stark * show . Stark attempted to find whether / 8-rays did produce 7-rays.f He used for this purpose 6 milligrammes of radium bromide contained in a very thin glass tube , which let most of the / 3-rays out . The 7-rays from this ionised the air in an electroscope , the walls of which were thick enough to absorb all the / 8-rays . He looked for an increase in the ionisation when various materials were placed just behind the radium . He found practically no difference in the reading , and , from that and a similar experiment in which he deflected the / 3-rays away from the electroscope by a magnetic field , concluded that no measurable 7-radiation was caused by the ^-rays of radium C. * H. Stark , ' Le Radium , ' February , 1908 , p. 35 . t In this paper a distinction is drawn between primary y-rays and secondary y-rays . By primary y-rays are meant y-rays coming from the radioactive atom . By secondary y-rays , y-rays produced by the impact of / 3-rays on external materials .

rspa_1911_0027

0950-1207

Secondary \#x3B3;-rays produced by \#x3B2;-rays.

131

139

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

J. A. Gray, B. Sc.|Prof. E. Rutherford, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1911.0027

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1911_0027

10.1098/rspa.1911.0027

Atomic Physics

Electricity

Atomic Physics

Secondary y-Rays produced by / 3-Rays . 131 changing its position with respect to the sides of the pipe , and the water which is flowing near the centre at one part approaches the sides as it moves through the pipe , and flowing near the sides it exerts a " scouring " action on the pipe walls , thus increasing the effectiveness of the pipe surface in transferring heat . Secondary y-Rays produced By J. A. Gray , B.Sc. , 1851 Exhibition Scholar , University of Melbourne , ( Communicated by Prof. E. Rutherford , F.R.S. Received February 4 , \#151 ; Read February 23 , 1911 . ) When the cathode rays of a vacuum tube impinge on any material they produce the X-rays , which are not deviated by a magnetic field , and are much more penetrating than the cathode rays which produce them . We might , therefore , expect that when the / 3-rays from radioactive substances impinge on a plate , similar penetrating rays would be emitted from the-plate . Such a penetrating type of rays , the 7-rays , is almost invariably associated with the / 3-rays , but it has generally been thought that these-7-rays are due to the expulsion of the / 8-ray from the radioactive atom . In-some cases they are certainly not due to the impact of / 3-rays on external ! objects , the 7-rays of radium C being an instance of this . Here the 7-rays come ; from the radioactive atoms , and in such amount that they effectually mask the possible production of 7-rays by / 3-rays as the experiments of H. Stark * show . Stark attempted to find whether / 8-rays did produce 7-rays.f He used for this purpose 6 milligrammes of radium bromide contained in a very thin glass tube , which let most of the / 3-rays out . The 7-rays from this ionised the air in an electroscope , the walls of which were thick enough to absorb all the / 8-rays . He looked for an increase in the ionisation when various materials were placed just behind the radium . He found practically no difference in the reading , and , from that and a similar experiment in which he deflected the / 3-rays away from the electroscope by a magnetic field , concluded that no measurable 7-radiation was caused by the ^-rays of radium C. * H. Stark , ' Le Radium , ' February , 1908 , p. 35 . t In this paper a distinction is drawn between primary y-rays and secondary y-rays . By primary y-rays are meant y-rays coming from the radioactive atom . By secondary y-rays , y-rays produced by the impact of / 3-rays on external materials . Mr. J. A. Gray . [ Feb. 4 , His experiments show that , if 7-rays are produced , they form a very small proportion of those coming from the radioactive atom . Subsequently Davisson* * * S used a different arrangement . He utilised the property of a magnetic field , which turns the path of the / 3-rays into spirals around the lines of force , to direct the / 3-rays from some radium C on to a lead plate . He found some slight but not very definite evidence of the formation of secondary 7-rays in the lead . There are other substances , however , emitting / 3-rays , in which the emission of 7-rays is very weak compared with that observed in the case of radium C. Soddy and Russellf have shown that with specimens of uranium X and radium C of equal / 3-ray intensity , the 7-rays of uranium X are only about 2 per cent , of those from radium C. Again , Schmidt ! found that the 7-rays of radium E produce initially only 0'016 per cent , of the ionisation caused by the / 3- and 7-rays from radium E in an electroscope . Meyer and SchweidlerS found a ratio 0033 per cent. , whereas in the case of the 7-rays of radium C the ratio is about 2 per cent. Substances like uranium X and radium E are therefore much better suited for an examination of the production of secondary 7-rays . Especially is this the case with radium E , for the 7-rays , as well as being present in small quantity , are very easily absorbed by lead ( see fig. 4 referred to later , p. 138 ) . The writer , during the course of some experiments on the 7-rays from radium E , has shown that 7-rays are produced by / 3-rays . The material used was a very active preparation of radium D with its products , radium E and F , and was initially used in magnetic experiments on the velocity of the / 3-rays from radium E.|| It was provided by Prof. Rutherford , and had been separated from a large quantity of radium by Prof. Boltwood , preparatory to the determination of the rate of production of helium by radium by Rutherford and Boltwood.1T The radium D was mixed with lead , which had been added to the radium to ensure the complete separation of the radium D , so that 90 per cent , of the material consisted of lead sulphate . For the magnetic experiments , it was placed in a groove in an aluminium plate , the groove being l-2 cm . long , 04 mm. wide and deep . A sheet of mica was placed over the material , which for safety was hermetically sealed . Special care had been taken by Prof. Boltwood to * Davisson , ' Phys. Rev. , ' 1909 , vol. 28 , p. 469 . t Soddy and Russell , ' Phil. Mag. , ' October , 1909 , p. 620 . I H. W. Schmidt , 'Phys . Zeit . , ' 1907 , vol. 8 , p. 361 . S Meyer and Schweidler , ' Wien . Ber . , ' May , 1906 , vol. 115 , Abt . ii a. || Gray , ' Roy . Soc. Proc. , ' A , 1910 , vol. 84 , p. 136 . IT Rutherford and Boltwood , ' Manchester Lit. and Phil. Soc. , ' 1910 . 1911 . ] Secondary y-Rays produced by ( 3-Rays . remove all traces of radium , and an examination of the 7-rays showed that there was practically none present . The production of secondary 7-rays by yS-rays was shown in the following mannerThe aluminium plate , which was T25 mm. thick , 3 cm . long , and 1 cm . broad , was placed below the / 3-ray electroscope E ( fig. 1 ) , the active material facing downwards . Between it and the electroscope was placed a sheet of iron FE 0'6 mm. thick , a thickness sufficient to cut off the / 3-rays of radium E. The radiator PB was placed directly below the active matter , and any radiation coming from it had to pass through the aluminium and iron plates before entering the electroscope . Readings were taken with and without the radiator , the difference being a measure of the secondary radiation . Using 0T35 mm. of lead as radiator , it was found that this difference was P25 divisions per minute , the respective readings being 5'65 and 4-40 . An absorption experiment with iron sheets , 0'6 mm. thick , showed that this radiation was not due to penetrating / 3-rays , and the results are tabulated below:\#151 ; Table I. Absorber . Reading ( no radiator ) . Lead radiator . Secondary radiation . * One iron sheet 4*40 5-65 1-25 Two iron sheets 3*20 4-10 0-90 Three iron sheets 2-61 3-32 0*71 This table shows that the rays are of the same order of penetrating power as those coming from the active material . They cannot be caused by the a-rays from radium F , and are in rather too large a quantity to be scattered 7-rays from the active material , so it was thought that they were caused by the impact of the / 3-rays . The following experiment differentiated between the last two probable causes . Sheets of paper were placed just below the active matter to cut off the / 8-rays from the lead radiator . The secondary radiation was measured as before , and the results are given in the following table:\#151 ; Table II . Absorber of / 3-rays . Transmission of / 8-rays by paper . Secondary radiation . Per cent. 0 100 1 25 4 sheets of paper 54 0-75 12 sheets of paper 0*29 Mr. J. A. Gray . [ Feb. 4 , The paper can absorb very little of the 7-rays , yet it is seen that when the intensity of the / 3-rays is cut down to 54 per cent. , the secondary radiation is reduced to 0'75 , or 60 per cent. Similarly , when the intensity is cut down to 18 per cent. , the secondary radiation is reduced to 23 per cent. Most of the penetrating radiation formed in the lead plate , therefore , is due to the / 3-rays , the amount due to the 7-rays from the active matter being very small . A separate experiment , in which the yS-rays were cut off by graphite , gave the amount as 0T0 division per minute . The / 3-rays thus form 7-rays in the lead plate which , passing through the aluminium and iron plates , give a reading of IT5 divisions per minute approximately . The formation of secondary 7-rays in other materials has been examined Fig. 2 . Fig. 1 . in a similar manner . The results are given in the following table , and expressed in divisions per minute of the electroscope :\#151 ; Table III . ( -rraphibft 0 *20 Silver 0-55 Aluminium 0 *26 Gold 1 -19 Iron 0 *31 Lead 1 -25 No correction has been made for the scattered 7-radiation from the active material , which is about OTO division . The numbers show that the secondary radiation from the " incident " side of a radiator increases with the atomic weight , being roughly proportional to it . The relative effects would also depend on the penetrating power of the radiation from different 1911 . ] Secondary y-Rays produced by / 3-Rays . 135 materials . It is probably softer the lower the atomic weight , but the effects are too small for accurate measurement . The formation of these secondary 7-rays has been verified by other methods , in which the / 3-rays are turned away from the radiation by means of a magnetic field . One arrangement used is shown in fig. 2 . The electroscope E was placed above the poles of an electromagnet which gave a field perpendicular to the plane of the figure . The bottom of the electroscope consisted of sufficient aluminium and cardboard to cut off the / 3-rays , the rest being of iron 1 mm. thick . A lead radiator PB of section shown in the figure was placed below the active matter A and between the pole pieces , which were 10 cm . apart . The lead N absorbed most of the direct radiation from A. The cardboard LM prevented the / 3-rays striking the sides of the electroscope . The pole pieces were covered by cardboard . The following are the readings , M.F. referring to a magnetic field of 1000 Gauss:\#151 ; Table IY . Disposition . Reading . ( a ) Radium D uncovered , no radiator ( b ) " lead radiator ( c ) " " M.F. tending to turn / 8-rays to the left ( d ) With the M.F. in opposite direction ( e ) Radium D covered so as to cut off / 8-rays ( / ) " " M.F - 0-76 1 -12 0*77 0-98 0-76 0 *76 The difference between ( a ) and ( b gives the amount of 7-radiation entering the electroscope from the lead plate . With 5 mm. of wood , as well as the cardboard , under the electroscope , this difference was 0*32 . It is seen from ( c ) that , when a strong enough magnetic field is applied to turn the / 8-rays away from the lead plate , this penetrating radiation is not set up . Readings ( e)and ( / ) show that the magnetic field in itself has no effect on the electroscope reading . The experiment therefore confirms the result found by the other method . The presence of 7-rays on the other side of a plate struck by / 3-rays , or emergent 7-rays as they may be called , was shown as follows:\#151 ; The bottom of the electroscope E ( fig. 3 ) consisted of 1 mm. of aluminium and 1*35 mm. of cardboard . Directly below was the radiator R. The active matter was placed between the poles N , S , and 6 cm . below R. Readings were taken with and without a magnetic field . The magnetic field was of about 1000 Gauss . The results are collected in Table Y. Mr. J. A. Gray . [ Feb. 4 , Fig. 3 . Table V. Eadiator . Eeadings . Secondary- radiation . Without field . With M.F. 1 Cardboard , 2 mm. thick 4-13 3'85 0-28 2 Aluminium , 1 mm. " 3-80 3-42 0'38 3 Iron , 0 *55 mm. " 2-20 1'84 0'36 4 Lead , 0 *12 mm. " 2 -70 1 -83 0'87 5 Lead , * 0 *12 mm. " 2-09 1 -37 0'72 6 Aluminium ( / 3-rays cut off ) 3 -12 3-12 7 Iron ( / 3-rays cut off ) 1-73 1 '73 * In this case an extra millimetre of aluminium was placed between the radiator and electroscope . In ( 6 ) and ( 7 ) the same radiators were used as in ( 1 ) and ( 2 ) , but aluminium and cardboard were placed directly above the active material to cut off the / 3-rays . These readings again show that the magnetic field in itself has no effect on the electroscope reading . This table , therefore , shows the production of secondary 7-rays , the more being formed the greater the atomic weight of the radiator . In comparing ( 2 ) and ( 3 ) allowance must be made for the greater absorption of the secondary radiation in the iron . Experiments ( 4 ) and ( 5 ) show again that 1911 . ] Secondary y-Rays produced by fi-Rays . 137 the secondary 7-rays from lead have the same order of penetrating power as the 7-rays from the active material , being , if anything , harder . That these rays are not deflected by a magnetic field was shown in the following manner . The aluminium plate ( fig. 3 ) was reversed so that the active material was on the lower side . Readings were taken with a lead radiator just under the active material , and are given below . Table VI . Disposition . Eeading . 1 Lead radiator underneath 4-00 2 " magnetic field of 1000 G-auss applied ... 4-00 3 No radiator 3-17 The table shows that , when the radiator was present , there was no difference in the readings whether a magnetic field was applied or not , and thus , that the rays formed in the lead are not deflected by a magnetic field . The figures for the secondary 7-radiation from lead show that the / 3-rays escaping from the active material produce 7-rays to the extent of 25 per cent , of the 7-rays coming from the active material used . * The material with which the radium D is mixed is mainly lead sulphate . As the material is in the form of a thick layer between 0'3 and 0-4 mm. thick , only a comparatively small percentage of the / 3-rays can escape . There must , therefore , be a production of 7-rays in the material , mainly in the lead , comparable with that produced in a lead plate by the issuing / 3-rays . These results indicate that the 7-rays ordinarily observed from a preparation of radium E may be largely , if not entirely , secondary in origin ; but before coming to a definite conclusion it will be necessary to examine the 7-radiation , if any , emitted from a thin film of radium E , spread on a very thin plate of low atomic weight . Experiments in this direction are now being made . It is also intended to continue experiments with uranium X and actinium in order to test how far the 7-rays produced may be secondary in origin . It may be of interest to compare the relative / 3- and 7-radiations of radium E and uranium X. Correcting for absorption in the aluminium and iron plates , the incident 7-rays from the lead radiator PB ( fig. 1 ) would give a reading of about three divisions per minute . The / 3-rays producing them give a reading of 7500 per minute , the initial ionisation , then , due to the 7-rays being one part in 2500 of that due to the / 3-rays producing them . It has been stated above that Soddy and Russell found that the 7-rays from a specimen of uranium X were about 2 per cent , of the 7-rays from 138 Secondary y-Rays produced by / 3-Hays . radium C , the intensity of the / 3-rays from the two substances being equal . The 7-rays of radium C cause in an ordinary iron electroscope about 2 per cent , of the initial ionisation due to the / 3- and 7-rays , so that the initial ionisation due to the 7-rays from their preparation of uranium X would be about 0'04 per cent , of that due to the / 3-rays , or one part in 2500 . This is the order one would expect from the secondary 7-rays produced by the / 3-rays in the platinum on which it had been placed . The curves in fig. 4 show the results of some absorption experiments . The activity has been plotted against the mass in grammes per unit area of MASS OF ABSORBER per SQ . CM . Fia . 4 . the absorbing materials . No correction has been made for the production of secondary 7-rays in the absorbing materials , but since more of these are formed in materials of higher atomic weight , this only serves to make the differences in the curves less marked ( see Table V ) . The curves , therefore , show the much greater absorption of soft 7-rays by materials of high atomic weight than by materials of low atomic weight . In this respect the 7-rays of radium E are similar to X-rays . The results of the experiments on the secondary 7-rays are summarised below:\#151 ; On the Measurement of Specif cInductive Capacity . 139 1 . 7-rays are produced by the / 3-rays of radium E in different materials , the greater in amount the greater the atomic weight of the material . 2 . The 7-rays of radium E may be . entirely secondary in nature . At all events , the 7-radiation can be greatly increased by a suitable disposition of the material and apparatus . In conclusion , the writer wishes to express his best thanks to Prof. Butherford for his kind interest in and advice during these experiments , and also to Prof. Boltwood for the preparation of the material employed . On the Measurement of Specific Inductive Capacity . By Charles Niven , F.E.S. , Professor of Natural Philosophy , University of Aberdeen . ( Eeceived February 9 , \#151 ; Eead February 23 , 1911 . ) 1 . The discrepancy between Maxwell 's theory of refraction and the values of the specific inductive capacities of some of the commoner liquids is well known , and the idea which naturally suggests itself is that the first values deduced for these capacities were obtained by using slowly alternating electric forces , and that if the period of alternation were greatly increased , a closer approximation to the values required by Maxwell 's theory might be gained . Among other methods employed is one by Thwing , founded on the principle of resonance , in which the period of the oscillations set up in a discharging circuit , which may be called the primary , is gradually altered till it agrees with the period of another fixed circuit , here called the secondary , in inductive connection with it . When the two periods are the same , it is assumed that the value of CL is the same for both , C being the capacity of one system and L the inductance of the circuit connected with it . If we reverse Thwing 's arrangement we may suppose the primary circuit fixed and modify the secondary till resonance is got . The measurements to be subsequently recorded were obtained in this way , using Fleming 's cymometer as the adjustable resonator . In this way alternations were used whose frequency was comparable with a million per second , but the cymometer was only used to give comparative readings , the capacity of a

rspa_1911_0028

0950-1207

On the measurement of specific inductive capacity.

139

145

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Charles Niven, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1911.0028

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1911_0028

10.1098/rspa.1911.0028

Electricity

Thermodynamics

Electricity

]\gt ; The two circuits are connected inductively by the two straight conduetors AB , DE , the coefficient of induction , , between which is very small , so , though currents are set up which are apparent in the sensitive cymometer , their reaction on the primary system is probably entirely negligible . The currents in the primary discharging circuit are therefore still given by the equation the solution of which is given by , and the equation for is that given in the preceding article . If we put , we see that if and be the two values of . The current in the cymometer circuit is given by being the inductance , resistance , and capacity in this circuit ; and substituting for I If we substitute for . its value , the denominator becomes which may be , where The for is ; its amplitude , therefore , will be a maximum when is least . In dealing with this expression , we must remember that and are approximately proportional to each other , each being nerly proportional respectively inside measurement ) and cm . Its capacity in electro static units was therefore , with air as dielectric . outer sphere had two taps inserted at the top and bottom , and the lower tap was connected with a copper spiral , through which the liquid examined allowed to flow , the whole system , piral and condenser , being immersed in a large vessel containing water at a known temperature . When pure water , twice distilled , was run through the condenser , the cymometer reading gave a value for of , the temperature in the outer contaimng vessel being C. , being kept constant by filling it with a mixture of snow and water . This was compared with the cymometer reading for an air-leyden formed of nine plates of glass coated on both sides with tin foil overan area 20- cm . by 25 cm . , and separated by small pieces of glass each cm . thick . The capacity of this condenser in electrostatic units is therefore cm . The cymometer reading for this condenser was The value for , the dielectric capacity of water at ia thus given by , By varying the temperature of the surrounding water the values of may be got those temperatures . The following table is a record of some results thus obtained : Dielectric Capacity , , of Water .

rspa_1911_0029

0950-1207

Note on the electrical waves occurring in nature.

145

150

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

W. H. Eccles, D. Sc., A. R. C. S.|H. Morris Airey, M. Sc., F. R. A. S.|Sir A. W. R\#xFC;cker, F. R. S.

article

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http://dx.doi.org/10.1098/rspa.1911.0029

en

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1911_0029

10.1098/rspa.1911.0029

Meteorology

Electricity

Meteorology

Note on the Electrical Waves occurring in Nature . 145 the scale , and the readings are perhaps not so accurate as in the case of water . A new form of condenser with a larger electrostatic capacity with air would have been preferable . The following were the results obtained with this substance :\#151 ; At 12 ' C ... ... ... ... ... . . K = 24-5 " 64'*2 C ... ... ... ... ... K = 1(3-0 giving a variation between 12 ' and 64 ' of \#151 ; 0161 per 1 ' C. I have pleasure in acknowledging the assistance which I received from Mr. A. E. M. Geddes , B.Sc. , in conducting the above experiments . Note on the Electrical Waves occurring in Nature . By W. H. Ecoles , D.Sc . , A.R.C.S. , and H. Morris Airey , M.Sc . , F.R.A.S. ( Communicated by Sir A. W. Riicker , F.R.S. Received February 10 , \#151 ; Read March 9 , 1911 . ) It has often been pointed out that whenever a lightning discharge occurs between a cloud and the earth , or between two charged clouds , it must give rise to a violent disturbance of the local electrical field , which will spread outwards as an electric wave from the region of the discharge . A lightning discharge may be aperiodic or oscillatory ; accordingly a solitary wave or a train of waves , as the case may be , travels in all directions from the centre of discharge till its energy is dissipated by divergence into space or by the absorption of the atmosphere , and thus the disturbance may reach great distances . In wireless telegraphy these vagrant waves are a source of great trouble to the telegraph operator . Being often very intense pulses or trains they frequently set the receiving autenna , whatever its natural period may be , into more violent vibration than do the signals being listened for , and not infrequently they compel the complete suspension of traffic . By those engaged in wireless telegraphy , all these and similar disturbances are called , variously , " atmospherics , " " strays , " " statics , " or " X 's . " When the usual telephonic method of receiving the Morse dots and dashes is employed , the strays are heard in the telephone as sharp clicks , as rattling noises , or as prolonged grinding or fizzing sounds . There is no doubt that some of these noises are due to other causes than vagrant waves . For example , it is well VOL. LXXXV.\#151 ; A. L Dr. W. H. Eccles and Mr. H. M. Airey . [ Feb. 10 , known that wind-driven hail , snow , or rain , produce in an earthed antenna transient currents that can affect the resonant circuits and the telephone of the receiving apparatus , and other very local causes are conceivable . But the travelling waves mentioned above , it has sometimes been surmised , form a considerable proportion of the strays heard on any occasion . It is the purpose of the observations described below to settle whether the proportion of strays due to vagrant waves of distant origin is indeed of importance . If it is , then the general properties of these waves , the limits of distance through which they can travel , and their meteorological significance ( if any ) , all seem worthy of investigation . The particular point we are here enquiring into does not seem to have been investigated'before . The sum total of the work published on the whole subject is very small , and no investigations specially directed towards the discrimination of the various causes are known to us . The study of these natural electric waves was begun by Popoff shortly before the rise of practical wireless telegraphy . In 1895 Popoff* * * S made use of a long vertical conductor ( such as a lightning rod ) in combination with a coherer in order to follow the motions of lightning storms through the atmosphere . A filings coherer was used and was automatically tapped back after registering the effect of each lightning stroke . In 1898 Boggio Leraf improved on Popoff 's apparatus as regards sensitiveness , and arranged that feeble and strong disturbances should be recorded separately . His experiments with this apparatus in 1899 showed that the approach of electrical storms was heralded by frequent operation of the apparatus several hours in advance of their arrival in the locality of the observing station . These results were confirmed by TominasinaJ in 1900 , using his carbon autocoherer . In 1901 FenyiS showed that the thunderstorms occurring within a radius of 100 kilometres of his station at Kaloska , Hungary , were all recorded by his coherers . Finally , Turpain , || in 1903 , made a long series of observations that proved the possibility of utilising these radio-telegraph apparatus and methods in the forecasting of thunder weather for hours and even days in advance . We may remark at this point that the occurrence of numerous strays at a particular station is not necessarily followed by a thunderstorm in the locality\#151 ; the storm may pass wide of the station . As a fact there are few days at any wireless telegraph station without its * Popoff , 'Journal of Russian Physico-Chemical Soc. , ' 1895 , vols . 28\#151 ; 29 , p. 899 . t Boggio Lera , ' Atti della Accademia Gioenia di Scienze di Catania , ' January , 19 00 . X Tommasina , 'Comptes Rendus , ' November 25 , 1900 . S Fenyi , 'Comptes Rendus , ' January 27 , 1902 . || Turpain , " La T616graphie sans Fil , " p. 314 . 1911.1 Note on the Electrical Wav 147 burden of strays . Whether these are due to very distant lightning strokes , or to extra-terrestrial causes , is a problem as yet unsolved , and is indeed one of the points to whose elucidation our own observations are tending . The plan of attack adopted by us in these preliminary experiments was as follows:\#151 ; One of us in London , and the other in Newcastle , arranged receiving apparatus just as for the telephonic reception of wireless telegraph signals . Then we listened , at times agreed upon , to the strays that happened to he audible . We recorded the principal atmospherics by an agreed system of pencil marks on paper which was ruled so that 6 inches represented a minute , each stray being recorded in its proper position on the paper by aid of the seconds hand of a watch . The period of recording was about half an hour , and was usually arranged so as to terminate or begin at or uear a time when a regularly working long-distance transmitting station , such as Poldhu , Norddeich , or the Eiffel Tower , started or finished its signals . The time signals from the two last-named stations proved exceedingly useful . In this manner a fairly perfect time correlation was established between the records made by the two observers . The observers exchanged " carbon " copies of their records , and made independent comparisons of them . Fig. 1 is a reproduction of a portion of such hand-made records Ik A . \#171 ; A d A / k* a A. K ft AA Av f\ A A A. a. . X ONDO K m A A Ia Aa Jl. . AM MiAfV IM A ft A M A M NEWCASTLE -/ w M U K ^_ _ A Fig. 1 . JL A/ L a X ONE ON m Mw . ^ ( V\#187 ; , M A. A ^ A h ^ ! L . * Mfau Aaa NEWCASTLE Fig. 2 . obtained on a day when there were many loud strays ; fig. 2 shows records of a less crowded day . It should be explained that the height of the mark above the datum line represents the intensity of the sound in the telephone as judged by the ear of the observer . The record may be described as a rough endeavour to chronicle graphically the strength of the strays as ordinates with the time as abscissae . A comparison of the records shows that many of the marks made by the two observers coincide in time and , besides , bear a strong likeness to one another . Other marks , again , bear great likeness , but are recorded as belonging to slightly different instants of time . This last remark gives point to the principal weakness of the method , namely , that large errors may be Dr. W. H. Eccles and Mr. H. M. Airey . [ Feb. 10 , made by each of the observers in deciding quickly the exact point of the axis of time at which to make the mark representing a stray . In consequence , reasonable allowance must be made for these personal equations in counting the number of coincidences . Table I is a summary of our results . This table gives the total number of strays recorded in London ( M ) , the total number in the same time at Newcastle ( N ) , and the number of coincidences ( Ci ) between marks that possess a decided similarity . The column headed " Percentage of coincidences " gives the percentage proportion that the number of coincidences Table I. Date . Duration of record , in seconds . London . M. Newcastle . N. Coincidences . . Cv Percentage of coincidences . 1910 . July 26 560 57 ( 1000 ) 52 ( 2000 ) 27 52 " 26 640 62 ( 2000 ) 53 ( 2000 ) 26 49 " 26 540 46 ( 2000 ) 50 ( 1000 ) 20 44 Aug. 24 1360 293 ( 2000 ) 382 ( 2700 ) 227 77 " 25 1680 293 ( 2700 ) 353 ( 2700 ) 197 67 " 26 1720 282 ( 2700 ) 420 ( 2700 ) 205 73 " 31 895 184 ( 40a ) 196 ( 2700 ) 106 58 5 ) 660 158 ( 2700 ) 160 ( 2700 ) 98 62 Sept. 1 955 175 16000 ) 245 ( 2700 ) 122 74 " i 665 120 ( 2700 ) 185 ( 2700 ) 96 74 " 8 840 96 ( 2600 ) yD ( 2800 ) 234 ( 600 ) 72 75 " 8 780 102 ( 2600 ) ( 2800 ) 210 ( 2700 ) 72 71 " 9 1660 300 ( 2700 ) 346 ( 2700 ) 191 64 " 1+ 1652 356 470 ( 2700 ) 289 81 " 16 980 229 ( 6000 ) 299 ( 2700 ) 151 69 " 16 603 105 ( 2700 ) 177 ( 2700 ) 67 65 " 22 1700 331 ( 2700 ) 312 ( 2000 ) 204 65 Bracketed numbers refer to the wave-length expressed in metres . bears to the smaller of the two numbers M or N. The figures in brackets show in metres the wave-lengths to which the receiving apparatus was tuned at each station . From these latter figures it will be seen that both the antenna and its associated resonant circuit at one station were normally tuned to the same wave-length as the two circuits at the other station , but sometimes the antenna and resonant circuit at one station were , tuned to a wavelength different from those at the other station , and on a lieu occasions the antenna and resonant circuit at one and the same station had different wave-lengths . Broadly speaking these differences in the adjustments ot the receiving apparatus had little perceptible effect on the number of coincidences afterwards found in the records , which indicates that the vagrant waves come in very short trains or as solitary waves . 1911 . ] Note on the Electrical Waves , 149 To meet a possible objection to the above method of analysing the records , we give in Table II the results of analysing in a manner which purposely takes no cognisance of the fact that strong resemblances exist between individual strays . Let T be the duration of the record at both stations in seconds , and suppose that M/ T and N/ T are small compared with unity , then the chance of one of the M marks falling within a time L/ 2 on either side of any assigned mark is LN/ T. This being true of every one of the M marks , provided that the time L rarely includes two of the M or of the 1ST marks , the probable number of coincidences in a random distribution of marks is therefore LMN/ T , a " coincidence " being defined as the occurrence of two marks with a time L/ 2 or less between them . Now , if any of these coincidences are due to the operation of the same cause , as , for example , a distant lightning flash , these ought to be excluded from the application of the above formula . Let their number be X. Let the number of observed coincidences be C. Then the chance coincidences are C \#151 ; X. But the random marks are M \#151 ; X and N \#151 ; X respectively ; and by the above formula the chance coincidences are in number L(M \#151 ; X ) ( X \#151 ; X)/ T. Equating this to C \#151 ; X , we get the quadratic equation , X3+{T\#151 ; ( M + N ) }X\#151 ; ( CT-MN ) = 0 . This has a positive root , which is the probable number of atmospherics due to the same lightning stroke or discharge . The number thus obtained is offered merely as a rough estimate ; the assumptions on which the formula is obtained are , of course , not strictly fulfilled . In Table II , the results of applying the formula are set out . There are columns headed C and X that did not appear in Table I. The latitude L Table II . Date . 1 Duration of record , in seconds . London . M. Newcastle . N. Coincidences . C. X. Aug. 24 1660 293 I 382 254 249 " 25 i 1680 293 353 220 212 " 26 1720 282 420 218 210 " 31 895 184 196 108 100 \#187 ; 31 660 158 160 101 96 Sept. 1 1620 295 430 224 213 " 2 1620 347 334 152 121 , , 8 1630 198 444 149 137 " 9 1660 300 346 201 189 \#187 ; 14 1590 356 470 294 287 " 15 1650 349 337 189 171 " 16 1628 334 476 231 211 \#187 ; 22 1695 331 312 235 230 VOL. LXXXV.\#151 ; A. M 150 Note on the Electrical Waves occurring in Nature . allowed in counting coincidences was 1 second . It will be seen that almost the same conclusions are reached by this method of analysis as by the method of counting only strays wdiose graphs display some resemblance . All the above observations , excepting those of July 26 , in Table I , were made during the half hour between 12.30 midnight and 1 a.m. ; those of the date named were made between 10.30 and 11 a.m. From a large number of forenoon observations , such as those of July 26 , we concluded that it was best to work at night . This fact may be in some part due to the " strays " produced , possibly , by electric trains and trams or other local users of large currents . Neglecting these daytime observations , the conclusion to be drawn from the above tables of results is that between 60 and 80 per cent , of the atmospherics audible at Newcastle and London , about 270 miles apart , are due to the same cause . This cause is probably a discharge of atmospheric electricity at places whose distances from the stations are possibly of the order of several hundreds of miles . We consider that these preliminary experiments are sufficiently encouraging to justify our extending the work by adopting automatic recording apparatus and by enlisting the aid of other wireless telegraph stations . The Newcastle observations were made partly at the Armstrong College and partly at Cullercoats . We take this opportunity of thanking the authorities of the Amalgamated Radio-Telegraph Company for permitting us to use their Cullercoats station for the purpose of the experiments described in this communication .

rspa_1911_0030

0950-1207

A theory of the chemical action of the electric discharge in electrolytic gas.

151

174

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Rev. P. J. Kirkby|Prof. J. S. Townsend, F. R. S.

article

6.0.4

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10.1098/rspa.1911.0030

Electricity

Atomic Physics

Electricity

]\gt ; necessary to determine the chemical activity of the positive columns of various discharges . Thus the experiments recorded in this paper chiefly deal with positive lumns and were undertaken to determine simultaneously both the chemical activity and the electric force within positive columns corresponding to different currents and pressures . The Apparatus . The scheme of the apparatus is shown diagrammatically in fig. 1 . The mixed gas was generated . in the closed vessel by the electrolysis was a D'Arsonval galvanometer such that the corresponding to a deflection of the spot of light through about 67 mm. was ampere , which was the order of the currents used ( see Table I previous values , since the positive column contributes to the total chemical effect an amount proportionate to its length . It was determined as a cation of the other two values and will help to indicate their accuracy , but was not used in deducing the chemical activity of the positive column . Results of the Experiments . The values of , determined in the manner just described , with.two or more rent distances between the electrodes , but the same current are given in Table I for various pressures . The significance of depends of course upon the cubical capacity of the part of the apparatus where the falls of pressure produced by the current took place , viz. , the part to the right of the tap , fig. 1 . This capacity was , or rather it varied within about per cent. of this value , changing slightly with the barometer and with the of the rod supporting the anode above the mercury . It is , however , convenient to express the results absolutely , i.e. independently of the apparatus . This might be done by multiplying by 1000/ 474 so as to give the fall of pressure per coulomb that would take place in an apparatus of capacity 1 litre . But the simplest course , in view of the subsequent discussion , is to find how many molecules of water vapour*are formed by the passage through the gas of the atomic quantity of electricity , namely , the charge carried by a negative ion . This number is denoted by W. Now it is easy to show that approximately For if is the number of molecules in 1 . of gas at 760 mm. pressure and temperature , and the charge on an ion ip eleotrostatic units . It follows that . is a function of , and that the relation between these two variables is independent of the current , for the current was arbitrary and varied by several hundred per cent. , while the points plotted in fig. 4 fall upon the curve within the limits of experimental error . This result proves definitely that the observed chemical effects in the positive column are not directly due to recombination*of ions , for the number of recombinations per cubic centimetre would increase with the square of the current , since the force and therefore the velocity of the ions are very little affected by the current . It also proves that these chemical effects are not due to any internal radiation , such as perhaps the " " entladungstrahlen set up in the positive column by the recombination of ions , for the intensity of such a radiation would probably be proportional to the of the current , and certainl could not have a chemical effect dependent only upon the quantity of electricity passed the gas . Another result , which is quite independent of any theory of the chemica : According to this theory , then , , which was defined to be the number ' molecules of water vapour formed by.the transit of the atomic charge through 1 cm . of the positive column , becomes the number of molecules of water vapour formed by the motion of a negative ion through cm . , where , are the velocities of the negative and positive ions in the column . Now is quite negligible in regions where the ratio of electric force to pressure is so great as in the positive columns of Table Therefore the theory makes the number of water-vapour moleoules formed by an electron 's motions through 1 cm . ; and it remains to show that the observed values of are connected with those of and as the theory requires . In what follows it is assumed that . owing to their very small mass the electrons are brought practically to rest by their colJisions with the gas molecules . It is also assumed ( an assumption usually made and easy to justify ) that the fields of force here considered impress such a bigh velocity upon the electrons that the gas molecules may be considered relatively at rest . Now the collision of an electron with a molecule of oxygen cannot have the effect of separating the atoms unless the energy of the electron at collision exceeds the energy of formation of the oxygen molecule , which will be denoted in this paper by ergs . But besides this condition it is natural to suppose that the electron will not dissociate the molecule unless it collides with a certain minimum velocity . I Let Yolts represent the potential difference through which the ion must fall to acquire this velocity , then being the charge in electrostatic units of the electron . Hence in a field of force , volts per centimetre , the electron must traverse a free path of or more before colliding with an oxygen molecule if it is to acquire the T. Lattey , ' Roy . Soc. Proc , 1910 , . His numbers make ] when this ratio is . Hence , when is so large as in Table I , is smalL Cf . J. S. Townsend , ' Phil. Mag February , 1901 , Inethd is here genesis of uncharged atoms from the of oxygen by the impart of the apparatus and not confined to positive columns but existing been the chemical effects of . an electron 's motion , through electrolytic gas and in any field of electrostatic force , and and is true that special conditions prevail in the positive column where these effects have been observed , and that a certain amount of recombination may be going on , so as to terminate the course of a percentage of electrons that traverse it . That percentage is , however , probably* ble ; and in any case , ions are produced at exactly the same rate as they disappear , since everything is quite steady , so that the mean chemical effects attending the passage of the atomic charge through 1 cm . of the positive column must be the same as though that charge was carried by the same , electron . Thus there is no reason to suppose that the relation ( 10 ) between , in the positive column would not equally exist anywhere else where there may be an electrostatic force Deduchons from the Theoretical Equation . The equation leads to several results which will now be deduced . ( 1 ) to the Energy of Formatim of an Oxygen Molecule.\mdash ; Since and by equations ( 8 ) and ( 7 ) , therefore V volts . That is , an electron must fall freely through at least 4 volts to acquire sufficient velocity to dissociate by impact an oxygen molecule into atoms . Hence by the inequality ( 1 ) , the energy of formation of an oxygen molecule , is less than ergs , the charge of an electron seems to be nearly electlostatio units ; and since the present theory assumes that the electron is practically stopped by its collisions , so that nearly all its energy is imparted to molecule struck , the limit , ergs , should be fairly near to : actual value of . This estimate is independent of quantity of walo the hydrogen to the nascent or atomic state , would not be suffloient t produce more than molecules of water vapour . On the other hand see ation ( an electron in moving through 1 cm . of electrolytic gas at 1 mm. pressure makes oollisions with molecules , so that if only 4 out of these collisions dissociated the moleenlae into atoms , there would still be enough detached oxygen . atoms for the . production of the molecules of water . It follows from these considerations that an atom of oxygen is capable of uniting directly with a molecule of hydrogen . In other words , if the atoms in a hydrogen molecule need to be relatively displaced previous to formation of water , such a displacement can be effeoted by the colIision of , the free atom of oxygen . This conclusion is supported by the form of equation , which requioea that only one of the gases need be brought to the active state . For if the hydrogen had also to be atomised by ionic impact , the amount of water vapour would be proportional to the product of and a similar term applicable to hydrogen ( see equation . Henoe would constants ) , and would be a function of : the latter result inconsistent with one or two observations in this aird the last paper , and former does not appear to be reconcilable with the rest . ( 3 ) Energy of Formation of a Molecule of Water Vapour.\mdash ; From the previous conclusions ( 1 ) and ( 2 ) it is possible to form an estimate energy of formation of a lecule of water vapour . For , as -well know4 1 . of hydrogen , uniting with oxygen to produce water laboratory temperature , liberates 29,000 calories of heal , that molecule into ions . It follows from the numerioal results that the collision might at once both atomise and ionise a molecule ; another consioq might have either of these two effects without the according to the velocity and other circumstances of the impact . For the works required to ionise a molecule of a gas , except in peculiarly favourable circumstances iouic impact , is much greater than the work needed to dissociate a molecule of oxygen into atoms : , and , on the other hand , ionisation may occur at every impact , if the velocity is great enough , but not dissociation into atoms . Again , since positive ions have also the power of iomsing molecules by collision , il is highly probable that they can perform the task , lighter in respect of work to be done , of breaking up of oxygen into atoms , if they ars moving in a strong enough field of force . Thus it is possible that the great chemical activity in a discharge across the cathode fall may be the work of the positive ions , though there is no direct evidence of this . With regard to other reactions produced by an electric discharge , it is natural to assume that the part played by it in promoting chemical action the same . The collisions of the ions , probably both kinds , with the molecules of gas bring the gas into the active state , either by dissociating or displacing the atoms , so that it can form new comb.inations . It follows that different chemical products might be formed in the same gaseous mixture by the motion of ions under different fields of force . This theory does not dispense with the postulate of chemical forees acting vely , only explains how the discharge prepares the way for their action . On the contrary , it was pointed out above that the experimental results , quite independently of theory , lead certainly to the conclusion the atoms of oxygen when separated are not charged electrically . so it is necessary to postulate some other force that binds them into a molecule . The connection between , and , expressed in equation ( 4 ) , owes its form partly to the fact involved in the theory that only one of the constituents of electrolytic gas viz. , oxygen has to be brought to the product would not be detectable . It is only in the case of very much larger currents , such as those maintained through a gas by a battery , or obtained by connecting the electrodes to the secondary terminals of a Ruhmkorff coil , as in the case of the silent discharge , that a sufficient number of effective collisions are made by the ions traversing the gas to produce a measurable effect . of Principat Conclusions . ( 1 ) When a steady discharge passes through electrolytic gas at pressure mm. , the number of molecules of water vapour formed by the passage of the atomic charge through 1 cm . of the positive column , where the electric force is , is approximately . This number , which is independent of the current , appears to be absolute ( i.e. independent of the apparatus and -not confined to positive columns ) and to depend only upon the field of force . ( 2 ) The atoms of oxygen , when separated , are not charged electrically . This is proved by experiments independently of theory . Hence the atom of oxygen is not bound in a molecule of water vapour by electrostalic force . ( 3 ) The chemical effects , within the positive column , are due to the collisions of the ( corpuscular ) negative ions with the oxygen molecules , which are dissociated into atoms , under certain conditions , by those collisions ; and so enabled to combine with hydrogen . ( 4 ) The energy of formation of an oxygen molecule is less-than ergs , and is nearly equal to ergs . ( 5 ) Water vapour produced by the collision of an atom of oxygen with a molecule of hydrogen . ( 6 ) The energy of formation of a molecule of water vapour is nearly ( 7 ) Only half the collisions that an electron makes with a molecule of

rspa_1911_0031

0950-1207

Atmospheric electricity over the ocean.

175

199

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

G. C. Simpson, D. Sc.|C. S. Wright, B. A.|Arthur Schuster, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1911.0031

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1911_0031

10.1098/rspa.1911.0031

Meteorology

Electricity

Meteorology

]\gt ; 8 Dr. G. more fundamental cause . It is possible that the daily range of the potential-gradient is dependenton latitude . Our observations on the sea were all obtained within about of the Equator , and they show in common with land observations within the same latitudes a predominant minimum at about mid-day ; in higly latitudes land observations show the predominant minimum at 4 , while between these two extremes we have the two minima occurring ether , but with varying relative intensities . May not therefore the afternoon minimum be of equal importance with the morning one , instead of being a disturbanoe caused by dust-changed convection currents ? If this found to be the case , then the 4 . minimum may be considered the polal minimum and the mid-day one the equatorial minimum . Non-periodic Changes.\mdash ; With regard to minor fluctuations of the gradient it may be remarked that just as is the case over the land the . potential over the sea undergoes changes from minute to minute . As . an example , the following readinga taken at minute intervals from 14 . to 14 . on , have been extracted haphazard from our notebook ; at the time the sky was cloudless except for a few small cumulus clouds on the horizon : , 30 , 40 , 47 , 43 , 57 , 50 , , 31 , 35 , 47 , 30 , , 35 . The effect of rain was found to be the same on the sea as on the land . As the rain approached the potential-gradient generally decreased , and during one period of steady rain , negative potential-gradient was noted . When , however , the rain was associated with a squall the potential-gradient took large values , which changed rapidly from one sign to the other just as it doea during a thunderstorm on land . It will be noticed that over the Atlantic in both hemispheres the emanation increases from latitude towards the Equator , but in the equatorial itself , i.e. within of the Equator , the emanation has a low . The explanation of this interesting observation may probably be as follows:\mdash ; Between and in both hemispheres a belt of high pressure is situated in which air descends to feed the trade winds blowing towards the low pressure near the Equator . The air descending from above must be almost free from emanation owing to the short life of the latter ; this no doubt accounts for the low values of A measured between and . As the air travels towards the Equator over the sea , it takes up emanation from the sea-water , so that the emanation content will inclease in amount as the air gets further away from the place where it descended . As soon , however , as the air reaches the Doldrums it.becomes thoroughly washed by the frequent heavy showers of rain , and in consequence smanation decreases long and cm . in diameter , and fits directly on to a Wulf electrometer . The aspirator is of the usual form supplied by this firm . When working , litres of air pass the condenser in a minute , the electrical capacity of the condenser being cm . According to the makers it is my necessary for the instrument to run for 5S minutes in order to get a satisfaotory determination of the ionisation . Experience showed , however , that a really satisfactory observation could not be made under 33 minutes , and most of our observations extended to 44 minutes . Our usual method was to charge the instrument with positive electricity and leave it for half am hour or so without the aspirator running in order to determine the insulation , leak . The aspirator was then set in motion and when the bell attached to the revolution counter rang a reading was taken . After each 2500 turns of the fan the bell rang again , and the instrument was wound up . After the bell had rung six times ( about 11 minutes after starting ) a reading of the electroscope was taken . The observation was continued for another similar interval and then again for a third . Ifjthe three readings were in good agreement , the instrument was discharged and recharged with negative electricity . If , however , the readings did not agree well the observation was continued for a fourth intervaL In the same way a measurement was made with a negative charge on the condenser , and afterwards the observation with positive charge was repeated . Thus each complete observation ( leaving out the period of insulation test ) extended over a period of between 1 . and 2 . Only those observations have been used in the following discussion in which the complete sequence as just sketched was carried out . With the Wulf electroscope good observations were possible even when the ship was rolling to a considerable. . extent . Owing to unforeseen difficulties , satisfactory determinations of the 2 ) the large amount of spray and salt might decrease the total ionisatiou , just as fog and dust have been proved to do . A division of the : acoording to wind strength indicates the latter effect , for , as the following table shows , both the ionisation and ths ratio are less with high wind ' than with light winds:\mdash ; The value of the ionisation measured on this voyage agrees fairly well with the only two other sets of observations made over the ocean . Eve , in a journey from Canada to England , *ffiuud I and . Boltzmann found over the Atlantic Ocean The ionisation over the land is so dependent on meteorological conditions that it is difficult to choose data to compare with our results . Perhaps the most suitable are those of one of us observed in Karasjok , in Lapland . At that place the ionisation was found to depend very largely on temperature and the results of observations at temperatures comparable with those encountered on the " " Terra Nova\ldquo ; are shown in the following table:\mdash ; Karasjok ( Lapland ) . of the ionisation current . As the rate of decrease during the second hour was always appreciably the same as during the no correction has been applied for defective insulation . FIG. 2 . }

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On the ionic solubility-product.

200

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Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

James Kendall, M. A., B. Sc.|Prof. James Walker, F. R. S.

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10.1098/rspa.1911.0032

Biochemistry

Chemistry 2

Biochemistry

]\gt ; On the Ionic Solubility-product . By JAMES KENDALL , M.A. , B.Sc. ( Vans Dunlop Scholar in Chemistry , University of Edinburgh ) . ommunicated by Prof. James Walker , F.R.S. Received February 16 , \mdash ; Read March 9 , 1911 . ) The theory of a constant ionic solubihty-product was first advanced Nernst , * from the analogy of the laws governing dissociation in gasea According to the principle of mass action , if the dissociation pressure of a system in equilibrium be changed by the introduction of an excess of of the dissociated gases , combination takes place between them unhl equilibrium is restored . Thus , on the addition of either or HC1 to a system consisting of ammonium chloride in equilibrium with its dissociation products , ammonium chloride is produced . For each temperature , the product of the pressures of and HC1 is a constant . Similarly , : Nernst found that the solubility of an electrolyte in water was reduced by addition of any salt containing a common ion . The variations in the solubility of silver acetate ( a sparingly soluble salt ) in water knoWn amounts of silver nitrate or sodium acetate were investigated , results obtained confirmed the view that a corresponding equilibrium law was here applicable . If we confine ourselves to substances of the simplest , type , the law may be stated thus : " " At a given temperature the solubility . of a sparingly soluble electrolyte is dependent upon a constant , hich is proportional to the product of the of the ions of the electrolyte The fundamental assumption made in the application of this law is that in a saturated solution of an electrolyte the undissociated salt in solution plays the part of an intermediary even the ions and the solid , being equilibrium with the ions on the one hand and with the solid on the othgr. . Consequently , so long as the solvent remains the same , the concentration the undissociated salt is constant , however much the ionic lations in subsequent experiments . With picric and methyl picric the end point was at firsb difficult to distinguish , owing to the disturbiqg colour , but after some practice the first permanent change of tint could be detected quite accurately by using a comparison solution . In most cases the saturation point was soon reached ; methyl picric acid , however , attained its full value only after two months , picric acid not even then . It was found that the presence of a few drops of ligroin or benzenr in the solution shortened the necessary time for methyl picric to a few days , but the end points reached differed from that obtained with pure water . Ligroin , in which the acid is moderately soluble , increased its solubility by 2 per cent. ; benzene , in which it is freely soluble , by 6 per cent. A considerable difference was thus caused by the presence of the extremely small amounts of each in solution in the water . This is note worthy in view of results afterwards obtained . In Table I below the concentrations of the saturated solutions of the acids are given in normalities ; from these , by means of the dissociation constant , the solubility-product and the " " constant value\ldquo ; of each acid are obtained . The above values for the molecular conductivities of the acids are in general greement with those given for picric acid by Ostwald* and Bothmund ; f but the degree of error may be fully 1 per cent. This would affect degree of dissociation to the same extent ; but , by trial from the equations , it was found that an errot of 5 per cent. was required to affect the solubility determinations , afterwards made with the acids , beyon.d the limits of , experimental errol . The conductivities were determined with a rotating commutator and galvanometer , more satisfactory results being obtained with this apparatus than with the usual induction coil and telephone , especially for the more dilute solutions . In the determination of the solubility of one acid in the presence of. . another , the method of procedure was exactly similar to that already described for single acids . The experiments were of two classes : in the first , two solid acids were taken with water ; in the second , one acid was present as a solid , the other as a solution in water of known strength . In all cases the end point was quickly reached , even methyl picnc , in the presence of another acid , attaining the steady state in a few days . The first investigations were of the simplest type , the two aoids obeying Ostwald 's dilution law . Of these , salicylic and -nitrobenzoic acids are good examples , and a full series of experiments with these two acids was carried out , the results of which are shown in Table II ( p. 207 ) . Since they serve to illustrate the other cases , they are commented upon in detail . It will be seen that the amount of acid in solution is in every case in excess of the theoretical . The divergences in Sections and increase with the strength of the original solution taken , and the greatest divergence is obta.ined in Section , where both acids are present in the soIid form . All the differences are far beyond the limits of experimental error . There are , however , some small corrections to be made in the above The results are given in normalities , whereas to be strictly comparable 208. . The " " effective\ldquo ; correction is thus , even in the last case , only . This is less than per cent. of the whole titre . In Sections and of Table II it will be seen that not only does the divergence from theory increase with increase of concentration , but . that , the actual amount of acid dissolved , instead of decreasing , at first rapidly and then more slowly , as demanded by the theory , either shows an increase or becomes practically constant . The divergences from theory are therefore fundamental . The result of another experiment will show this more A saturated solution of -nitrobenzoic acid , of strength , free from solid , was added to solid salicylic acid and shaken in the thermostat until constant . strength was now N. the concentration of the hydrogen ion had been increased , the solution should be supersaturated with respect to -nitrobenzoic acid . But on solid -nitrobenzoic acid to the solution , and shaking again until the titre was constant , the concentration rose to , i.e. the solution was not supersaturated , but unsaturated . A comparison of the three results of Sections , and is int.eresting . The concentrations of the solutions originally taken in and are , as nearly as possible , those shown by A to be ' theoretically , saturated in presence of the other acid . The final titre should therefore be the same in all three cases . Instead of the theoretical value of however , the three values obtained are , and respectively , which differ widely not only from the theoretical value bul also from each other . The presence of solid acid allows excess beyond theory to be dissolved ; this is allowed in the case of both acids in , in the case of -nitrobenzoic only in , and in the case of salicylic only itive divergences . in all cases within error limits of the theoretical result- A typical loriea ot corrections is given in Table IIIA . Table IIL\mdash ; Remaining Experiments with Two Weak Acids . The " " effective\ldquo ; correction is only at the greatest concentration . This is less than per cent. of the whole titre . In the next table there are given the results of experiments with two strong acids . For the calculation of the theoretical results the following table of dissociation values for hydrochloric acid was used : , The dissociation values of picric and methyl picric acids at various dilutions have already been given . Table \mdash ; Experiments with Two Strong Acids . Here also divergences from theoretical results are obtained ; negative in the case of methyl picric and hydrochloric , positive in the case of methyl picric and picric acids . Table V gives examples of weak acids ( salicylic and -nitrobenzoic ) Mr. J. Kendall . The differences in Table VI are all large and positive . that methyl picric acid is more soluble in salicylic acid solutions than pure water . In none of the above tables is the theory exactly followed , and a further experiment was performed , to ascertain whether the divergences obtained were superposable . A known solution of hydrochloric acid was taken , and two weak acids ( salicylic and -nitrobenzoic acids ) added : The differences to be expected from theory estimated by interpolation from the results of the preceding tables , and compared with the difference experimentally 'obtained . Table \mdash ; Two Weak Acids in Hydrochloric Acid Solution . The following divergences were to be expected ( see Tables II and ) ( o ) Due to solid salicylic and solution of -nitrobenzoic N. Due to solid -nitrobenzoic and solution of salicylic N. ( c ) Due to solid salicylic and solution of hydrochloric N. ( d ) Due to solid -mitrobenzoic and solution of hydrochloric N. The solution should therefore be approximately of theoretical strength if the various differences are superposable . Seeing that the accuracy of a large number of experiments is inyolved in the values of the expected divergences given above , the experimental result agrees with this supposition well within the limits of error . A general consideration of the results in Tables II to VII shows that the theory holds strictly in none of the possible combinations of acids . It makes no difference whether they are both weak , both strong , or one of each type ; similar ergences of several per cent. obtained in every oaae . And these divergences , though usually numerically small , are that of the acid dissolved , in which latter small variations were impossible to measure . The method employed was that of evaporation . The solutions were . prepared in the same manner as already described , 25 . of the liquid pipetted out into a weighed evaporating dish , and evaporated down to dryness . The amount of the dissolved solid was then found by weighing , and its titre in the solution directly calculated . The case investigaM were :\mdash ; ( a ) In solutions of formic acid : Salicylic acid , hippuric acid . ( b ) In solutions of acetic acid : Salicylic acid . ( c ) In solutions of : Salicylic acid , -nitrobenzoic acid . utions c hippuric acid could be evaporated down on steam-bath without loss of solid by volatilisation ; those containing salicylic . and -nitrobenzoic acids , since these proved to be more or less volatile with steam , were allowed to evaporate slowly at the ordinary temperature . The residues obtained weighed from to of a gramme ; the limit in the latter case is per cent. Experiments performed in duplicate gave results agreeing together within this limit , and the results of this method , as tested with some of the more dilute solutions , were closely concordant with those obtained volumetrically . The results obtained are shown in both tabular and graphic form . Some volumetric determinations are also given in the tables , both for the purpose . of comparison with the gravimetric results and for use in the accompanying curves . Results are expressed , as before , in normalities . The corrections in the volumetric determinations , although much here owing to thu greater concentrations of the solutions used , are not apply \amp ; That due to . oduct . \fnof ; g Acid . Acid . ( a ) An undissociated portion ( below the line ) , increasing or decreasing : regularly , according as the acid is more or less oluble in the solvent acid : than in water . ( b ) A dissociated portion above the ecreasing more or kss rapidly . according to the ionic strength of the solvent acid . This decrease is not regular , but is proportionally greater the less concentrated the solution is , falling off as the dissociated portion is suppressed by increase of concentration . The solvent effect , acting directly upon the undissociated portion , will also indirectly affect the dissociated part of the substance in solution , since this must remain in equilibrium with the undissociated part . In the curves given , the acids exist in solution mainly in the undissociated state , hence this indirect effect is but small , and soon becomes negligible with increase of concentration , to the almost total suppression.of the ionised part . In solutions of strong electrolytes , however , the indirect may be greater than the direct effect ; hence the solubility curves in such cases will not..-finally approximate to lines which cut the axis , when produced backwards , at or very near to the " " constant undissociated value The case of salicylic acid in solutions of acetic acid is another example of the inapplicability of the rule in the eYent of the ionised portion persisting appreciable quantity at all concentrations of the solvent acid , The experimental diyergences obtained from the . values indicated by the theory of the constant solubility-product can thus be accounted all cases by this solvent effect . The divergences , positive or negative , are :

rspa_1911_0033

0950-1207

Bakerian Lecture.\#x2014;A chemically active modification of nitrogen, produced by the electric discharge.

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229

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Hon. R. J. Strutt, F. R. S.

lecture

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10.1098/rspa.1911.0033

Thermodynamics

Atomic Physics

Thermodynamics

A Chemically Active Modification of Nitrogen . 219 determination must be uncertain , since a wide variation in the assumed degree of dissociation corresponds in most instances to a very small change in the solubility , any decrease in undissociated substance dissolved being almost entirely balanced by an increase in dissociated , and vice versa . This fact explains also why , although the degrees of dissociation of the strong acids used in the above research are not yet accurately determined , being liable to an uncertainty of several per cent , in dilute solutions , the solubility results of other acids with them , as calculated from these values , are subject to a much smaller degree of error . In conclusion , I have much pleasure in expressing my thanks to Prof. Walker , at whose suggestion and under whose direction the above research was carried out , for his advice and assistance during the whole period of its execution . Bakerian Lecture.\#151 ; A Chemically Active Modification of Nitrogen , Produced by the Electric Discharge . By the Hon. B. J. Strutt , F.B.S. , Professor of Physics , Imperial College of Science , South Kensington . ( Received March 16 , \#151 ; Lecture delivered April 6 , 1911 . ) [ Plate 8 . ] . ) , \#166 ; UP S 1 . Afterglow It is known that vacuum tubes frequently show a luminosity of the\gt ; contained gas after discharge is over . In a previous paper* I was able to show that this effect , as it occurs in air , is of the nature of a phosphorescent combustion , and is due to the mutual reaction of nitric oxide and ozone , each formed in the discharge . In a second paperf it was shown that other phosphorescent combustions can be observed in ozone , notably of sulphur , sulphuretted hydrogen , acetylene , and iodine . Some of these give continuous spectra , but the majority band spectra . In the first paper it was stated that pure nitrogen gives no afterglow whatever , and , with the simple induction coil discharge with which I was then working , this has been frequently verified since . Mr. Percival Lewis has however , described an afterglow obtained in nitrogen when a jar * ' Phys. Soc. Proc. , ' Dec. 15 , 1910 , vol. 23 , p. 66 . t Ibid. , Feb. 15 , 1911 , vol. 23 , p. 147 . Hon. R J. Strutt . A Chemicallij [ Mar. 16 , discharge with spark-gap is used.* I had no difficulty in obtaining this glow as soon as the jar discharge was used , and have applied to its examination the method used in the former papers . This is due to Sir James Dewar , f and consists in drawing a current of gas through the vacuum tube into an observing vessel , where the glow is developed , and thence into an air pump , which must be a mechanical one of good construction , driven by power . It is thus possible to examine the properties of the glowing nitrogen much more satisfactorily than can be done by intermittent examination after successive discharges . As Lewis observed , the glow has a characteristic band spectrum not known in any other connection . Its most conspicuous features in the visual region are a green , a yellow , and a red band , of not very unequal intensity . The yellow one is usually the brightest , and imparts a yellow colour to the glow , not very dissimilar to that of the afterglow in air , due to the union of nitric oxide and ozone . The two glows are , however , instantly distinguished by the spectroscope , the air glow giving a continuous spectrum . I have obtained the nitrogen afterglow intense enough to be conspicuous to an observer 30 feet off , when it was 18 inches below a 32-candle electric lamp . With regard to the conditions for its production , my observations do not altogether agree with those of Lewis . He obtained it with nitrogen from sodium nitrite and ammonium chloride , but was unable to do so from atmospheric nitrogen . He was disposed to regard the presence of a trace of nitric oxide as necessary . I obtained it first from air which had passed over red-hot copper , and afterwards from air which had been freed from oxygen in the wet way by Hempel 's copper and ammonia method . J It has been shown by Yon Mose'ngeilS that nitrogen completely freed from oxygen by sodium can give the afterglow . I have confirmed this by bubbling atmospheric nitrogen through melted phosphorus , and thence into the vacuum tube . The glow seemed rather improved than otherwise by this treatment . No luminosity was observed in the phosphorus . Nitrogen prepared by burning phosphorus in air under a large bell-jar gives the glow , but not well . It is not free enough from oxygen . In short , all the evidence obtained points to the conclusion that the glow is connected with nitrogen , and nothing but nitrogen . For experiments on the glow7 , particularly if they are to be prolonged , it is * 'Ann . d. Phys. , ' 1900 , vol. 2 , p. 466 ; 'Phys . Zeit . , ' 1904 , vol. 5 , p. 546 . t 'Roy . Inst. Proc. , ' 1888 , and 'Engineering , ' June 18 , 1909 . f It is necessary to remove carbon dioxide and ammonia by appropriate absorbents when using this method , or the glow fails . Special drying of the nitrogen , on the other hand , seems to be of no advantage . S ' Ann. d. Phys. , ' 1906 , vol. 20 , p. 833 . Active Modification of Nitrogen . 1911 . ] convenient to make use of commercial cylinders of compressed nitrogen , provided with the usual automatic regulators as used in connection with the limelight . Commercial nitrogen is not free enough from oxygen for immediate use , but it can readily be made so by passage through a tube filled with freshly cut or cast fragments of phosphorus . A glow is seen where the nitrogen enters , indicating that an absorption of residual oxygen is in progress . This only extends a short way down the tube , and the darkness of the remainder is a guarantee that absorption is complete , and that the issuing nitrogen is fit for use . The phosphorus tube should not be unnecessarily exposed to daylight , as this causes deterioration of the absorbent surface . S 2 . Effect of Temperature . If a long tube , through which a stream of glowing nitrogen passes , is moderately heated , the glow is locally extinguished . As the gas passes on to a cooler part of the tube its luminosity is recovered . If , on the other hand , the gas is led through a tube immersed in liquid air , it glows out with increased brilliancy where it approaches the liquid air . The luminosity is completely and finally extinguished when , or before , the fully cooled portion of the tube is reached . This increased brilliancy is obviously the counterpart of the temporary obscurity observed with heat . Whatever the atomic or molecular change may be , of which the afterglow is a sign , these experiments show that it is accelerated by cooling , and retarded by heating . The kind of change which may be expected to behave in this way is an association , e.g. of dissociated nitrogen atoms into molecular nitrogen . It may be doubted , however , whether the visual glow is a perfect measure of the changes in progress . I find that if a tube carrying the glow is strongly heated the glow is permanently extinguished . It is clear that the view suggested above is incomplete . S 3 . Effect of an Electric Field . The question will naturally present itself whether the gaseous ions of the discharge , which no doubt remain in the glowing nitrogen , have any direct connection with its peculiarities . If this were the case , we should expect that by passing the glowing gas through an electric field so as to remove the ions , the glow , and its power of exciting metallic spectra , to to be presently described , would be destroyed . Glowing nitrogen was passed down a tube about 40 cm . long and 2 cm . in diameter , provided internally with tin-foil strips along the whole length on the opposite sides . The glow was in no way affected at any part of the tube , if an E.M.F. Hon. II . J. Strutt . A Chemically [ Mar. 16 , of 200 volts was applied to these strips . Nor was its power of exciting the spectrum of some sodium vapour at the further end at all diminished , ( see below , S 5 ) . S 4 . Action of the After-glowing Nitrogen on the Non-metcds . The glowing nitrogen has remarkable chemical properties . Drawing it by the pump over a small pellet of phosphorus a violent reaction occurs , red phosphorus is formed , * and the yellow glow is quenched . At the same time the gas is absorbed . This latter experiment can readily be shown by means of a tube illustrated in fig. 1 . The tube is in this case closed , and has no current of nitrogen through it . The discharge passes between the electrodes A and B as indicated by the dotted line . The afterglow diffuses into the annex C , where its characteristic colour and spectrum may be seen . On the other hand , phosphorus vapour diffuses out from the pellet of that substance at D , and they meet at a point E , where the reaction occurs , and red phosphorus is deposited as a film along the walls of the tube . The changed appearance of the discharge shows that absorption is in progress . Beginning with enough nitrogen to give a threadlike discharge , in a few minutes the pressure is sufficiently reduced to broaden out the discharge so as to fill the tube . Shortly after that the vacuum becomes quite high , and conduction ceases . Pteturning to the experiment where a continuous stream of nitrogen is maintained by the pump , it is found that if the Leyden jar is suppressed , and the ordinary coil discharge employed , a piece of phosphorus in the stream of nitrogen is very little acted on . There is just perceptible action in a few minutes , and a faint greenish flame may be seen round the phosphorus . The same flame may be seen more conspicuously with the jar discharge , but only for a moment ; for it is almost immediately obscured in this case by the opaque deposit of red phosphorus on the walls of the tube . No doubt the ordinary coil discharge has the same kind of effect as the jar discharge , but in a degree too slight to make the afterglow visible , and only apparent by prolonged action on phosphorus . * Other cases are known where the reaction of phosphorus with another body convert the excess into red phosphorus . Iodine behaves thus . FIG. 1 . Active Modification of Nitrogen . 1911 . ] The novelty of these observations lies in the fact that the phosphorus vapour employed has no access to the region of discharge . It has long been known that phosphorus vapour in the region of discharge would combine with nitrogen , and the fact has been made use of since 1893 in the exhaustion of incandescent lamps.* Discharge takes place through the rarefied air between the ends of the filament . The E.M.F. of , say , 100 volts between these is amply sufficient to produce it with a white-hot cathode . Sir Oliver Lodge , too , has used phosphorus in exhausting his vacuum valves.f No one , however , seems to have suspected that nitrogen could continue to react with phosphorus after it had left the discharge , and even after it had been deprived of ions by passing through an electric field . Nor has the reaction been connected with the afterglow . I have made use of the reaction with phosphorus to determine what percentage of active nitrogen is present in the gas shortly after leaving the discharge tube . The principle of the method is to determine the gain in weight of the phosphorus after a measured volume of nitrogen has been passed over it . Fig. 2 shows the apparatus . Active nitrogen enters from a vacuum tube attached by a short indiarubber connector to the stopcock A. It passes over fragments of phosphorus at B , where it is absorbed with deposition of red phosphorus , and the glow disappears . The gas then passes through a U-tube C , cooled in liquid air . This is to prevent any phosphorus vapour being carried off . Finally , the gas leaves through a stopcock D. The entire arrangement can be detached and hung on the balance by the wire loop E. The phosphorus is originally introduced through F , which is then sealed . The weighings were always carried out with the tube vacuous , and every precaution was taken against the entrance of moisture , which might lead to erroneous results . In a typical experiment 2540 c.c. of nitrogen were passed , and the gain in weight was 15'5 mgrms . Thus the nitrogen absorbed was 12'2 c.c. , , * See , for instance , J. Rodet , 'Lampes a Incandescence , ' p. 107 , Paris , Gauthier-Villars , 1907 . . ? + Patent No. 25047 , 1905 . FIG. 2 . Hon. R. J. Strutt . A Chemically [ Mar. 16 , 1/ 210 part of the whole . It appears that the percentage of nitrogen converted into the active form is comparable with the percentage of oxygen converted in an ozoniser . The glowing nitrogen also exhibits remarkable phenomena when led over iodine . Its normal yellow glow is replaced by a magnificent light blue flame , at the place where it mingles with the iodine vapour . The appearance is represented in the coloured plate . A slight rise of temperature is observed where the blue glow originates . The iodine is quite volatile enough without the application of heat . I have not succeeded in demonstrating the absorption of nitrogen in this case , nor have I been able to see any signs of a compound deposited further on in the tube . It may be masked by the excess of iodine . The flame gives a magnificent spectrum of broad bands . Details will follow in a later paper . Brief notes will now be given on the behaviour of a few other non-metallic elements . Sulphur , when warmed in the current of glowing nitrogen , extinguished it ; and , with somewhat stronger heating , a blue flame or glow was apparent , though not comparable in volume or intensity with that of iodine . A transparent green deposit is formed on the glass . Selenium had no effect . Arsenic , heated in the glow , gave a not very conspicuous green flame , with a spectrum which seemed continuous , or , at all events , lacking in conspicuous features , and extended over the whole visual region . Antimony and carbon gave no effect . When hydrogen is admitted to mix with the glowing nitrogen , after the latter has been through the vacuum tube , no effect is produced , beyond a mere dilution of the glow . Oxygen , on the other hand , destroys the glow without any other luminosity being developed in the process . | 5 . Action on the Metals\#151 ; Production of Metallic Line Spectra . When the glowing nitrogen is led over a fragment of sodium , which is heated a little above its melting point , the sodium spectrum is developed with great brilliancy . Indeed , the power of developing the D line is a more sensitive test for the presence of the active nitrogen than any other . When the sodium is more strongly heated , say , to 250 ' C. , a curious effect is observed . The denser vapour in the immediate neighbourhood of the metal becomes visually green , showing the green line E very strongly , while the D line is scarcely visible . On either side of the central green light is an outer luminous region in which the D line predominates . Strutt . Koy . ooc . Froc . , vot . 8d , 8 . 19H . ] Active Modification of Nitrogen . I have been able to observe the absorption of the glowing nitrogen by sodium , by the same method as was employed with phosphorus . The sodium vapour was not allowed to penetrate into the discharge , and its spectrum was not observed there.* There seems to be no reason for doubting that the sodium spectrum seen in these experiments is simply the flame spectrum of sodium burning spontaneously in the active nitrogen , to form the nitride . It opens up a new field of experiment to be able to produce metallic spectra in a vessel at so low an average temperature , and in the absence of an electric field . The line spectra of many other metals have been obtained similarly . The following have been observed:\#151 ; Cadmium , magnesium , mercury , potassium , zinc , lead . Thallium was tried in the form of chloride , and gave a magnificent green light , in striking contrast to the yellow afterglow which it replaces . The sodium spectrum , too , can be obtained when the glow passes through a soda glass tube , heated to near the softening point , but in this case the I ) line alone appears . In the case of metallic mercury , absorption of nitrogen was proved , as with sodium and phosphorus , though , working in a closed vessel without a current of gas , it was not found feasible in practice to prevent mercury vapour finding its way into the discharge . There is no doubt that this is the action described by Threlfall.f He observed the absorption of nitrogen when a jar discharge was passed through it at a low pressure in presence of mercury , though there is no reference to the afterglow in his paper . He observed , too , the formation of a compound which decomposed with a slight explosion when moderately heated . Although in the absorption experiments mercury could not be prevented from getting into the discharge , it was easy to avoid this when the air pump was used , and a continuous current of nitrogen drawn through . Working thus , I have observed that Threlfall 's explosive nitride is formed when the mercury spectrum is developed by the afterglow . This seems conclusive evidence that the production of these spectra is a direct result of the chemical union of the metal with the active nitrogen . It may be remarked that , though the hot metals ( . , zinc ) are rapidly skinned over with nitride , cold metals remain bright in the nitrogen glow . This was tried particularly with sodium , and with mercury\#151 ; the latter in the form of a bright film on a copper plate . The clean cold metals have no unfavourable influence on the luminosity of the glow itself . * This distinguishes the present action from the well-known absorbing power of the alkali metals when used as cathode in a discharge . + 'Phil . Mag. , ' Jan. , 1893 , p. 1 . Hon. R. J. Strutt . A Chemically [ Mar. 16 , S 6 . Action on Compound Bodies . Some gases and vapours mixed with the glow merely dilute it . Water and carbon dioxide are examples . In one case an obvious chemical attack has been observed . This was with naphthalene , which turns brown , a brown deposit forming also in the walls of the tube where the nitrogen is passed over it . The nitrogen glow was destroyed , but no luminous phenomena accompanied the action . Heat was not applied . Ammonia was another case where the original glow was destroyed without attendant luminous effects . It seems likely that a chemical action occurs here , but proof has not been obtained . It is certain , however , that in some cases destruction of the glow by contact with another substance may occur without chemical action . Manganese dioxide and copper oxide are at once fatal to it . The analogy to the known destruction of ozone by these substances cannot fail to attract attention . A small roll of superficially oxidised copper gauze was placed in a glass tube and carefully weighed . It was then inserted between the vacuum tube and the pump by means of indiarubber connectors , and a stream of the glowing nitrogen passed over it for about half an hour . The glow abruptly stopped at the surface of the copper oxide . The tube was detached and reweighed . No change of weight amounting to 1/ 10 mgrm . could be detected , though the quantity of active nitrogen passed , judged by the phosphorus experiments described above , must have amounted to several milligrammes . I conclude that the glow is destroyed in these cases by a catalytic action . Another class of compound substances become luminous with characteristic band spectra when vaporised in the glow . Stannous and stannic chloride both give the same brilliant and voluminous blue glow . Most of the light comes from one broad symmetrical band in the blue and violet regions . There are , in addition , a number of lines in the ultra-violet , chiefly due to tin . Mercuric iodide gives a violet glow with a strong unsymmetrical violet band distinct from any in the iodine afterglow spectrum mentioned in S 4 . Distinctive glows have also been obtained from other mercury salts . Mercurous chloride gives a green one . Cuprous chloride gives a blue-green glow , with a spectrum agreeing with that shown by the same compound in the Bunsen flame , but with additional features not present in the latter . Cyanogen gas fed into the glow gives the lilac flame of cyanogen with its well-known spectrum . Active Modification 1911 . ] The band spectrum of iodine in the afterglow ( see S 4 ) should probably be regarded as of similar origin with these compound spectra . They are I think , essentially flame spectra , as are also the line spectra of metals produced in the afterglow ; but the afterglow must be regarded as a much more searching kind of flame than the ordinary high-temperature flames . In much of the literature of flame spectra it is implied that temperature is a measure of the spectrum-developing quality of a flame , and no doubt the fact that the oxy-acetylene and oxy-hydrogen flames are , each in its own degree , capable of developing more lines than the Bunsen flame , is favourable to this view . Yet the balance of evidence is greatly against the idea that heat alone is capable of exciting line and band spectra at all ; and if we reject this idea it is evidently unreasonable to assume that temperature alone governs the number of lines or bands emitted . Regarding , then , the afterglow as a flame capable of developing spectra , we have the means of examining the spectra of a number of compounds which will not endure the temperature of an ordinary flame without decomposition . Moreover , the spectrum is better developed.- Cuprous chloride , which gives a characteristic spectrum in the Bunsen flame , gives the same spectrum , with additional details , in the afterglow . Compounds like mercuric iodide , instantly decomposed in the Bunsen flame , give in the glow a spectrum not before recognised . It may be possible to obtain valuable generalisations from the examination of a long series of such spectra . Nitric oxide , allowed to mix with the active nitrogen , shows a very strange behaviour . A greenish flame , possessing a continuous spectrum , is produced , and heat is developed at the point of confluence . To test whether any gas condensable at \#151 ; 180 ' was produced , the gases from the flame were led through a U-tube cooled in liquid air , and a dark blue substance was condensed out . This melted to an indigo-blue liquid , and finally revealed itself as nitrogen peroxide by evaporating off into an orange gas , soluble in caustic alkali . It is very surprising that a reaction between nitrogen and nitric oxide should lead to the formation of a substance , not less , but oxidised than the latter . A critic may naturally object that the formation of nitrogen peroxide may have been due to oxygen which accidentally gained admission to the nitric oxide , quite independently of the active nitrogen . I wish to emphasise a test experiment , which disproves this hypothesis . The influence of the active nitrogen may be removed by simply turning off the electric discharge . The apparatus being in adjustment , with a suitably regulated flow of the gases , the U-tube was kept cool with liquid air for Hon. R J. Strutt . A Chemically [ Mar. 16 , 10 minutes , after which the liquid air was removed , and the tube allowed to warm up somewhat , for the removal of hoar frost from the outside . No trace of the indigo liquid could be seen . Now the discharge was started , and the tube kept in liquid air for only two minutes . At the end of this time the indigo liquid was extremely conspicuous . The tube could be warmed up to allow the stream of gases to wash out the product , and the experiment could be repeated , on and off , as often as desired . The supply of gas , adjustment of taps , etc. , were left absolutely untouched throughout . It would seem that the reaction which occurs may be of this kind :\#151 ; 2NO + N = N02 + N2 . However , I lay no stress on this . I wish only to insist on the definite facts above stated . Brilliant glows are obtained from some carbon compounds containing the halogens , for instance , a lilac glow from ethyl iodide . This , examined spectroscopically , shows a magnificent cyanogen spectrum . The fact is evidence that the active nitrogen attacks the carbon compound , combining with the carbon ; iodine is set free , and may be collected as a conspicuous sublimate by cooling the resulting vapours in liquid air . What becomes of the hydrogen has not yet been determined . Chloroform and carbon tetrachloride also give a fine cyanogen spectrum . In this case the glow is visually orange , owing to greater relative intensity in the red portion of the cyanogen spectrum . Chlorine is set free , and can be collected in liquid air . Again , the lilac cyanogen glow is obtained when acetylene is fed in . The experiment mentioned above , where cyanogen itself is shown to give this glow under the same conditions , suggests very strongly that in all these cases the active nitrogen attacks the carbon compound , forming cyanogen , which is merely stimulated , without further change , by the peculiar conditions existing in the glow . The formation of cyanogen was proved more directly as follows:\#151 ; The gases from the acetylene experiment were condensed by liquid air , and afterwards collected through a Toepler pump . They were agitated with caustic potash solution to absorb any cyanogen present from the excess of acetylene . The presence of a cyanide in this solution was readily proved by abundant formation of Prussian blue , and by the ferric sulphocyanate reaction . It should be mentioned that , in addition to the condensed gases , some black tarry substance was present in the tube . Finally , the cyanogen spectrum has been observed when the active nitrogen is allowed to react with methane , pentane , ethylene , Icohol , ether , and 1911 . ] A dive Modification of Nitrogen . benzol . It is not , however , so conspicuous in these cases , and probably does not indicate the main course of the reaction . S 7 . Summary and Conclusion . The leading facts established are:\#151 ; ( 1 ) That pure nitrogen , from whatever source , subjected to the jar discharge , undergoes some modification which causes it to glow for a short time after it has left the discharge . ( 2 ) The glow which is emitted while the gas returns to its normal condition is not affected by the removal of ions . It is weakened by heating , intensified by cooling . This seems to favour the view that it is due to the recombination of dissociated atoms . ( 3 ) The modified nitrogen acts on ordinary phosphorus , combining with it , and at the same time forming much red phosphorus . ( 4 ) It combines with sodium and also with mercury at a gentle heat , forming in the latter case an explosive compound , and in each case developing the line spectrum of the metal concerned . It also develops the line spectra of other metals , probably combining with them too . ( 5 ) It develops the band spectra of compounds when they are vaporised in it , giving , in many cases , spectra of substances tot ) unstable to be examined at the temperature of the Bunsen flame . ( 6 ) It attacks nitric oxide , with formation , strangely enough , of nitrogen peroxide , a more oxidised substance . ( 7 ) It attacks acetylene and the halogen derivatives of organic radicles , setting free the halogen , where one is present , and combining with the carbon to form cyanogen . This is proved by the brilliant cyanogen spectrum produced , and by direct chemical tests . It may perhaps be felt that more detailed study of the compounds produced by the active nitrogen should have been made . The importance of this is not underrated , but the difficulties of working with such small . quantities of material are considerable , and have led to a postponement of this branch of the work . It may be pointed out how little has been done in studying the compounds produced by ozone . The spectroscopic data in this paper are merely general and preliminary . An accurate investigation of the various spectra by photographic methods , in collaboration with Prof. A. Fowler , F.R.S. , is in progress . VOL. lxxxv.\#151 ; A. s

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The ionisation of heavy gases by X-rays.

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239

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

R. T. Beatty, M. A., B. E.|Sir J. J. Thomson, F. R. S.

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10.1098/rspa.1911.0034

Tables

Atomic Physics

Tables

]\gt ; FIG. \mdash ; Ionisation in Radiator . Also from equation 2 ) it appears that the final slope of the curve divided by its initial slope , i.e. , , is equal to Hence we can calculate and . These numbers were calculated in several cases and found be in reement with those found by the more direct method which ill now be described . Method of Investigation . In equation ( 4 ) the term results from the fact that corpuscular produced in the gas in the layer next to the bounding walls aoe stopped produced should entail quite a small effect and only at low ; Indeed , in the experimental culves it was found impossible to deUei irregularities due to this cause . When curves connecting ionisation and pressure were now drawn , it found that in every case the curve was a straight line through the ( fig. 4 ) . Since a curve representing equation ( 5 ) can only be obtained it FIG. \mdash ; Se Radiator . coefficient of the corpuscular rays from the films , can be determined from th6 curve in fig. 5 in the manner described in a previous paper . * The values of are given in Table I , Column 4 . To obtain the total ionisation in relative to that in air , the ionisation in the vessel was measured at different pressures when the vessel was occupied by 1 ) , ( 2 ) air . The ratio of the slopes of the linear parts of the thus obtained gives the total ionisation in relative to that in air for any particular radiator . The values the relative total ionisation are given in Table , Column 5 . Table I.\mdash ; Ionisation in relative to that in Air .

rspa_1911_0035

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The variation of ionisation with velocity for the \#x3B2;-particles.

240

248

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

W. Wilson, M. Sc.|Prof. E. Rutherford, F. R. S.

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Atomic Physics

Tables

Atomic Physics

]\gt ; in a Vessel . Nearly all measurements of ionisation have been made with vessels enough to reflect a large proportion of the rays which fall on the walls , and the connection between the ionisation in the thick copper vessels used abov . and velocity is shown in Tables III and IV , which correspond respectively the two sets of results given in Tables I and II . The values given in Table are shown graphically in fig. 3 . Table IIL : The Association of Lead with Uranium in Rock-Minerals , : Application to the Measurement of Geological Time . By ARTHUR HOLMXS , A.B.C.S. , B.Sc. , Imperial College of Science and Technology . ( Communicated by Prof. the Hon. R. J. Strutt , F.R.S. Received March 20 , \mdash ; Read , April 6 , 1911 . ) 1 . Introduction.\mdash ; The study of radioactive minerals is of great importance from two points of view . Such minerals may be regarded as ' for the various series of genetically connected radioactive elements . them the parent element slowly disintegrates , while the ultimate of the transformation gradually accumulate . The analysis of these

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The association of lead with uranium in rock-minerals, and its application to the measurement of geological time.

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256

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Arthur Holmes, A. R. C. S., B. Sc.|Hon. R. J. Strutt, F. R. S.

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Chemistry 2

Geography

Chemistry

248 Mr. A. Holmes . Association of [ Mar. 20 Conclusions . 1 . The ionisation produced per centimetre by / 3-particles in free air varies inversely as the square of the velocity between the limits examined . 2 . The ionisation in a thick copper vessel is not connected with the velocity by any simple power law , but is approximately given by I = where k and c are constants and v the velocity of the ^-particles . In conclusion , I wish to express my best thanks to Prof. Rutherford for proposing this research , and for his suggestions from time to time during its progress . The Association of Lead with Uranium in Rock-Minerals , and its Application to the Measurement of Geological . By Arthur Holmes , A.R.C.S.8 , B.Sc. , Imperial College of Science and Technology . ( Communicated by Prof , the Hon. R. J. Strutt , F.R.S. Received March 20 , \#151 ; Read April 6 , 1911 . ) 1 . Introduction.\#151 ; The study of radioactive minerals is of great importance from two points of view . Such minerals may be regarded as storehouses for the various series of genetically connected radioactive elements . In them the parent element slowly disintegrates , while the ultimate products of the transformation gradually accumulate . The analysis of these minerals ought , then , in the first place , to disclose the nature of the ultimate product of each series ; secondly , a knowledge of the rate of formation of this product , and of the total quantity accumulated , gives the requisite data for a calculation of the age of the mineral . It has been shown that the disintegration of uranium results in the formation of eight atoms of helium.* In 1907 Bolt wood brought forward strong evidence suggesting that lead is the ultimate product of this disintegration . ' ] ' In this paper it is hoped to produce additional evidence that such is the case , according to the following equation:\#151 ; U \#151 ; 8He + Pb . 238-5 32 2-069 . * See Strutt , ' Roy . Soc. Proc. , ' A , 1908 , vol. 81 , p. 276 . t Boltwood , 'Am . Journ. Sci. , ' 1907 , p. 77 . Lead with Uranium Rock-Minerals . 1911 . ] On the assumption that helium is produced to this extent , Butherford has given data* from which it may be calculated that 1 gramme of uranium produces 10'7 x 10~8 c.c , of helium per annum . Strutt has verified this theoretical estimate by a direct appeal to experiment . ' ! ' Actually measuring the annual production of helium , he obtained a corresponding result of 9-9 x 10~8 c.c. Accepting the theoretical figure , which is equivalent to 1-88 x 10"u grm. , it is easily calculated that the amount of lead which would remain is 1*22 x 10-10 grm. per gramme of uranium per annum . If this rate of production were constant , a gramme-molecule of lead would take the place of a gramme-molecule of uranium in 8,200 million years . However , the rate is not constant , but is proportional to the amount of uranium remaining unchanged . If the latter is large compared with the total amount of lead produced , the rate may be taken as nearly constant , and the age of the mineral in which this disintegration has occurred is given by Pb/ U. 82 00 x 106 years , where Pb and U represent the respective percentages of these elements at the present day . In many cases , however , this constancy cannot be assumed , and it is necessary to substitute for the present-day percentage of uranium its time-average for the period considered . Thus , in the minerals described in this paper , the difference between the uranium now present and that originally present amounts to about 5 per cent. , and , in calculating the age , corresponding values are obtained . In this case a sufficiently accurate approximation to the time-average is given by the mean . Por minerals of the same age , the ratio Pb/ U should be constant , if all the lead has originated as suggested . Further , for minerals of different ages , the value of Pb/ U should be greater or less in direct proportion to those ages . Collecting all the known analyses of primary uranium-bearing minerals which included a determination of lead , BoltwoodJ showed that the above conditions were generally found to hold . Unfortunately , he omitted to give the geological ages of the several occurrences . In a summary of his analyses , to be given in a later section , these will be indicated as accurately as at present is possible . 2 . Selection of Minerals.\#151 ; In order that the suggested relations between lead and uranium should be detectable , and that lead should be confidently used as a reliable age-index , certain assumptions require to be made . The selection of minerals must be such that for them these assumptions are justifiable . They will be considered as follows:\#151 ; * Cited by Strutt , ' Roy . Soc. Proc. , ' 1908 , p. 276 . t Strutt , ' Roy . Soc. Proc. , ' A , 1910 , vol. 84 , p. 388 . X ' Am . Journ. Sci. , ' 1907 , p. 77 . Mr. A. Holmes . The Association of [ Mar. 20 , ( a ) That no appreciable amount of lead was present when the mineral was formed . ( b ) That no lead has originated by any other radioactive process than that suggested . ( c ) That no lead nor uranium has subsequently been added or removed by external agencies . ( a ) Previously to the consolidation of a rock magma , the uranium in the latter must , of course , have been generating helium and lead for an unknown period . It is probable that much of the lead then present would , at the time of crystallization , be carried away in hot sulphide solutions to form the hydatogenetic and metasomatic deposits of lead which provide our supplies of that metal . Doubtless , however , a certain amount of lead would be retained in the molecular network of crystals , and consequently analyses of a rock as a whole should give values of Pb/ U higher than that corresponding to the period since consolidation . This difficulty may be avoided by considering particular minerals . Thorite , zircon , in some cases apatite and sphene , and other rarer minerals segregate within themselves on crystallization a much larger percentage of uranium than remains to the rest of the magma . Within these minerals lead accumulates to such an extent that the amount originally present becomes negligible . ( \amp ; ) It may be objected that lead may perhaps originate as a product of some element other than uranium . Boltwood shows that it is highly improbable that thorium should give rise to lead , and the results submitted in this paper add further proof to that independence . Wherever lead occurs in primary minerals it is associated with uranium , and there is little doubt that it can be completely accounted for in this way . ( c ) It may seem unlikely that for periods of hundreds of millions of years a mineral should remain unchanged by external chemical agencies . In the earth 's surface materials , making up the belt of weathering , solution is the dominant process . Lower down , in the belt of cementation , re-deposition is more characteristic.* Can we be sure that these processes have not dissolved out lead or uranium at one time , depositing the same elements at another time ? In some cases we cannot , but , fortunately for our purpose , many of the uranium-bearing minerals , like zircon , are dense and stable , and capable of withstanding great changes in their environment without undergoing alteration . But an appeal to analysis will rarely fail to dispel this difficulty . If such changes have occurred , it is inconceivable that they would always have affected lead and uranium in the same proportion , * See Van Hise , " Treatise on Metamorphism , " 'Mon . United States Geol . Survey , ' 1904 , vol. 47 . Lead with Uranium in Rock-Minerals . 1911 . ] and hence the results obtained from different minerals should show marked discrepancies . On the other hand , if the analyses give consistent results one can only assume that any alteration has been inappreciable . A microscopical examination of the minerals in question affords a useful guide to the extent of alteration . Unless one can be sure in this way that the mineral is fresh , it is clear that reliable results can only be expected when a series of minerals are examined . Still another possible objection may be treated here . Under the high temperatures and pressures which rocks have undergone during their geological history , is it safe to assume that radioactive changes proceed at the same rate ? All that can be said is that experimental evidence consistently agrees in suggesting that these processes are quite independent of the temperatures and pressures which igneous rocks can have sustained without becoming metamorphosed . Arrhenius has supposed that radioactive processes may be reversed under the conditions prevailing at great depths . This idea has nothing but analogy to support it . There is abundant evidence that molecular changes are reversed at greater depths , e.g. , in the upper zones of the earth 's crust silicates are replaced by carbonates , while in the lower zones carbonates are decomposed and silicates are formed . But that interatomic changes should 'reverse , or even proceed more slowly or quickly , there is no evidence . From these considerations , it is obvious that the only minerals to be chosen are fresh , stable , primary rock-minerals . Secondary and meta-morphic minerals could not be relied upon to satisfy the required conditions . There occurs in the Christiania district of Norway , * a geologically depressed area of nearly 4,000 square miles , which is separated on every side by faults from the surrounding Pre-Cambrian gneiss . In this area there is a nearly complete sequence of early palaeozoic rocks . Above these strata there are a few beds of red sandstone of Lower Devonian age . Over these beds and intercalated with them are lava flows ; and , finally , penetrating the whole mass , representing a later phase of this period of igneous activity , are great intrusions of plutonic rocks . Amongst the earliest of the intrusions is a series of thorite-bearing nepheline-syenites . Brogger believes them to be of Middle or Lower Devonian age , most probably the latter . The minerals occurring in them are , in many instances , notably radioactive , and thus they afford an admirable series in which to investigate the consanguinity of lead and uranium . Several of these minerals were obtained from Brevig , and estimations of these elements in each case were made . * See Brogger , ' Zeit . fur Kryst , ' 1890 , vol. 16 . Mr. A. Holmes . The Association of [ Mar. 20 3 . Methods of Analysis.\#151 ; ( a ) Uranium.\#151 ; This constituent was estimated by Strutt 's method , * in which radium emanation is directly measured , and the constancy of its ratio to uranium used to give the amount of the latter . From 0*3 grm. to 2-0 grm. of the finely powdered mineral was used for each estimation , according to the relative richness of the mineral in uranium . From preliminary electroscopic tests this could be roughly measured . The powdered mineral was fused with borax in a platinum crucible , and the resultant glass dissolved in dilute hydrochloric acid . After boiling , and standing for several days in a corked flask , the radium emanation was boiled out , collected in a gas-holder , and ultimately transferred to an electroscope . Knowing the normal leak and constant of the electroscope , a measurement of leak sufficed to give the necessary data for the calculation of the equivalent amount of uranium . Blank experiments were made with the reagents used , and the normal leak was determined at suitable times throughout the investigations . In no case was any appreciable difference observed . Two solutions of each mineral were made , and two estimations of each . Without exception , the results obtained agreed closely . ( b ) Lead.\#151 ; Several methods of estimating lead were attempted , but the most constant and reliable results were found to be attained by weighing it as sulphate , and in cases when the quantity of lead present was too small for the gravimetric method , colorimetric estimations were made . Gravimetric method.\#151 ; Quantities varying up to nearly 100 grm. of the finely powdered mineral were intimately mixed with four or five times as much fusion mixture , and fused in a platinum basin . On allowing the melt to cool completely , the cake could usually be easily separated by treating with boiling water . A second heating and cooling always resulted in a successful separation . The cake was broken up by boiling with water in a beaker . Dilute hydrochloric acid was gently heated in the platinum basin to remove any still adherent portions of the cake . The contents of the basin were then washed into the beaker , and more hydrochloric acid added . The solution thus formed ( with a colloidal mass of silica ) was evaporated to dryness , and , dilute hydrochloric acid having been added , this was repeated a second time . On again adding dilute acid and heating , the silica was easily filtered off , leaving a clear solution . From the latter lead was precipitated as sulphide , by heating and adding ammonium sulphide . The precipitate was collected on as small a filter paper as possible , dried and ignited . The residue was treated with a little nitric acid , and boiled to convert any reduced lead to nitrate . Sulphuric acid was finally added , and the whole heated until all nitric * ' Roy . Soc. Proc. , ' A , 1906 , p. 473 et Lead with Uranium in Rock-Minerals . 1911 . ] acid fumes had ceased . A tiny white precipitate then remained . This was collected on a very small filter , of which the weight of the ash was accurately known , washed with alcohol , dried , ignited , and weighed with the greatest possible accuracy . Colorimetric method*\#151 ; Standard solutions containing known quantities of lead , as nitrate , were prepared by dissolving the lead compound in a slightly acidified solution containing ammonium acetate and grape sugar , known as the " diluting solution . The lead to be estimated having been concentrated in a nitric acid solution as already described , the latter was evaporated to dryness , or nearly so . The residue was then taken up with a little of the diluting solution . This was treated with a known quantity of well-diluted ammonium sulphide , the liquids being contained in a graduated glass vessel . A brown coloration was produced . One of the standard solutions was similarly treated in an exactly similar vessel . The diluting solution was then added to one vessel or the other until the colours produced in both were indistinguishable , care being taken that the amount of ammonium sulphide in each was proportionate to the respective volume . After a little practice with solutions of known strengths , this could be done with confidence , and concordant results were obtained . Tested by the sulphate methods slightly higher results were given in general . The colorimetric method obviously assumes the absence of copper and bismuth . From Yogt 's estimates of the average amount of these metals in 100 grm. of rock :\#151 ; *j* Grm . Lead ... ... ... ... ... ... . . 0*000# Copper ... ... ... ... ... ... 0*0000# Bismuth ... ... ... ... ... . . 000000# it might be anticipated that the latter two would not have much influence . Tests were , however , applied to detect any very small quantities which might be present . By testing for copper^ with hydrobromic acid , about 0*00002 grm. was probably the greatest amount indicated . Schneider 's test applied for bismuth S failed to detect that element . To the fourth decimal the amount of lead was therefore unaffected by its non-separation from copper or bismuth . The smallest amount of lead estimated , viz. , 0*0003 grm. in 100 grm. of * V. Harcourt , ' Journ. Chem. Soc. , ' 1910 , vol. 97 , p. 841 . + ' Zeit . prakt . Geol . , ' 1898 . + ' Select Methods of Chemical Analysis , ' Crookes , 1905 , p. 295 . S Ibid.,1905 , p. 355 . Mr. A. Holmes . The Association of [ Mar. 20 , felspar , approaches the limit to which the colorimetric method can be applied quantitatively , although smaller quantities than this can easily be detected . 4 . Experimental Results.\#151 ; The results obtained are tabulated below:\#151 ; Mineral . Uranium . Grin , per 100 grm. mineral . Lead . Grm . per 100 grm. mineral . Pb/ U. Thorite ( 1 ) 10 -1040 0 -4279 0-042 Orangite ( 1 ) 1 -2437 0 -0570 0-046 Orangite ( 2 ) 1 -1825 0 -0542 0-046 Thorite ( 2 ) 0 -4072 0 -0196 0-048 Homelite 0-2442 0 -0121 0-049 Zircon 0 -1941 0 '0085 0-044 Pyrochlore ( 1 ) 0 -1923 0 -0120 0-062 Pyrochlore ( 2 ) 0 -1855 0 -0093 0-050 Biotite 0 -1602 0 -0069 0-043 Tritomite 0 -0631 0 -0026 0-041 Freyalite 0 -0526 0 -0028 0-053 Mosandrite 0 -0432 0 -0024 0-056 Eagerine 0 -0253 0 -0015 0-060 Astrophyllite 0 -0140 0-0007 0-050 Catapleite 0 -0132 0 -0009 0-068 Nepheline 0 -ooio 0-0004 0-400 Felspar 0 -0006 0-0003 0-500 With the exception of pyrochlore , specimen ( 1 ) , and astrophyllite , the number of lead estimations varied from two to five . Of the minerals named , only one determination was made , owing to lack of material . It will be noticed that with few exceptions the value of Pb/ U increases as the uranium content decreases . This may be due to the possibility of the lead originally present in the magma having a gradually increasing relative importance as the lead generated from uranium decreases in amount . Thus it would seem in the case of nepheline and felspar that the lead so generated is of no importance whatever when compared with that originally present . Such minerals are , of course , valueless in age-estimations , and of the results given here only eight of the first nine will be used for determining the age . Omitting that of pyrochlore ( 1 ) , since the single rather anomalous determination of lead could not be verified by a second estimation , these results give 0046 as their mean , and if the uranium percentage be replaced by its approximate time-average the mean becomes 0D45 . This gives an age of 370 million years , and is probably the most reliable estimate that can be deduced from the evidence . 5 . Summary of Analyses collected by \#151 ; ( a ) The analysis of five specimens of uraninite from Glastonbury ( Conn. ) gives a ratio of Pb/ U = 0-041 . The minerals occur in a pegmatite associated with a * Boltwood , 'Am . Journ. Sci. , ' 1907 , p. 77 . 1911 . ] Lead with Uranium in Rock-Minerals . 255 granite intruding Lower Carboniferous strata , and probably itself of Carboniferous age . ( b ) Uraninite from Branchville ( Conn. ) gives four closely agreeing ratios , 0'053 . The geological evidence here is similar to that at Glastonbury , with the exception that the intruded strata are of Silurian or Ordovician age . ( c ) Material from dykes of pre-Carboniferous age in Carolina gives less consistent results , of which the mean ratio is 0*05 . ( d ) In Llano Co. ( Texas ) , there occurs a group of metamorphosed sedimentary rocks of early Algonkian age . Into these the Burnet granites are intrusive , and are therefofe somewhat younger than the schists and quartzites . The ratio of minerals from these igneous rocks is 0T6O . ( ie ) Another group of minerals from Burnet Co. ( Texas ) and Douglas Co. ( Colorado ) gives a ratio of 0T75 . Geological evidence is similar to that of Llano Co. , and it is impossible to say whether or not the rocks are older . ( / ) The pre-Cambrian rocks of Sweden are divided by Hogbom into three main divisions , Jotnian , Jatulian , and Archaean , in order of increasing age . Above the Archaean , but younger than the Jatulian , is a series of igneous massives known as the Sen-archsean granites , and with these are associated the famous uranium-bearing pegmatites of Scandinavia . In a series of 17 minerals from these pegmatites , taken from all parts of Norway and Sweden , there appear to be two clearly marked groups . One gives a ratio of 0T25 and the other of 0-155 . Amongst these rocks geological correlation is very speculative , but it is agreed that there is nothing by which any difference in age could be detected , and provisionally the two groups are regarded geologically as one . ( , g)The greatest ratio is given by thorianite from Ceylon , for which Pb/ U = 0*20 . Here the only evidence for the pre-Cambrian age of the minerals is derived from the similarity of the rocks to those of the fundamental complex of India . These latter underlie a vast series of sedimentary strata considered to be of pre-Cambrian age . It should be observed that in calculating the above ratios U represents the time-average , and not the amount actually present . The difference is , however , not great . G. Conclusion.\#151 ; Evidence has been given to prove that the ratio Pb/ U is nearly constant for minerals of the same age , the slight variability being what theoretically one would anticipate . Eor minerals of increasing geological age the value of Pb/ U also increases , as the following table clearly shows :\#151 ; The Association of Lead with Uranium in Rock-Minerals . Geological period . Pb/ U. Millions of years . Carboniferous 0 -041 340 Devonian 0-045 370 410 430 1025 1270 1310 1435 1640 Pre-carboniferous 0 -050 Silurian or Ordovician 0 053 Pre - Cambrian\#151 ; a. Sweden b. United States c. Ceylon 0-125 0-155 0-160 0 175 0-20 % Wherever the geological evidence is clear , it is in agreement with that derived from lead as an index of age . Where it is obscure , as , for example , in connection with the pre-Cambrian rocks , to correlate which is an almost hopeless task , the evidence does not , at least , contradict the ages put forward . Indeed , it may confidently be hoped that this very method may in turn be applied to help the geologist in his most difficult task , that of unravelling the mystery of the oldest rocks of the earth 's crust ; and , further , it is to be hoped that by the careful study of igneous complexes , data will be collected from which it will be possible to graduate the geological column with an ever-increasingly accurate time scale . In conclusion , I wish to express my thanks to those gentlemen who in any way have helped to make this investigation possible . I am indebted to Profs . Sir T. H. Holland , Brogger , and Hbgbom , and to the Director of the United States Geological Survey , for information regarding the geological position of many of the occurrences cited in S5 ; and to Dr. Prior for his permission to make preliminary electroscopic tests of several minerals in the collection of the Natural History Museum . Finally , I owe my best thanks to Prof. Strutt , at whose suggestion the work was attempted , for his ever-ready help and criticism , and for his kindness in obtaining for me the suite of minerals and allowing me the use of apparatus in their investigation .

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On some mineral constituents of a dusty atmosphere.

271

275

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

W. N. Hartley, D. Sc., F. R. S.

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10.1098/rspa.1911.0039

Atomic Physics

Chemistry 1

Atomic Physics

271 On some Mineral Constituents of a Dusty Atmosphere . By W. N. Hartley , D.Sc . , F.R.S. , Royal College of Science , Dublin . ( Received April 4 , \#151 ; Read May 11 , 1911 . ) During the past 12 months I have had occasion to ascertain the nature of the mineral constituents of an ordinarily turbid atmosphere . By means of a small portable quartz spectrograph several series of spark spectra were photographed with graduated exposures of 1 , 5 , 10 , 20 , 40 , and 60 seconds , all on the same plate . The electrodes in the first series were cadmium , iron , nickel , and copper , a self-induction coil being interposed to eliminate the air spectrum and the short metallic lines . Several plates taken from only the cadmium electrodes exhibited features of particular interest when minutely examined . Though the spectra are small , the instrument gives fine definition from the red potassium line about \7665'6 to that of cadmium A.2194'7 . With Wratten and Wain wright 's panchromatic plates , an exposure of one second renders all the principal lines of cadmium , including W 4800 and 2265 , with 10 seconds all the rays from X 6438 are obtained . The solar spectrum from b to M is faintly visible at all exposures from 1 to 60 seconds inclusive . The conspicuous H and K lines seen in the first three exposures have their usual appearance ; but , on the third spectrum , exposed 20 seconds , the K line has , at its exact centre , an extremely narrow sharp black line ; in succeeding exposures this line becomes longer and intensified . With 40 seconds ' exposure a similar black line is just discernible on H , and it is stronger with 60 seconds . Other parts of the solar spectrum are overlaid by exceedingly fine dark lines which it was proved do not belong to the cadmium spectrum , but were caused by solid matter in suspension in the atmosphere being vaporised by the spark . The dark lines on H and K are easily explained by the presence of calcium carbonate in very minute particles of dust suspended in the air . I have called attention to this in former publications.* It was proved in these experiments that the lines did not originate from impurities in the metallic cadmium , because the same electrodes with longer exposures yielded spectra without any impurity lines , when the sparks were passed in an atmosphere of hydrogen . It was also found that whether in the open air , or in a quiet room near a window , the most prominent lines of calcium were always present . * Hartley , 'Phil . Trans. , ' 1884 , Part I , pp. 49\#151 ; 62 , and Part II , pp. 325\#151 ; 342 . Also 'British Association Report , Aberdeen , ' 1885 , and ' Journ. Soc. Arts , ' 1886 , pp. 396\#151 ; 415 . Dr. W. N. Hartley . On Mineral [ Apr. 4 , A line , rather more refrangible than G , was carefully measured , and proved to he that of calcium , X 4226'9 ; it is the ultimate line of the element in oxyhydrogen flame spectra . There are two lines just on either side of M ; there is no doubt that these are the calcium lines XX 3737'2 and 3706*3 . It has been shown by Hartley and Adeney 's wave-length determinations* that the line of cadmium measured by Mascart ( No. 12 ) is a triple line , the components being distinguished by the following letters and wave-lengths:\#151 ; a 3261*2 , / 33252'6 , and 7 3250-5 . With a self-induction coil the ft line disappears . On examining plates photographed on three successive days , with exposures varying from 1 to 60 seconds , it was seen that two plates showed only two lines a and 7 . The third plate showed , at an exposure of one second , an extremely fine and very sharp black line , more refrangible than the other two , which , by very careful measurements , was proved to be the ultimate line of copper , X 3274 . With five seconds ' exposure this and all other succeeding spectra on the plate showed another line less refrangible than the cadmium group , which was proved to be the penultimate line of copper , X 3247'7 . A comparison of the plates of spectra showed that with the same exposures on each succeeding day the five lines of calcium and the two lines of copper became stronger ; in other words , the increased strength of the lines showed that the outside air became more dusty . This was seen to be actually the case , under the conditions of a dry atmosphere and a hot sun continuing for six or seven days in the month of May . To ascertain the origin of the copper was an enquiry attended with some difficulty , the quantity diffused in the atmosphere of the city being comparatively large . Copper has been proved to be a constituent of coal ashes , and of the flue-dust from gasworks and chemical works , of soot , and of dust from the clouds in hail , snow , and sleet.f These sources , however , contain other constituents , notably lead , nickel , and iron . The constant traffic of tram-cars and motor-cars in the street raised dust , which caused an increased haziness of the atmosphere day by day , and corresponding increase in the number and intensity of the calcium lines in the spectra . While making these observations , the prevalence of copper in the dust was accounted for by the repeated flashes on the overhead cable , which is in the centre of a wide street ( St. Stephen 's Green ) at a distance of 54 feet from the * 'Phil . Trans. ' 1884 , Part I. t Hartley and Ramage , 'Roy . Soc. Proc. , ' 1901 , vol. 68 , p. 97 . Constituents of a Dusty Atmosphere . 1911 . ] window of my private room . The condensation of the vapour of copper after each discharge must yield a dust of extreme tenuity such as could not arise from mechanical action , such as scraping or abrasion of the solid metal . The lines identified from their proximity to , or coincidence with , solar lines , are as follows ; the wave-lengths of calcium are taken from Eder and Valenta 's spark lines :\#151 ; X X Near G 4308 4226-9 Calcium . HI KJ Coincident 3968-61 3933-3 J \ Calcium . Near M 3727 3737-21 3706-2 Calcium . Near Q 3284-7 3274-01 3247-7 I Copper . Of seven plates of spectra photographed in the months of April and May two were very carefully measured with the micrometer . Twenty-two lines were positively identified with those of elements known to be contained in atmospheric dust . The lines are principally the ultimate lines of the respective elements . The following is a list of the wave-lengths found and the wave-lengths adopted:\#151 ; Wave-lengths found . Wave-lengths adopted . Origin of lines . 4227 -5 4226 -9 Calcium.* 4058 -5 4057 -8 Lead* 3965 5 3932 -5 3968 -61 3933 -8 j Calcium.* 3878 -0 3870 -0 3876 -2 1 3871 -2 / Carbon . 3733 -0 Yery faint . 3735 -0 Iron.* 3683 -5 3643 3683 -1 \ 3639 -7 J Lead* Yery faint . 3495 3484 -5 3496 \ 3483 J Manganese . 3416 3415 Nickel* 3274 -8 3274 -0 \ Copper.* 3247 -9 3247 -7 J 2802 -1 2794 *5 2802 -4 \ 2794 -5 J Magnesium.* 2614 -5 2614 -8 Lead . 2594 -0 2575 -O 2594 -0 \ 2576 -2 J Manganese.* 2480 -0 2478 -7+ Carbon.* * * Ultimate lines . t A. de Gramont , 4 Comptes Rendus , ' 1908 , vol. 146 , p. 1260 . This line appears distinctly with an exposure of 60 seconds , but as a short line . Of the other two lines one corresponds with \ 3876*5 , Living and Dewar , the other with 3871*5 , Kayser and Rung , and 3872 , Eder and Yalenta , the second edge of the cyanogen band No. 3 . See 4 Proc. Roy . Soc. , ' 1896 , vol. 60 , p. 216 . The first edge 3883*8 is obscured by a nitrogen band . 274 On some Mineral Constituents of a Dusty Atmosphere . Spectra were photographed from portions of the same cadmium electrodes , six months later , in a part of the college as far removed from the frontage as possible , close to a large garden , and with no street thoroughfare within 100 yards . There had been heavy rain , which had washed out much of the dust from the air . Not withstanding , the wave-length measurements of two feeble strange lines identified them with copper , and the five calcium lines were very distinct . Spectra were photographed from cadmium electrodes in hydrogen with exposures of one , two , three , and four minutes ; cadmium in air exposed one minute . The spectrum taken in the hydrogen atmosphere , and exposed minutes , Avas in all respects of similar intensity to that taken in air in minute , except beyond \ 2418'5 , where the continuous rays between the lines commenced to fade away . The spectra taken in hydrogen showed no trace whatever of the lines of either copper or calcium , and many other feeble lines were entirely absent which undoubtedly are representative of the other constituents of atmospheric dust . It is thus proved , absolutely , that . the copper and calcium were the constituents of dust diffused through the atmosphere of the city . Determinations of the weight of material necessary to give the lines of these spectra in the manner described , and with such short exposures , have been completed . From the loss of weight of the dry electrodes by the passage of the spark during successive intervals of 10 minutes , the weight of metallic calcium volatilised in one minute , and in one second , was calculated . The number of spark discharges per second was accurately determined , and likewise the number of discharges necessary to render the lines of calcium , as photographed from atmospheric dust , with an exposure of 60 seconds . Similarly with copper , the number of discharges necessary to render the ultimate line and the two lines respectively , as measured on plates exposed to atmospheric dust for one second and for five seconds , was ascertained , and the weight of copper volatilised at each spark discharge was accurately determined . It was found that , in order to render the five principal lines in the spectrum of calcium , the weight of the metal passing between the electrodes in 60 seconds was from 00001 to 0-00014 mgrm . , or , as calcium carbonate , from 0-00025 to 0-00035 mgrm . Similarly , the quantity of copper which passed between the electrodes in one second was from 0-0005 to 0-0007 mgrm . , and in five seconds from 0-001 to 0-0014 mgrm . These quantities yield the spectra photographed , and the proportion of copper in the dust thus appears to be 10 times as great as that of the calcium . Both the calcium and copper reactions in the spark are more delicate than On the Absolute Measurement of Light . the sodium test by the yellow flame , or even by the photography of the ultimate lines of sodium in the oxyhydrogen flame and spark . Metallic sodium renders no lines with one spark when photographed , and with five sparks the lines X 3301*1 and X 3302*5 are both stronger than the yellow lines ( mean X 5893*2 ) . These lines do not appear on any of the cadmium plates . The reactions of lead , manganese , and magnesium in the spark are much more sensitive than those of sodium , calcium , or copper . For instance , 0*00003 mgrm . of manganese is volatilised by one spark discharge , and yields a spectrum with the following ultimate group of lines : 2949*3 , 2939*4 , and 2933*1 . As no atmosphere is free from dust , and that of cities is particularly dusty , these mineral constituents must be regarded as possible reagents in cases where there is evidence that very minute quantities of basic substances can initiate chemical reactions and isodynamic changes , such as have generally been considered as spontaneous , and in all cases where a solution in contact with air is liable to be affected . On the Absolute Measurement of Light : A Proposal for an Ultimate Light Standard . By R. A. Houstoun , M.A. , Ph. D. , D.Sc . , Lecturer in Physical Optics in the University of Glasgow . ( Communicated by Prof. Andrew Gray , F.R.S. Received April 5 , \#151 ; Read May 11 , 1911 . ) The measurement of the intensity of a source of light is , it is well known , a somewhat unsatisfactory process . The eye cannot estimate light intensity ; it can only tell when the illumination of two adjacent surfaces is equal . If , for example , we desire to measure the intensity of a metal filament lamp , we compare it with a Hefner lamp and say that the intensities are inversely as the squares of the distances from the photometer head , when equal illumination is obtained . In strictness , however , this method is applicable only when the colours of the two sources , or more accurately when the distribution of energy in the spectra of the two sources , is exactly the same ; for the relative luminosity of the different colours of a spectrum varies with the intensity of that spectrum . Abney has two well-known curves illustrating

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On the absolute measurement of light: A proposal for an ultimate light standard.

275

284

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

R. A. Houstoun, M. A., Ph. D., D. Sc.|Prof. Andrew Gray, F. R. S.

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10.1098/rspa.1911.0040

Optics

Tables

Optics

On the Absolute Measurement of Light . the sodium test by the yellow flame , or even by the photography of the ultimate lines of sodium in the oxyhydrogen flame and spark . Metallic sodium renders no lines with one spark when photographed , and with five sparks the lines X 3301*1 and X 3302*5 are both stronger than the yellow lines ( mean X 5893*2 ) . These lines do not appear on any of the cadmium plates . The reactions of lead , manganese , and magnesium in the spark are much more sensitive than those of sodium , calcium , or copper . For instance , 0*00003 mgrm . of manganese is volatilised by one spark discharge , and yields a spectrum with the following ultimate group of lines : 2949*3 , 2939*4 , and 2933*1 . As no atmosphere is free from dust , and that of cities is particularly dusty , these mineral constituents must be regarded as possible reagents in cases where there is evidence that very minute quantities of basic substances can initiate chemical reactions and isodynamic changes , such as have generally been considered as spontaneous , and in all cases where a solution in contact with air is liable to be affected . On the Absolute Measurement of Light : A Proposal for an Ultimate Light Standard . By R. A. Houstoun , M.A. , Ph. D. , D.Sc . , Lecturer in Physical Optics in the University of Glasgow . ( Communicated by Prof. Andrew Gray , F.R.S. Received April 5 , \#151 ; Read May 11 , 1911 . ) The measurement of the intensity of a source of light is , it is well known , a somewhat unsatisfactory process . The eye cannot estimate light intensity ; it can only tell when the illumination of two adjacent surfaces is equal . If , for example , we desire to measure the intensity of a metal filament lamp , we compare it with a Hefner lamp and say that the intensities are inversely as the squares of the distances from the photometer head , when equal illumination is obtained . In strictness , however , this method is applicable only when the colours of the two sources , or more accurately when the distribution of energy in the spectra of the two sources , is exactly the same ; for the relative luminosity of the different colours of a spectrum varies with the intensity of that spectrum . Abney has two well-known curves illustrating Dr. R. A. Houstoun . [ Apr. 5 , this.* One , which represents the relative luminosity of the different colours of a spectrum at ordinary intensity , has a maximum in the orange ; the other which is for a spectrum with the same distribution of energy , but with an intensity of less than 1/ 100 candle-foot , has its maximum in the green . If , therefore , we have an extremely long photometer bench , and an experimenter with normal colour vision compares the intensities of the metal filament lamp and the Hefner lamp , at first placing the Hefner lamp one foot from the photometer head and afterwards placing it more than 100 ft. from the latter , he should not obtain the same result both times . In the first case , owing to the reddish tint of the Hefner lamp , the intensity of the metal filament lamp should appear less . If , again , a second observer , whose colour vision is slightly abnormal , compares the lamps at the first distance , he gets a third result . Of course the difficulty does not arise in practice , because the sources to be compared have usually the same colour and the illumination of the field of the photometer does not vary over a wide range . Still , a standard unit of light should meet all conceivable cases , and we are at present unable to state satisfactorily in terms of our standards , once for all , the candle power of , for example , a mercury vapour lamp . In order to be definite we must specify , first of all , normal colour vision on the part of the observer , and then we must state the illumination of the fields he compares . It is , of course , the Purkinje effect , the change from rod to cone vision , that causes all this trouble . And it is precisely within the range of illumination in common use , 1 to 100 metre-candles , that this change from rod to cone vision takes place . I think it is now possible to place the photometry of different coloured lights on an exact footing , at least as far as ultimate measurements are concerned , by removing it out of the field of physiology altogether into the field of electricity , which is a much more exact science . Why can we not measure candle power by means of a thermopile ? Simply because the thermopile measures the total energy radiated , irrespective of wave-length . The energy of every radiation receives the same value . How infra-red and ultra-violet radiations produce no effect at all on the eye , and the light-producing effect of the same quantity of energy is much greater in the middle of the spectrum than at its ends . If we place in front of the thermopile a light filter which has the property of stopping entirely all the infra-red and ultra-violet radiation and of cutting down the energy of the visible spectrum in inverse ratio to its light-producing effect , that is , if we weight each radiation according to its , then the deflections will be proportional to the light received . This combination of filter and * ' Colour Vision , ' p. 103 . On the Absolute Measurement of Light . thermopile is then a kind of electric eye , which has a property that the human eye has not , namely , the property of registering the intensity of the light to which it is exposed.* The relative visibility of light of different wave-lengths for different intensities of that light has as yet been determined only for one eye , namely , that of Prof. A. Ivonig , and the results are given in a very convenient table in a paper by P. G. Nutting , f Prof. Konig 's colour vision was normal , and so in default of other data we can take this table as applying to the average human eye . In choosing a filter we must fix on something capable of accurate reproduction . This rules coloured glasses out of the question , unless they are made under standard conditions . We are therefore restricted to liquids in glass cells . Commercial dyes of ill-defined composition are subject to the same objection as coloured glasses . Solutions of salts which can be varied in strength give us more latitude , and are therefore to be preferred to liquids of a fixed composition . A series of researches on the absorption of light by aqueous solutions of inorganic salts in the ultra-violet , visible spectrum , and infra-red is now being carried out in the Physical Laboratory of the University of Glasgow , as a result of which I am in possession of a considerable amount of data not at present accessible to others , and from it I have no hesitation in concluding that the most suitable filter is a 3 cm . thickness of copper sulphate in water of concentration 0'200 gramme-molecule per litre , followed by a 1 cm . thickness of potassium bichromate of concentration 0-0025 gramme-molecule per litre . I have examined eight * After writing this paper my attention was called to the fact that an attempt to put this method into practice has already been made by Ch. Fdry ( " Photometrie a lecture direct : Rendement optique de quelques luminaires , " 'Journ . de Pliys . , ' 1908 , vol. 4 , p. 638 ) . He used a solution of copper acetate in water with a radiomicrometer , and has selected the same total thickness of water as myself , namely , 4 cm . He has not , however , gone into the matter fully , and does not give the fraction transmitted by his filter throughout any part of the spectrum . Copper acetate alone cannot give the proper absorption in the violet . I have also used a radiomicrometer , and my experience is that it is inferior in sensitiveness to the apparatus described in this paper , although possessing the advantages of simplicity and cheapness . J. E. Petavel , in a well-known paper ( " A Preliminary Study for a New Standard of Light , " ' Electrician , ' 1902-3 , vol. 50 , p. 1012 ) , proposes to let the radiation from incandescent platinum fall upon two thermopiles , one with a glass filter and the other with a filter of " black fluorspar " in front of it , and to use the ratio of the deflections as a means of determining the temperature of the platinum . The brightness of the latter as measured by a photometer at a definite temperature is to be the standard . His work is thus altogether on different lines . Black fluorspar seems to me altogether too indefinite a substance for his purpose . + " The Luminous Equivalent of Radiation , " 'Bull . Bureau of Standards , ' 1908 , vol. 5 , p. 279 . VOL. LXXXV.\#151 ; A. X Dr. R. A. Houstoim . [ Apr. 5 , different kinds of commercial coloured glass , but none of them is of the least use for the purpose , owing to not stopping the near infra-red . The absorption of light in aqueous solutions of inorganic salts obeys the following equation , I = I0 . 10-^ , which also defines A , the molecular extinction coefficient of the salt for the wave-length considered . I0 is the initial intensity of the light , I its intensity after passing through a thickness d of solution , d being measured in centimetres , and c is the concentration of the solution in gramme-molecules per litre . We may take A as independent of c except for wide ranges and at particular points in some spectra . The following tables give the values of A for the two salts in question in the ultra-violet and for the copper sulphate in the infra-red . The values Infra-red . A. A. CuS04,5H"0 . \lt ; ? = 0-03435 . A. A. CuS04,5Ho0 . c = 0-03435 . M- fX . 0-684 6-36 0-910 9-1 0-720 9-8 0-980 7-1 0-750 11 -5 1-07 5 -8 0-794 11 -7 1-17 4-1 0-850 11 1 1 -27 3-0 Ultra-violet . CuS04 ; 5H20 . K2Cr207 . c. A. A. c. A. A. n. M " 7160 o-oi 0-267 52 -0 0 *0001 0-241 0-03 0-278 34 -0 \#151 ; 0-269 11100 0-05 0-282 20 -2 \#151 ; 0-284 7440 0-287 13-0 \#151 ; 0-291 5070 o-io 0-291 10 -1 * \#151 ; 0-300 2720 0-292 8-6 0 *0005 0-308 2320 0-296 6-5 0 *0003 ? 0 -316 2080 0*30 0-299 3-37 0 -0005 0-325 2320 , j 0-309 1 -48 0 '0001 0-331 2720 0-313 0-78 \#151 ; 0-336 5070 ? 0 -322 0-08 \#151 ; 0-349 7440 ? 0 -375 10000 0-397 7440 0 '0003 0-410 3080 0 '001 0-416 1030 On the Absolute Measurement of Light . 1911 . ] for the visible spectrum have already been determined by Griinbaum* and by A. S. Bussell and the author.f The values for copper sulphate in the infra-red were obtained with a linear thermopile , the source of light being a Nernst glower . The values for the ultra-violet were obtained by means of a quartz photometer of original design which has recently been worked out by John S. Anderson and the author , and a description of which is already in course of publication . It is , of course , impossible to give values further into the infra-red owing to the absorption of water . At the strength and thickness used in the filter potassium bichromate does not exercise any appreciable absorption in the infra-red . The values of A cdfor the two filters have been calculated from the table ? and are shown in the following diagram . The values for copper sulphate art . shown by \#169 ; 's and the values for potassium bichromate by x 's ; Griinbaum 's values are taken for the copper sulphate and our own for the potassium bichromate . The smooth curve is the sum of the ordinates for each salt . The logarithms of the columns D and E in Nutting 's table were then calculated , their sign was changed , and they were plotted on the diagram as the dotted curves . In order to facilitate comparison with the smooth curve , the vertical scale for the dotted curves is displaced 008 up . Of course , we can add any constant quantity to the ordinates of the smooth curve without altering the relative absorption of the different colours . o o o o. * 'Ann . d. Phys. , ( 4 ) 1903 , vol. 12 , p. 1004 . t 'Roy . Soc. Edin . Proc. , ' 1908-9 , vol. 29 , p. 69 . X Dr. R. A. Houstoun . [ Apr. 5 , On the one side the smooth curve agrees with E , on the other side with D. D is for an illumination of 2 30 metre-candles and E for an illumination of 9'22 metre-candles . We are therefore justified in assuming that our filters weight the radiation of the visible spectrum correctly according to its visibility to normal colour vision , the illumination of the field being about 6 metre-candles . If we take as our standard another illumination of the field , it is easy to shift the minimum of the curve by diminishing the concentration of the copper sulphate and increasing the concentration of the potassium bichromate or vice versa . The strength of the copper sulphate , however , cannot be weakened much unless an additional thickness of water or of , say , ferrous ammonium sulphate is used , otherwise there will not be a sufficient margin of safety in the infra-red . Aqueous solutions of ferrous ammonium sulphate are , it is now known , very effective in stopping heat rays while allowing the light rays to pass.* They are much more efficient than alum , which in this respect is no better than water . If we neglect the light absorbed in the glass , the fraction of light transmitted by our filter is equal to 10-'-6Ac x j[0~0'0025Ak x jc\gt ; where Ac is the molecular extinction coefficient of the copper sulphate , AK is the molecular extinction coefficient of the potassium bichromate , and the fraction that would be transmitted by 4 cm . of pure water alone . In order that the effect due to the different constituents of the filter may be seen , I have calculated 10-0'6Ac , lO-0'0025^ and k throughout the spectrum , using for k the values of E. Aschkinass.f The results are given in the second , third , and fourth columns of the following table . The product of the three factors , that is , the transmissivity of the whole filter , is given in the fifth column . Of course , in addition to the above , the absorption of the glass of the cells has to be considered . Glass absorbs all radiations below ( \gt ; 330 ya and above 3-00 ya. The filter is weakest in the infra-red at E27 ya. In the normal energy spectra of our ordinary light sources the ordinates at 1*27 ya are about twenty times or thereabouts the ordinates at 05 ya. With the strength used , the stopping power of the filter is hence ample , but this point in the spectrum must be watched if the concentration of the copper sulphate is diminished much . Having found by calculation that the radiation received by a thermopile * R. A. Houstoun and J. Logie , ' Phys. Zs . , ' vol. 11 , p. 672 . t ' Wied . Ann. , ' 1895 , vol. 55 , p. 401 . 1911 . ] On the Absolute Measurement of Light . A. 10-0-6AC . 10 -0-0025Ak . 0*227 \ \lt ; 6*3110~n \lt ; 1-3 10-1S 0-241 J 1 -3 10~18 0-284 6-3110"11 2 -5 10-19 0-300 1 -20 10-2 1 -6 10~7 0-308 0-107 1 -6 10~6 0 *325 0-89 1 -6 10-\#174 ; 0-336 1 -9 10-13 0-397 2 -5 10-19 0-416 2 -6 10~3 0-463 \ \lt ; 0-986 0-105 0-471 J 0-158 0-480 0-986 0-234 0-489 0-977 0 -355 0-499 0-968 0-501 0 -5086 0-951 0-661 0 -5461 0-792 0-982 ' 0 -5780 0-521 1 -oo 0-6004 0-292 \#151 ; 0-6239 0-108 \#151 ; 0 -6452 0-0336 \#151 ; 0-684 1 -54 10~4 0-720 1 -32 10~6 \#151 ; 0-750 1 -26 10_* \#151 ; 0-794 9 -55 10~8 \#151 ; 0-850 2 -2 10- 7 \#151 ; 0-910 3 -5 10-fi \#151 ; 0-980 5 -5 10~5 \#151 ; 1 -09 3 -3 10-4 \#151 ; 1-17 3 -5 10~3 \#151 ; 1 -27 1 -6 10~2 \#151 ; 1 -40 k. \ 10"0*6 Ac X 10-0*0025 Ak x k. 0-99 \ \lt ; 8 10-29 0-99 J 0-99 1 -6 10-'29 1 -oo 1 9 10~9 \#151 ; 1 -7 IO-7 \#151 ; 1 -5 10~7 \#151 ; \lt ; 1-9 10-13 \#151 ; \lt ; 2-5 10"19 \#151 ; \lt ; 2-6 lO"3 \lt ; 0-105 \#151 ; \lt ; 0-158 \#151 ; 0-229 \#151 ; 0-347 \#151 ; 0 -485 \#151 ; 0-63 \#151 ; 0-77 \#151 ; 0-52 0-99 0-29 0 -99 0-107 0-99 0 -034 0-99 1 -53 10-4 0-95 1 -25 KT6 0-91 1 -14 10"7 0-92 8 -8 10-8 0*86 1 9 10- ? 0-73 *2 -5 10-\#174 ; 0-20 1 -5 10~5 0-48 1 -6 10~4 0-054 1 -9 IQ"4 0-0085 1 -3 lO"4 2 10"41 \lt ; 2 10~41 Never \gt ; lO^18 all the way to 8 " 5 fx . through this filter should be proportional to the light incident on the filter , I proceeded by direct experiment to determine if this actually was the case . I had three thermopiles at my disposal , a Rubens linear one with iron-constantan couples and two older ones , of different types , but both with antimony-bismuth couples . The Rubens thermopile consists of 20 couples on a length of 2 cm . , the wires being soldered together with silver beads , which are flattened into discs of 1 mm. diameter . Hence its receiving area is about 0*157 sq . cm . In the case of each of the other two , the receiving area was about 1 square inch , and the number of couples was greater , yet the Rubens thermopile was as sensitive , even without its reflectors , reached the steady state in a shorter time , and had a very much steadier zero . Only the Rubens thermopile was used . The galvanometer was a Du Rois Rubens ironclad one , of resistance 10 ohms , the property of the Carnegie Trust for the Universities of Scotland . Dr. R. A. Houstoun . [ Apr. 5 , In order to protect it from vibration , it was suspended from a bracket in the wall by three wires each about H metres long , and hung with its three levelling screws clearing the table by about 1 cm . Between the table and levelling screws loose wads of cotton wool were placed for the purpose of damping any vibrations that might arise . The lamp and scale were \\ metres from the mirror . The resistance of the thermopile was 5 ohms . At the sensitiveness used , the period was 3 seconds and ^ mm. on the scale indicated a current of 10~9 amperes . It soon became evident that this high sensitiveness was to be fully utilised . When the thermopile was set up at a distance of 33 cm . from a 32 c.p. carbon glow lamp with the filters in front , the deflection was only 17 |-mm . When this lamp is run at its marked voltage , 250 volts , about 2-6 per cent , of its total radiation is light , that is , lies between 0-400 [ x and 0760 / x , but only a fraction of this 2'6 per cent , gets through the filter . Perhaps altogether about 1/ 1000 of the total radiation passes through the filter . The thermopile was , then , set up at a distance of 33 cm . from the 32 c.p. carbon glow lamp with the filters in front , the K2O2O7 filter being next the thermopile . On the other side of the lamp was a photometer bench , at the other end of which there was a 125 volt tantalum lamp that was run off a storage battery . The carbon lamp and the tantalum lamp were compared by a wedge photometer . When this comparison was being made the tantalum lamp was always shunted by a current balance and constant resistance , the latter being chosen so that the open part of the scale of the balance was in use , and from the indications of the balance the voltage on the tantalum lamp could be kept constant to 1/ 800 by means of a rheostat . At the voltage used the horizontal candle power of the tantalum lamp , measured by a Hefner lamp , was 7T3 British candles . Headings were then taken for different voltages alternately with the thermopile and with the photometer . One set of results is given in the following table and plotted in the following curve . Test of a 32-candle power Glow Lamp . I Voltage . Galvanometer readings . Photometer readings . Throws . Mean . Individual settings . Candle power . 207 -1 5-5 4-0 4-0 3-0 4-5 4 -2 117-5 114-5 112-5 114-5 6-15 222 *5 8-0 7-0 6-5 6-7 7-0 96 -5 98 -5 96 -5 98 -5 11 -2 251 -6 18 -0 16 -0 17 -5 18 -0 17 -4 77 -5 76 -5 76 -5 76 -5 24 -9 283 -7 38 -0 38 -0 36 .5 36 '5 37 -2 59 -5 57 -5 59 -5 58 5 53 -8 ' 304 *7 56-5 56-5 60-0 59 58-2 48-5 47*5 49-5 49 5 88 -1 ' ' \#166 ; : 1911 . ] On the Absolute Measurement of Light . Every reading taken is given . At each voltage two readings were first taken with the thermopile , then two settings of the photometer were made ; the remaining thermopile readings were then made , and , finally , the last two photometer readings were taken . The numbers given in the table as photometer settings are the distances of the wedge in centimetres from the comparison lamp . The total distance between the two lamps was 220 cm . The curve should , of course , be a straight line . The agreement is very good when we consider that the galvanometer readings are ^ mm. at 1^ metres distance from the mirror , and that for the last point the photometer was getting rather near the comparison lamp for the inverse square law to hold . I have altered the strength of the K2C12O7 to 0'0125 and of the CuS04,5H20 to c = 0'350 , and the proportionality still holds . A thermopile used with such a filter can therefore be employed for measuring candle power , more especially mean spherical candle power , because it is only necessary to set up equally sensitive thermopiles over the sphere and to connect them in series with the one galvanometer . All difficulties connected with the integration thus vanish . The method works also quite as well in broad daylight as in a darkened room , the deflections being the same in each case . I think , however , that it is not suitable for commercial application , on account of the high sensitiveness of the galvanometer required . Its importance lies in the fact that it can be used for defining our unit of light and for providing a satisfactory basis on which lights of different colour can be compared , irrespective of intensity and of idiosyncrasy on the part of the observer . The amount of light lost by reflection at the glass surfaces and by 284 On the Absolute Measurement of Light . absorption in the glass of the cells can be easily determined by filling the cells with water and using a spectrophotometer to determine the fraction of the incident light transmitted . It is sensibly the same throughout the visible spectrum , and has the value 084 for both of the cells employed . It is easy to determine what the galvanometer deflections would have been , had there been no reflection losses or absorption losses in the glass ; we have only to multiply by l/ ( 084)2 . In determining the distance of the thermopile from the source of light , we have , of course , to multiply each thickness'of glass and liquid traversed by its index of refraction . I propose therefore to define the unit of light intensity as follows :\#151 ; The unit of light intensity is that source the total intensity of radiation from which at an optical distance of 1 metre after passing through an ideal filter would be x ergs/ cm.2 sec. , the ideal filter to be one possessing the light absorbing properties of a 3 cm . thick aqueous solution of CuS04,5H2(A of strength 0200 gramme-molecules per litre and a 1 cm . thick aqueous solution of K2Cr207 of strengthO '0025 gramme-molecules per litre , but neither to reflect nor to absorb any light in any other way . I think it better to eliminate the properties of the glass in this way . Different cells have quite an appreciable difference in absorption and the transmission coefficient of a cell is easy to determine . The definition , has the advantage of connecting up light closer with the C.G.S. system . By means of his pyrheliometer K. Angstrom* has been able to measure the radiation from terrestrial sources to less than 1 per cent. , the chief difficulty being to allow for want of " absolute blackness " on the part of the receiving surface . The radiation-receiving surface in my experiments was about 0157 sq . cm . , and the distance from the source 33 cms . By increasing the light-receiving area and using Angstrom 's method it should be possible to determine x with sufficient accuracy . For the standard candle in the units specified it is roughly 0*8 . * 'jAstrophys . Journ. , ' 1899 , vol. 9 , p. 332 ; 'Phys . Rev. , ' 1893 , vol. 1 , p. 365 .

rspa_1911_0041

0950-1207

On a method of making visible the paths of ionising particles through a gas.

285

288

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

C. T. R. Wilson, M. A., F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1911.0041

en

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1911_0041

10.1098/rspa.1911.0041

Atomic Physics

Thermodynamics

Atomic Physics

285 On a Method of making Visible the Paths of Ionising Particles through a Gas . By C.T. R. Wilson , M.A. , F.R.S. ( Received April 19 , \#151 ; Read May 11 , 1911 . ) [ Plate 9 . ] The tracks of individual a- or / 3-particles , or of ionising rays of any kind , , through a moist gas may be made visible by condensing water upon the ions set free , a suitable form of expansion apparatus being used for the purpose . In order that the clouds formed should give a true picture of the trails of ions left by the ionising particles , it is necessary that little or no stirring up of the gas should result from the expansion . It is desirable that no interval long enough to allow of appreciable diffusion of the ions should elapse between their liberation and the production of the super-saturation necessary for the condensation of water upon them ; and that the cloud-chamber should be free from all ions other than those in the freshly formed trails . The apparatus which has proved effective for the purpose differs from that used in my former experiments on condensation nuclei mainly in the form of the cloud-chamber . This is cylindrical , with flat horizontal roof and floors , its diameter being 7'5 cm . , and its height between 4 and 5 mm. before expansion , and about 6'2 mm. after expansion . The expansion is effected by the sudden downward displacement of the floor of the cloud-chamber ; this is constituted by the flat top of a hollow brass piston open below , and set in motion by the method described in former papers . The clouds are viewed through the roof of the cloud-chamber , which is of glass , coated below with a uniform layer of clear gelatine . The floor is also covered by a layer of gelatine , in this case blackened by the addition of a little Indian ink . Besides serving as a cement to attach the glass roof of the cloud-chamber , , the gelatine lining avoids altogether one of the principal sources of trouble in all cloud experiments\#151 ; the deposition of dew on the inner surface of the glass . In addition it forms , when moist , a conducting layer which may be maintained at a constant potential ; the connection with a source of potential being made through an annular strip of tinfoil fixed by means of . the gelatine round the margin of the glass plate which forms the roof , and ! extending to just within the cylindrical glass wall of the cloud-chamber . 286 Mr. C. T. K. Wilson . Method of making Visible [ Apr. 19 , The potential difference applied between the roof and floor , in the observations described below , amounted to 8 volts . Any ions set free before an expansion were thus exposed to a field of about 16 volts per centimetre , and had at the most about | cm . to travel . The only ions " caught , " on expansion , were thus those which had been produced within less than 1 / 40th of a second before the expansion , and such as were set free in the short interval after the expansion during which the super-saturation exceeded the limit necessary for condensation upon the ions . A horizontal stratum of the air in the cloud-chamber was illuminated by a suitable source and condensing lens ; for eye observations a Nernst lamp is a convenient source . For the purpose of photographing the clouds a Leyden jar discharge through mercury vapour at atmospheric pressure was employed , the mercury being contained in a horizontal capillary quartz tube , of which the central portion was heated to vaporise the mercury . The spark was fired by the mechanism which started the expansion , and took place one- or two-tenths of a second later . The camera was inclined at .an angle of 30 ' to the horizontal , the distances being arranged to give a picture of approximately the natural size , and the photographic plate being tilted so that the whole illuminated layer might be approximately in focus . Results . Clouds with Large Expansions.\#151 ; The clouds formed with large expansions in the absence of ions ( v2/ vi'\gt ; 1'3\amp ; ) showed , so far as the eye could judge , a uniform distribution of drops . Ionisation by a-Rays.\#151 ; The radium-tipped metal tongue from a spinthariscope was placed inside the cloud-chamber , and the effect of expansion observed after removal of the dust particles . The cloud condensed on the ions , wdiile varying infinitely in detail , was always of the same general character as that of which fig. 1 ( Plate 9 ) is a photograph . The photograph gives , however , but a poor idea of the really beautiful appearance of these clouds . It must be remembered , in interpreting the photographs , that trails of all ages , up to about l/ 40th of a second , may be present , the most sharply defined being those left by particles which have traversed the air while super-saturated to the extent required to cause condensation upon the ions . The trail of ions produced by a particle which traversed the gas before the expansion may have had time to divide into a positively and a negatively charged portion under the action of the electric field , and in each of these a certain amount of diffusion of the ions may have taken place before expansion . It is possible , therefore , that the few remarkably .sharply defined lines , about 1/ 10 mm. wide , alone represent the actual C. T.R , Roy . Soc. Proc. , A. 85 , Plate 9 . Fig. 1 . Cloud formed on Tons due to a-Kays . Fig. 2 . Cloud formed on Ions due to X-Rays . 1911 . ] the Paths of Ionising Particles through a Gas . 287 distribution of ions immediately after the passage of the a-particles , before any appreciable diffusion has had time to take place . Ionisation by/ 3-liays.\#151 ; A small quantity of impure radium salt in a thin glass bulb was held against a small aperture , closed by aluminium weighing about 1 mgrm . per sq . cm . , in the cylindrical vertical wall of the cloud-chamber . On making an expansion sufficient to catch all the ions , two or three absolutely straight thread-like lines of cloud were generally seen radiating across the vessel from the aperture . In addition , other similar lines were occasionally seen crossing the vessel in other directions , probably secondary / 3-rays from the walls of the vessel . Ionisation by y-Iiays.\#151 ; The 7-rays from 30 mgrm . of radium bromide , placed at a distance of 30 cm . on the same horizontal level as the cloud-chamber , produced on expansion a cloud entirely localised in streaks and patches and consisting mainly of fine , perfectly straight threads , traversing the vessel in all directions\#151 ; the tracks of / 3-particles from the walls of the vessel . Ionisation by X-Rays.\#151 ; When the air is allowed to expand while exposed to the radiation from an X-ray bulb the whole of the region traversed by the primary beam is seen to be filled with minute streaks and patches of cloud , a few due to secondary X-rays appearing also outside the* primary beam . A photograph shows the cloudlets to be mainly small thread-like objects not more than a few millimetres in length , and many of them being considerably less than 1/ 10 mm. in breadth . Few of them are straight , some of them showing complete loops . Many of them show a peculiar beaded structure . In addition to the thread-like cloudlets , there are minute patches of cloud which may be merely foreshortened threads . Other fainter and more diffuse patches and streaks are also present , possibly representing older trails , in which the ions have had time to diffuse considerably before the expansion . The droplets composing the threads have been deposited on the ions produced along the paths of the actually effective ionising rays . These are probably of the nature of easily absorbed secondary - or cathode-rays ; some doubtless starting from the roof or floor of the cloud-chamber , others , however ( the larger number when a limited horizontal beam of X-rays is used ) , originating in the gas . The results are in agreement with Bragg 's view that the whole of the ionisation by X-rays may be regarded as being .due to / 3- or cathode-rays arising from the X-rays . The question whether the original X-radiation has a continuous wave front , or is itself corpuscular as Brag supposes , or has in some other way its -energy localised around definite points in the manner suggested by Dr. F. Horton . [ Apr. 26 , Sir J. J. Thomson , remains undecided . The method already furnishes , however , a very direct proof that when ionisation by X-rays occurs corpuscles are liberated , each with energy sufficient to enable it to produce a large number of ions along its course . The few preliminary photographs which have been taken were not obtained under conditions suitable for an examination of the relation of the initial direction of the cathode rays produced in the air to that of the incident Rontgen radiation . I hope shortly to obtain photographs which will admit of this being done . The Vacuum Tube Spectra of Mercury . By Frank Horton , D.Sc . , M.A. , Fellow of St. John 's College , Cambridge . ( Communicated by Sir J. J. Thomson , F.R.S. Received April 26 , \#151 ; Read May 25 , 1911 . ) The ' Proceedings of the Royal Society ' for 1860 contain a paper by Plucker , * which gives an account of the first observations of the spectrum of the luminous discharge through mercury vapour at a low pressure . Plucker used a vacuum tube with mercury electrodes , and he observed and made measurements of the wave-lengths of ten lines . A few years later , working with Hittorf , f he found that the mercury spectrum may be obtained more brightly when a Leyden jar and spark gap are used in parallel with the tube . Other conditions affecting the lines observed in the vacuum tube spectrum of mercury have since been recorded by various investigators ; for instance , the widening of the lines with increased pressure was observed by Ciamician , * and the effect of the presence of different gases in the vacuum tube on the brightness of the mercury lines was investigated by Sundell , S who found that the mercury lines were visible when the tube contained hydrogen at considerable pressures , but that with oxygen or nitrogen they could only be seen when the pressure was very low . The spectrum of the light from the mercury arc was first investigated by Liveing and Dewar , || and afterwards very completely by Kayser and * Plucker , ' Roy . Soc. Proc. , ' 1860 , vol. 10 , p. 256 . + Plucker and Hittorf , ' Phil. Trans. , ' 1865 , vol. 155 , p. 1 . + Ciamician , \#163 ; Wien . Ber . , ' 1878 , vol. 78 , p. 867 . S Sundell , ' Phil. Mag. ' [ 5 ] , 1887 , vol. 24 , p. 98 . I ] Living and Dewar , ' Phil. Trans. , ' 1883 , vol. 174 , p. 187 .

rspa_1911_0042

0950-1207

The vacuum tube spectra of mercury.

288

302

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Frank Horton, D. Sc., M. A.|Sir J. J. Thomson, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1911.0042

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1911_0042

10.1098/rspa.1911.0042

Atomic Physics

Thermodynamics

Atomic Physics

288 Dr. F. Horton . [ Apr. 26 , Sir J. J. Thomson , remains undecided . The method already furnishes , however , a very direct proof that when ionisation by X-rays occurs corpuscles are liberated , each with energy sufficient to enable it to produce a large number of ions along its course . The few preliminary photographs which have been taken were not obtained under conditions suitable for an examination of the relation of the initial direction of the cathode rays produced in the air to that of the incident Rontgen radiation . I hope shortly to obtain photographs which will admit of this being done . The Vacuum Tube Spectra of Mercury . By Frank Horton , D.Sc . , M.A. , Fellow of St. John 's College , Cambridge . ( Communicated by Sir J. J. Thomson , F.R.S. Received April 26 , \#151 ; Read May 25 , 1911 . ) The ' Proceedings of the Royal Society ' for 1860 contain a paper by Plucker , * which gives an account of the first observations of the spectrum of the luminous discharge through mercury vapour at a low pressure . Plucker used a vacuum tube with mercury electrodes , and he observed and made measurements of the wave-lengths of ten lines . A few years later , working with Hittorf , f he found that the mercury spectrum may be obtained more brightly when a Leyden jar and spark gap are used in parallel with the tube . Other conditions affecting the lines observed in the vacuum tube spectrum of mercury have since been recorded by various investigators ; for instance , the widening of the lines with increased pressure was observed by Ciamician , * and the effect of the presence of different gases in the vacuum tube on the brightness of the mercury lines was investigated by Sundell , S who found that the mercury lines were visible when the tube contained hydrogen at considerable pressures , but that with oxygen or nitrogen they could only be seen when the pressure was very low . The spectrum of the light from the mercury arc was first investigated by Liveing and Dewar , || and afterwards very completely by Kayser and * Plucker , ' Roy . Soc. Proc. , ' 1860 , vol. 10 , p. 256 . + Plucker and Hittorf , ' Phil. Trans. , ' 1865 , vol. 155 , p. 1 . + Ciamician , \#163 ; Wien . Ber . , ' 1878 , vol. 78 , p. 867 . S Sundell , ' Phil. Mag. ' [ 5 ] , 1887 , vol. 24 , p. 98 . I ] Living and Dewar , ' Phil. Trans. , ' 1883 , vol. 174 , p. 187 . 1911 . ] The Vacuum Tube Spectra of Mercury . Rung , * * * S but the first thorough investigation of the spectrum of mercury in vacuum tubes was that of Eder and Valenta , f published in 1894 . These observers found that the lines obtained from a vacuum tube at low pressures were much sharper than those given by the arc or spark . The number of lines obtained depended on the current density and on the temperature of the vapour . The spectrum richest in lines was obtained by having one part of the vacuum tube hot and the rest cold , so that the mercury distilled through the capillary . Using a Leyden jar they were then able to measure a great many new lines . From the wider parts of the vacuum tube they obtained a banded spectrum , but this ( which was first observed by them ) was seen best in the capillary when the discharge was passed without a Leyden jar . Introducing capacity into the circuit had the effect of breaking up these bands into an immense number of fine lines\#151 ; the " rich line spectrum " \#151 ; some 670 lines are recorded in their paper . The observations of Eder and Yalenta have since been confirmed by Huff.* As the result of a detailed study of the effects of capacity , self-induction , and temperature on the spectrum , he came to the conclusion that , by suitably regulating the temperature of the tube and the conditions of the discharge , the spectrum could be made to change gradually from that consisting of bands to that richest in lines . A background of continuous spectrum was obtained , especially when capacity was placed in the circuit and strong discharges were passed at rather high temperatures . A thorough investigation of the spectrum of mercury has also been made by Stark , S who came to the conclusion that mercury possesses two distinct line spectra , viz. , that given by an arc in vacuo , and that given by a vacuum tube discharge . The lines obtained in the arc spectrum were those previously observed by Kayser and Rung , together with a few others of small intensity . Those obtained in the spectrum of the glow discharge Stark compares with the " rich line spectrum " of Eder and Yalenta . The latter observers give more lines in the less refrangible part of the spectrum , but Stark records many more in the ultra-violet . The spectrum given by the mercury arc light is called by Stark the first line spectrum of mercury , that given by the glow discharge is the second line spectrum . He puts forward the hypothesis that the first line spectrum is due to monovalent , and the second line spectrum to divalent mercury atoms\#151 ; atoms which have lost respectively one and two negative corpuscles . * Kayser and Rung , ' Wied . Ann. , ' 1891 , vol. 43 , p. 384 . + Eder and Yalenta , ' Denksclir . Wien . Akad . , ' 1894 , vol. 61 , p. 401 . I Huff , 'Astrophys . Journ. , ' 1900 , vol. 12 , p. 103 . S Stark , ' Ann. d. Phys. , ' 1905 , vol. 16 , p. 490 . Dr. F. Horton . [ Apr. 26 , A very complete investigation of the vacuum tube spectrum of mercury has been made by Stiles , * who gave particular attention to the red end a region of the spectrum which has not been so closely investigated as those which more readily affect a photographic plate . While investigating the discharge of electricity for a hot lime cathode in a vacuum tube , the author- ] was struck by the appearance of five sharp , bright lines in the red and orange regions of the spectrum , lines which could not be found recorded in any of the ordinary tables of wave-lengths , although two of them agreed roughly with faint lines observed by Stark in the vacuum tube spectrum of mercury . It now appears that these lines had been previously observed and measured by Hermann ! in the arc spectrum of mercury . They have since been measured by Stiles and their wave-lengths recorded in the paper already referred to . These lines are so sharp and bright in the spectrum of the discharge from a hot lime cathode through mercury vapour , that I was tempted to investigate the spectrum of the discharge in an ordinary vacuum tube under different electrical conditions . It was found that under certain conditions several new red and orange lines could be obtained . These appeared when a condenser was used , and the discharge was sent through the vapour at a low pressure . I therefore tried the effect of varying the pressure of the vapour through which the discharge from a hot lime cathode passed , in order to see if a different spectrum could be obtained . The discharge tube used was of the form figured in my previous paper , except that the platinum anode was covered with mercury . The amount of vapour present in the tube could be varied by warming or cooling it . When the lime cathode was heated and a discharge from a battery of cells passed through the tube , the five red and orange lines were seen quite brilliantly , the other bright lines observed being the two yellow lines 5791 , 5770 , the green 5461 , the blue 4916 , and the violet 4359 . On increasing the vapour pressure by warming the mercury , all the lines became wider and blurred and , with the exception of the wavelengths just mentioned , they finally became indistinguishable in a brilliant background of continuous spectrum . On reducing the pressure of the vapour by cooling the tube in liquid air , the whole spectrum became very faint and finally disappeared as the luminosity ceased , the lines in the red and orange regions being the first to go . It thus appears that the normal spectrum produced by the lime cathode discharge through mercury vapour contains these five red and orange lines * Stiles , ' Astrophys . Journ. , ' 1909 , vol. 30 , p. 48 . t Horton , 'Camb . Phil. Soc. Proc. , ' 1908 , vol. 14 , p. 501 . ! Hermann , 'Ann . d. Phys. , ' 1905 , vol. 16 , p. 684 . 1911 . ] The Vacuum Tube Spectra of Mercury . in addition to the other bright ones mentioned above ; a few faint lines are also visible\#151 ; the complete spectrum is given in Column II of the table on p. 295 . As will be seen in the following pages , this spectrum can also be-obtained , under certain conditions , from the induction coil discharge through an ordinary vacuum tube . The Preparation of the Vacuum Tubes . In the investigations of the spectrum of the induction coil discharge through mercury vapour the vacuum tubes employed were of the shape indicated in the accompanying diagrams :\#151 ; Fig. 1 shows the tube before being filled with mercury ; fig. 2 shows it sealed off from the pump and ready for use . The bulbs A and B containing the mercury were each about 2 cm . in diameter . The capillaries were about 2 mm. wide , but differed slightly in width in the different tubes used . The method of getting the mercury into the vacuum tube in a high state of purity may be gathered from fig. 1 . The glass tubing used to make the apparatus there shown was most carefully cleaned with chromic acid , and when complete the apparatus was cleaned out with boiling nitric acid , and finally with distilled water . Boiling nitric acid in the bulbs A and B served to remove hydrogen from the small platinum electrodes fused into them. . After careful drying , the discharge tube AB with the bulb I ) was sealed on to a mercury pump with a phosphorus pentoxide drying tube and the tube E containing cocoanut charcoal in connection . The large bulb C was carefully cleaned , dried , and nearly filled with purified mercury . It was then sealed on to the bulb D as shown in the diagram . The whole apparatus was exhausted as completely as possible by means of the mercury pump , the evacuation being finally completed by cooling the carbon tube E in liquid air . The tube AB and the bulb D were then heated all over by means of a blow-pipe flame to remove gas occluded on the inside surface of the glass . :292 Dr. F. Horton . [ Apr. 26 , The heating was continued for half an hour or more , and the glass was made so hot that in places it softened and sank in on account of the vacuum -inside . The bulb C was then very gently warmed by means of a small flame placed about 20 cm . below it , and the mercury began to distil over and to collect in the bulb D. When about two-thirds of the mercury in C had distilled into D the small connecting tube was fused up by a blow-pipe flame , and C was removed from the apparatus . D was then gently warmed , and two-thirds of the mercury in it was distilled over into the discharge tube AB . D was then sealed . off and removed . The mercury in the bulbs A and B was heated , and a discharge from an induction coil was passed through the tube . After this had been going on for some time the temperature of the discharge tube was considerably raised by gentle heating with a blow-pipe flame , and a quantity of the mercury distilled over into the tubes leading to the pump and collected there and in the tube E , which , throughout these operations , remained in a vessel of liquid air . Finally the connecting tube was melted at F , where previously it had been drawn down , and the discharge tube was separated from the pump and was ready for use ( fig. 2 ) . In this manner tubes could be prepared containing mercury only , all traces of foreign substances being completely excluded . At the ordinary room temperature the vacuum in the tube was so complete that no discharge could be sent through it by a large Marconi coil giving a 10-inch spark . In one of the tubes used the mercury was prepared from pure mercuric oxide supplied by Kahlbaum . This was decomposed by heating it in a vacuum , the oxygen being continually pumped away . The mercury was distilled into the discharge tube in the manner already described . All the tubes used gave similar spectra , but in one or two of them the carbon monoxide band spectrum was sometimes seen after they had been in use for some weeks , and , strangely enough , generally when the pressure of mercury vapour in the tube was rather high . I think that this gas came from the glass of the discharge tube , for the inner surface of the bulbs A and B at the level of the mercury became broken up by the passage of the discharge , and this might lead to a liberation of CO2 ( which gives the band spectrum ) from carbonates used in the manufacture of the glass . This would account for the spectrum appearing when the pressure of the mercury vapour was high , for then the tube was being most strongly heated . However , I have one tube , made over two years ago , which has never shown anything but mercury lines . 1911 . ] The Vacuum Tube Spectra Mercury . The Spectroscope , etc. The spectroscope used to measure the wave-lengths of the lines was one of Hilger 's direct wave-length reading instruments . This was very carefully calibrated by means of a helium-hydrogen-mercury tube . It was further calibrated in the red , orange , and yellow , by means of a neon tube . A curve of corrections was plotted showing the correction to be applied to any reading when the instrument was adjusted so that the reading of the mercury orange line , 6152 , was correct . The mercury vacuum tube under observation was held in a wooden stand , and under each of the bulbs A and B , but some 20 cm . below them , was placed a small flame which could be adjusted in size . The coil used to produce the discharge was a large Marconi instrument , taking 3 to 12 amperes through the primary , and capable of giving a 10-inch spark in the secondary circuit . When extra capacity was required in the circuit , two large Leyden jars of gallon size , joined in parallel , were included . This was done by lessening the size of a spark gap until sparks passed between the knobs , or sometimes by screwing these knobs up together . It was found that the two jars in parallel had more effect on the spectrum than one jar alone , and the effect was not noticeably increased by using six jars . The appearance of the spectrum varied greatly with the size and nature of the spark between the knobs in the Leyden jar circuit , the spectrum with most lines being observed when sharp , bright , intermittent sparks passed . Experimental Besults . In the experiments with the mercury vacuum tubes described in this paper , several spectra were obtained which appeared to be produced by quite definite conditions . These spectra contained , in some cases , the same lines , but with different relative intensities . Each spectrum was quite distinct and easily recognisable , and could be made to appear on arranging the electrical conditions known to produce it . The- methods of obtaining the different spectra will now be described . The simplest spectrum is that which I have called the five-line spectrum of mercury , consisting of the yellow pair 5791 , 5770 , the green 5461 , the blue 4916 , and the violet line 4359 . This spectrum is always obtained when both limbs of the tube are fairly hot and the discharge is running easily , the interrupter of the induction coil working quietly and without much sparking . Under these circumstances , even with the knobs of the spark gap in connection with the Leyden jars close together , no spark ( or a very small and quiet one ) passes between them , and screwing them together until they touch VOL. LXXXV.\#151 ; A. Y Dr. F. Horton . [ Apr. 26 , causes no difference in the spectrum of the discharge . During these observations , mercury condenses and collects in the upper , horizontal part of the tube . This suddenly runs over into one or other of the limbs of the tube , and some of it falls down into the mercury in the bulb , but generally a blob remains , blocking up a portion of the capillary . This immediately changes the nature of the discharge ; sparks are heard between the knobs of the spark gap , and usually the induction coil works more noisily . Instead of the simple five-line spectrum , the lines recorded in column II of Table I appear . This spectrum is the one given by the discharge from a glowing lime cathode through mercury vapour , and its characteristic feature is that the three orange lines 6235 , 6124 , 6074 , are present and are equally bright . During this experiment both bulbs , A and B , fig. 2 , have been gently warmed . If , now , the flame under bulb A is turned out , so that the temperature of that limb of the tube falls and the mercury distils over from B to A , and if the tube is then gently tapped with the finger so that a blob of mercury is made to collect in one of the capillaries , at the instant the blob forms the luminosity of the tube increases , and the spectrum observed is that given in column III of Table I. The most noticeable features of this are the presence of the mercury orange line 6152 , and that , of the other three orange lines , which in Spectrum II are equally bright , 6235 is now brighter than 6124 or 6074 . The order of luminosity of the two red lines is now reversed , and many more lines appear in the more refrangible parts of the spectrum . On the other hand , the two faint , but sharp , lines 5352 , 5319 , of Spectrum II are now no longer seen . In this experiment the mercury vapour is at a fairly high pressure , though , of course , not at quite so high a pressure as in the first experiment , in which both bulbs were heated . The spectrum obtained before the blob appears in the tube is the five-line spectrum , and , as before , this is not altered by putting the capacity in the circuit by screwing up the spark gap . Spectrum III is given by the light from either capillary after the blob has formed in one of them . There is a lot of continuous spectrum as a background to these lines ; this disappears when the blob falls out of the capillary , and the five-line spectrum then becomes very bright again . The other lines generally persist faintly for a short time , but they soon disappear . This seems to indicate that the systems emitting them are no longer being produced in the vapour , but that those which existed at the moment the blob fell out of the capillary are not immediately destroyed when the electrical conditions are changed . The formation of the blob of mercury in the capillary has the effect of making the tube " harder " ; for the two fresh surfaces of mercury formed across the tube act as an extra 1911 . ] The Vacuum Tube Spectra of Mercury . Table I. I. ii . III . IV . V. 1 Spectrum Lines of measured Five-line Intensity . glowing Intensity . Intensity . Intensity . 1 by Eder Intensity . spectrum . lime and discharge . Valenta . 6908 i 6908 3 6717 4 6717 2 6235 8 6235 8 6152 8 6152 8 6152 9 6124 8 6124 5 6074 8 6074 5 5890 6 5890 3 5889 4 5873 2 5873 3 5872 6 5819 1 5819 1 5806 2 5804 1 5791 9 5791 8 5791 8 5791 8 5791 10 5770 9 5770 8 5770 8 5770 8 5770 10 5728 , I 5728* 5 5679 1 5679 4 5679 I 6 5679 8 5596 2s 5596 6 5461 10 5461 ! io 5461 10 5461 10 5461 10 5427 1* 5427 8 5427 8 5409 1 5366 6 5366 4 5356 1 ' 5356* 1 5352 1,9 5352* 1 5319 1,9 5207 n 5207 4 5128 1 5047 3 5047 1 4960 4 4960 u 4960 6 4916 j 4 4916 4 4916 6 4916 lb 4916 4 1 4797 1 . lb 4797 2 4359 10 4359 6 4359 8 4359 8 4359 10 The lines of Eder and Valenta marked with an asterisk were only observed in the many lined spectrum . b signifies that the line was blurred . s signifies that the line was sharp . anode and extra cathode respectively , and there is consequently a double anode fall and a double cathode fall of potential to be overcome by the E.M.F. applied from the induction coil . The result of this is that a larger potential difference is established between the terminals of the tube . The Leyden jars become charged to a higher potential , and the energy of the discharge is now much greater than before , as is shown by the difference in the sparks . This increase in the energy of the discharge is possibly the cause of the production , and certainly the cause of the agitation , of those vibrating systems which are the origin of the extra lines appearing in the spectrum when the mercury collects in the capillary of the tube . That an increase in the energy of the discharge , due to an increase in the difference of potential between the terminals of the tube , is the cause of the Y 2 Dr. F. Horton . [ Apr. 26 , appearance of these extra lines may be shown in another way , for , starting with both bulbs fairly warm and the discharge running easily , we can increase the potential gradient in the tube by lowering the flames and allowing the temperature , and therefore the pressure , of the mercury vapour to fall . Doing this , we find that the five-line spectrum changes into Spectrum II , without the blob of mercury forming in the capillary . The temperature at which this happens is lower than that at^which Spectrum III is produced in the experiment described above . Having obtained Spectrum II in this manner , we can suddenly still further increase the potential gradient by tapping the tube so that the mercury collects in the capillary . The spectrum at once changes in a remarkable manner ; the orange Hne 6152 comes out brilliantly , and is the only line in that part of the spectrum\#151 ; the other orange and the red lines disappear . The visible lines are recorded in column IV of Table I. When the mercury falls out of the capillary the spectrum changes back again to Spectrum II . It is interesting to note that just as Spectrum II could be produced without the formation of the blob of mercury in the capillary , so , at still lower pressures , Spectrum IY would appear in the same way . It was seen| on several occasions after turning out both the Bunsen burners under the tube and allowing it gradually to cool down . On these occasions there was a small spark gap ( about 0'5 mm. ) in the Leyden jar circuit , and feeble sparks passed across . If the pressure falls too low , heavy sparking occurs and many more lines appear in the spectrum . The behaviour of the orange line 6152 is peculiar . Its appearance seems to depend upon circumstances which only slightly affect other lines usually appearing with it . For instance , when one limb only of1* the tube was warmed and the pressure of the vapour inside was not too low , the five-line spectrum normally changed into Spectrum III when a blob of mercury collected in the capillary , but sometimes all the lines of this spectrum would appear except 6152 . On these occasions , by careful observation , the line could usually be seen very faintly , and it would suddenly flash out quite brilliantly for an instant , probably during some slight change in the electrical conditions . At the same time several of the other lines would momentarily increase in brightness , notably the yellowish-green line 5679 . It might here be mentioned that I made some experiments with mercury vacuum tubes containing a little helium gas , in order to have present some lines of known wave-length for standardising the readings of the spectrometer . It is well known that the presence of helium brings out the mercury orange line very brightly , when otherwise only the five-line spectrum would appear . I found that the helium lines and the mercury line 6152 always The I acuumTube Spectra of Mercury . 1911 . ] appeared and disappeared together as the electrical conditions were changed . They were visible when an induction coil discharge was passed with the mercury electrodes cold , but when these were heated so as to increase the vapour pressure in the tube , the helium lines would gradually get fainter and finally disappear , and so also would the mercury orange line ; at the same time the other five mercury lines ( Spectrum I ) would gradually increase in brightness . Similar results were obtained when the discharge from a glowing lime cathode was used to produce the luminosity , although in this case the helium spectrum was always faint , and in this case , too , the other lines of Spectrum II appeared at first , but faded away as the temperature was raised . The normal cathode fall of potential in helium gas is considerably less than that in mercury vapour , and the presence of helium would therefore probably increase the potential gradient along the rest of the tube , but it is evident that neither a decreased cathode fall nor an increase in the potential gradient along the luminous discharge can be the cause of the production of the line 6152 , for in the absence of helium it does not appear in the spectrum of the glowing lime discharge , although the cathode fall is always very small and the potential gradient can readily be varied , nor would such an explanation account for the intimate connection of this particular mercury line with the brightest lines of the helium spectrum . In regard to the lines recorded in Table I , it should be stated that those down to the bright yellows 5791 , 5770 , were measured as accurately as possible with the spectrometer used , which had been standardised in the manner already described . The more refrangible lines were merely identified from the measurements of Eder and Valenta , which are given In the last column . It has already been stated that at very low pressures a spectrum was obtained containing several new red and orange lines . This spectrum in the more refrangible portions corresponds to the many lined spectrum discovered by Eder and Yalenta . It was first observed on turning out both the flames used to heat the vacuum tube and allowing it to cool down , but under these circumstances the tube soon becomes so hard that the discharge through it ceases . However , by careful regulation of the size of the flames and the distance of them from the tube , the temperature can be so adjusted that the many lined spectrum is continually present . It is necessary to have the Leyden jars in the circuit , and the spectrum is brightest when loud intermittent sparks pass between the knobs of the spark gap . If the sparks are weakei and give a continuously hissing noise ( as they do when the pressure is not sufficiently low ) only about half the number of lines are seen . The Dr. F. Horton . [ Apr. 26 , many-lined spectrum can be obtained at a slightly higher pressure by arranging that some mercury should collect in one of the capillaries of the tube . Under these circumstances the spectrum is brighter than at the very low pressure , but under the latter condition the lines are all quite sharp , whereas some of them appear blurred and obscured by bands at the higher pressures . The red and the orange lines only of this spectrum are given in Table II , which for comparison also contains the lines previously observed by Hermann and by Eder and Valenta . Table II.\#151 ; The Red and Orange Lines of the Many Lined Spectrum . Lines measured in the present research . Intensity . Lines measured by Hermann . Intensity . Lines measured by Eder and Valenta . Intensity . 1 7083 i ( 6908 ) 6908 4 ( 6717 ) 6717 1 6524 3 6521 2 6504 4 i 6421 2 6397 3 6386 2 6363 4 6364 2 6347 3 i 6318 6i 6298 1 62921 . 6i 6290 J It 6268 1 6242 2 ( 6235 ) 2 6235 10 6219 2 6187 1 6171 . 3s 6152 10 6152 10 ( 6124 ) 2 6124 10 6101 2 6090 2 ( 6074 ) 2 6073 10 6046 2s . 6023 2s 6018 2 5963 1 5948 1 5936 Is 5890 7 5890 2 5889 4 5881 2 5881 2 5873 7 5872 1 5872 6 i signifies that the line was intermittent ; the intensity given is that of the line at its biightest . s signifies that the line was sharp . The lines 6292 , 6290 , usually alternated , first one , then the other , appearing in rapid succession . On a few occasions lines were seen in the red beyond 6o24 , but I was unable to measure the position oi these with any accuracy on account of 299 ' 1911.]* ' The Vacuum Tube Spectra of Mercury . their feeble intensity . They appeared to be the two lines 6908 , 6717 , each of intensity less than 1 , with other rather brighter , but very indistinct lines at about 6642 , 6604 , and 6555 . I am inclined to think that the five red and orange lines of the spectrum of the glowing lime discharge ( which are placed within brackets in the table ) do not properly belong to the many-line spectrum , for they were absent when the spectrum was at its best . If the conditions of the discharge slightly changed , however^the three orange lines 6235 , 6124 , 6074 , would appear , and often when the mercury fell out of the capillary the spectrum would change to Spectrum II of Table I with these lines extraordinarily brilliant . After a few seconds\#151 ; probably as the temperature fell\#151 ; hissing sparks would be heard between the knobs of the spark gap and several lines of the many-lined spectrum would appear . The sparks would change to loud intermittent ones when the condensed mercury fell and stopped up the capillary , and then the complete many-lined spectrum could again be observed . In the table a few of the lines are marked as intermittent ; these , as a rule , kept flashing in at very frequent intervals , but in the case of 6318 the line was present all the time and kept flashing out more brightly . These intermittent lines were the last to appear in the many-lined spectrum as the pressure of the mercury vapour in the tube fell . It has been mentioned that when the many-lined spectrum was obtained at the higher pressure by waiting for a blob of condensed mercury to collect in the capillary of the tube , some of the lines were blurred and obscured by bands . As examples of this : a faint band occurs between the lines 5963 and 5936 , but when the many-lined spectrum is at its best this goes , and the line 5948 is seen quite plainly , while the line 5936 becomes extremely sharp . In the same way a band between the lines 6046 and 6018 at the higher pressure disappears when the pressure is reduced , leaving the line 6023 sharply defined . The many-lined spectrum may conveniently be obtained in another way , by passing an electrodeless ring discharge through mercury vapour . This was done with the tube shown in fig. 2 in the following manner:\#151 ; The tube was placed on its side and most of the mercury was collected in the bulb B. The bulb A was surrounded by a coil of 10 turns of well-insulated wire , the ends ot which were each connected to the outer coating of a large Leyden jar . The inside coatings of these jars were connected to the induction coil with an electric valve in series . An adjustable spark gap was arranged between the two inside coatings , and as each spark passed across this , there was a luminous ring discharge in the bulb A , if the temperature of the tube was fast adjusted so that the pressure of the mercury vapour was within certain Dr. F. Horton . [ Apr. 26 , limits . The author had previously found* that very bright luminosity may be produced in a gas in this way at pressures as low as 0-03 mm.\#151 ; corresponding in this case to a temperature of about 60 ' C. The electrodeless discharge only gives the complete many-lined spectrum when the slit of the spectroscope is directed to the outer edge of the luminous ring . Fewer lines were seen on looking nearer to the centre of the bulb , where the field is less intense , but these were always lines belonging to the many-lined spectrum ; the spectra recorded in Table I were never obtained from the electrodeless discharge . In addition to the red and orange lines recorded in Table II , 66 other lines were measured in the more refrangible parts of the many-lined spectrum . As nearly all of these were identified as lines measured by Eder and Yalenta , it was thought to be unnecessary to give them here . It should be mentioned that the lines in the second column of Table II were measured by Hermann in the spectrum of the mercury arc , produced in an Arons lamp . Hermann used a special method of rendering his photographic plates sensitive to the red rays . There can be no doubt that it was the absence of such sensitiveness in the plates used by Eder and Yalenta that was the cause of the lines now recorded in this region of the spectrum escaping detection in their experiments . Summary and Conclusion . The experiments described in this paper go to prove that mercury is capable of giving several distinct line spectra when subjected to an electric discharge in a vacuum tube . The particular spectrum appearing in any given case depends upon the energy of the discharge in relation to the mass of vapour through which it passes . The five-line spectrum is the one most easily produced , and as the energy is increased , or the pressure of the vapour is diminished , the other spectra recorded in the tables make their appearance in turn . The spectra of Table I are all perfectly definite in appearance , not only in regard to the actual lines they contain , but also as to their relative intensities when the spectrum is fairly bright ; moreover , on gradually increasing the energy of the discharge , all the lines of each spectrum in turn appear at the same moment as the electrical conditions become suitable to its production . The many-lined spectrum , on the other hand , is not quite so definite , for the number of lines appearing increases as the energy of the discharge is increased , until all are present . This is well illustrated by the case of the electrodeless ring discharge , in which , as has already been mentioned , the complete many-lined spectrum is only seen in the stronger parts of the field . A similar * Horton , 'Boy . Soc. Proc. , ' A , 1910 , vol. 84 , p. 434 . The Vacuum Tube Spectra Mercury . 1911 . ] result can be obtained with the ordinary vacuum tube discharge in which the electrical intensity is different at different points . It is much greater in the capillary portion than in the wider parts of the tube ; and , consequently , when the complete many-lined spectrum is seen in the capillary , there may be many fewer lines in the spectrum of the luminosity at other places . This is the result obtained by Huff , which is referred to at the commencement of this paper . Huff came to the conclusion that the change from the spectrum with fewest lines to that with the greatest number is quite gradual . This is so when we are dealing with the many-lined spectrum all the time\#151 ; and I class the two spectra of Eder and Yalenta ( and also those of Stark ) together , as being the same spectrum , with many more lines visible in one case than in the other\#151 ; but this gradual change does not occur in the case of the spectra of Table I , all of which contain many fewer lines . It will be noticed from the tables that the five lines of Spectrum I are common to all the spectra of mercury , though their relative intensities are not always the same . The spectrum of the glowing lime discharge consists of these plus some others , the brightest being the three lines in the orange region . Spectrum III is practically a combination of Spectra II and IY , together with a few extra lines , the brightest of which is 5366 . There are seven lines of Spectra II and IV which do not appear in Spectrum III , but all are of very small intensity . The many-lined spectrum contains all the lines of the other spectra , except the five red and orange lines 6908 , 6717 , 6235 , 6124 , 6074 . These , though sometimes visible , were always absent when the spectrum was at its best . In conclusion , the author would like to emphasize the importance , from a spectroscopic point of view , of two of the methods of producing luminosity in a gas which have been employed in these experiments , namely , by using the electrodeless ring discharge , and by the discharge from a glowing lime cathode . The first of these is a very convenient way of obtaining the spectrum with most lines , corresponding to that given by a heavy discharge with capacity in the circuit . The latter method of exciting luminosity is one which should be capable of many applications in spectroscopy , on account of the ease with which the electrical conditions can be controlled . In many respects mercury would appear to be an ideal substance to use for investigating the origin of spectra , for its vapour is monatomic and is very easily ionised ; moreover , it is possible to excite luminosity in it in several ways : by the electric arc or spark , or by the vacuum tube discharge . This latter may be produced ( a ) under a high potential difference , as with an induction coil and here the conditions may be varied by introducing capacity Messrs. W. R. Eousfield and W. E. Bousfield . [ Jan. 19^ and self-induction into the circuit ; ( b ) under a low potential difference by-means of the discharge from a glowing lime cathode ; and ( c ) by electromagnetic induction in the electrodeless ring discharge . Under these different conditions a continuous spectrum , a band spectrum , and spectra with various numbers of bright lines may be obtained . The difficulty is to correlate the observed spectra with the electrical conditions producing them . The author gladly takes this opportunity of expressing his thanks to Prof. Sir J. J. Thomson for his interest in these experiments , which were carried out in the Cavendish Laboratory , Cambridge . The Specific Heat of Water . By W. B. Bousfield , M.A. , K.C. , and W. Eric Bousfield , B.A. ( Communicated by Prof. Sir J. Larmor , Sec. R.S. , \#151 ; Received January 19 , \#151 ; Read February 23 , 1911 . ) ( Abstract . ) The object of this investigation was to obtain a basis curve for the specific heat of water , for comparison with specific heat curves of aqueous solutions . Former observers using different methods have obtained widely varying curves ; thus for the specific heat of water at 80 ' in terms of the 15 ' calorie , the following figures have been given , showing differences of 1 per cent.:\#151 ; Barnes , P0014 ; Regnault , P0081 ; Liidin , P0113 . For the value in joules of the 15 ' calorie the following have been found :\#151 ; Joule , 4T74 ; Griffiths , 4T98 ; Barnes , 4T84 . The first part of our investigation is concerned with the determination of the mechanical equivalent of heat in terms of the mean calorie from 13 ' to-55 ' , by a method of continuous flow calorimetry . Mercury thermometers were used which could be read to 0o,005 . An interval of 40 ' was taken , so that an error of 0'01 would not vitiate the result by more than 1 in 4000 . Through a Dewar vessel containing about 3 litres of water , in which was an electric heater , there was passed a current of water , entering at about 13 and passing out at about 55 ' . The vessel was immersed in a bath kept at the same temperature as the contents of the vessel . The top of the vessel was closed by a platinum box kept 10 ' higher . The electric heater , and the resistance used in series with it for determining the current by help of a battery of standard cells , were of novel type . Each consisted of a spiral glass tube of small bore into the ends of which were sealed platinum electrodes . The tube is connected with a thermometer tube so that

rspa_1911_0045

0950-1207

An optical method of measuring vapour pressures: Vapour pressure and apparent superheating of solid bromine.

306

308

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Clive Cuthbertson|Maude Cuthbertson|Prof. F. T. Trouton, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1911.0045

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1911_0045

10.1098/rspa.1911.0045

Thermodynamics

Tables

Thermodynamics

306 An Optical Method of Measuring Vapour Pressures Vapour Pressure and Apparent Superheating of Solid Bromine . By Clive Cuthbertson , Fellow of University College , London , and Maude Cuthbertson . ( Communicated by Prof. F. T. Trouton , F.R.S. Received April 20 , \#151 ; Read May 25 , 1911 . ) In the course of an investigation of the refractivity of gaseous bromine conducted with a Jamin refractometer it was observed that , as the temperature changed , very slight variations of the density of the vapour could be quickly and accurately recorded . This fact suggested that an optical method would be useful for measuring vapour pressures or densities at low pressures , especially in the case of substances which attack mercury . The following observations on the vapour of bromine serve as an illustration of the possibilities of the method , and have brought to light an interesting phenomenon , which is described below . A thin glass bulb , containing 1 or 2 c.c. of Kahlbaum 's pure bromine , was sealed to a tube communicating both with the pump and the refractometer tube . The temperature of the bromine was reduced to \#151 ; 80 ' C. , at which its vapour pressure is negligible , and the bulb was completely evacuated , so as to remove all traces of hydrobramic acid which might have formed by the action of the bromine on the tap-greasa since the previous experiment . The refractometer tube was separately evacuated , and the two were put in connection by opening a tap . The cooling bath was then slowly brought up to atmospheric temperature by stages , while an observer counted the interference bands which crossed the field of view of the refractometer . During each reading the temperature of the bulb was kept constant by stirring the hath . As the melting-point was approached numerous readings were taken , the rise of 1 ' from \#151 ; 8 ' to \#151 ; 7 ' sometimes occupying 20 minutes . A complete series of readings between \#151 ; 80 ' and 0 ' occupied about an hour . At the moment of each reading the temperature of the refractometer tube was also read . The light used was approximately monochromatic , and had the wave-length of the red Cd line , 6438 . In this experiment what is actually observed is the temperature of the liquid bromine and the corresponding refractivity of the vapour in the refractometer tube , which is at the same pressure as the vapour in contact with the liquid , though at a different temperature . The refractivity of bromine vapour for a known density had previously been determined by us , An Optical Method of Measuring Vapour Pressures . 307 and if we assume that the refractivity is proportional to the density , as Mascart 's work justifies us in doing , then the density of the vapour in the refractometer tube is known for various temperatures . It may further be assumed that , at the low pressures at which measurements were taken , the pressure of the vapour in the tube is proportional to its density . Hence , if we know one pressure and temperature absolutely , the whole curve of temperatures and pressures can be calculated from these observations . liamsay and Young* found for bromine at its melting point a pressure of 44*5 mm. Assuming this value , the table below shows the vapour pressures derived from a typical set of readings which are well supported by other series . Vapour Pressures of Solid Bromine . Temp. ( C. ) Pressures ( mm. ) Temp. ( C. ) Pressures ( mm. ) Observed . Calculated . Difference . Observed . i Calculated . Difference . -80 ' ! 0 -13 0-13 0 -15 ' *7 22 -9 22 -34 -0-56 -64'-75 0-52 0*43 -0-09 -15 ' -1 24 -35 23 -44 -0-9L -03 ' 0-66 9*5 -0-16 -12'-7 28 -8 28 -41 -0-39 -59 ' -9 0-79 0*65 -0-14 -12 ' -5 29*9 28 -87 -1 -03 -53 ' -3 1 -05 1*1 + 0-05 -10 ' 36 *15 35 -27 -0-88 -46'-9 1 -83 1 -83 0 - 9'-6 37 *1 36-42 -0-68 -41'-3 2-89 2-87 -0-02 - 7 ' *7 42-25 42 -41 + 0-16 -28'-8 7 -74 7 *82 + 0 *08 - 7 ' *5 42-9 43 -1 + 0-2 -28'-3 8*14 8 14 \#151 ; - 7 ' *2 43 -9 44 *14 + 0-24 -22'-6 13 -0 12 -82 -0-08 - 7 ' *1 44-5 44 *5 \#151 ; \#151 ; 19D -4 16*7 16 -61 -0-09 If the values of p are plotted against the absolute temperatures the points fall on an exponential curve p = where a = 2*485 x 10-8 and b = 1*0834 . The values of p , calculated from this equation , are shown in the third column . The constants were derived from the values p \#151 ; 44*5 and 8*14 . At \#151 ; 12c*74 C. , Bamsay and Young found p = 28*1 mm. The number calculated from the formula above is 28*3 . At \#151 ; 17'*12 they founds = 18*9 against 19*9 calculated . Thus the two sets of observations agree well . Numerous observations were taken at and about the melting point , both with ascending and descending temperatures , and on several occasions , though not on all , an interesting fact was observed . With steadily rising temperature of the bath the vapour pressure at the melting point increased * 'Chem . Soc. Journ. , ' vol. 49 , p. 457 . 308 An Optical Method of Measuring Vapour Pressures . above 44*5 mm. by 1 or 1-| mm. , and then , in the course of one or two minutes , fell back again . After remaining almost constant for a few seconds it then began to jump several times and fall back again , and at last it mounted steadily and rapidly . At each jump , which lasted one or two seconds , the pressure rose by 1 or 2 mm. A corresponding result was observed with falling temperature of the bath , the vapour pressure suddenly rising and then decreasing , but without jumping . These phenomena may possibly be due to differences of temperature between neighbouring portions of the solid in the bulb , vapour being formed at one place and condensed in another . But they are more probably explicable as the changes which might be expected to occur during the superheating of the solid and supercooling of the liquid . The superheating of a solid is stated by Chwolson to have been observed by Barus in the case of naphthalin ; and Duhem gives instances of a similar phenomenon in connection with the passage of a solid from one crystalline form to another . Whatever be the cause , the optical method seems to promise a valuable means of investigating the rapid and delicate changes of vapour pressure which must occur at the freezing point . Jamin 's form of interferometer is , of course , not indispensable . The simple design described by Lord Rayleigh , and used by Ramsay and Travers for the inert gases , would prove equally efficient .

rspa_1911_0046

0950-1207

The influence of planets on the formation of sun-spots.

309

323

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Arthur Schuster, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1911.0046

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1911_0046

10.1098/rspa.1911.0046

Tables

Agriculture

Tables

]\gt ; zoo zoo Jupit Dr. A. represents the number of spots generated in unit time in unit of longitude , and the number of those which are first observed range , we have third have with Oommunicated by Sir J. J. Thomson , F.R.S. Received April \mdash ; Read NIay 25 , 1911 . ) know farkla athers tanyphenomena ionnection wmission oecondary Bontgen r explained quite simply by supposing that there are two distinct ways S matter subjected to the action of primary rays may itself become a tree of radiation:\mdash ; ( 1 ) primary rays may be scattered\mdash ; an effect which is always very

rspa_1911_0047

0950-1207

The production of characteristic R\#xF6;ntgen radiations.

323

332

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

R. Whiddington, B. A.|Sir J. J. Thomson, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1911.0047

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1911_0047

10.1098/rspa.1911.0047

Tables

Agriculture

Tables

]\gt ; third have with Oommunicated by Sir J. J. Thomson , F.R.S. Received April \mdash ; Read NIay 25 , 1911 . ) know farkla athers tanyphenomena ionnection wmission oecondary Bontgen r explained quite simply by supposing that there are two distinct ways S matter subjected to the action of primary rays may itself become a tree of radiation:\mdash ; ( 1 ) primary rays may be scattered\mdash ; an effect which is always very

rspa_1911_0048

0950-1207

Experiments on the compression of liquids at high pressures.

332

348

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Hon. C. A. Parsons, C. B., F. R. S.|S. S. Cook, B. A. Cantab.

experiment

6.0.4

http://dx.doi.org/10.1098/rspa.1911.0048

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1911_0048

10.1098/rspa.1911.0048

Thermodynamics

Tables

Thermodynamics

]\gt ; Hon. C. A. Parsons and Mr. S. S. Cook . Summary of Experimental Results . ( 1 ) The energy emitted in the form of Rontgen radiation by a cathode particle when suddenly stopped is proportional to the fourth power of its velocity . ( 2 ) The primary rays from a Rontgen ray tube can only excite the radiation characteristic of a radiator of atomic weight when the velocity of the parent cathode rays exceeds cm . This law holds fairly closely for the radiators Al , Cr , Fe , Ni , Cu , and Se . It gives me pleasure to thank Prof. Sir J. J. Thomson for the interest he has taken in these experiments . Experiments on tloe Compression of Liquids at High Pressures . By the Hon. C. A. PARSONS , C.B. , F.R.S. , and S. S. COOK , B.A. Cantab . ( Received May 10 , \mdash ; Read May 25 , 1911 . ) 1 . Introduct During the experiments on the behaviour of carbon under high pressures and temperatures , of which an account was given in the paper read before this Society by the Hon. C. A Parsons on June 27 , 1907 , very considerable volumetric compressions were observed , and the apparatus then employed appeared to be equally suitable for the direct measurement of the compressibility of liquids at higher pressures than had previously been attempted . The measurement of the compressibility of liquids has received the attention of a great many investigators ; the most comprehensive researches in this subject appear to be those of Amagat , who determined the coefficients of compressibility of water and ether for )ressures up to 3000 atmospheres and for a variety of temperatures . Amagat 's experiments are given in various numbers of ptes Rendu In the experiments about to be described , the were carried up to about 40 tons per square inch , or over 6000 atmospheres . 'Comptes Rendus , ' vol. 103 , p. 429 ; vol. 105 , p. 1120 ; vol. 10 ; vol. 108 , p. 228 ; vol. 111 , p. 871 . 1911 . ] On the Compression of Liquids High Pressures . 333 The experiments were commenced in 1908 , but , the first experiments showing some modification of the apparatus to be desirable , principally with a view to making temperature measurements , it is the results of the later experiments carried out during the last year that are chiefly brief reference is desirable , however , to the preliminary readings obtained , by way of explaining the method adopted to eliminate friction , and in order to indicate how these experiments suggested an extension of the research to the investigation of the effects of internal molecular forces of the liquids tested . 2 . Apparatus . The apparatus consisted of a steel mould of about 4 inches bore and 12 inches external diameter , placed under a heavy hydraulic press , capable of exerting a pressure of 2000 tons , with a main ram of 29 inches diameter and a 6-inch lifting ram . In the first series of these experiments the mould was constructed of gun steel , having an elastic limit of about 40 tons per square inch . Greater strength could have been obtained , and still higher pressures applied , by the employment of special steel with a higher elastic limit . Water was supplied to the upper side of the ram at pressures up to 2000 lbs. per square inch by a three-throw hydraulic pump driven by an electric motor . The pressure on the ram was recorded by a carefully Kialibrated Bourdon gauge , and the depression of the liquid in the mould measured by a pair of multiplying callipers , inserted between the top of the mould and a projecting collar on the plunger . One of the outer arms of the callipers moved over a graduated scale attached to the other arm , and the readings of this scale were for safety observed through a telescope outside the armoured building in which the press and mould were set up . A sketch of the apparatus is given in , fig. I. Between the plunger and the liquid was placed a leather cup backed by a thin-edged cup of brass , this combination making an effective packing ( see fig. II ) . 3 . Elimination of Errors . In such an apparatus certain errors would arise in a experiment , but the experiments were carried out in such a manner as to practically eliminate them . The sources of error were the friction of the , the compression of the cup leather and brass and of the plunger below the point of measurement , and the lateral expansion of the mould . All these , with the exception of that due to friction , would be eliminated if an experiment could first be made with the mould filled with an incompressible fluid , and the apparent 334 Hon. C. A. DIAGRAM I. compressions so obtained deducted meant . But as there was no order to obtain in an indirect manner apparatus of a substance of negligib 1911 . ] On the Compression of Liquids at High Pressures . 335 cedure was adopted . A steel cylinder was prepared of half the volume of the liquid and of smaller diameter than the bore of the mould . In a first experiment this steel cylinder was inserted in the mould , which was then filled with distilled water up to a mark corresponding to a total volume of 2000 , so that it then contained 1000 . of water and an immersed volume of 1000 . of steel , both of which could be subjected together to bulk compression , and the apparent compression observed . A second experiment was then made with the steel cylinder removed , and the mould filled to the same mark with 2000 . of distilled water , the apparent compression being read as before . Since the volumetric compression of the water in the first experiment is only one.half of its value in the second ( the original volume of the water compressed being only one-half ) , by subtracting the compression readings of the second experiment from twice those of the first , the compression of the water is eliminated , and the differe11ce thus obtained gives the constant error of the apparatus on the supposition that the inserted steel cylinder is incompressible . A small correction is then necessary for the compression of this steel cylinder . The coefficient of compressibility of steel at ordinary pressures , as deduced from modulus of rigidity and Young 's modulus , by the usual formula for the relation between the moduli , ' per atmosphere of pressure . Since this is only a small percentage of the compressibility determined below for water , etc. , the reduction in volume of the steel . cylinder under a pressure of atmospheres may be assumed , to a near enough approximation , to be cp times its original volume , where . In the compressibility of water by the difference between the apparent compressions obtained in the two experiments , it is obvious that it is greater by approximately this amount ( viz. , than it would be on the assumption of absolute constancy of volume of the immersed steel cylinder . A further small correction has been necessary owing to the expansion of the mould taking effect upon htly different volumes in different experiments . This correction has been estimated by the usual theory of the bursting strains of thick cylinders , its magnitude at the highest pressures employed never exceeding 1 per cent. 4 . Elimination of the Bffects of Frietion . Curve 1 gives the readings without corrections obtained with the mould containing 2000 . of distilled water at C. The vertical ordinate * See Thomson and Tait 's ' Natural Philosophy , ' S683 . 1911 . ] On the Compression of Liquids at High Pressures . 337 represents the volume of the liquid as indicated by the depression of the plunger , and the abscissa the pressure in atmospheres . The cyclic nature of the curve will be noticed , the upper branch of the loop being plotted from the readings obtained when the pressure was increasing , and the lower from those obtained whilst the pressure was being reduced ; the difference between the readings of the upper and lower branches is concluded to be due to friction , the horizontal breadth of the loop being twice the pressure needed to overcome the friction of the packing and of the working parts of the press . Loops of this nature were traced for all the experiments . To guard ainst leakage , after the pressure had been raised to its highest value and reduced back to zero , it was again raised so as to repeat a portion of the higher branch of the loop ; if any leakage had taken place it was thus at once detected , and the experiment ected . By drawing a curve midway between the two branches of the loop we obtain a curve of compression with the effects of friction eliminated . Curve 2 is the curve plotted for 2000 . of water in this manner . Curve 3 is a curve of errors of the apparatus obtained by a calibrating experiment with the immersed steel cylinder as described above . Curve 4 gives readings plotted for a heavy cylinder oil of mean density about at C. It will be noticed that the loop of Curve 4 is very similar to that for water , Curve 1 , in spite of the greater viscosity of the oil , so that it would appear that the loop obtained in all the experiments with liquids is entirely due to friction of the press and packing , and not to internal friction . 5 . of Graphite under Pressure . Similar measurements were attempted with powdered Atchison graphite of specific gravity and containing per cent. of ash . The obtained are plotted in Curve 5 . It was thought possible that under high pressure graphite would behave as a fluid , but the character of the curve obtained indicates an increasing degree of consolidation as the pressure is increased . The consolidated graphite appears to show considerable rigidity , that is to say , the stress was not equal in all directions . The lower portion of the cycle was repeated , applying and removing the pressure a great number of times , the dotted Curve 6 representing the readings subsequently obtained . On opening up the mould the graphite was removed in biscuit-like ' fragments , often separating along a conical surface at about to the axis , so that it appears to have relieved itself during expansion along lines of cleavage at this angle . Similar results were obtained with Ceylon graphite of specific gravity and containing about 15 per cent. of ash . The readings for this graphite au plotted in Curve 8 . 6 . Effects of Heat of Compression . It will be observed that in the curves plotted for the experimental readingS , the readings for the pressures ascending a second time for the purpose , as explained above , of detecting leakage , are in general very slightly below the readings for the previous application of the pressure . Subsequent examination of the apparatus showing no trace of leakage , and this phenomenon persisting in subsequent experiments , it was concluded to be due to temperature variation , the work done during compression transformin heat and rendering the substance , whilst under high pressures , slightly hotter than its surroundings , so that at the end of the cycle it had lost some heat to the surroundings , and during the second compression was slightly colder than during the first . This heat effect being therefore a possible source of error , it was desirable to make some measurement of its amount . As a preliminary , a volume of 2000 . of heavy cylinder oil was pressed to a pressure of 6300 atmospheres , which was maintained for two hours to allow the heat due to compression to leak away . At the end of this time the pressure was suddenly released , and the liquid was found to be 1/ 5 inch lower in the mould than it was before compression , corresponding to a reduction in total.volume of about 2 per cent. The heat effect was further investigated by allowing 2000 . of thin machine oil to cool under high pressure for hours with an external temperature of about C. , and after sudden removal of the pressure opening up the mould for examination . With the method of packing employed at this time it was not possible to open up in less than about a quarter of a hour , owing to the difficulty of removing brass cup and the cup-leather from the mould . The temperature after up was read , however , at regular intervals of time , by which means , a logarithmic law , the temperature immediately after release and expansion could be estimated , and appeared at the moment of release to have been about C. It was evident from this that the loss of heat was considerably in excess of 1911 . ] On the Compression of Liquids at High Pressures . 341 about 41bs . , which is equivalent only to heat units per lb. , leaving units per lb. to be accounted for by internal forces . This point having been reached , the experiments were continued with a twofold object , namely , ( 1 ) to ascertain the compressibilities of various liquids for both adiabatic and isothermal compression , the experiments last referred to showing it to be necessary to discriminate between these modes of compression , and ( 2 ) to determine the amount of the heat developed from internal forces during compression and absorbed by the same agency during .expansion . Various attempts were made to measure the instantaneous temperature of the contents of the mould during compression by electrical methods with platinum coils and terminals brought outside the mould to a galvanometer . None of these were successful ; the oeadings interference from galyanic action and from conduction in the liquid , and constant difficulty was experienced through of the coils with congealed oil and through leakage of the fluid past the terminals , in spite of many precautions taken to avoid these difficulties . In the meanwhile an accumulator had been installed , and it was now possible to put on or remove the full pressure almost instantaneously ; further , by attaching the packing to the ram in such a way that it could be withdrawn mmediately on the removal of pressure ( see Diagram I , fig. III ) , it was possible to insert a quick-reading mercury thermometer immediately after release . The mould was also surrounded by a water jacket so that the temperature could be varied as required and measured by a mercury thermometer . Isothermal curves were plotted by allowing the pressure to remain applied long enough for the liquid in the mould to assume the temperature of the jacket , after which the pressure was varied slightly above and slightly below its recorded value sufficiently to overcome the friction . For adiabatic compression the pressure was raised to the required value in a few seconds . In these later experiments the ressures were not carried higher than from 4500 to 5000 atmospheres , the adoption of which lower values , together with the experience acquired in with these high pressures , rendered it safe for the observer to work inside the building close to the apparatus , which greatly facilitated the readings . 7 . Bxperiments with Wate Curve 9 is an isothermal curve obtained for the compression of distilled water at C. plotted to a base of pressure in atmospheres , the vertical ordinates giving the volumes of a kilogramme in cubic centimetres . In the case of water the adiabatic compression was found to be only about VOL. LXXXV.\mdash ; A. 2 3 per cent. less than the isothermal . With other substances , as will be below , the difference was greater , on account of lower specific heat and apparently higher internal forces . Curve 10 is a curve of adiabatic expansion of water from a temperaturg of C. at 4550 atmospheres pressure . The temperature at the end of this cent. lesstetHon . C. A.Parsons and Mr. Cook . , as [ May process of adiabatic expansion was found to be C. , so that 1 calories per kilogramme have to ) restored to bring the water back to C. at atmospheric pressure . The external work done during expansion is given by the shaded area under the curve and amounts to 2700 per kilogramme . But the 13 calories of heat which have to be added per ramme are equivalent to 5500 kilogramme-metres , so that in passing from the initial state of C. temperature and 4550 atmospheres pressure to a final state at the same temperature and atmospheric pressure 2800 kilogramme-metres of energy have become latent , or in other words have been converted into internal potential energy . The increase of volume between these two conditions is 130 , and this disappearance of energy is therefore equivalent to the work that would be done against an internal force of average value , or 2150 atmospheres . 1911 . ] On the Compression of Liquids at High Pressures . 343 It will be seen that by increasing the pressure from 1 up to 4500 atmospheres water at C. is compressed to 87 per cent. of its original volume . At 3000 atmospheres it is per cent. This agrees closely with per cent. given by Amagat for 3000 atmospheres pressure at C. An endeayour was also made in the case of water to find the influence of temperature upon compressibility . For this purpose the water was compressed adiabatically at various temperatures . Readings were taken of the compression at 600 atmospheres and immediately afterwards at spheres , the interval elapsing being only a few seconds . The amount of the compression between these pressures is plotted in Curve 11 , the units adopted being of volume in cubic centimetres per kilogramme for the vertical ordinate and temperature before compression for the horizontal base . The compressibility is reduced with increase of temperature , from which it follows that the coefficient of heat expansion at high pressures is htly greater than at atmospheric pressure . This is in agreement with Amagat 's results . 8 . Experiments with Ether . Curve 12 shows the compressibility of pure ether at C. , the vertical ordinate being the volume iu cubic centimetres of a quantity whose volume is 1000 . at C. The compression for 4000 atmospheres is from . to 840 c.c. , the final volume being 80 per cent. of the , so that the compression in this case is practically double that obtained for water . The agreement with Amagat 's results in this case also is fairly good . the latter giving a compression from 1050 to 863 for 3000 atmospheres at C. , whilst by the present experiments it appears to be from 1050 to 870 , the disagreement being only about 4 per cent. of the total compression measured . Hon. C. A. Parsons and Mr. S. S. Cook . [ May 10 , Neither for ether nor for water can the curves showing the results of these experiments be said to definitely indicate the existence of a limiting value to the compression . In the case of ether , as in the case of water , experiments were made to ascertain the heat absorbed through the action of intermolecular forces by sudden expansion . Curve 13 is the curve of adiabatic expansion after cooling at 4400 atmospheres to C. The final temperature was C. This drop of C. , assuming the specific heat of ether to be corresponds Hon. C. A. Parsons and Mr. S. S. Cook . [ May 10 , to 871 , or about 84S per cent. of its original volume at C. ; the compressibility is therefore greater than for water by about 20 per cent. The , drop in temperature on expansion from 4600 atmospheres to atmospheric pressure was found to be C. Taking the specific heat at ) energy extracted per 1000 . is made up of 2055 kilogramme-metres of external work and 4645 kilogramme-metres work against internal forces , the latter corresponding to a pressure of 2920 atmospheres . 10 . Conclusion . To exhibit the comparison between them , the curves of isothermal compression have been replotted in Diagram II , reduced to a common basis of 1000 . original volume . Expressing compressibility in atmospheric units , that is to say , as the ratio of the decrease of volume per atmosphere of pressure to the volume of the liquid , from the foregoing experiments the following values have been deduced for the isothermal coefficients of compressibility of water , ether , and paraffin oil aterEther The average values of the molecular force deduced from the heat lost during adiabatic expansion as described above are as follows.\mdash ; Molecular force . atmos . Water ( for pressures between and 4550 atmos . ) 2150 Ether , , , , , , 4000 , , 2440 Paraffin , ; , , , , 4600 , , 2920 The authors wish to record their thanks to Mr. Robert Howe with the mechanical work in connection with the experiments . 1911 . ] On the Compression of Liquids at High Pressures . .347 ( June 3 ) . The method adopted in the paper for determining the equivalent internal pressure corresponding to the excess of heat extracted over the external work done is based on the following considerations:\mdash ; Suppose a closed cycle on a pressure volume diagram , made up of the following processes in isothermal compression at temperature ; ( b ) adiabatic expansion to atmospheric pressure and temperature ; ( c ) restoration to temperature by addition of heat at atmospheric pressure . The external work during process ) is negligible . Hence the excess of the heat given out over external work done during ( a ) can be measured by the excess of the heat absorbed during ( c ) over the external work done during The excess thus determined in has been expressed as the product of an average internal pressure into the change of volume occurring during the isothermal compression . The rate of rise of temperature of fluids under compression can be determined from the thermodynamic relations resulting from the first and second laws of thermodynamics . When there is no emission of heat , we have with the usual notation , ( 1 ) from which . ( 2 ) Using to denote the coefficient of expansion at constant pressure , or ' we have . ( 3 This formula will ordinarily only bear application in the neighbourhood of atmospheric pressure , the values of and under the high pressures employed in the foregoing experiments being unknown . Thus , for the adiabatic curve plotted for water , in the neighbourhood of atmospheric pressure , we have for the various expressions in equation ) kgrm.-cm . per kgrm . . per kgrm . from which there results , or a rise of C. per atmosphere of pressure . The rise in temperature will , however , in the case of water , proceed more rapidly in the later stages of the compression as higher pressures reached , since increases both with the temperature and with the pressure . On the Compression of Liquids at High Pressures . With the help of Curve 11 it is possible to obtain an approximate estimate of the value of of the fluid when under compression . Denoting by the compressibility at constant temperature , since and it follows that The slope of Curve 11 gives for the value of , with the unit adopted for ( viz. , change of volume per unit volume per atmosphere of pressure ) , , and if we assume this as the approximate rate of increase of throughout the range of pressures covered by the adiabatic compression from C. at atmospheric pressure to C. at 4550 atmospheres pressure , we have for the value of at the beginning of the compression , and at the end , or an average value of The expressions in equation ( 3 ) then assume the following average values over the whole range of this compression\mdash ; . per kgrm . , giving per atmosphere . The measured drop in temperature during the reverse process of adiabatic expansion , from a pressure of atmospheres at C. to atmospheric pressure , was C. , or per atmosphere , thus agreeing even closely with the estimate .

rspa_1911_0049

0950-1207

Energy transformations of X-rays.

349

365

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Prof. W. H. Bragg, M. A., F. R. S.|H. L. Porter, B. Sc.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1911.0049

en

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1911_0049

10.1098/rspa.1911.0049

Atomic Physics

Tables

Atomic Physics

]\gt ; Energy Transformations of -Rays . By Prof. W. H. BRAG , M.A. , F.RS . , and H. L. PORTER , B.Sc. , Demonstrator of Physics , University of Leeds . ( Received May 15 , \mdash ; Read May 25 , 1911 . ) The manner of our attack upon the problems of radioactivity , including the action of the Rontgen rays , depends materially on whether suppose that an atom can or can not be made to yield energy from an internal store . In the former case we have nothing to guide us to an estimate of how much energy may be expected to be put into circulation in this way . If , for example , a -ray in passing through an atom prompts the atom to emit new secondary radiation with energy drawn from a source usually beyond the reach of transformation into physical or chemical or other known forms , or if the atom sometimes absorbs energy from that of the -ray motion and locks it up , then the quantities of energy thus added to or subtracted from the amounts we may hope to measure must be no more than subjects of experiment . We shall have to be content with registering them without accounting for them . But if we take the second of the two alternatives the problem is immensely simplified , and we may work for a more complete solution . An -ray or -ray begins its career with so much energ ) . While we cannot , of course , explain this initial liberation of energy , we may try to account completely for its subsequent expenditure in various ways , since we have no unknown or unexpected items to take into account on either side of the balance-sheet . Exactly the same statement can be made in respect to each X- or -ray , since each such ray , as has been shown in previous papers , be considered by itself , being independent of all its companions in what we call a " " beam of X-or of -rays.\ldquo ; Energy considerations lead us directly to the supposition that the X- and -rays are corpuscular in nature in so far as each ray is a separate identity moving space unaltered in form and content , just as an unhindered projectile would do . No X- or -ray spends energy in its passage through matter ; the only way in which the existence of such rays is made manifest is through their replacement by swiftly moving electrons which ionise the gas through which they pass . The single X-ray disappears as such , and in its place is a cathode ray , an electron moving with energy inherited from the -ray . Ionisation by X- or -rays is an indirect process . * For a summary of the argument , see a paper by Brag , 'Phil . September , 1910 . Prof. W. H. Brag and Mr. H. L. Porter . [ May 15 , It is not necessarily an exception to this rule that sometimes the absorption of a primary stream of -rays of definite quality or penetrating power is marked by the appearance of secondary X-rays of different quality . Barkla has shown that many such cases exist , that the secondary rays are characteristic of the substance from which they come , and not of the rays which excite them , and that they can only be excited by rays more penetrating ( as measured by absorption in aluminium screens ) than themselves . The corpuscular theory leads us to suppose that the more penetrating -rays as defined in this way are simply those with the most energy . The quality of any -ray is completely defined by the energy of the cathode particle to which it gives rise . At any rate there seems no ground at present for supposing any other qualification to be required . Barkla 's law , then , amounts to this , that many substances under the stimulus of primary -rays emit secondary -rays which are characteristic of the substance and not of the stimulating rays , and that a secondary -ray can only be brought into existence by one having more energy than itself . On the view of the energy question which we are adopting the last assertion in this statement is to be anticipated . As we have said , this production of secondary -rays is not necessarily an exception to the rule that absorption of -rays implies the conversion of their energy into , that of cathode rays , and into nothing else . It may well be that the secondary rays are due to a reconversion of the cathode rays into X-ray form , after they have lost energy in moving through the gas in which they arise , or in some other way . Let us , for example , consider the history of a secondary -ray emitted by zinc under the stimulus of -rays from a Rontgen bulb . It is an identity of definite energy , and is liable to be replaced in traversing some atom by a cathode ray of definite initial energy ; we may speak of the " " zinc X-ray\ldquo ; and the ' zinc cathode ray The electron of the zinc cathode ray is not different to other electrons , but it has a definite initial speed and a definite penetrating power . Let us imagine a -ray penetrating a nickel plate ; in some cases the -ray is replaced by a Ni -ray , which is an identity of less energy . This change may have taken place in one atom of nickel , which has then absorbed energy equal to the difference between the energies of a -ray and a Ni -ray . Or there may be no exception*to the rule that -rays are replaced by cathode * In a recent paper Mr. J. Crosby Chapman ( Phil. Mag April , -1911 ) describes experiments which convince him that this cannot possibly be the process by which the secondary ionisation is excited . Allowing X-rays to fall on bromine vapour he finds that the preseltce of or makes little difference in the amount of secondary radiation arising in the bromine ; whereas , since the must get in the way of many 1911 . ] Enerqy Transformations of -Rays . rays only , and in that case we must suppose an intermediate stage , in which the -ray has been replaced by a moving electron ; in this stage some of the energy is frittered away in ionisation , and only a remainder handed on to the Ni X-ray . We are here supposing that the X-rays are really homogeneous , and consist of a number of " " corpuscles\ldquo ; all alike . The homogeneity is taken to be proved by the fact that they are absorbed , according to Barkla , under an exponential law , which naturally implies that , however many rays have been removed from a stream , the remainder possess the same properties . Perhaps there is room to suppose that the quality of -rays is only an ayerage quality , but it is certainly difficult to understand the exponential absorption that case . The foregoing statements are intended to be introductory to the description of certain experimental results . We have attempted to consider and to measure the transformation of X-ray energy in a few cases , since the corpuscular theory would suggest the possibility of success in this direction . If the absorption of -rays means their conversion into cathode rays , then we ought to find that the production of cathode ray energy is proportional to the disappearance of -ray energy , at least where there is no production of seco1ldary -rays . In the latter case we may avoid the uncertainty as to the exact way in which these secondary rays arise , by for the energy contained in them . Whatever energy of the primary rays is then left unaccounted for must be proportional to the cathode ray energy they can produce . Lastly , we can show that -rays , when they go through a gas , produce enough cathode radiation to cause all the ionisation which is observed , and the1e is no need to ascribe any direct action to the -rays themselves . We take first a pencil of the secondary X-rays from tin , which are relatively energetic , and give rise to penetrating cathode rays . On this account the cathode rays which emerge from a plate on which the Sn cathode rays and the cannot do so , the CO : ought to interfere with the conversion of cathode rays into -rays . This does not seem to me concIusive . If the production of X-rays is a consequence of the encounters of cathode rays with bromine atoms there will be opportunity for the effect to take place even though the molecules are scattered among the Br atoms . If an eIectron meets a molecule first it is not arrested there but deflected , and may have hundreds of encounters still before it : so that its chauce of meeting a Br atom is practically as great as ever . If it is argued that the cathode ray is " " absorbed\ldquo ; by the bromine and the in proportion to weight , it must be answered that whatever " " absorption \ldquo ; may mean there is no clear evidence of the universality of Lenard 's law . I do not assert that the idea of the intermediate corpuscular stage is established.in the simple form in which I have stated it ; but it se to simplify the theory , and is not , I think , disproved by Mr. Chapman 's experiment.\mdash ; W. H. BRAGa . Prof. W. H. Brag and Mr. H. L. Porter . [ May 15 , X-rays fall have a considerable ionising effect , for even those which have their origin in relatively deep layers of the metal can make their way into the open . Our first object is to find the cathode radiation which the Sn -ray can arouse in different substances , and to compare the various amounts with the absorption coefficients of the substances for those -rays . The apparatus is shown in fig. 1 . A primary pencil of rays from the bulb passes down a tube lined with tin , and falls upon a plate of tin in a box made of tin . The primary rays fall on nothing but tin , the object being to make the pencil of rays issuing from the box as free as possible from all but Sn -rays . The secondary rays pass into an ionisation chamber through an FIG. 1 . opening AA closed with paper . They excite emergence cathode rays in sheets of metal laid on the paper , or incidence cathode rays in plates laid on top of the chamber if such sheets or plates are placed in position . The ionisation current is balanced against a similar current in a second ionisation chamber crossed by a pencil of rays from the same radiator . The second chamber is closed by an adjustable opening worked by a micrometer screw ; the values of the readings are determined by a special calibration . A Wilson tilted electroscope is used as a detector . The arrangement works well ; consecutive readings rarely differ by as much as lper cent. The results of experiment differ by far more than this at different 1911 . ] Energy of -Rays . times , but it seems as if the bulb at fault rather than the measuring apparatus . There are various ways of finding out what fraction of the ionisation current observed is due to the action of the cathode rays at incidence or emergence . It may be done by gradually increasing the depth of the chamber , a method employed by Townsend* long ago . Sadler . has used the same method . varied the air pressure , which is more convenient in ways , because it no moviDg parts in the apparatus and makes no change in the geometrical conditions . In some cases it is convenient to increase gradually the thickness of the metal sheet , and to observe the consequent increase in the cathode radiation . and MadsenS employed this method when investigating the production of -rays from -rays . It is also very convenient to find the difference between the current when the metal under investigation is bare to the ionisation chamber , and the current when the metal is covered over with a very thin sheet of tissue paper , which cuts off all cathode rays and interferes very little with any others . For this purpose we generally employ carefully flattened plates of metal , one face of each plate being bare and the other covered with tissue paper fixed on with as little adhesive as possible . In order that results obtained at different times , or with different pieces of apparatus , may be comparable with each other , it is convenient to express each result as the ratio of the ionisation caused by the cathode radiation to the ionisation caused by the -rays in crossing 1 cm . of air . For example , in one experiment where the plate was made of Sn , with the bare side towards the chamber the current was 247 on an arbitrary scale , and when the plate was turned over so that the tissue paper cut off the cathode rays , the current was 122 . Hence the cathode radiation was 125 , and , since the chamber was cm . across , the ratio required was . There was no secondary radiation in this case ; it is not excited by tin in tin . In the same way we may find the corresponding figure for the " " emergence\ldquo ; cathode radiation . In the case of Ni , Fe , Cu , and , the results are complicated by the presence of the characteristic secondary radiations . The tissue paper no longer cuts off all the radiation from the metal ; the cathode rays are absorbed , but the secondary -rays should be very little affected in passing through the paper . To make sure that this was the true explanation we PhiL Soc. Proc 1899 , vol. 10 , p. 217 . 'Phil . Mag March , 1910 . . Phil. Soc. Proc , vol. 15 , p. 416 . S PhiL Mag December , 1908 . Prof. W. H. Brag and Mr. H. L. Porter . [ May 15 , stretched a piece of paper over the top of the ionisation chamber so as form the upper wall of it . The ionisation current then observed was nol increased when plates of tin or aluminium were placed over the chamber on top of the paper , but it was increased when any one of the other metals was placed there . By interposing thin sheets of aluminium or paper between the plate and the paper top to the chamber , it was possible to find an absorption curve . This curve is not exponential ; it is of a more complicated form , which we must examine presently when we compare the energy of the secondary radiation with that of the primary . At this stage it is only necessary to say that when the plate on top was a copper one the curve showed an absorption such as would be expected if the secondary -rays were Cu -rays . We may assume , therefore , that we have here an example of the effect described by Barkla , and that the secondary rays excited by the Sn rays are characteristic of the metal in which they arise . The amount of the secondary radiation is conveniently expressed by the ratio of the ionisation it causes in the chamber to the ionisation caused by the primary rays in the same chamber . For example , in an experiment when the rays entered the chamber through a paper screen and fell upon an aluminium plate with the papered face down , the current was 136 . When nickel with the papered face down was substituted for the aluminium , the current was increased to 177 , and if the nickel plate was turned er so as to present its bare side to the -rays the current became 296 . Thus there was an incidence cathode radiation of 119 , and a secondary -ray effect of 41 . The former is recorded as and the latter as 41/ 137 or The ratio of the emergence to the incidence cathode radiation was determined separately . The following table ( p. 355 ) sho ws a set of results obtained in this way . In the case of zinc the ratio of e1nergence to incidence cathode rays was not actually measured , but assumed to be the same as for copper . The total cathode ray effects and the absorption coefficients ] run parallel to each other , allowing for the fact that in the case of some of the metals part of the primary -ray energy is spent in exciting secondary X-rays . But there are several points to be considered before a true rison can be made . In the first place the cathode ray effects are caused by such of the cathode radiation as emerges from a plate on which the rays , fall . This is not exactly what we want ; we are trying to compare the cathode radiations excited in equal weights of different metals by Sn -rays , and we have really no measures of these as yet , for we have not allowed for the Energy Transformations of -Rays . Table I.\mdash ; Sn Rays . Column I refers to the metal in which the X.rays excite cathode rays . II gives the intiidence cathode ladiation expressed as already explained . III gives the ratio of emergence to incidence cathode IV gives the total cathode radiation . V gives the secondary -radiation expressed as already explained . VI gives the absorption coefflcient of the Sn rays in each metal . loss of energy of the cathode rays in their way out of the body of the metals . If the proportionate loss is the same for all metals , it is unnecessary to find it , and there are rounds for believing that in many cases it is . Lenard showed that the cathode rays which he employed were equally absorbed by all substances with atomic weights between those of carbon and gold . The value of the coefficient which he found was 3000 nearly , so that his rays must have been about as penetrating as the Sn cathode rays . * Hydrogen was an exception , having a larger coefficient . Lenard also compared the absorption coefficient of less penetrating cathode rays in some gases , of which the only one with a large atomic weight was argon . Though the coefficient was still much the same in , and , the atom had increased its difference . These experiments do not cover the penetration of the slower cathode rays in metals such as Fe , Cu or ; and we do not know that the law of equal penetration holds ill these cases . They are very difficult to investigate since the absorption coefficients are so high . Confining , however , our attention to the Sn rays for the time being , it seems right to assume Lenard 's law to hold to a first approximation . If we do this , the amount of cathode radiation emerging may be taken as a true relative measure of the amount of cathode radiation made . We must now try to allow for the energy spent in making secondary X-rays . Barkla has shown that suoh secondary rays are radiated uniformly in all directions about their origin . Let a pencil of rays of energy I enter the upper plate of the ionisation chamber and let be the absorption coefficient of the plate for these rays . Let be the absorption coefficient *Beatty , . cit. Prof. W. H. Brag and Mr. H. L. Porter . [ May 15 , for the same plate in to its own rays . The loss of energy of the primary in crossing a of weight is , where is the mass penetrated previously . Of this the amount that gets back into the chamber is where is the fraction of the primary energy which is directly or indirectly converted into secondary X-ray energy , and the factor in brackets is necessary to allow for the absorption in the stratum of weight when the rays are distributed uniformly , having been obtained by measurement with rays normal to the absorbing plate . * The divisor 2 is introduced because half the energy must go each way . The whole of secondary radiation which comes back and crosses the chamber is therefore and is a function , therefore , of The value of the integral can be found for a few values of by plotting the curve and finding the area . The result is shown in fig. 2 , and 'Phil . Mag. , 'May , 1910 , p. 735 . Values of the constant have been already found for a number of cases by Sadler , ' PhiL Mag July , 1909 . 1911 . ] Energy of -Rays . a smooth line drawn through the calculated points gives us the value of the integral sufficiently well for all values of In the case for example of Sn rays incident on Cu , since and so that , the value of the integral is found from the curve to be ; or Now the absorption coefficient of Sn rays in is nearly , and of Cu rays in is , and the ratio of the coefficients in air will be the same practically as in C. Also the ionisation of the air is proportional to the absorption coefficient of the air ; hence By actual experiment the ratio of these ionisations is found to be and therefore . That is to say , of the absorbed energy of the primary is spent in producing secondary Cu rays , and only of the energy remains to be accounted for in cathode ray } . There is still one correction to be made , which is only of importance , however , in the case of aluminium . When we measure cathode rays in this way we measule actually the difference between the cathode radiation from the etal in question and the cathode radiation from the tissue paper with which we have covered one face of it . The results we obtain are therefore comparable with the difference between the absorption coefficients of the metal and the paper . In the case of Sn rays the absorption coefficient of [ carbon is about . Making all these allowances we obtain a set of results which are set out in Table II . On the whole the figures in the last column agree very well , quite as closely as we can expect considering the sources of uncertainty which we have pointed out . So far , therefore , we may conclude that the relationship between the cathode radiation and the absorption coefficient is as it should be . Experiments with arsenic X-rays gave the results set out below in Table III . Only the incidence cathode rays were taken into account , for the measurement of emergence cathode rays is unsatisfactory unless the plate through which the X-rays enter the chamber is very thin indeed . The thinnest sheets obtainable of most substances were sufficient to harden the X-rays a little in spite of their approximate homogeneity , and there was a certain small fraction of scattered primary X-radiation included in the secondary radiation from the arsenic . A very little penetrating radiation in VOL LXXXV.\mdash ; A. 2 Prof. W. H. Bragg and Mr. H. L. Porter . [ May Table II.\mdash ; Sn Rays . Column I. Name of metal in which the cathode and secondary -rays are excited . II . Amount of cathode radiation measured as described above . III . Amount of secondary -radiation . IV . Calculated value of ratio of secondary to -ray energy . V. Absorption coefficient of primary X rays by the metal . VI . PropQrtion of the absorption which should go to the production of cathode VII . The same , less the absorption coefficient of paper ( see above ) . VIII . Ratio of VII to II . a fairly homogeneous beam produces a material alteration in the cathode radiation . For example , Beatty 's figures on p. 324 of the paper already quoted and published in the ' Phil. Mag August , 1910 , show that a stream of Sn -rays producing the same efiect in air as a stream of As -rays produces seven times as much cathode radiation in silver . As it happens , there is very little difference between the emergence and incidence cathode rays in such ctises as we have examined , and it seems justifiable therefore to work with the incidence rays only . The arsenic radiator was made of the same form as the tin radiator ; tube , box , plate and all parts on which the primary rays could fall were made of thick card on which metallic arsenic in a powdered form had been fastened by a little gum . Perhaps the gum scattered a little hard prinlary radiation , for our absorption coefficients were somewhat smaller than those of Barkla and Sadler . We know hardly anything of the absorption coefficients of As cathode rays . Assuming that they also follow Lenard 's ] , the figures in the last column should be all the same . They are so approximately . Some results obtained with Zn rays may be given . As with arsenic rays , they are difficult to interpret fully until more is known of the absorption of the special cathode rays in different metals . Ihere is also more liability to experimental error since the cathode radiations are so small in many cases . We have , therefore , following Beatty 's plan , worked at low pressures so as to make the cathode ray effect , reater relative to the effect of the -rays . Even then it is difficult to find accurate results , for when zinc rays fall on a metal such as aluminium Prof. W. H. Brag and Mr. H. L. Porter . [ May 15 , covered with tissue paper and the broken one shows the effect when the metal is bare . The lines are drawn straight though clearly they should all be slightly curved in order to fit the points ; the figure seems easier to examine with the lines drawn as they are . The results are collected in the following table:\mdash ; Table Rays . For description , see notes to Table II . The parallelism between the absorption coefficients and the production of secondary radiations is quite clear ; and when due allowance is made for the energy which reappears as secondary -rays , there is a fair agreement between thep production of cathode rays and the energy which presumably goes to make them . Copper does not agree with the others ; and we have no reason to as yet for the divergence . It is to be remembered that agreement cannot be expected unless cathode rays are equally absorbed in all substances , and we no sure knowledge that they are . Beatty*has traversed the field in a cross direction . He has allowed -rays of various types , viz. , those from Fe , Cu , , As , and Sn to pass through a silver leaf , and has measured the " " emergence\ldquo ; cathode radiation arising from the silver in each case , expressing the result as a ratio of the ionisation caused by it to the ionisation caused by the -rays in a layer of air 1 cm . thick immediately after through the silver . It is necessary , of course , to use some such standard of reference . The ratio is called in Table I of his paper ( p. 324 ) . He also measured the absorption coefficient ( ) of the cathode rays in air by finding the thickness of air stratum required to reduce the cathode radiation to half value ( in the same table ) and dividing this into . This process depends on the assumption of an experimental law of absorption . The absorption does not really fulfil this law , as his own diagrams show ; but for the purpose of argument it was no doubt justifiable to make 'Phil . Mag August , 1910 . 1911 . ] Transformations of ] the assumption for the sake of convenient expression , and he was concerned only with the relative amounts of the cathode radiations produced in silver by the different rays . If the assumption of the exponential law made an error in one case , it probably made the same error in the others . He then assumes , further , that the in silver is proportional to the in air for all these types of X-rays , so that while is a measure of the emergence cathode radiation only , is a measure of all the cathode radiation that is produced , not of what gets out of the silver . It is the ratio of the ionisation due to this radiation ( if it could all get out ) the ionisation due to the -rays in 1 cm . of air . He assumes , still further , that the ionisation of the air by the -rays is proportional to the absorption of those rays by the air ; and , again , that the absorption of -rays by the air is proportional to their absorption by silver . The constancy of the quantity therefore enables him to draw his final conclusion that , " " in the case investigated , a constant fraction of the homogeneous radiation is spent in producing cathode particles Some of Beatty 's assumptions are certainly justifiable , the third , at auy rate , and probably fourth ; the first is permissible for the occasion , and the second may very well be true , but there is no definite proof of it . The corpuscular theory would lead us to anticipate Beatty 's result : it would , indeed , further still , and assert that the constant fraction is unity , at least in the case where there is no secondary -radiation in addition to the cathode radiation . There was none in Beatty 's experiment . If we aim at an experimental verification of this simpler but more comprehensive deduction from the corpuscular theory we cannot assume an exponential law for the absorption of the cathode rays in the silver . We must make some attempt to find the true law . We pass Sn rays into an ionisation chamber through an opening closed by a card . The whole of the chamber , which is made of brass , is lined with Al and paper , so that there is no radiation from the walls to be taken into account . Silver foils then laid on the card , and the increase in ionisation is observed as the number of foils is increased . The curve obtained is shown in . If we can find the slope of this curve at the origin we shall know the cathode radiation for extremely thin sheets , which is what we really require ; for if the sheets were very thin all the cathode rays would get out . Unfortunately silver foil is not to be had thin enough to any points nearer the origin than are shown in the figure , and we are left to draw the curve through the experimental points as we think it ought to be drawn . Beatty assumed the exponential curve passing through the point for which the current measured is half the final value . This is represented by the Prof W. H. Brag and Mr. H. L. Porter . [ May 15 , dotted line in the figure , and OQ is the tangent at the origin . The true curve would seem to be somewhat different and less steep initially . The simplest form to assume is parabolic , viz. , , and such a curve has been drawn so as to pass through the origin and the first two points ; it then FIG. 4 . breaks away as shown . Adopting this form , it is easy to find the at the origin , OP ; and it appears that initially emergence cathode rays are produced and make their way into the open at the rate of 208 to a weight ( of screen of . The maximum reading due to cathode rays is 309 . We derive from this curve the fact that when the maximum emergence radiation is 309 , the actual production of emergence cathode rays is or 832 per milligramme of silver . The ratio of these two numbers , , and is all that is required for future calculation . If we had assumed an exponential curve passing through the point on a curve at which the ordinate is half its greatest height we find that the tangent at the origin , , gives a value for this ratio about 15 per cent. higher . In order to find the full amount of the cathode radiation produced in silver we must also take into account that which would be found on the incidence side of a very thin sheet . We must do the same thing in regard to incidence cathode rays as we have just done in regard to emergence . This might be done by gradually thickening a silver sheet on top of the chamber on which the X-rays fall : but there is always some uncertainty about this method , since some of the -rays which enter the chamber might \mdash ; through scattering or otherwise\mdash ; strike the walls than the top plate . When dealing with the emergence cathode radiation no such thing can happen . It is perhaps simpler to compare the incidence and emergence cathode rays by laying one or more silver foils on a card and placing this in 1911 . ] Energy Transformations of . 363 the middle of the ionisation chamber , so that the -rays must go through it . The cathode radiations are then found by subtracting the current for a bare card from the current when there are silver foils on one side or the other . We found the ratio between incidence and emergence to be for one , two , or three foils ; and we conclude that this ratio may be supposed to hold for extremely thin films . The distribution of the cathode rays about the silver atom is therefore unsymmetrical from the first , though it is by no means so uni-directional as in the case of the -rays caused by -rays . The measurements made so far were obtaiued in air , because it was con- venient to adjust the silver foils in a chamber which could be easily opened and closed . But the remaining part of the experiment was carried out with oxygen instead of air , since it was necessary to compare the absorption coefficient of the Sn rays in the silver and in the gas employed . It is difficult to measure accurately the absorption of Sn rays in a gas since it is so very small , and air can only be used as gas . But the absorption in oxygen can be found by using solid absorbing screens containing known quantities of oxygen . This part of the experiment will be described presently . It was necessary to find the ratio of the emergence radiation from the silver , measured by the ionisation it causes in oxygen to the ionisation in a given layer of oxygen due to the Sn -rays . Employing the same method as Beatty , we passed Sn rays into an ionisation challlber which could be filled with gas at any pressure . The rays passed in through ten silver foils , which were amply sufficient to give the full cathode radiatiolL The depth of the chamber was cm . The curve obtained is given in fig. 5 , and gives us Prof W. H. Brag and Mr. H. L. Porter . [ May 15 , the means of calculating the ratio we require . The ionisation due to the emergence cathode rays is 344 , while that due to the -rays crossing cm . of oxygen at 76 cm . pressure . Hence the ratio of the effect of the emergence cathode radiation to the effect of the -rays crossing 1 milligramme of oxygen is the density of oxygen being We have already found that the cathode radiation per milligramme of silver is times the emergence cathode radiation from silver , result which was found by the use of air , but must be just the same when oxygen is used . Combining these figures with the ratio of the whole cathode radiation to the emergence radiation ( viz. , we have finally that in equal weights of silver and oxygen there is times as much* ionising power in the cathode rays produced by the X-rays in the silver as there is ionisation actually effected by the -rays going through the oxygen . We nexb require the ratio of the absorptions of the Sn rays in silver and in oxygen . Using the same apparatus and keeping all the conditions the same in the absorption experiment as in those that went before , we found the absorption coefficient of the -rays by the silver to be . The very soft portion ' of the Sn rays was intercepted by a wooden plate which closed the ionisation chamber , and was used throughout because it stood air pressure without cutting out many Sn rays . The absorption coefficient of was found to be and of oxalic acid to be . From Beatty 's results the absorption coefficient of is negligible . Hence we can calculate the absorption coefficient of oxygen from the equation and therefore Consequently silver absorbs Sn rays , or times as much as oxygen . From the earlier results in this paper we therefore conclude that Sn rays produce times as many thode rays in silver as in , so that the ionising power of the cathode rays produced by the Sn -rays in 1 milligramme of silver is times the ionising power of the cathode rays produced by the same -rays in 1 milligramme of oxygen . Comparing this with the result of the last paragraph we see that the ionisation effected in * That is to say , the total ionisation they would cause in oxygen if they could complete their whole courses in the gas . For , allowing for water of crystallization , there is one carbon atom to three of gen and three of hydrogen .

rspa_1911_0050

0950-1207

The mechanical viscosity of fluids.

366

376

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

T. E. Stanton, D. Sc., M. Inst. C. E.|R. T. Glazebrook, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1911.0050

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1911_0050

10.1098/rspa.1911.0050

Fluid Dynamics

Tables

Fluid Dynamics

]\gt ; The Mechanical Viscosity of Fluids . By T. E. STANTON , D.Sc . , M.Inst . C.E. ( Communicated by R. T. Glazebrook , F.R.S. Received May 16 , \mdash ; Read June 29 , 1911 . ) ( the National Physical Laboratory . ) The experiments described in the following paper were undertaken in order to yate the relation between shearing stress and rate of distortion in fluids which are in eddying or sinuous motion , that is , motion in which the frictional resistance , at the boundaries of the solid over which they move , varies approximately as the square of the relative velocity , as distinguished from that steady or laminar motion in which the frictional resistance is proportional to the first power of the relative speed . This shearing stress has been called by Osborne Reynolds* ' ' mechanical viscosity i.e. , " " viscosity arising from the molar motion of the fluid and which is not a property of the fluid independent of its motion as is its physical viscosity Thus , to quote Reynolds ' statement , in the eddying motion of a fluid in a parallel channel , " " although the meaIl motion at any point taken over a sufficient time is parallel to the axis of the pipe , it is made up of a succession of motions crossing the pipe in different directions In this case , the shearin stress at this point on a cylindrical surface coaxial with the pipe will include the momentum per second parallel to the pipe carried by the cross streams across the surface on which this shearing stress is measured On the other hand , ' the coefficient of physical viscosity is the coefficient of instantaneous resistance to distortion at a point with the fluid As far as the author is aware , no attempts have yet been made to measure the shearing stress in fluids which are in eddying motion , but Osborne Reynolds has assumed that this stress is proportional to the mean speed of flow , and is also a function of the dimensions of the channel in which the motion takes place . For experimental purposes , it appeared obvious that the conditions under which the phenomenon could be most conveniently studied were those of the motion of air or water in parallel pipes of circular cross section , and as all the appliances used for the determination of the friction of air in pipes at the National Physical Laboratory were available , air was the fluid chosen for the " " Theory of Lubrication ' Phil. Trans 1886 , p. 165 . viscosity of Fluids . experiments . Another reason for the choice of air was that in Threlfall's* observations on the distribution of mean axial velocity in air flowing through large pipes this distribution . at any cross section appeared to be independent of the rate of flow . Further , although in Threlfall 's experiments the general form of the velocity curve does not appear to have been investigated , yet the observed values of the ladial gradient of velocity some hope of the possibility of an accurate determination of the rate of distortion . If this was found to be the case , a further determination of the variation of pressure along and across the pipe would furnish the data necessary for the estimation of the ratio of the stress to the rate of distortion . Thus , if is the average shearing stress on the surface of any cylindrical portion of radius of the fluid coaxial with the pipe through which it flows , and the mean axial velocity of the fluid at this radius ; , writing , the object of the experiments was the determination of which may be called the coefficient of mechanical viscosity , as a function of and the dimensions of the pipe . The Method of Estabtishing the Air Current and Estimating the Values of and The arrangement of one of the experimental pipes and the air fan used to set up the current is shown in fig. I. The air fan discharges into a horizontal pipe metres in length . This pipe is connected by a bend to a vertical pipe metres high . The experimental portion , 61 cm . long , is at the upper extremity of the vertical pipe . It was found by experiment that this length of outlet was sufficient to set up the limiting distribution of the velocity across the pipe as long as the diameter did not exceed cm . The fan was driven by an electric motor , which was provided with a sensitive speed indicator , and during the observations at any given speed of flow the speed of the motor was kept constant by hand regulation of a carbon resistance in the armature circuit of the motor . The values of were determined from the difference between the pressure in a small Pitot tube facing the current and that in a small orifice in the side of the pipe . The Pitot tube was of rectangular section , the dimensions at the orifice being:\mdash ; In the direction of the radius of the pipe Perpendicular to the radius of the pipe mm " " Motion of Gases in Pipes ' Inst. Mech. gineers Proc 1904 . Dr. T. E. Stanton . [ May 16 , This tube was fixed to a micrometer , and could be moved across a diameter of the pipe . The pressure difference was measured by a sensitive oil and water gauge , whose indications could be relied upon within an accuracy of mm. of water . The final calibration of the Pitot tube was made by a comparison of its readings with the measured discharge of the pipe through a gas meter . The determination of the shearing stress on any cylindrical portion of the fluid of radius was made by a direct measurement of the drop of pressure at the surface the pipe , together with the measurement of the variation of pressure along the radius . The former was observed by taking the difference in two small tubes let into the sides of the pipe . -As regards the latter , it has been shown by Osborne Reynolds*that although in steady motion , when the motion is sinuous , whexe 'Nature , ' 1898 , p. 468 . 1911 . ] The Viscosity of Fluids . is the component of sinuous motion normal to the surface . To detect such a variation , a small tube of radius mm. , with a hole in its side connected to a sensitive gauge , was moved across a diameter , but no variation of pressure could be found up to a distance of 20 mm. from the walls . It was therefore assumed in the reductions that the pressure was constant across any section , and that the shearing stress was , therefore , proportional to the radius . ( A ) EXPERIMENTS 0N ARTIFICIALLY ROUGHENED PIPES . As in ordinary smooth pipes it is known that the frictional resistance varies as a lower power of the velocity than the square , and that in consequence , as shown by Lord Rayleigh , friction is given by , where kinematical coefficient of viscosity , linear dimension of the pipe , and the velocity at the axis of the pipe . In order to simplify the problem , an attempt was made to eliminate any effect due to a variation in by artificially roughening the pipes used until the friction was proportional to the square of the velocity . This was done a double screw-thread on the inside surface of the pipes , and so the pitch and depth that the surfaces of pipes of different diameters were geometrically similar . After several trials , two pipes were produced , of diameters and cm . , in which the friction varied as the square of the velocity , and consequently the friction per unit area at the same velocities was found to be the same for each pipe , the numerical value being dynes per square centimetre . The results of a large number of expeI'iments on these two pipes were as follows:\mdash ; Effect oVelocity of Flow on the Radial Distribution of Velocity . To test the constancy of the velocity distribution in a radial direction , two sets of observations were made at the hest and lowest centre filament velocities which could be satisfactorily obtained . These were 2220 and 546 cm . per second respectively . The two sets of reduced velocities for the cm . diameter pipe are plotted in fig. II , and it will be seen that for this range of speed there is no definite change in the form of the curve , which , from the centre up to a distance of about 3 mm. from the wall of the pipe , is a parabola with its vertex in the axis of the pipe , the equation to which may be written Report of Advisory Committee for Aeronautics , ' 1909-10 , p. 38 ; also ' Phil. Mag fkic Dr. T. E. Stanton . [ May 16 , Table I.\mdash ; Reduced Values of the .From the oregoing results the follow pipes are derived:\mdash ; ( a ) In such a pipe , through which critical value , it follows from the pa mechanical viscosity , as defined above , within a relatively small distance from 1 ( b ) Considering the variations in th surface coaxial with the pipe due to evident that , since the value of is centre filament , and the shearing force therefore is directly proportional to ] ( c ) In two pipes in which the velocity diameters the values of on two whose linear dimensions are proportion It follows , therefore , that , since the re squares of the corresponding velocities different pipes , be directly proportional The equation to the velocity curve being is known to be proportional to , it foUows tha The Viscosity Fluids . It appears , therefore , that the expression for the coefficient of mechanical viscosity in the artificially roughened pipes considered may be written where is the velocity of flow at the axis of the pipe , the linear dimension of the pipe , and is a constant depending on the extent of the eddying motion , i.e. , the roughness of the surface . ( B ) EXPERIMENTS ON OBDINARY SMOOTH PIPES . For these experiments two smooth brass pipes of approximately the same diameters as the artificially roughened ones were used . ( These were and cm . diameter . ) As in the case of the rough pipes , two sets of observations , . . VOL. LXXXV.\mdash ; A. Dr. T. E. Stanton . [ May 16 , one at the highest speed of flow obtainable and the other at the lowest , were made on one of the pipes , and the distributions of axial velocity in the cases are shown in fig. . It will be seen that , for a region extending the axis up to a value of the radius of approximately , the distributions are identical , but that beyond this radius the curves separate , indicating apparently a regiotl of viscous flow near the walls , in which the slope of the curves necessarily increases at a greater rate than the centre filament velocity , since the resistance varies as a of the speed greater than unity . It may be mentioned that in the earlier experiments the corresponding curves plotted from the observations were not anywhere coincident , except at the axis , but , as a possible explanation of this was the insufficient length of the pipe between the fan and the portion under observation , further experiments were made with an increased length of pipe , and it was ultimately found that with a total length of 9 metres there was practical coincidence within the region mentioned . It is of course possible that even then the coincidence was not exact , but the difference , if any , was too small to be detected by the . It evident , therefore , that in the case of smooth pipes the region of viscous flow was of considerably greater area than in the case of the roughened pipes , in which it } ) eared to be nearly destroyed . It was , however , found that the central portion of the velocity distribution curve in smooth pipes up to a radius of was parabolic in form , as in case of the roughened pipes , thus indicating that the value of was constant up to this limit . As regards the effect of the size of the pipe , a precisely similar tion to that used for the hened pipes showed that , for two pipes in which the centre filament velocities were proportional to the respective diameters , the velocity distributions were strictly similar throughout the central portion of the flow referred to above . * , therefore , this region , since the values of for arly given value of the radius are proportional to the velocity of flow , and since the friction per unit area at this radius is known to be proportional to , it is evident that in the case of the smooth pipe is proportional to . Further , since for two smooth pipes in which the centre filament velocities are proportional to the respective diameters the values of at . points in the central region are the it follows that is proportional to the external diameter of pipe , and the * The two velocity curves for this case have not been plotted as in case of the rough pipes ( fig. III ) , because the difference in the radii is too small to bring out their divergence in the region of viscous flow . The values of the velocitieH determined are given in Table II . 1911 . ] The Viscosity of f'tuids . complete expression for the mechanical viscosity for the region in question is . where is a constant . This is , of course , in agreement yith the value found for the roughened pipes , as in the latter case was a constant quantity for all values of Table II.\mdash ; Reduced Values of the Velocities in the two Smooth Pipes for Experiments in which is constant ( columns ( 1 ) and ( 2 ) ) and is constant ( colunns ( 1 ) and ( 3 ) ) . Radius . ecVelocity i Badius . It appears , therefore , that the yeneral character of the flow of air in pipes consists of a central region in which the ratio of the shearing stress to the rate of change of distortion is constant for any particular value of the flow , and that in the neighbourhood of the walls this alters rapidly until it becomes equal to the physical viscosity at the boundary . In such a composite state of motion as this , it is clear that exact similarity over the whole section of the motions of air in two smooth pipes of different diameters can only exist when the values of both and are the same for each . From the value of here determined this condition can only be satisfied if the values of and are the same for the two pipes . To illustrate this similarity , experiments were made on the distribution of velocity in the two smooth pipes used for this work and in the filament velocities were respectively 1625 cm . per second in the cm . pipe and 1017 cm . per second in the cm . pipe . The expsrimental results for both pipes are given in Table II and are also plotted in fig. , and it will

rspa_1911_0051

0950-1207

Spectroscopic investigations in connection with the active modification of nitrogen.\#x2014;I. Spectrum of the afterglow.

377

388

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

A. Fowler, F. R. S.|the Hon. R. J. Strutt, M. A., F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1911.0051

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rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1911_0051

10.1098/rspa.1911.0051

Atomic Physics

Tables

Atomic Physics

]\gt ; Spectroscopic Investigations in connection with the -4ctire of Nitrogen.\mdash ; I. Spectrum of the Afterglou . By A. FOWLER , F.B.S. , Assistant Professor of Physics , Imperial College of Science and Technology , and the Hon. B. J. }STRUTT , , F.R.S. , Professor of Physics , Imperial College of Science and Technology , South Kensington . ( Received May 20 , \mdash ; Read May 25 , 1911 . ) Method of Observation . The method of producing and isolating the nitrogen adopted in the observations dealt with in the present paper was that described by one of us in the recent Bakerian lecture . * A continuous stream of nitrogen was passed at low pressure through the exciting discharge tube , from which it was drawn into a side tube which was viewed end-on through a quartz window . The source of nitrogen was the commercial compressed gas , but it was purified to the required degree by through a tube chips of phosphorus and other tubes containing caustic potash and phosphorus pentoxide . The purer the the more brilliant was the luminosity of the afterglow ; a small amount of oxygen in the nitrogen sufficed to destroy the deep yellow glow , and only a bluish-white luminosity was then visible . Three spectrographs have been employed in the investigation ; ( 1 ) a small quartz spectrograph , giving a linear dispersion of cm . from to a larger quartz spectrograph giving cm . for the same extent of spectrum ; ( 3 ) a Littrow spectrograph , with a prism of light flint glass , giving 16 cm . for the region 7000 to 3800 . For the determination of wave-lengths , comparison spectra of copper ( with impurities of lead , etc. ) were chiefly used . General Description of the Spectrnm . As seen and rapbed with instruments of small dispersion , the spectrum of the afterglow produced by the above method appears to be identical with that described by Lewis . The luminosity , however , is so great , and its maintenance so easy , that considerable dispersion may be employed , and long exposures given , so that the spectrum can now be examined in much greater detail . J. Strutt , ' Roy . Soc. Proc 1911 , vol. 8 p. 219 . ' Astrophys . Jourlt 1904 , vol. 20 , p. 49 . . A. Fowler and Hon. R. J. Strutt . [ May 20 The spectrum may be convenient]y considered to consist of three groups of bands , namely:\mdash ; Group .\mdash ; Three very conspicuous bands in the red , yellow , and green , with the htest parts about wave-lengths , 5804 , and 5407 . Another faint band 5054 also to this group . series of 11 bands in the violet and ultra-violet , extending from 4312 to 2503 . These are degraded towards the red , and have double heads . Other fainter series of hands of similar structure also belong to thia group . series of flutings , egraded to the more refrangible corresponding in every particular with I)eslandres ' " " third positive\ldquo ; group of nitrogen bands . These have double-double heads and extend from 3009 to 2155 . The stronger members of the second positive group of nitrogen bands raded to the , and extending from about 5000 to ) appear in the spectrum of the afterglow , but they may have been introduced by internal reflections of the ] ight from the exciting discharge tube , or by stray discharges in the afterglow tube itself , as Lewis did not find them by his method of observing the afterglow only ) the discharge was interrupted . The first head of the cyano , en band at 3883 was frequently present , but it may be accounted for by a slight carbon impurity , * and is not to be regarded as a part of the afterglow spectrum of pure nitrogen . The presence of carbon compoumds was sometimes shown in another way by the line of cal.bon at in the spectrum of the , tube when the condenser was in circuit . of Group The three barlds of roup , in the less refrangible part of the visible spectrum , are the most striking feature of the lowo spectrum when the nitrogen is as pure as possible . Iheir true characters and relationships were not revealed umtil they were raphed with the comparatively great dispersion of the Littrow . It was then found that their structure was identical with that of the ' first positive\ldquo ; bands of nitrogen , and further investigation revealed the previously unsuspected fact that they are also identical in position with hands of nitrogen . This result is shown by the photographic comparison iven in Plate 10 , fig. 1 , which indicates the extraordinary selection of first positive ba\amp ; nacute ; ds for special enhancement in the afterglow . It will be seen that the afterglow bands * See Stl'utt , loc. , p. 228 . 1911 . ] llodification oVitrogen . are not merely a survival of the htest of the firsG positive band represent a special development of the more rible parts of the three groups into which the first positive spectrum is visibly divided . The positions of the various bands are roughly shown by the ] scale marked on the photographs . Von Helm 's values for the nitrogen bands , the wave-lengths and oscillation frequencies of the first heads of the principal bands which occur in the spectrum as indicated in Table I. Table I.\mdash ; The Visual Bands of the After , ( Group ) . Green Green { *Measure by Hasselberg . Identified by visual The requency differences and second differences the heads of the bands are given in the and fifth columns of the table , and similar figures are obtained for the other corresponding heads . Tbese differences are of interest as showing that the bands not been selected at random from the numerous series which build up the first positive spectrum of nitrogen , but that they COIlstitute three definite series of the usual character . They are , in fact , identical vitl ) three consecutive series in Cuthbertson 's eIuenC of the first positive bands of nitrogen in 13 series , The faint bands less refrangible than 6322 shown in the photograph probably do not form part of the true afterglow spectrum , but represent part of the normal first positive spectrum accidentally superposed on that of the afterglow . 's ' Handb . der ) vol. p. 828 . Phil. Mag 1902 , [ 6 ] , vol. p. 348 . Mr. A. Fowler and Hon. R. J. Strutt . [ May 20 , Series 3 . Series4 . Series6 . Series7 . Series Series 16163 The association of the bands in the afterglow suggests that of the various possible ements of the first positive bands the horizontal series in the above table are perhaps specially significant . It will be observed that , the frequency scale , a of one of the horizontal series by an appropriate amount will result in its superposition on one or other of the remaining series , thus resembling the five series into which the second ositive bands of nitrogen have been divided by Deslandres . * The relation between the bands is shown in another way by the application of Deslandres ' general formula for the first positive bands,1 namely:\mdash ; The first horizontal series of the above table is obtained when and , 43 , 44 ; the second when and , 43 , 43 , 44 ; and the third when and , 41 , 42 , 43 . The bands shown in fig. lb which are less efraugible than 6322 do not belong to either of these series , and , as already pointed out , they probably do not form part of the afterglow spectrum , but have been introduced by accident . lt thus appears that , in the less refrangible part of the spectrunl , the afterglow shows no new bands , and only differs from that of the ordinary discharge nitrogen in the concentration of the luminous energy into a small selection of the numerous series into which the first positive spectrum can be divided . It should be noted also that first positive bands of nitrogen are reatly 1educed in intensity in the condensed discharge , which generates the afterglow , as compared with the uncondensed discharge , so that the artly abolished first positive hands may be considered to reappear in the , bnt with greatly modified intensities . Apart from the modification of intensities , for which we can offer no explanation at present , this observation is in accordance with the view that nitrogen is partially dissociated in the condensed discharge , and that the afterglow is produce , during the of ordinary nitrogen . 'Comptes Bendus , ' 1887 , vol. 104 , p. 'Comptes Rendus , ' 1902 , vol. 134 , p. 74 Mr. A. Fowler and . R. J. Strutt . [ May 20 , second difference is about equal to that which appears to be commo to the first and second positive nitrogen series , but otherwise the series is quite distinct , and the have a strncture which is different from that of any of the other bands attributed to The oscillation frequencies of the more oible heads of the bands are closely represented by the formula where ? has values rano 5 to 65 . The calculated from the observed values by amounts which only once reach as much as three units . In adclition to this chief series of bands , are several fainter ones of similar structure , particulars of which are fiven in Table III ( see also Plate 10 , figs. and ) . These also form series , which may be conveniently designated , etc. , as in the last column of the table . The intensities are roughly on the same scale as those of the main series in the prsvious table . Table III.\mdash ; Fainter Bands of Group * This heacl is hidden by the mercury line , accidentally present , and its position been estimated by co1lsideration of the intervals rating the component heads . These secondary series are related to the chief series and to each other in the same way that the constituent series of the first or ' second positiye groups are related , such that a general displacement of one series by the proper amount will superpose it upon one of the other series . This is shown in he following arrangement of the frequencies:\mdash ; 1911 . ] Active Nitrogen . 39404 It follows that the , formula for the main series may be adapted to the secondary series by an alteration of one of the constants thus\mdash ; Series The values of for the several vertical columns are shown in the tabular arrangement above . Series fails to show the band corresponding to , although there is no other band at this place which could mask it . The several series of tJroup must clearly be regarded as forming a connected system , but they have no evident relation to the other series of nitrogen bands . As in the case of the group , however , the group does not represent a spectrum which exists exclusively in the . The bands were observed faintly by Lewis in the ordinary through nitric oxide , and our own experiments have indicated that they occur under suitable conditions in similar disoharges through air or . This is illustrated in the case of air in Plate fig. . The original negatives show the five bands of group ( 3377 to 2748 ) and the four bands of the series , and it is remarkable that the latter are relatively more developed than the chief series in the air discharge . The bands of group foumd in association with the third positive bands of , dealt with in the next section , and , as in the case of those bands , we have not found sufficient evidence co show that but nitrogen is necessary for their development . The general result of the ation of the group of bands is to show that , like roup , they tend to disappear from the spectrum of the exciting discharge , and they reappear with somewhat modified intensities in the afterglow . Mr. A. Fowler and Hon. R. J. Strutt . [ May 20 , The of As already remarked , the third group of afterglow bands is identical with the third positive band spectrum of nitrogen . This is indicated by the photographs reproduced Plate 10 , fig. 3 , which show the spectrum of the afterglow in comparison with that of air . For convenience of reference , the positions of the less refrangible heads , from the data given by Schniederjost , indicated in Table Table \mdash ; Chief Heads of Third Positive Bands of These bands occur strongly in several other sources besides the afterglow and the uncondensed discharge in air or nitrogen . They are found in the spectrum of an uncondensed spark in air at atmospheric pressure , in the arc between metallic poles , in the flame of cyanogen , and in the flame of ammonia burning in oxygen . Deslandrcs has suggested that they may be due to an oxide of developed by traces of oxygen in the case of a supposed nitrogen tube\mdash ; as he found them to disappear from the spectrum when the nitrogen had ' been passed heated sodium . The absence of the bands from the discharge in nitrogen is also regarded by Lewis as their oxide origin , the idea being that the bands vanish because of the decomposition of the compound which is thought to produce them . We have not been able to convince ourselves , however , that these third positive bands require anything more than nitrogen for their production . With all precautions to exclude oxygen , bands have always been present in the afterglow spectrum , even when the nitrogen was passed through melted phosphorus before it entered the tube . In the discharge tube itself , it was found that the presence or absence of the bands seemed to depend only upon the intensity of the discharge . In the condensed discharge , and in the uncondensed discharge , if of sufficient intensity , the bands in question are wanting , but with other things remaining the same they made their appearance when the strength of the discharge was sufficiently reduced . It would thus appear that the third positive bands are more sensitive to changes in the discharge than the of the first and second positive groups , and are the first to be abolished as the discharge approaches that necessary to produce the line spectrum . 'Zeitsch . . wiss . Photog 1904 , vol. 2 , p. ) . 19 ] ] . ] Active of Nitrogen . The general behaviour of these bands in relation to the afterglow is very similar to that of the and . They occur in the uncondensed discharge , disappear in the stronger discharge which produces the afterglow , and reappear in the afterglow ; they differ from the other two groups , however , in that there is no notable change in the relative intensities of the component bands . Spectrum of Exciting Discharge . It seemed important to compare the spectrum of the condensed discharge which develops the afterglow with that of the uncondensed discharge which ordinarily fails to do so . In the first place it was foumd that a discharge iving only the line spectrum does not excite the afterglow . A special tube was constructed with a very narrow capillary . The electrodes projected almost into this capillary , so as to avoid any development of the band spectrum in the wider palts of the tube , which might have made the result ambiguous . A current of pure nitrogen was passed through this tube , excited by the condensed discharge , but no afterglow was observed . The same current of rarefied nitrogen passed on its way to the pump through a wider tube capable of giving the band spectrum . When the discharge was transferred to this tube , the afterglow was well developed . This served as a check , to prove that the failure to obtain the in the previous instance had not been due to any defect in the quality of the gas . It was accordingly only necessary to the modifications of the band spectrum which occur in passing from a discharge of moderate intensity without condenser to a discharge with the condenser . It was already known that the effect of the condenser is to reduce the intensity of the first positive bands , to brighten the second positive bands , and to abolish those of the third positive group . We have found in addition that a new series of seven bands in the ultra-violet appears in the spectrum of the condensed discharge . There appears to be no previous record of these bands in the observations made by Deslandres and others , but there seems to be no reason to doubt that they belong to nitrogen . For purposes of reference , this series may be conveniently called the " " fourth positive\ldquo ; group of nitrogen . As photographed with the larger quartz spectrograph Plate , each of the fourth positive hands shows five principal heads , of which the most refrangible is the in each case , and the middle one next in order of brightness . The flutings are degraded towards the more refrangible end of the spectrum . The wave-lengths of the bands , their relative intensities , oscillation frequencies , and frequency differences are shown in Table 1911 . ] Active Vitrogen . The difference is constant within the limits of error , and 1ltmerically , at least , the fourth positive bands are related to the second positive as the several series of the latter are related to each other . The figures in the first and second cohlmns of the foregoing table may be respectively calculated from the formulae here m from 54 to 60 . The positive hands appear to be the most characteristic feature of the spectrum of the discharge which produces the afterglow , but a change of state in the nitrogen is also indicated by the modified intensities of the other three positive groups . The bands are also found , but with less intensity , in the condensed discharge a tube air , and if they are characteristic of the gas , it may be presumed , in accordance with other experiments , that the absence of the nitrogen afterglow in air tubes is due to the presence of oxygen . ( 1 ) The paper gives a detailed account of the spectrum of the afterglow of pure nitrogen , with wave-length determinations of sufficient accuracy to indicate the series relationships of the various bands . ( 2 ) The characteristic bands of the afterglow ill the red , yellow , and green are complex groups which have been found to be identical with some of the bands the sequence ' as the first positive group of . They represent a special development of three of the numerous series into which the first positive bands have been divided . ( 3 ) The second group of bands , extending from 4312 to 2503 , corresponds with a group of faint bands which occur in the uncondensed discharge in air or nitrogen , and the third group is identical with the third positive group of nitrogen bands , as previously by Lewis . The most characteristic feature of the condensed discharge tt'hich Active Modification of Nitrogen . . 1 , produces the fterglow is a series of seven complex bands , occupying the region 2904 to 2256 , which have not previously been recorded as belonging to nitrogen . It is suggested that these should be designated the " " fourth positive\ldquo ; group of nitrogen bands . ( 5 ) No is when the discharge is such as to give only the line spectrum of The authors are indebted to Mr. H. Shaw , A.RC . S. , for valuable assistance in the computation of wave-lengths , and in enlarging the for reproduction . I)ESCRIPTION OF PLATE . Uncondensed discharge in nitrogen , showing the first positive bands in the red , yellow , and green . I . Afterglow bands of Group , showing reIation to first sitive bands . . Uncondensed discharge in air , violet and ultra-violet region , showing second positive bands of nitrogen , part of the third positive , etc. . Afterglow bands of Group , which are also seen faintly in the spectrum of air , . Uncondensed discharge in air , ultra-violet region , showing the third positive bands of nitrogen , etc. . Afterglow bands of Group and Group ( third positive nitrogen ) . . Uncondensed discharge nitrogen , ] -violet region . . Condeused discharge in nitrogen , which excites the afterglow , showing the new ' ' fourth positive\ldquo ; bands . 1 and lb were taken with the Littrow spectrograph and the remainder with the larger quartz spectrograph . The scales attached to the photographs are strictly only applicable to the upper spectrum in each pair , owing to difficuIties of mounting .

rspa_1911_0052

0950-1207

The constitution of the alloys of aluminium and zinc.

389

392

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character

Walter Rosenhain, B. A., D. Sc.|Sydney L. Archbutt, A. I. C.|R. T. Glazebrook, C. B., F. R. S.