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rspa_1908_0069

0950-1207

The spectrum of the lighter constituents of the air.

181

194

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

Herbert Edmeston Watson B. Sc., (Lond. )|Sir William Ramsay F. R. S.

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6.0.4

http://dx.doi.org/10.1098/rspa.1908.0069

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0069

10.1098/rspa.1908.0069

Atomic Physics

Thermodynamics

Atomic Physics

181 The Spectrum of the Lighter Constituents of the Air . By Herbert Edmeston Watson , B.Sc. ( LoncL ) . ( Communicated by Sir William Ramsay , F.R.S. Received June 23 , \#151 ; Read June 25 , 1908 . ) In 1900 , Professors Living and Dewar published a paper on " The Lighter Constituents of Air , " * and gave a table of wave-lengths for nearly 300 lines . Some of these were shown to be produced by hydrogen , helium , and neon , but the greater number were of unknown origin . A few years later the spectrum of pure neon was published by Baly , + and it was shown that many of Living and Dewar 's lines were due to that gas , but at the same time 162 lines remained which , in the opinion of that observer , did not belong to neon . With the view of throwing some light on the matter , and ascertaining more definitely whether there was a constituent of the air of lower atomic weight than helium , CoatesJ fractionated a large quantity of air , but could find no constituents other than hydrogen , helium , and neon on examining the lightest fractions with a small prism spectroscope . In order , however , to make quite sure of this point , Sir William Ramsay requested me to photograph the spectrum with the Rowland grating at University College , and the results of this work form the material of the present communication . The main object of the research , namely , definite proof of the existence of a new gas , has been unsuccessful , as was to be expected from the preliminary work , but incidentally it has been shown that the neon spectrum is considerably more complicated than was formerly supposed , and a number of new lines have been measured . Experimental . The method of fractionation of the gas has already been fully described by Coats , S but it may be as well briefly to recapitulate it . About 73,000 'litres , of air were continually circulated through the liquefying apparatus at University College until greatly reduced in volume by the condensation of the least volatile portions . The residue was then condensed in portions of about 80 litres in a glass bulb immersed in liquid air boiling * 'Roy . Soc. Proc. , ' vol. 67 , pp. 467\#151 ; 474 , 1900 . + ' Pbil . Trans. , ' A , vol. 202 , pp. 183\#151 ; 242 , 1903 . f 'Roy . Soc. Proc. , ' A , vol. 78 , pp. 479\#151 ; 482 , 1906 . S Loc . cit. Mr. H. E. Watson . The Spectrum of the [ June 23 , under reduced pressure . Light fractions were boiled off , and the process repeated several times until the volume was reduced to 4700 c.c. The portion of this gas which was not absorbed by charcoal at \#151 ; 190 ' C. was separated into several fractions . Fraction 1 was pumped off charcoal at \#151 ; 205 ' C. , and fraction 2 at \#151 ; 190 ' C. These were the two fractions examined spectroscopically . It is worthy of note that analysis showed neither of them to contain any appreciable quantity of hydrogen , this gas only boiling off at a higher temperature . The form of vacuum tube used was one in which the capillary portion was viewed end on through a quartz plate cemented on with sealing wax . The electrodes wTere situated in side tubes , so that the spectrum of the gas surrounding them was not photographed as in the experiments of Liveing and Dewar . They were made of stout aluminium wire , and mounted as described by Baly.* Baly 's methods of filling the tubes and adjusting the pressure in them were also adopted , except with regard to removing the last traces of hydrogen from the electrodes , this gas being present in small quantities in the gas to be examined . The Rowland grating used has a focal length of 10 feet , and is ruled with 14,438 lines to the inch . When finally adjusted , it was found that the centres of lines of different orders upon the same plate were not in the same horizontal line , and consequently it was easy to distinguish lines of different orders . This displacement was slight , and does not appear to have affected the relation between wave-lengths measured in different orders . The spectra obtained were remarkably free from ghosts , and , in fact , when first set up , the grating was supposed to be perfect in this respect . I have found , however , that on prolonged exposure all the very intense lines are accompanied by four ghosts , the outer pair being some distance from the true line . They were recognised by the property of symmetry about the principal line , and were in several cases used to determine the true position of the latter . If one ghost were masked by another line , the position of the corresponding ghost was calculated by means of the fact that the distance from the principal line is proportional to the wave-length . It is hoped that by this means all spurious lines have been removed from the table of wave-lengths . The whole spectrum was photographed in the first order , but lines of wave-length less than 4100 were measured in the second order as well . The plates used were Wratten and Wainwright 's " Panchromatic , " the sensitiveness of which is practically equal for all portions of the spectrum below 7000 . For the red region the " spectrum " plates of the same firm * Loc . cit. 1908 . ] Lighter Constituents of the Air . were used , these being sensitive to at least 7900 . I am greatly indebted to Dr. Mees for personally making them for me . It was found preferable to make exposures during the night , as there was less vibration and the temperature remained more constant . The second condition was very important , since it was found possible to obtain first-class plates only when the temperature variation was less than 1 ' ; but the grating being situated in the basement , the variation during one night seldom exceeded 3 ' , and was usually much less . All the plates were taken between the temperatures 11 ' and 18 ' C. Exposures of about 16 hours were given , this comparatively long time being necessary to show many faint lines which exist in the spectrum . The very strong lines in the orange region were photographed with tubes which had partially run down , in order to avoid over-exposure . In all cases a weak current from an induction coil without a Leyden jar was used , so as to prolong the life of the tubes as much as possible . After each exposure an iron spectrum was photographed below that of the gas , the slit being screened so that the points of the longer lines in the two spectra just met . As the relative positions of the principal neon lines and standard iron lines had been already determined by Baly , it was considered unnecessary to repeat this work . The wave-lengths of iron lines given by Kayser and Bunge* were , however , used to eliminate errors , according to the method described by Baly , f with the exception that the correction applied to the wave-length of a gas line differed from the value deduced from the correction curve by a small number which was constant for any one plate , and of such a magnitude as to make the corrected wave-lengths agree as nearly as possible with Baly 's . This procedure is necessary , because the gas and iron spectra were photographed through different portions of the slit and consequently were apt to suffer a slight relative displacement . The error in the wave-lengths given is difficult to estimate . All the plates were measured at least twice , and the readings in nearly every case o agreed within 0*001 cm . , a distance corresponding to 0*05 Angstrom unit . Usually the agreement was much better . The wave-lengths , as determined from different plates , agreed in general within 0*04 A.U. , but those of the very strong and very wreak lines sometimes differed by as much as 0*1 A.U. , and in such cases they were remeasured . Any values which differed much from those given by Baly were also carefully revised . In the red part of the spectrum , and the region from 5000 to 4000 , a number of plates were taken , and it is hoped that the error in the wave-lengths is not greater than * 'Brit . Ass . Reports , ' 1891 , p. 161 . t 'Spectroscopy , ' p. 221 . Mr. H. E. Watson . Spectrum of the [ June 23 , 0 03 A.U. This also applies to lines of shorter wave-length than 4000 , as they were measured in two orders . Baly has measured nearly all the lines in the remainder of the spectrum , and his results are probably the more accurate since they were deduced from photographs in the second order . The hydrogen , helium , and mercury lines which were found in the spectrum afforded a means of checking the absolute wave-lengths , and the agreement was found to be good throughout . The Constituents of the Gas . As before mentioned , two fractions of gas were examined , one pumped off charcoal at a temperature of \#151 ; 205 ' C. and the other at \#151 ; 190 ' C. After a complete series of photographs of each fraction had been taken the gases were sparked for a considerable time with oxygen , and the latter removed by means of phosphorus . This procedure had no effect on the spectrum beyond removing the hydrogen lines , and moreover the two fractions appear to be identical as regards their constituents , the only difference being in the relative intensities of some of the lines . The spectrum consisted entirely of bright lines , and no trace of nitrogen or carbon compounds could be detected . Three of the brightest mercury lines were obtained from freshly filled tubes , but were only just visible . The small quantity of hydrogen present in the gas before sparking was a source of considerable difficulty since there appears to be at present no reliable table of the vrave-lengths of the secondary hydrogen spectrum . Ames* has published a list of lines obtained from a vacuum tube of hydrogen , and about half these appeared on my plates . No trace of the weaker lines was to be seen , and hence it appeared unlikely that any other hydrogen lines would be present . There were , however , several faint lines on my plates which appeared only occasionally , and these were all found in a list given by Frostf of lines which appeared in a helium tube after running for some time . The region of the spectrum embraced is only from 4723\#151 ; 4358 , but from comparison with Hasselberg 's original secondary hydrogen spectrum } it is concluded that these lines are due to hydrogen . The number of them is 90 , of which only nine are given by Ames . It appears , therefore , that there is a spectrum of hydrogen which is seen only under exceptional circumstances , one of the most favourable of which is the presence of a monatomic gas . A further investigation of this point is in progress . Owing to the limited range of Frost 's values it is possible that a * ' Phil. Mag. , ' vol. 30 , p. 33 , 1890 . t * Astropliys . Journ. , ' vol. 16 , p. 104 , 1902 . } Watts , ' Index of Spectra , ' p. 50 . 1908 . ] Lighter Constituents of the Air . 185 few hydrogen lines have not been removed from the table of wave-lengths , but their number is not likely to be great because the relative intensities of nearly all the lines given were constant on different plates taken with different tubes . All the helium lines given by Rung and Paschen , * except the very weakest , were seen and measured , but the helium spectrum was not nearly as strong as that of the neon . In some cases the former was very faint indeed owing to the selective absorption of the helium by the electrodes , and on one plate no trace of the line 5875-8 was to be seen . The lines at 6678 and 3447 , however , were very bright on the same plate , and it must be concluded that these are two neon lines almost coincident with the helium lines . The line at 3447 is , moreover , given by Baly as a strong line , though in his tubes the helium was always allowed to run out before a photograph was taken . There appears to be"a similar pair at 4713 , though I was unable to obtain a plate on which the neon line alone was present . The wavelengths of the lines concerned are :\#151 ; He ... ... ... . . 6678-37 4713-25 3447-73 He ... ... ... . . 6678-50 4713-51 3447*83 and no reason can be at present assigned to their close proximity . Argon was present in minute traces , even after the exhaustive fractionation the gas had undergone ; it is not surprising , therefore , to find that Baly 's gas also contained argon , and several lines given by him are due to this substance . All that have been found are given in the tables , and have not been eliminated as have the lines due to gases previously mentioned . The question which now arises is : What is the origin of the remaining lines ? Their number is 321 , of which only 115 are given by Baly , and 132 by Living and Dewar , and it might well be supposed that some of them are due to elements as yet unknown . Accordingly their wave-lengths were carefully compared with those of the chief nebular lines as measured by Wright , f and the coronal lines given by Lockyer.^ There was not the slightest indication of the existence of any of these lines in my spectrum . Marshall Watts , in a list of auroral lines , S assigns some to neon , but the wave-lengths given are not sufficiently accurate to enable definite conclusions to be drawn . In addition , Dyson's|| list of 1200 lines in the chromosphere * 'Astrophys . Journ. , ' vol. 3 , p. 4 , 1896 . t 'Astrophys . Journ. , ' vol. 16 , p. 53 , 1902 . \ ' Roy . Soc. Proc. , ' vol. 66 , p. 191 , 1900 . S ' Monthly Weather Review , ' vol. 35 , p. 408 , 1907 . || 'Phil . Trans. , ' A , vol. 206 , pp. 403\#151 ; 452 , 1906 . Mr. H. E. Watson . The Sp of the [ June 23 , of the sun was examined . A certain number of approximate coincidences were observed , and are noted in the table of wave-lengths , but it is highly probable that they are merely accidental , for the lines in question are remarkable neither for their intensity nor their character . This being so , another explanation was looked for . It will be observed that all the lines not given by Baly are of comparatively low intensity , and occur largely in the ultra-violet , and hence it is quite probable that they are really neon lines which were not previously obtained owing to insufficient exposure . Baly 's photographs were all in the second order , which for the particular grating used is not nearly as bright as the first , and , moreover , his vacuum tube had a thin glass end which would naturally obliterate much of the ultra-violet light . To confirm this supposition a different sample of neon and helium containing considerably more helium than the former one was photographed . The lines ascribed to neon were all seen , and were identical in intensity with those formerly obtained , so that it appears very unlikely that any gases other than helium and neon were present in either sample . There is , of course , the possibility that a gas very similar to neon in physical properties exists , but the periodic table renders this unlikely , and it is to be expected that a gas with lower atomic weight than helium would resemble this gas substance rather than neon , with the result that its spectrum would be relatively stronger in the second sample examined . It may consequently be stated fairly conclusively that the spectrum of a new gas has not been photographed , but this is by no means synonymous with saying that such a gas does not exist . There are at least three reasons for this . Firstly , it was remarked by Coates that the fractions of air distilled from charcoal at \#151 ; 190 ' C. contained hardly any hydrogen , this gas boiling off only at a higher temperature . Consequently , it is possible that another gas might behave similarly , and if this were the case its spectrum would probably be masked by that of the nitrogen in the later fractions . Secondly , as already mentioned , the helium in the gas was absorbed by the electrodes more readily than the neon , and a third gas might he absorbed almost at once before its spectrum could be photographed . Thirdly , it has been observed by Cameron and Bamsay* that helium is absorbed by glass and silica even in the cold , and it is therefore just possible that a monatomic gas of very low atomic weight might pass through these substances with ease , and if this be so it seems unlikely that a lighter constituent of air will ever be isolated . It still remains to make a few remarks about the tables of Baly , and Liveing and Dewar . Baly makes no mention of the strong line 6334 , * 'Chem . Soc. Trans. , ' vol. 91 , p. 1279 , 1907 . 1908 . ] Lighter Constituents of the Air . although it is assigned to neon by Living and Dewar . I have been unable to find the reference for this , but it seems likely that the omission is due to a clerical error . The same author also gives several lines not in my list . Some of these I have identified as argon lines , some as ghosts , and a few as belonging to a different order , but the most careful search has failed to reveal any trace of the rest . The origin of many of Living and Dewar 's lines is by no means clear . Since these observers liquefied only about 200 litres of air , less than a three-hundredth part of the amount treated by Coats , it does not seem at all likely that they can have obtaiued any gas which was unnoticed by the latter . Their gas , however , contained considerable quantities of hydrogen , and though it is stated that the hydrogen lines wTere not usually visible when photographs were taken , owing to the passage of this gas to the positive pole , yet it may have happened that there was hydrogen round the negative pole as well , but that this yielded a hitherto unrecognised spectrum . If this be not admissible , it must be supposed that the negative pole has some peculiar influence upon the gas in its immediate neighbourhood which complicates the spectrum considerably . The following tables show the wave-lengths obtained , those of Baly , and Living and Dewar being added for the sake of comparison . The intensities are given in the usual way , with 10 as maximum , although this method of representing them is wholly inadequate , and in fact misleading . Many lines of apparently the same intensity differ greatly in reality , and the strongest lines are many hundred times as intense as the weakest . 0 represents a line which can just be measured with a low-power microscope . A few weaker lines could be seen with a small lens , but could not be measured , and are omitted . Anything noticeable about a particular line is placed in the column headed " Remarks . " In conclusion , I should like to tender my warmest thanks to Sir William Ramsay for the great interest he has taken in this work , for personally sparking down and repurifying the gases , and for frequently undertaking the laborious process of remaking and refilling the vacuum tubes . Also to Mr. Baly for advice with regard to the use of the grating , and to Mr. Coats for some help in the earlier part of the work . Note added July 28.\#151 ; Since going to press , the hydrogen spectrum has been completely photographed . Only one hydrogen line was found in the table of wave-lengths , and this has now been removed . Mr. H. E. Watson . The Spectrum of [ June 23 Wave-length . Intensity . Baly . | Intensity . Liveing and Dewar . Remarks . 7245 -47 2 7247 The wave-lengths of these 7174 -25 2 \#151 ; \#151 ; 7174 red lines carefully standard- 7059 -50 2 \#151 ; \#151 ; 7058 vw ised from the helium lines 7032-65 3 \#151 ; \#151 ; 7034 7065*48 , 6678*37 , 3705 T5 , 7024 -38 2 3613 *79 , and 3354 *67 6929 *78 6 \#151 ; \#151 ; 6931 i 6759 72 1 6738 -17 2 s 6717 -22 7 .20 i 6716 6678 -50 9 \#151 ; \#151 ; 6678 -4 Not Helium 6678 *37 6667 -05 3 6652 -20 4 \#151 ; \#151 ; \#151 ; Very weak in first fraction 6640 -23 1 6603-10 3 6599 -18 9 .16 4 6601 6533 -08 6 .10 4 6535 6506 -69 9 .72 i 6 6508 6444-88 4 .90 1 6446 v w 6421 -89 2 6409 -93 3 .90 1 6202 -43 10 .40 10 6404 6401 -24 6 .26 1 6383 -14 9 .15 8 6382 6365 -23 2 6352 -08 4 .04 1 6334 -65 9 \#151 ; \#151 ; 6334 L. and D. remark that this is a neon line 6331 -11 5 .13 1 6328 *39 6 .38 6 6313 -89 5 .94 1 6304-97 6 .99 8 6304 6293 -98 5 4-04 1 6276 -23 3 6273 -23 3 .26 6266 -69 6 .66 10 6266 6258 -98 3 9*06 1 6246 -90 4 7-00 1 6244 6232 : 6225 -90 3 6217 -44 6 .50 8 6217 6214 -04 5 .13 2 6205 -94 5 6-01 1 6203-08 1 \#151 ; \#151 ; 99 -34 1 1 6193 -23 3 6189 -24 3 .30 1 6182 -28 5 .37 10 6183 \#151 ; \#151 ; 79 -90 1 6175 -09 5b .15 2 6176 vw Intensity variable 6173 -01 1 .02 1 \#151 ; \#151 ; 66 -81 1 6163 73 6 .79 10 6163 \#151 ; \#151 ; 57 -12 1 j 6156 -36 1 6150 -46 3 .49 1 6143 -31 7 .28 10 6144 6142 -63 2 \#151 ; \#151 ; \#151 ; Not a very accurate value , the line being so near the last/ 6128 -63 5 .63 8 6128 vw 6118 -20 4 .22 2 6096 *36 6 .37 10 6097 6074 -51 6 .52 10 6075 1908 . ] Lighter Constituents of the Air . Wave-length . Intensity . Baly . Intensity . Living and Dewar . Remarks . 6064 -70 3 .36 i \#151 ; " 1 Baly 's values for 6046 -31 3 .06 i \#151 ; \#151 ; 1 these four lines \#151 ; \#151 ; 43 -20 i \#151 ; Are . 6043 *68 [ about 0 *3 too \#151 ; \#151 ; 32 -32 2 \#151 ; Ar . 6032 *69J low 6030 -20 5 .20 10 6031 \#151 ; \#151 ; 26 -03 1 \#151 ; Second order . \#171 ; . 3013 *02 \#151 ; \#151 ; 24 -40 1 \#151 ; " 3012 *20 6001 -15 3 .00 1 6001 5991 -80 4 .72 2 5991 5988 -10 4 .00 4 5987 w \#151 ; \#151 ; 84 -94 1 \#151 ; Second order . 2992 *47 5982 -71 1 5975 -76 5 .78 8 5976 5974 -80 5 .73 6 5966 -44 1 5965 -64 3 .50 4 5964 w 5961*85 2 .64 1 \#151 ; \#151 ; 49*51 1 \#151 ; Second order . 2974 *76 5945 -02 6 .91 10 5945 s 5939 -49 2 .44 1 5934 -65 2 5919 -11 4 .08 1 5919 w 5913 -81 4 .82 1 5914 w 5906 -60 5 .54 2 5905 w 5902 -65 5 .57 4 5898 -48 1 5891 -68 0 5882 -06 5 .04 8 5882 5873 -02 5 .04 1 5872 -27 4 5868 -59 3 5852 -62 10 .65 20 5852-7 vs 5829 -08 2 5820 -29 5 .29 4 5820 s 5816 -76 2 . 5811 -62 3 5804 *62 5 .57 1 5804 s 5770 *45 0 | 5764 -55 7 ! .54 8 5763 s \#151 ; \#151 ; 64-20 1 5760 -74 4 .72 1 5748 -47 5 .44 4 5747 5719 -35 5 .42 1 5718 5689 -96 5 .96 2 5689 5662 -72 4 .76 1 5662 w 5656 -81 4 .80 4 5656 5656 -16 2 5652 -69 2 .67 1 \#151 ; \#151 ; \#151 ; 5592 5589 -40 1 \#151 ; \#151 ; Not 2794 *72 5562 -90 4 .96 2 5561 5538 -73 1 5533 -73 1 \#151 ; \#151 ; 5532 \#151 ; \#151 ; \#151 ; \#151 ; 5503 vw 5494 -52 1 5448 -64 2 \#151 ; 5447 tw 5433 -78 4 .86 1 5432 w 5420 *29 0 5418 -70 2 \#151 ; 5417 vw 5412 -80 2 \#151 ; \#151 ; \#151 ; \#151 ; 5409 vw 5400-70 6 .77 4 5400 1 These lines probably not \#151 ; 00-50 4 \#151 ; J separable in first order o VOL. LXXXI.\#151 ; A. Mr. H. E. Watson . The Spectrum the [ June 23 Wave-length . Intensity . Baly . Intensity . Living and Dewar . Remarks . 5383 -35 i 5375 -15 3 5372 -47 4 \#151 ; \#151 ; 5372 5360 -16 4 \#151 ; \#151 ; 5360 5355 -37 3 \#151 ; \#151 ; 5355 5349 -36 1 5343 -40 5341 -24 7 7 .41 .25 1 4 CO A pair . L. and D. 5333 -44 0 \#151 ; \#151 ; 32 -33 4 5330 -90 8 \#151 ; \#151 ; 5330 5326 -55 4 5316 -92 1 5314 -93 0 5304 -91 3 \#151 ; \#151 ; 5304 w 5298 33 4 \#151 ; \#151 ; 5298 w 5280 -25 1 \#151 ; \#151 ; 78 -50 1 5274 -24 0 \#151 ; \#151 ; 71-50 1 5234 -14 4 \#151 ; \#151 ; 5234 5222 '45 5 \#151 ; \#151 ; 5222 \#151 ; \#151 ; 18 -30 1 5214 -44 1 5210 -68 3 | 5209 5208 -93 4 \#151 ; \#151 ; 5203 *97 5 .12 1 5204 5193 -33 4 \#151 ; \#151 ; 5192 5191 -44 2 5188 -68 5 .79 1 5188 5158 -99 1 5156 -77 0 5154 -54 3 5152 -07 4 \#151 ; \#151 ; 5152 5150 -24 0 5145 -06 5 *15 1 5145 5122 -40 4 \#151 ; \#151 ; 5122 5120 -72 0 5116 -64 6 .72 1 5116 5113 -80 3 5105 -84 1 5080 -52 6 .54 1 5080 5076 -73 0 5074 -35 4 \#151 ; \#151 ; 5074 5037-87 6 .95 1 5038 s 5036 -12 0 5031 -48 5 \#151 ; \#151 ; 5031 5023 -03 0 5005 -28 2 4995 -02 0 4957 -18 3 \#151 ; \#151 ; 4958 w 4955 -56 0 4945-05 2 4939 -12 2 4892 -18 2 4885 -05 4 \#151 ; \#151 ; 4884 y w 4868 -35 0 \#151 ; \#151 ; \#151 ; Chromosphere 4068 *20 , int . 2 4866 -60 1 4865 -67 2 4864 -52 0 4863 -22 3 4852 -81 2 1908 . ] Lighter Constituents Air . ! Wave-length . i Intensity . Baly . Intensity . Living and Dewar . Remarks . 4852 -56 0 4843 '01 0 4838 vw 4837 -49 5 .54 i 4827 -52 3 4823 -35 1 4822 -06 3 4819 vw 4818 -94 2 \#151 ; \#151 ; 4817 -80 3 4811 -85 0 4811 vw 4810 -22 3 \#151 ; \#151 ; \#151 ; \#151 ; 06 -24 i 4800 -29 1 4791 w 4790 -36 2 \#151 ; \#151 ; 4789 -66 0 \#151 ; \#151 ; \#151 ; Chromosphere 4789 -70 , int . 2 4789 -07 4 .07 i 4780 -45 i \#151 ; \#151 ; \#151 ; " 4780 -39j int . 1 4758 -84 i 4754 w 4752 -91 5 .88 i 4749 *74 4 \#151 ; \#151 ; \#151 ; 4749 -58 , int . 1 4725 -32 i 4721*72 i 4717 -77 0 4715 -50 5 .49 4 4715 4714 -59 1 4713 -31 6 *51 2 ! \#151 ; My reading probably the mean of Baly 's and He 4713 '25 4712 -22 3 .23 2 4710 -21 4 .21 2 4710 4709 -00 5 .00 4 4704 -55 5 .56 4 4704 4702-68 1 4687 -79 1 \#151 ; \#151 ; 4687 w 4680 -50 0 \#151 ; \#151 ; 4680 w 4679 -30 0 4678 -37 1 4671*09 0 4667-58 0 ! 4661 -27 2 \#151 ; \#151 ; ? 4664 4656 -57 3 \#151 ; \#151 ; 4657 w 4650 -07 1 \#151 ; \#151 ; \#151 ; i 4647 w 4645 -59 3 \#151 ; \#151 ; \#151 ; 4640 w 4636 -82 0 \#151 ; \#151 ; 4636 w 4636 -27 0 4628 -50 2 \#151 ; \#151 ; 4628 w Hardly visible in fraction 1 . Are . 4628 -60 4618 -04 0 4614 -55 1 \#151 ; \#151 ; 4616 w 4610 -07 1 \#151 ; \#151 ; \#151 ; : 4589 4582 -61 2 \#151 ; \#151 ; 4583 w 4582-18 1 4575 -27 3 \#151 ; \#151 ; Brighter in second fraction 4573 -14 1 \#151 ; \#151 ; \#151 ; )9 99 4566 -04 0 4540 -55 3 .48 1 4540 ! 4538 -49 1 4537 -93 4 .39 1 4538 4536 -40 3 1 4534 -28 1 \#151 ; \#151 ; \#151 ; First fraction only 4526 -04 0 \#151 ; \#151 ; 4526 w Very faint o 2 Mr. H. E. Watson . The Spectrum of the [ June 23 Wave-length . Intensity . Baly . Intensity , j Liveing and Dewar . Remarks . ! I i 4523 w 4517 -88 0 - _ 4518 w Very faint . 4515 -04 0 \#151 ; \#151 ; 4510 -85 0 .86 i \#151 ; " Ar . 4510 -90 \#151 ; \#151 ; \#151 ; 4508 w \#151 ; \#151 ; \#151 ; \#151 ; 4500 w 4591 -97 0 4588 -23 3 \#151 ; \#151 ; 4488 w 4483 -43 0 4477 -65 0 \#151 ; \#151 ; ~ Doubtful 4475 -78 0 . 4467 -01 1 4465 -79 0 \#151 ; \#151 ; \#151 ; 4460 -03 0 \#151 ; \#151 ; 4460 vw * \#151 ; 59 -68 1 4457 4433 -89 2 \#151 ; \#151 ; 31 -14 1 4431 Ar . 4431 -16 , int . 2 \#151 ; \#151 ; 30-33 1 4429 Ar . 4430 *35 , int . 4 \#151 ; \#151 ; 26 -15 2 \#151 ; Ar . 4426 *16 , int . 6 4425 -57 2 .57 1 4424 -96 2 .98 2 4424 4422 -70 3 .69 2 4422 \#151 ; \#151 ; 14 -44 1 4413 L. and D. probably H 4412 *35 4395 -79 0 \#151 ; | \#151 ; \#151 ; Very faint . L. and D. give 4409,4398,4392,4380,4370 w , and 4365 vw 4363 -69 0 \#151 ; 4363 w 4348 -37 0 \#151 ; ! 4347 vw Very faint . P Ar . 4348 'll , int . 8 4345 -33 0 \#151 ; \#151 ; \#151 ; Ar . 4345 *27 , int . 7 4336 -46 0 4335 -57 4334 -31 0 \#151 ; \#151 ; Very faint : Ar . 4335 *42 , Chromosphere 4335 *49 2 \#151 ; i \#151 ; 4334 w 4306 -48 1 \#151 ; \#151 ; 4306 vw L. and D. 4322 vw , 4315 vw , 4275 -78 and 4290 w 2 \#151 ; \#151 ; 4276 Chromosphere 4275 *71 4274 *88 1 4270 -41 0 \#151 ; i 4270 w 4269 '92 1 4 4268-18 1 4259 -55 4200 -84 1 .53 6 4261 w Ar . 4259 *50 , int . 9 L. and D. 4258 , 4251 , 4241 , 4234 , 4232 , 4220 , 4218 , and 4206 , last being a H line 0 1 -03 4 \#151 ; Ar . 4200 *80 , int . 10 , Chromo- 4198-35 sphere 4200 *73 0 .71 4 4198 vw Ar . 4198 *40* , int . 10 , Chromo4191 -08 sphere 4198 *73 0 .44 2 \#151 ; Ar . 4191 -02* , int . 10 \#151 ; \#151 ; 90 *86 2 \#151 ; Ar . 4190 *85 , int . 7 4182 -10 4175 -40 0 0 .00 2 \#151 ; Ar . 4182 *03 , int . 7 4174 -60 0 \#151 ; \#151 ; \#151 ; Chromosphere 4174 *48 \#151 ; \#151 ; 58*68 4 \#151 ; Ar . 4158 63* int . 10 4157 -74 0 \#151 ; \#151 ; \#151 ; L. and D. 4151 , 4134 4131*06 4071 -51 0 \#151 ; 4131 Chromosphere 4130 *97 L. and D. 4128 , 12 , 4099 , 86 , 80 0 \#151 ; \#151 ; One plate only L. and D. 4063 , 43 , 37 , 3985 , 80 , 33 , 05 * Kayser 's values are 98 '162 , 91 '841 , 58 '722 , and 67 -78 respectively . 1908 . ] Lighter Constituents of the Air . Wave-length . Intensity . J Baly . Intensity . Living and Dewar . Bemarks . 3899-21 i 3900 Baly 's line a ghost \#151 ; \#151 ; 86 -26 i \#151 ; A ghost , \#151 ; 79 -49 i \#151 ; L. and D. 3856 , 42 , 40 , 30 , 00 , 3777 , 66 3754 32 3 .31 2 3754 * 3733 -54 i \#151 ; \#151 ; \#151 ; L. and D. 3751 , 45 , 38 , 35 , 28 3713 -27 0 \#151 ; \#151 ; 3713 s L. and D. 3710 3701 -31 5 .30 6 3701 3694 -38 0 \#151 ; \#151 ; 3694 s 3685 -86 4 .84 4 3686 3682 -37 4 .33 4 3683 L. and D. 3664 s , 55 , 51 3633 *80 5 .78 6 3634 A pair . L. and I ) . Other constituent of pair He 3634 '39 3609 -33 3 .27 2 3609 w L. and D.3628 \#151 ; \#151 ; 06 -61 1 \#151 ; Are . 3606 " 69 , int . 3 3600 -32 6 .24 4 3600 3593 -69 8 .67 10 3593 s \#151 ; \#151 ; 88 -60 1 \#151 ; Are . 3588 '64 , int . 2 3587 -50 0 87-52 1 3587-5 vs A pair . L. and D. \#151 ; \#151 ; .24 1 \#151 ; 1 These lines possibly obscured \#151 ; \#151 ; 86 -62 1 \#151 ; J by halation from 3593 \#151 ; \#151 ; 67 -73 1 \#151 ; Are . 3567 '88* , int . 7 \#151 ; \#151 ; 54 -39 1 \#151 ; Are . 3554 '48 , int . 5 L. and D. 3575 , 71 , 69 , 61 , 58 , \#151 ; \#151 ; \#151 ; 1 \#151 ; 48 , 43 \#151 ; \#151 ; 32-30 1 \#151 ; \#151 ; 29 '95 1 \#151 ; A ghost \#151 ; \#151 ; 22 -92 1 \#151 ; 3520 -61 9 .57 8 3521 vs 3515-32 5 .30 6 3515 3510 -87 4 .87 2 3510 w L. and 1 ) . also give 3504 w 3501 -34 5 .34 6 3500 3498 -19 5 .19 6 3498 \#151 ; \#151 ; 81 '94 1 \#151 ; A ghost . L. and D. give 3482 , 3481 3472 -68 6 .70 8 3473 s 3466 -70 5 .72 6 3467 3464 -46 4 .48 6 3464 3460-61 5 .67 6 3460 3454 -31 5 .30 6 3454 3450 -88 4 .87 4 3451 3447 -83 5 .83 8 3447 -7 Not He 3447 '73 \#151 ; \#151 ; 38 '66 1 \#151 ; A ghost 3424 -08 3 .05 2 3424 Much brighter in second fraction 3418-03 5 .05 8 3418 s L. and D. 3417 , 07 , 04 , 3393 , 3388 3378-27 0 \#151 ; \#151 ; 3378 s Doubtful 3375 -74 2 .72 1 3370 -02 1 5 .01 6 3370 L. and D. 3374 , 72 , 67 , 63 , 62 , 60 , 58 , 45 s , 44 , 35 s , 29 , 27 , 24 s , 19 s , 15 , 13,11,10 , 3297 , 54 , 50 , 44 s , 33 , 30 , 25 , 18 s , 14 , 09 , 3199 3167 -62 2 \#151 ; \#151 ; 3165 3153 -51 2 3148 -70 2 .76 1 3147 -82 1 \#151 ; \#151 ; ? 3142 3126 -33 2 .33 1 \#151 ; ! 92-84 1 \#151 ; 80 -05 1 1 1 # For footnote , see p. 192 . 194 Spectrum of the Lighter Constituents of the Air . Wave-length . 1 Intensity . Baly . Intensity . Living and Dewar . Remarks . 3079 -31 i ! \#166 ; 3079 -02 i 3077 *08 2 .08 1 3063 -83 2 3057 :51 3 .50 1 3030-44 2 3017 -47 3 3013 -09 3 3012 -25 3 2992-57 3 2982 -81 3 2981 -06 1 2980 *81 1 2979 -94 2 2975 *65 1 2974 -89 3 2949 -32 lb 2947 -44 | 3 2932 -82 2 2929 -47 1 2913 -28 2 2911 -55 1 2872 -74 1 2862-28 0 2835 -32 1 2833 -04 0 2825 -75 0 2825-37 0 2814-77 1 2796 -06 1 2794 -72 0 2792-39 1 2775 -09 0 2766 -35 0 - 2736 -19 | 1

rspa_1908_0070

0950-1207

An investigation of the heavy constituents of the atmosphere.

195

209

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

Richard B. Moore, B. Sc.|Sir William Ramsay, K. C. B. F. R. S

article

6.0.4

http://dx.doi.org/10.1098/rspa.1908.0070

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0070

10.1098/rspa.1908.0070

Thermodynamics

Chemistry 2

Thermodynamics

195 An Investigation of the Heavy Constituents of the Atmosphere . By Bichard B. Mooiie , B.Sc. ( Communicated by Sir William Ramsay , K.C.B. , F.R.S. Received June 23 , \#151 ; Read June 25 , 1908 . ) When Ramsay and Travers* first separated krypton and xenon from liquid air residues , they obtained about 12 c.c. of the former gas and 3 c.c. of the latter . On sparking the xenon with oxygen over caustic potash and removing the excess of oxygen with phosphorus , a density of 64 was obtained , which would make this element , on the assumption that it is a monatomic gas , have an atomic weight of 128 . This would place it in its proper place in the periodic table\#151 ; above iodine . Consequently , if any other element of greater density were present in the xenon , the quantity would necessarily be very small . Afterwards Ramsayf obtained 0'87 c.c. of xenon from 191T kilogrammes of air , which plainly indicated that any attempt to look for elements in the atmosphere of greater density than xenon would involve the handling of very large quantities of liquid air . This difficulty has been surmounted through the courtesy of M. Georges Claude , and M. Andre Helbronner , of Paris , who very kindly furnished the necessary material . The liquid air apparatus used by them is shown in % . IThe cooled air , under a pressure of about 5 atmospheres , enters H , and ascending the series of tubes P , which are surrounded by liquid oxygen , is liquefied there progressively , that is to say , the oxygen being converted into a liquid at a higher temperature than the nitrogen , liquefies first and drips back into the receiver A. This liquid contains about 48 per cent , of oxygen . The nitrogen meanwhile reaches B , and descending the tube F ' , is liquefied and collects in C , as almost pure liquid nitrogen . The liquid in A ascends the tube R , and enters the fractionating tower , where the oxygen passes down and ultimately reaches the reservoir M. The nitrogen , carrying traces of oxygen , meanwhile ascends and meets with the nitrogen from C , which has arrived at the top of the tower by means of the tube R ' . The last traces of oxygen are thus fractionated from the nitrogen , and the latter gas escapes through E practically pure . This nitrogen and also the oxygen from M , which is used for commercial purposes , is led through " exchangers " ( not * 'Trans . Roy . Soc. , ' Series A , 197 . t 'Roy . Soc. Proc. , ' vol. 71 , p. 421 , 1903 . Prof. B. B. Moore . An Investigation of the [ June 23 , shown ) which are used to lower the temperature of the air , which enters at H. These exchangers completely surround the apparatus shown in fig. 1 , o\#151 ; and serve to prevent loss of heat energy . This loss , although small , is appreciable , and in order to replace it small quantities of liquid air may be run into the fractionating tower through the pipe N. The efficiency of the whole plant is about 95 per cent. Heavy Constituents of the Atmosphere . 1908 . ] It can be seen at once that the light gases , helium and neon , would escape through E with the nitrogen , whilst the heavy gases , krypton and xenon , would be concentrated with practically no loss whatever , in the oxygen contained in the reservoir M. The majority of the argon accompanies the nitrogen ; a little is retained by the oxygen . Therefore , at the end of any period of operation the oxygen in the reservoir M would contain all of the krypton and xenon , in addition to any other heavier gases which were originally in the air , passed through the apparatus . In this way the krypton and xenon in several tons of air can be concentrated in 10 or 15 litres of liquid oxygen . The first consignment of oxygen received represented the residues from 3 tons of air . It was contained in a 5-litre vacuum flask , and was allowed to evaporate into the air until only about 1 litre of liquid remained . The flask was then connected with a large gas-holder in which the oxygen was collected as it evaporated . It was expected that the 5 litres of gas which remained behind in the Dewar flask would be very rich in the heavy rare gases , as it constituted the last fraction from 3 tons of air . A preliminary test with a small portion of this gas showed that it was explosive , due to the presence of vapour of pentane which was used for lubricating the compressors at the liquid air plant . The presence of this hydrocarbon was unfortunate , as the 5 litres of gas in the vacuum flask did not contain as much rare gas as it would otherwise have done . The same trouble was met with in all the air that was subsequently worked up . The pentane was got rid of by passing the gas over heated copper oxide , first passing it , however , through a capillary tube sealed on to another tube 5 mm. in diameter , completely filled with a roll of fine copper gauze . When the gas reached the heated copper oxide it exploded back , but only as far as the copper gauze . The flow of gas was regulated so that the explosions took place regularly , but not violently . In this manner most of the oxygen present was used up in oxidising the pentane . The gas obtained from this treatment was passed over heated copper and a strongly heated mixture of magnesium and lime , in order to remove the last traces of oxygen and nitrogen . It was then stored over mercury . Meanwhile , another consignment of liquid oxygen had been received from Paris . It represented the residues from 16 tons of air . The oxygen had been allowed to evaporate until it just filled a 5-litre vacuum flask . The process of evaporation was continued at University College until 2 litres only of liquid remained , the gas from this last portion being collected in the same large gas-holder as before . About 2500 litres of gas were thus stored 198 Prof. R. B. Moore . An Investigation of the [ June 23 , over water . The last fraction in the vacuum flask was worked up in exactly the same manner as described above , and the resulting rare gas was added to that already obtained . The gas in the large reservoir consisted principally of oxygen , and in order to obtain the rare gases present this oxygen had first of all to be removed . Using copper to absorb large quantities of oxygen is an extremely slow and laborious process . If a small apparatus is used the copper is very soon oxidised and must be reduced . Each time this change in procedure is made the gas in the apparatus must be pumped out and stored . Large tubes containing a considerable amount of copper are almost equally objectionable . It was therefore determined to make use of melted phosphorus as an absorbing agent instead of copper . The apparatus used is shown in fig. 2 . Fig. 2 . C is a wash-bottle containing concentrated sulphuric acid , which served the double purpose of drying the gas and of indicating its rate of flow , which is regulated by the stop-cock G. D and E are phosphorus pentoxide tubes , and E is a bubbler , preferably containing concentrated sulphuric acid . A is a round-bottomed Jena flask of 1 litre capacity , the delivery tube reaching to almost 2 inches above the surface of the melted phosphorus . It is provided with a pressure gauge H. The whole apparatus must be , of course , perfectly air-tight . Connections are made by good pressure tubing fastened with copper wire . At first the apparatus was disconnected from the Heavy Constituents of the Atmosphere . 1908 . ] receiving reservoir B and completely filled with carbon dioxide . The stopper of H was then quickly removed and half-a-pound of dried phosphorus sticks dropped in . The stopper was then reinserted , wired down , and connection made with the reservoir B , which was filled with dilute sodium hydroxide solution . The temperature of the water bath was then raised to about 55 ' C. , and maintained at that point with only slight variations . The oxygen from the large reservoir was then led slowly through the apparatus . Its advent was at once signalled by a bright glow in the flask , which was maintained as long as the gas passed . After once regulating , the apparatus needed very little attention , practically running-alone . Bor the sake of safety , the work was carried on out of doors , but at no time was there an accident or trouble of any kind . When one charge of phosphorus was used up , the gas in the apparatus was displaced by carbon dioxide , after which another flask with a fresh charge of phosphorus was substituted for the old one . This apparatus was run practically continuously in the day-time for six weeks , during which time 5 pounds of phosphorus were used . If the gas is rich in oxygen , phosphorus pentoxide is the chief product , some red phosphorus being also found . In the case of a gas poor in oxygen , a good deal of trioxide is produced which distills over and tends to stop up the exit tubes . About 100 litres of gas remained unabsorbed by the phosphorus . This gas was passed over soda-lime , metallic copper , magnesium-lime mixture , and copper oxide . This last substance oxidised any hydrogen or carbon monoxide given off by the magnesium and lime . Sixteen combustion tubes containing magnesium and lime were required to remove the nitrogen present . The residues in these tubes were kept for further examination . By this means 6 litres of inactive gas were obtained and stored over water . During the storage of the gas and during the progress of the work itself , nearly 3000 litres of water had been in contact with the gas . Practically all of this water was kept . Although the solubilities of krypton and xenon are not at present known , it is probable that the solubilities of the inactive gases increase with the densities and that the solubility of xenon is something like three times that of argon . That being true , any new gas which might be present of a still higher density would be more soluble than xenon . Although the partial pressure of such a gas in the large gas-holder would be very small , it was deemed advisable to boil at least a portion of the water used in this gas-holder , and all of that used in the smaller ones . This was accomplished by means of an apparatus designed by Lord Kayleigh.* About * 'Phil . Trans./ A , vol. 186 , p. 225 , 1895 . Prof. R. B. Moore . An Investigation of the [ June 23 , 1000 litres of water were boiled in this manner and the evolved gas carefully collected . This gas was passed over copper , magnesium lime mixture , and copper oxide , and the residue added to the stock of inactive gas already obtained . Any further quantities of water with which the gas came into contact during this process were also boiled and the gas worked up in the same manner . Nearly 1 litre of inactive gas was thus obtained from the whole amount of water boiled . The mixture of the rare gases from the two vacuum flasks was fractionated first . This had been stored over mercury and was run into a bulb immersed in liquid air . The gas readily liquefied . It was then allowed to boil back into the mercury reservoir until a solid began to appear in the fractionating bulb . The liquid air in which the bulb was immersed was removed , and as the solid changed to gas the latter was taken through a Topler pump and run into another mercury reservoir ( fraction 13 below ) . The volume thus obtained was 200 c.c. The argon , with traces of krypton and xenon , was added to the main body of gas . The latter , which consisted mostly of argon , was then fractionated . The same apparatus was used . The gas was run over soda lime and phosphorus pentoxide , and liquefied readily under the water pressure which could be exerted on the gasometer . The ease with which the gas liquefied was due to the large percentage of krypton and xenon present . It was then allowed to evaporate back under reduced pressure into a mercury reservoir and when this was full the gas was readily transferred to the water reservoir . This was continued for two hours , at the end of which time 'about 1 c.c. of liquid was left in the fractionating tube . This then began to solidify . The surrounding liquid air was removed , and the gas taken through the pump , where it was collected in three fractions , the last one of 15 c.c. ( fraction 5 below ) showing the xenon spectrum but no krypton lines . The argon ( fraction 2 below ) was refractionated in the same way once more , and a further supply of heavy gas obtained . The argon this time was allowed to evaporate back into a different gas-holder ( fraction 6 ) containing fresh water , so that the water which had stood in contact with the gas in the other gas-holder could be boiled . The gas obtained from this boiled water was fractionated separately and yielded 3 c.c. of xenon and 9 c.c. of krypton . The general plan of fractionation followed is illustrated by the following scheme:\#151 ; * 1908 . ] Heavy Constituents of the Atmosphere . p6 ( argon ) f7 n " i 1 1 1 ; u 8 1 " 91 \#151 ; ik r16- L 4---- L5 # rJ i-1 | fbt L-15- 11\#151 ; I j\#151 ; 21r24 ( argon ) |-2S ( argon ) [ \#151 ; 26 | ( \#151 ; 30 L2Q- , \#151 ; | 22\#151 ; 20-1 1\#151 ; 23\#151 ; j T- L27-\lt ; 1-32 * Krypton and xenon obtained from vacuum flasks . 11 , 14 , 17 , and 20 , which constituted the middle fractions and were mixtures of krypton and xenon , were refractionated together . 30 consisted of krypton containing some argon , 31 was krypton , and 32 xenon . 30 and 31 weer still further fractionated in the following manner :\#151 ; -33------- , [ -39 ( argon ) . 7-1 r 30 | ! \#151 ; 34\#151 ; j p37-35\#151 ; T l\#151 ; 38\#151 ; [ 1-36- |-40 ( krypton ) . The total amount of krypton thus obtained was 293 c.c. Fractions 5 , 12 , 15 , 18 , and 32 were all fairly pure xenon and were mixed together . The total volume was 70 c.e. Since xenon boils at 164 ' abs . , in order to fractionate it a temperature was required at which xenon had a moderate vapour-pressure . This could be obtained by ethylene boiling under reduced pressure , but as the amount of ethylene required to fractionate 70 c.c. of xenon would be considerable , an easier method of fractionation was looked for . When liquid air is added to petroleum ether , the temperature of the latter gradually falls until a point is reached at which , on adding more air , the petroleum ether at the surface freezes to a white solid . If this is stirred down into the liquid below , a temperature of 143 ' abs . may ultimately be reached . By adding more liquid air every few minutes the temperature may be kept constant within two or three degrees . At 143 ' abs . the liquid is thick and " mushy , " and difficult to stir , but at 153 ' abs . it is not nearly so thick and may easily be stirred . The xenon was run from the mercury gas-holder into a small fractionating bulb connected with a Topler pump . All the connections were of glass Prof. P. B. Moore . An Investigation of the [ June 23 , sealed on . The bulb was immersed in petroleum ether and a temperature of 148 ' to 151 ' abs . was maintained during the fractionation . At a higher temperature than 151 ' abs . the xenon comes off too rapidly . The method employed for fractionation was as follows :\#151 ; r41 r46 42 47 Xenon . 1-45 i-50 The five fractions ( 41 to 45 ) first obtained were stored in test-tubes over mercury . 41 was run into the fractionating bulb and about two-thirds of the gas pumped off , constituting 46 . 42 was then run into the bulb , where one-third of 41 still remained . Two-thirds of the whole volume was pumped off to form fraction 47 . 43 , 44 , and 45 were added in the same manner . An examination of the spectrum of 46 showed that it contained traces of nitrogen and krypton . It was therefore fractionated separately at the temperature of liquid air to remove these impurities . The fractionation of the xenon was carried still further at a slightly lower temperature , viz. , between 143 ' and 145 ' abs.:\#151 ; i-51 L-53 -54 r59 57 1-62 r63 64 61 r67 68 L58 No. 58 , which had a volume of about 18 c.c. , was fractionated at the same temperature as before . Three or four cubic centimetres were obtained by the first 10 minutes ' pumping , and constituted fraction 63 ; the rate then decreased considerably , two or three bubbles coming off with each stroke of the pump when there was an interval of half a minute between the strokes . This gas was collected in two fractions\#151 ; 64 and 65 . When the gas was Heavy Constituents of the Atmosphere . 1908 . ] obtained at the rate of only one bubble for each stroke , the ether bath was removed and the last fraction pumped off ( No. 66 ) . The final fractionation , giving fractions 67 and 72 , was carried out under the same conditions . No. 72 , whose volume was about half of 1 c.c. , was sparked with oxygen over caustic potash solution , and the excess of oxygen removed with phosphorus . The photograph of the spark spectrum of this gas was compared on the same plate with that obtained from fraction 59 , which was entirely free from krypton . There was no difference whatever in the spectra . No lines occurred in one spectrum which were absent in the other , and the relative intensities of the lines were about the same in the spectra . In other words , no difference was discernible . The density of fraction 66 was taken in a 7-c.c . bulb , and found to be 63 . A density determination was attempted with fraction 72 , but the volume was too small to allow of an accurate determination being made . These negative results were disappointing , but because no new element could be found in 19 tons of air , it did not prove that a positive result could not be obtained with 100 tons . In addition , the large quantities of water with which the gas was in contact at different times\#151 ; although most of this water was boiled\#151 ; might after all have been a source of considerable loss . Especially would this be the case if the solubility of the possible new gas were anything like that of the radium emanation , whose solubility coefficient at 18 ' is 0'270.* The residues from 100 tons of air were kindly furnished by M. Claude , but in order to eliminate any loss from water , an entirely new plan of procedure was decided upon . Six 5-litre vacuum flasks were filled with the liquid oxygen . Five of these were fitted with rubber corks through which ran glass delivery tubes with a double bend , the other end of each of these tubes dipping below the surface of the liquid oxygen in the sixth vessel , which was kept full during the progress of the experiment . The arrangement is shown in fig. 3 . As the oxygen in the vessels A to E evaporates , the krypton and xenon were condensed to a solid either in the tubes that dropped below the oxygen in F , or in the liquid oxygen itself . The gas left behind in the first five vessels , after evaporation was complete , was of course rich in krypton and xenon . This gas was displaced by a strong solution of caustic soda , and run into wine bottles , which were securely corked , about 10 c.c. of the soda solution being left in each bottle . When the bottle was inverted , this liquid formed an excellent seal . Unfortunately , one of the vacuum flasks was broken , and 5 litres of gas were lost . The glass delivery tubes , which contained a heavy * ' Phys. Zeit . , ' vol. 9 , pp. 6\#151 ; 8 , 1907 . Prof. R. B. Moore . An Investigation of the [ June 23 , white deposit , extending several inches above the surface of the liquid oxygen in F , were cut between F and the other vessels , and the open ends quickly closed by means of rubber tubing and Hofmann screw clamps . They were allowed to remain dipping in the liquid oxygen . This part of the work was kindly carried on at Paris by Mr. W. L. Alton . The bottles of gas , the caustic soda solution , and the vessel full of liquid oxygen and containing the five delivery tubes were sent from Paris to University College . The five delivery tubes containing solid krypton , xenon , carbon dioxide , etc. , were quickly dropped into a flask which was filled with carbon dioxide . This flask was connected with a gas-holder containing caustic soda solution , so that as the solids on the tubes evaporated the soda solution was displaced in the gas-holder . All of the gas in the flask was finally transferred by running into it sodium hydroxide solution . Meanwhile , the vessel F had been fitted with a rubber stopper and a wide delivery tube leading to the bottom of a vacuum tube containing about 300 c.c. of liquid air . This air was constantly replenished as it evaporated . The object was , as before , to concentrate the rare gases in a smaller volume of liquid air or oxygen . The Dewar tube used was an exceptionally good one , and by filling up late at night and early in the morning the liquid air was never allowed to get too low . At the end of a week , when the oxygen in the vessel F had evaporated , the vacuum tube was connected with a coiled glass condenser dipping in liquid oxygen as indicated in fig. 4 . In order to prevent the liquefaction of the oxygen from the vessel G in the tube H , the exit tube was connected with the pump and the pressure inside the apparatus kept a little below normal . Under these conditions , only krypton and xenon with traces of carbon dioxide and pentane were condensed in the tube H , oxygen with traces of nitrogen escaping through the pump , As krypton has a vapour-pressure at the temperature of liquid oxygen of 17'4 mm. , it seemed certain that the procedure adopted would result in the loss of most of the krypton , but as the vapour-pressure of xenon is only 0T7 mm. at the same temperature , it seemed equally certain that a large part of the xenon would be obtained . On the other hand , if the boiling points of the argon series be plotted against their atomic weights , it can be readily shown from the curve obtained that the boiling point of a member of the series with an atomic weight of about 175 would be approximately 183 ' abs . , 20 ' higher than the boiling point of xenon . How Kamsay has shown* that whereas xenon has a vapour-pressure of 0T7 at 90o,6 abs . , at 68 ' abs . a difference of 220,6 , its vapour-pressure is only 00005 mm. Therefore , a new element , the boiling point of which differed from that of xenon * 'Roy . Soc. Proc. , ' vol. 71 , p. 421 , 1903 . 1908 . ] Heavy Constituents of the Atmosphere . to about the same extent , would have at the same temperature of liquid oxygen , a vapour-pressure so small that practically all of the gas would be obtained by the method of fractionation used . As the object was not to prepare krypton , but to look for new elements in the atmosphere , the work was continued along the same lines . The solidified gases in the condenser H were allowed to evaporate into the reservoir in which was stored the gas obtained from the five delivery tubes , the last traces of gas being swept out with carbon dioxide . The combined gases in the reservoir were then worked up in the usual manner by passing them over soda-lime , metallic copper , magnesium-lime mixture , and copper oxide . The resulting gas was stored over mercury . On running it into a bulb immersed in liquid air , it solidified at once , but was not fractionated separately , being transferred back to the mercury reservoir through the pump . Its volume was about 50 c.c. The gas remaining in the large flask F ( fig. 3 ) , and in the small tube G-(fig . 4 ) , together with that in the wine bottles which contained the gas Fig. 3 . transferred from four of the other flasks shown in fig. 3 , was purified in the usual manner with magnesium-lime mixture , etc. The inactive gas was mixed with the 50 c.c. already obtained and stored over mercury . The total volume of water and caustic soda solution which had been in contact with the gas at any period was not more than 20 litres . All of this was carefully kept and thoroughly boiled , the evolved gases being worked up in VOL. lxxxi.\#151 ; A. p Prof. R B. Moore . An Investigation of [ June 23 , Fig. 4 . the usual manner , and the rare gas obtained added to the main supply . The latter was fractionated in the following manner:\#151 ; l~8 ( argon ) 1-4 L UH L5---1 Lnn -6\#151 ; 10 ( argon 4* krypton ) 14 ( krypton + argon ) 15 ( krypton ) 16 ( krypton + xenon ) L-7 r12 ( xenon + krypton ) L13 ( xenon ) The main body of the gas constituted fractions 13 and 15 , fractions 10 , 14 , 16 , and 12 occupying only a few cubic centimetres each . The volume of the krypton was 50 c.c. , and that of the xenon 220 c.c. The second method of extracting the heavy rare gases is therefore nearly as economical , as far as xenon is concerned , as the first , but from five times the amount of air only one-sixth the volume of krypton was obtained . The second method , however , involves very much less labour , and was the better of the two considering the object of the work . Ramsay has shown* that the proportion of krypton in the air , by volume , is 1 part in 20 millions , and that of xenon 1 part in * 'Roy . Soc. Proc. , ' vol. 71 , p. 422 , 1903 ; 'Roy . Soc. Proc. , ' vol. 80 , p. 599 , 1908 . Heavy Constituents of the Atmosphere . 1908 . ] 170 millions . According to these figures , 100 tons of air ought to yield 4 litres of krypton and 470 c.c. of xenon . The difference between these volumes and those obtained is very marked in the case of krypton . This is not surprising , considering what the vapour-pressure of krypton is at the temperature of liquid air . By the first method of separation 70 c.c. of xenon was obtained from 19 tons of air , by the second method 220 c.c. from 100 tons , but in the latter case the gas in one of the vacuum flasks was lost . Consequently , the difference in the volume of xenon per ton of air obtained by the two methods is not large . There is , however , loss in both cases , and as the amount of this loss is unknown , the data are insufficient to base a calculation on . The xenon , after being sparked with oxygen , was fractionated in the same manner as before , the temperature of the petroleum ether being maintained between 149 ' and 151 ' abs . The final ^ c.c. of gas which could be pumped off whilst the fractionating bulb was still at the above temperature was collected separately . On removing the vacuum tube and allowing the temperature of the bulb to rise , another small fraction of ^ c.c. was obtained . At the time it was thought that this behaviour was indicative of the presence of a new gas , but in reality it was probably due to the fact that the amount of gas was so small that the evaporation was insufficient to give as much as one bubble for each stroke of the pump . The bulb , therefore , appeared to have been pumped " dry , " although a small trace of gas remained . Both the ordinary and spark spectra of these two last fractions were photographed and compared on the same plate with the spectra given by the first fraction at the opposite end of the series . The lines obtained from the three samples of gas were identical . They were compared by using the negative as a lantern slide and throwing the images of the spectra on a screen . In this way the lines could very readily be compared . The results obtained indicate that if a stable element heavier than xenon does exist in the atmosphere , the volume present compared to that of xenon is extremely small . As at least 10 per cent , of a new gas could probably have been detected in the spectra examined , therefore , 0-03 c.c. of such a gas could have been detected . As this existed in 100 tons of air , it represents 1 part in 2,560,000,000 by volume . All of the magnesium and lime used to extract nitrogen had been kept in stoppered bottles . Bamsay and Travers tested the magnesium and lime used by them in the preparation of argon , but no tests had been made with such a mixture over which a gas containing a considerable proportion of krypton and xenon had been passed . It was thought possible that although argon and the lower members of the series did not react , those of higher p 2 Prof. R. B. Moore . An Investigation of the [ June 23 , atomic weight might do so . The magnesium and lime over which the gas containing most krypton and xenon had been passed was therefore treated in the following manner :\#151 ; It was placed in the round-bottomed Jena flask A ( fig. 5 ) which was connected with a large U-tube containing pure dilute hydrochloric acid . E is a phosphorus pentoxide tube , one end of which was connected with a Topler Fig. 5 . pump . The whole apparatus , after being made perfectly air-tight , was exhausted . Connection could be made between the two sides of the U -tube by opening the tap D. When exhausted , the tap D was closed , and water allowed to run in slowly through B. The evolved gas was passed through the acid in C by which the ammonia was retained and the unabsorbed gas was collected at the pump , sparked with oxygen over sodium hydroxide solution and the excess of oxygen removed by means of phosphorus . The two or three bubbles of gas left consisted of nitrogen derived from traces of air in the apparatus ( fig. 5 ) , and which had not been removed owing to insufficient sparking . There was no rare gas present . Another sample of the same gas was analysed , with the following result:\#151 ; Per cent. Carbon dioxide ... ... ... ... . 12T1 Carbon monoxide ... ... ... ... 2-20 Silicon hydride ... ... ... . . 86-34 100-65 1908 . ] Heavy Constituents of the Atmosphere . 209 The solution in C was evaporated to dryness in a platinum basin , and the equivalent of the ammonium radical in the residue found by estimating the chlorine present . My thanks are due to Dr. Gwyer for making this analysis , and for assistance in the work on the magnesium and lime residues . The figures obtained in the analysis were:\#151 ; Percentage of chlorine . , -------------A____________ Weight taken . Chlorine found . Found . In ammonium chloride . R2629 grm. 0T735 grm. 65'99 66'23 The results show plainly that there was nothing but ammonium chloride present . As Sir William Ramsay has pointed out in his Introductory Note , the negative results obtained in this work do not necessarily indicate that a final end has been reached , they simply indicate the improbability of the existence of a stable elementary gas in the atmosphere with a higher atomic weight than xenon . My cordial thanks are due to Sir William Ramsay for his suggestions and unfailing interest in the work , in a considerable portion of which he took an active experimental part .

rspa_1908_0071

0950-1207

The spectrum of radium emanation.

210

213

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

Alexander Thomas Cameron, M. A., B. Sc.,| Sir William Ramsay, K. C. B., F. R. S.

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10.1098/rspa.1908.0071

Atomic Physics

Thermodynamics

Atomic Physics

210 The Spectrum of Radium Emanation . By Alexander Thomas Cameron , M.A. , B.Sc. , and Sir William Ramsay , K.C.B. , F.R.S. ( Received July 2 , 1908 . ) In May , 1904 , one of the authors , in conjunction with Professor Collie measured the visual spectrum of the emanation accumulated in 14 days from 109 milligrammes of radium bromide , by means of a direct vision spectroscope . A subsequent measurement was made with 11 days ' accumulation . It was then stated* :\#151 ; " The spectrum was very brilliant , consisting of very bright lines , the spaces between them being perfectly dark ; it had a striking resemblance in general character to the spectra of the gases of the argon group . " This spectrum became rapidly faint , and had largely disappeared in less than a minute ; it was replaced by the spectrum of secondary hydrogen . We have now repeated this experiment several times with the emanation accumulated during 12 days from 477 milligrammes of radium bromide , with partial success ; and recently with perfect success , no other spectrum being visible at first but that of the emanation . It was intensely brilliant , and consisted of a number of green , blue , and violet lines , besides a very slightly refrangible live in the red . The spectrum was photographed ; but during the exposure , which lasted 4 to 5 minutes , it faded , and was replaced by that of hydrogen . The tube was photographed three times altogether ; the second and third exposures lasted about eight minutes ; the hydrogen lines , as a rule , were equally strong in the second and third photographs , and almost entirely absent from the first . On reducing the pressure , a number of lines appeared in the second photograph , which seem to be additional lines of the emanation . The action of the discharge is to drive the emanation into the negative electrode , where it is largely absorbed ; for the glowing , due to secondary products , was much more brilliant there than through the rest of the tube . The greater part of the lines previously observed have been confirmed ; and a number have been added to the list . The degree of exactitude is of course , very much greater than before ; in most cases the limit of error is O not greater than one or two Angstrom units ; the lines of secondary hydrogen already mapped , and apparently not with great accuracy , were taken as fiducial . * ' Proceedings , ' vol. 73 , p. 472 . The Spectrum of Radium Emanation . 211 The secondary spectrum of hydrogen is being re-mapped by Mr. Herbert Watson , and the lines will be corrected as soon as his measurements are complete.* The following table shows the results of two experiments ; in Column 1 are the wave-lengths of the lines ; in Column 2 their intensities when photographed during the first experiment ; in Columns 3 , 4 , and 5 , their intensities if observed on the first , second , and third photographs of the W ave-length . Intensity . Previous reading . Remarks . Experiment 1 . Experiment 2 . ( Ramsay and Collie . ) f\#151 ; 6350 faint 6307 \#151 ; \#151 ; 1 i 6307 evanescent Probably H. 6070* 0-5 \#151 ; 8 i 5995 \#151 ; \#151 ; 1 \#151 ; 5975 faint Doubtful 5955 " Probably H. 5887 \#151 ; \#151 ; 3 i 5890 " Uncertain 5805 persistent 5725 fairly strong 5686 faint 5595 strong 5584 1 \#151 ; 5580 faint , persistent 5430 faint 5393 " 5077* \#151 ; 3 1 \#151 ; 4977* \#151 ; 3 0-5 \#151 ; 4985 strong , persistent 4966 bright , transitory 4932* 0 5 \#151 ; 3 0*5 4926* \#151 ; \#151 ; 3 \#151 ; 4817* \#151 ; 2 \#151 ; \#151 ; 4723* 2 0*5 4 0*5 4704 \#151 ; 1 1 \#151 ; \#151 ; Doubtful 4680* 0*5 6 1 \#151 ; 4690 transitory 4669* \#151 ; 2 1 \#151 ; 4654* \#151 ; 2 1 \#151 ; 4644* 0*2 8 2 1 4650 transitory 4632* 3 0*5 10 1 4640 " 1 4624* 0*5 8 3 1 4630 4608* \#151 ; 2 7 1 1 4603* 2 3 4578* 1 2 9 3 4547 \#151 ; 1 \#151 ; \#151 ; Doubtful 4509* 1 2 4 1 4505 \#151 ; 1 \#151 ; \#151 ; 4440 \#151 ; 1 4435* 1 1 3 1 4310* 2 3 5 4208* 0*5 9 4 3 4170* \#151 ; 10 4 2 4114* \#151 ; 2 4057 5 3 15 20 4014* \#151 ; 3 0*5 3977* \#151 ; 6 2 3967* \#151 ; 5 3950* \#151 ; 2 \#151 ; \#151 ; * The corrected values are given in the addendum , , all except five lines , for which the corrected values are 6068 , 5887'5 , 4702 , 4634-5 , 4058-5 . Mr. A. T. Cameron and Sir W. Karnsay . [ July 2 , second experiment . Column 6 gives the wave-lengths and intensities of the lines observed visually by Collie and Ramsay . The photograph taken during the first experiment showed chiefly secondary hydrogen and some nitrogen ; it is somewhat remarkable that so many lines belonging to the emanation were photographed . The asterisked lines are undoubtedly those of the emanation . The greater number of these lines grow weaker with the duration of the discharge , and in some cases fade out , so that they are absent from the third column of Experiment 2 . But in some cases , and conspicuously in line 4058-5 , the intensity has increased astonishingly . This line is near a mercury line of wave-length 4047 , the intensities of which vary from 3 in the first plate to 6 in the second , and to 2 in the third ; it is given in spectrum tables as of intensity 10 . It looks probable , therefore , that the line 4058-5 is due to some product of the decay of the emanation , the quantity of which increases with length of passage of the discharge . Through the kindness of Sir William Huggins , we have been furnished with a list of the more important lines of the nebulae . No one of them appears to be due to radium emanation . Addendum.\#151 ; Received . August 5 , 1908 . In the experiments just described ordinary panchromatic plates were used . In two later experiments " spectrum " plates were employed . In the first of these the spectrum only lasted a minute and a-half . The lines in the photograph were all very weak . They included most of the emanation lines previously photographed , together with the slightly refrangible line in the red , already referred to ; the wave-length of this line is 7050 . In all these experiments the spectrum tubes were fitted with aluminium electrodes , and the rapid absorption of the emanation was undoubtedly connected with this . In a final experiment , on the recommendation of M. de Bort , we used copper electrodes . The result was entirely satisfactory . They apparently contain no hydrogen , and absorb emanation much more slowly . The tube became vacuous only after 7 to 8 minutes and a very good photograph was taken . It contained a large number of new lines belonging to the emanation spectrum , besides a number of mercury lines . The hydrogen lines were few , and their intensity were unaltered throughout . The unitalicised figures in the following table refer to lines measured in this last experiment with the corresponding intensities . Italicised figures refer to lines absent in this case , but measured previously . 1908 . ] The Spectrum of Radium Emanation . Wave- length . Intensity . Remarks . Wave- length . Intensity . Remarks . 7050 2 4592 i Doubtful 6150 2 4585 4 Observed before , weak 6101 2 4578 -5 3 Very strong previously 6055 2 4545 -5 2 5980 -5 2 4541 1 5679-5 2 4532 -5 2 5586 2 4524 4 Possibly H. 5446 1 4509 4 5419 4 4505 2 Doubtful 5370 2 4501 3 5335 3 4481 4 5289 6 4463 -5 8 1 5083 2 4449 4 ' 4979 2 4441 -5 \lt ; 1 1 4936 2 Possibly H. 4436 -5 \lt ; 1 4920 3 Observed before \lt ; 1 4416 -5 4 4883 2 " v \lt ; 1L 4391 3 4873 2 4 4349 6 Observed before 4843 -5 10 " " \lt ; 1 4331 4 4816 2 4307 2 4806 -5 1 4246 4 4768 2 " " weak 4239 3 Observed before \lt ; 1 4731 -5 2 JJ J ? 4204 5 4722 4 4189 3 4695 -5 2 \gt ; ) JJ J ) 4167 6 4681 5 4114 3 4672 7 4018 . 4 4652 -5 3 3982 8 4645 -5 6 3973 6 4626 -5 10 3958 3 i 4616 2 3879 . 10 i 4610 2 3866 -5 6 i 4605 1 10 3856 . 4 Since this paper was communicated to the Society Professor Rutherford and Mr. Royds have published a preliminary account of their work on the same subject.* Their figures show a very close agreement with those given above . Our thanks are due to Mr. Herbert Watson for some assistance in measuring the wave-lengths of the lines , and for placing at our disposal his results of measurement of the secondary spectrum of hydrogen . * 'Nature,3 July 9 , 1908 , p. 220 .

rspa_1908_0072

0950-1207

Further note on a luminous glow generated by electrostatic induction in an exhausted vessel made of silica.

214

216

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

Frederick John Jervis-Smith, M. A. (Oxon), F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1908.0072

en

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10.1098/rspa.1908.0072

Thermodynamics

Electricity

Thermodynamics

214 Further Note on a Luminous Glow generated by Electrostatic Induction in an Exhausted Vessel made of Silica . By Frederick John Jeryis-Smith , M.A. ( Oxon ) , F.R.S. ( Received June 15 , \#151 ; Read June 25 , 1908 . ) 1 . A glow-bulb rotating within a shallow cylindrical inductor made with a dome-shaped end ( devised by my son , E. J. Jervis-Smith , R.F.A. ) , placed symmetrically , with respect to the axis of rotation of the glow-bulb , exhibited the glow and magnetic phenomena described in the former paper and exhibited at the Royal Society on May 13 , 1908 . Sir Oliver Lodge has kindly repeated some of my experiments with glass bulbs , as set forth in the former paper , and also surrounded by a ring-shaped inductor , and has produced the same effects . 2 . Two bulbs , similar in shape and size to those described in the paper referred to , were made by the Silica Syndicate , London , of pure fused silica . Up to this time ( May 30 , 1908 ) , as far as I can discover , no highly exhausted tubes of pure silica have been made ; but now means have been found whereby such apparatus may be manufactured . The only difficulty which remained was to seal off ' an exhausted silica tube in such a manner as not to alter the condition of the vacuum by the introduction of hydrogen gas , since at a high temperature hydrogen passes through fused silica . By employing a means of sealing not involving the burning of hydrogen , this trouble may be avoided , if great accuracy is aimed at . 3 . The residual gas in the new silica glow-bulbs , after exhaustion to a Rontgen vacuum , was air . A glow-bulb was supported by its stem at the distance of 0-5 cm . from a disc-shaped terminal of an induction coil . Opposite to the bulb and disc , a pointed terminal ( negative ) was placed at such a distance that sparks did not pass when the point and disc were 10 cm . apart , but only a brush discharge , which played freely over the bulb . When the coil was in action , the bulb was illuminated with a brilliant emerald green glow . When the discharge was stopped , the bulb continued to glow , the glow slowly dying out in about fifteen minutes . This remarkable after-glow could be easily seen by a person at a distance of 3 or 4 metres from the bulb for the first eight or ten minutes after the excitation of the bulb . In one experiment a bulb showing the after-glow was carried about 80 metres , through a garden , at night ; it still retained its glow as it did when not moved in the laboratory . 4 . No glass glow-bulbs , treated in exactly the same manner , exhibit this after-glow phenomenon in the slightest degree . On a Luminous Gloiu generated by Induction . 215 5 . The silica glow-bulb , when under the influence of the above-mentioned discharge , showed green streaks of glow brighter than that of the whole bulb , slowly moving within the bulb . 6 . A silica glow-bulb was mounted in the rotating apparatus described in S ( 2 ) of the paper of January 30 , 1908 . The inductor . wras charged from about 1800 to 2000 volts . The silica glow-bulb gave out a glow quite unlike that of the glass bulbs described in the former paper . In the experiments with the glass bulbs the glow was not at all strong when the inductor was charged to about 1800 volts ; also , the magnetic phenomena could only be seen by some persons at a distance of 0'25 to 0'5 metre from the apparatus ; but when a silica bulb , similar in size and exhaustion to the glass bulbs , was rotated , it could be seen without difficulty in the dark at a distance of 5 metres , and when the inductor was charged up to 3000 to 4000 volts it was clearly visible at 15 metres from the glow-bulb . 7 . The magnetic phenomena appear to be the same as those which exist when a glow-bulb is employed made of glass . 8 . A silica glow-bulb was rotated ( as in the previous experiments , by means of a hollow mandrel ) with a portion of the bulb in contact with dry mercury , supported under the rotating bulb in a circular wooden dish . On rotating the bulb it was almost instantly filled with a bright greenish glow . The bulb was rotated about thirty times per minute ; on increasing the surface velocity of the bulb , so that the mercury was thrown out of the dish , the glow produced was but very slightly increased . 9 . A flexible brush of fine copper wire , supported on an insulator , was held in light contact with the bulb , about 1*5 cm . above the surface of the mercury . The brush was connected to a graduated electroscope . When the bulb was rotated , the electroscope was rapidly charged up to 1500 volts ; also a Leyden jar was easily charged from the copper brush and insulated conductor . 10 . This method of generating electricity placed in one 's hands an excellent method of gradually charging a body to any desired degree , from zero up to the highest potential attainable by the arrangement . Owing to the highly insulating nature of silica , practically no leakage back to the bulb through the brush takes place . The sign of the electricity so produced is negative . The brush should in all cases lightly touch the rotating bulb . 11 . Solid fused silica was employed , and electricity was generated as in ( 10 ) , but only the slightest trace of light was visible . 12 . A jet of mercury , falling through 4 cm . , was made to play upon the surface of a silica glow-bulb , when it instantly became luminous . On connecting the point of impact of the drops of mercury with the electroscope , Dr. E. C. Edgar . [ June 25 , it was at once charged , as in Experiment 9 . The same was the case when solid silica was employed , but hardly any luminosity appeared . 13 . All these experiments were repeated with glass glow-bulbs , but the effects were minute in comparison with those produced when silica was used , and it was found that considerable leakage back of a charge took place when glass was used . 14 . An electrical machine is now being constructed by me , in which silica and mercury will be used on a far larger scale than in the experiments described in this paper . I wish to thank Mr. H. G. Lacell , of the Silica Syndicate , for the great care with which the glow-bulbs have been prepared under his supervision . On the Atomic Weight of Chlorine . By Edward C. Edgar , D.Sc . , Assistant Lecturer in Chemistry in the University of Manchester . ( Communicated by Professor H. B. Dixon , F.R.S. Received and Read June 25 , 1908 . ) ( Abstract . ) Six years ago Professor Dixon and I began a research with the object of determining directly the weight of chlorine which combines with the unit weight of hydrogen . Our method was to burn a jet of hydrogen in an atmosphere of chlorine ; hydrogen being stored and weighed in palladium , the chlorine being condensed and weighed as liquid . The number we obtained for the combining weight of chlorine was appreciably higher than that found indirectly by Stas , and still higher than that approved by the International Committee on Atomic Weights . While this research was in progress , other determinations had been made bearing on the relative weights of silver , chlorine , and nitrogen , so that some modification in the accepted values of one or more of these elements appeared inevitable . The direct " joining up " of the two ends of the chain connecting hydrogen with chlorine thus became a matter of immediate importance . Since the method of burning one gas in an atmosphere of the other had been proved to be accurate within fairly narrow limits , I was encouraged to continue the investigation , and to modify the apparatus , with a view to

rspa_1908_0073

0950-1207

On the atomic weight of chlorine.

216

218

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

Edward C. Edgar, D. Sc.| Professor H. B. Dixon, F. R. S.

abstract

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10.1098/rspa.1908.0073

Thermodynamics

Chemistry 2

Thermodynamics

Dr. E. C. Edgar . [ June 25 , it was at once charged , as in Experiment 9 . The same was the case when solid silica was employed , but hardly any luminosity appeared . 13 . All these experiments were repeated with glass glow-bulbs , but the effects were minute in comparison with those produced when silica was used , and it was found that considerable leakage back of a charge took place when glass was used . 14 . An electrical machine is now being constructed by me , in which silica and mercury will be used on a far larger scale than in the experiments described in this paper . I wish to thank Mr. H. G. Lacell , of the Silica Syndicate , for the great care with which the glow-bulbs have been prepared under his supervision . On the Atomic Weight of Chlorine . By Edward C. Edgar , D.Sc . , Assistant Lecturer in Chemistry in the University of Manchester . ( Communicated by Professor H. B. Dixon , F.R.S. Received and Read June 25 , 1908 . ) ( Abstract . ) Six years ago Professor Dixon and I began a research with the object of determining directly the weight of chlorine which combines with the unit weight of hydrogen . Our method was to burn a jet of hydrogen in an atmosphere of chlorine ; hydrogen being stored and weighed in palladium , the chlorine being condensed and weighed as liquid . The number we obtained for the combining weight of chlorine was appreciably higher than that found indirectly by Stas , and still higher than that approved by the International Committee on Atomic Weights . While this research was in progress , other determinations had been made bearing on the relative weights of silver , chlorine , and nitrogen , so that some modification in the accepted values of one or more of these elements appeared inevitable . The direct " joining up " of the two ends of the chain connecting hydrogen with chlorine thus became a matter of immediate importance . Since the method of burning one gas in an atmosphere of the other had been proved to be accurate within fairly narrow limits , I was encouraged to continue the investigation , and to modify the apparatus , with a view to 1908 . ] On the Atomic Weight of Chlorine . 217 -eliminate some of the possible sources of error in the former series of experiments . The most important source of error lies in the weighing of the hydrogen . To diminish this error the weight of hydrogen employed was doubled ; and since Professor Dixon and I found , when water was used to condense the hydrogen chloride formed in the flame , that some of the water vapour was decomposed by the free chlorine , I avoided#this by burning a jet of chlorine in dry hydrogen , condensing the hydrogen chloride as it was formed in a tube dipped into liquid air . In some of the experiments the hydrogen chloride formed has been weighed . My experiments ( concluded in 1907 ) agree closely with the results previously obtained in 1905 . The method \#166 ; employed was briefly as follows:\#151 ; Hydrogen , made by the electrolysis of barium hydrate solution , and dried by potash and phosphorous pentoxide , was occluded , and weighed in palladium contained in a boro-silicate glass bulb . The chlorine , prepared by electrolysing fused silver chloride in a Jena glass vessel , was weighed as a liquid in a thick-walled boro-silicate glass bulb . Two ground joints attached these bulbs to a quartz combustion vessel , which was also connected with a vertical quartz tube , and with a steel bomb and-a pump . After a thorough evacuation of the whole apparatus , the vertical limb of the combustion vessel was immersed in liquid air . Then the vacuous vessel was filled with hydrogen from the heated palladium bulb . Chlorine was ignited by a spark at the tip of a quartz jet , and continued to burn in the atmosphere of hydrogen with a fine needle-shaped flame . The endeavour was made so to regulate the gases as to maintain the flame until nearly all the chlorine weighed had been burnt . Then the supply of hydrogen was cut off . As the atmosphere became more attenuated the flame died away until , just before it went out , the chlorine was turned off . The hydrogen chloride , immediately after it was formed in the flame , was condensed as a snow-white solid by the liquid air surrounding the vertical limb of the combustion vessel ; and a little chlorine , which had escaped burning , was also solidified . At the end of the combustion , the residual gas was extracted by the pump and analysed ; it proved to be practically pure hydrogen . Then the snow-white hydrogen chloride was allowed to evaporate . By passing the gas through a quartz tube filled with mercury vapour , the chlorine it contained was completely removed and the purified hydrogen chloride passed on to a steel bomb immersed in liquid air , where it was condensed in six experiments and successfully weighed in three ; in the other three the bomb leaked . In two other experiments the gas was absorbed by water and weighed as aqueous acid . The weights of hydrogen and chlorine burnt were On the Atomic Weight of Chlorine . obtained by subtracting from the total weight of each used the weight of hydrogen extracted by the pump and the weight of chlorine caught by mercury vapour respectively . The balance was specially made for this work by Oertling ; even under the load of the steel bomb , weighing over 1000 grammes , it gave very reliable readings . Each piece of apparatus weighed was tared with another of the same material and of very nearly equal volume and weight , and the small weights used in the weighings were reduced to a vacuum standard . Below are set out the corrected weights of hydrogen and chlorine burnt in eight experiments , and the weights of hydrogen chloride caught in five :\#151 ; ! 1 i Hydrogen burnt , in grammes . Chlorine burnt , in grammes . Hydrogen chloride caught , in grammes . Chloride burnt Hydrogen chloride caught \#151 ; Hydrogen burnt Hydrogen burnt Hydrogen burnt 1 2 -1452 75 -5026 77 -6469 35 196 35 -196 2 2 -0387 71 -7504 73 -7880 35 -194 35 -194 3 1 -7762 62 -5004 \#151 ; 35 -188 4 1 -9935 70 -1638 72 -1565 35 -196 35 -196 5 1 -6469 57 -9671 \#151 ; 35 -198 6 2 -1016 73 -9662 \#151 ; 35 -195 7 1 -7254 60 -7162 62 -4401 35 -190 35 -189 8 2 -0885 73 -4991 75 -5859 35 -192 35 -191 Mean 35 -194 \#177 ; 0-0008 35-193 \#177 ; 0-0009 If the atomic weight of hydrogen be taken as T00762 , the mean values for the atomic weight of chlorine , calculated from the numbers in the table above , are 35'462 + 0-0008 and 35-461 + 0-0009 . Dixon and Edgar , burning hydrogen in chlorine , found the equivalent of chlorine to be 35-463 + 0-0019 from their nine experiments . The concordance of the two sets of experiments is thus exceedingly close , and the number 35'462 may be taken as representing the result of the whole work . On the other hand Noyes and Weber , * by passing a known weight of hydrogen over weighed potassium chlorplatinate , noting the loss in weight of the salt , and condensing and weighing in water the hydrogen chloride formed , have recently obtained for the atomic weight of chlorine the mean number 35-452 + 0-0008 ( H = T00762 ) . In view of the promised recalculation of the atomic weights by the International Committee this year , I have not attempted to correlate my results with the recent determinations of silver , nitrogen , and chlorine . * ' Journal of the American Chemical Society , ' vol. 30 , p. 13 , 1908 .

rspa_1908_0074

0950-1207

The supersaturation and nuclear condensation of certain organic vapours.

219

220

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

T. H. Laby, B. A.|Prof. J. J. Thomson, F. R. S.

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6.0.4

http://dx.doi.org/10.1098/rspa.1908.0074

en

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10.1098/rspa.1908.0074

Thermodynamics

Chemistry 2

Thermodynamics

219 The Supersaturation and Nuclear Condensation of Certain Organic Vapours . By T. H. Laby , B.A. , Emmanuel College , Cambridge , Exhibition of 1851 Science Research Scholar of the University of Sydney , Joule Student of the Royal Society . ( Communicated by Prof. J. J. Thomson , F.R.S. Received April 10 , \#151 ; Read April 30 , 1908 . ) ( Abstract . ) The condensation of drops , which takes place when dust-free air saturated with an organic vapour is cooled by an adiabatic expansion , is the subject of this investigation . The experiments were made with the air and vapour ( 1 ) in their natural state , ( 2 ) ionised by Rontgen rays . The apparatus used was in principle the same as that of Mr. C. T. R. Wilson in his experiments with water vapour . The essential part of it is an expansion chamber in communication with a glass cylinder , in which a gas-tight piston slides freely . When a trigger is pulled the piston descends , and a very rapid ( adiabatic ) expansion of the air and vapour is obtained . The expansion was determined from the initial and final readings of a pressure gauge . The illumination of the expansion chamber was such as enabled any drops formed by the expansion to be readily seen . The liquids used in the experiments were carefully purified . When the air and vapour are expanded adiabatically their temperature falls , and the pressure of the vapour at this lower temperature is greater than that which it has over a plane surface of the liquid at the same temperature . This supersaturation , however , may not cause the condensation of drops in dust-free air . Expansions of increasing magnitude were made until condensation took place , and then the least expansion required to produce condensation for the conditions of the experiment was determined . In another series of experiments the expansion chamber was so made that in one part of it the positive ions produced by Rontgen rays were in excess , and in the other adjacent part the negative were in excess ; the expansion was identical in both and the result of it could be observed in the two parts simultaneously . In this way the relative efficiencies of the ions as condensation nuclei could be examined . The results of the investigation may be summarised as follows:\#151 ; ( 1 ) The least expansion , which causes condensation in air initially saturated with an organic vapour and ionised by Rontgen rays , has been 220 Super saturation , etc. , of certain Organic Vapours . -determined for five esters , six acids ( formic to iso-valeric ) , and iso-amyl alcohol . ( 2 ) In the case of acetic acid the expansion required was greater for feeble Eontgen rays than for more intense ones . ( 3 ) The supersaturation , S , existing at the end of each of the expansions mentioned in ( 1 ) has been calculated , and also for four alcohols and chloroform from Przibram 's experiments . ( 4 ) The acids are found to have the largest values of S and the alcohols the least . The isomers examined have the same value for S with one exception . In the case of the alcohols , ethyl to iso-amyl , a fairly regular decrease in S accompanies the addition of a CH2 group . ( 5 ) The existing theory of condensation on ionic nuclei has been given , values of S have been calculated from it , and compared with S deduced from the observed expansions . The agreement in the case of acetic , propionic , ^-butyric , and iso-butyric acids , and methyl alcohol is very close . ( 6 ) The expansion and supersaturation necessary for condensation on the natural nuclei have been determined for the same ( dust-free ) vapours . In the case of formic , acetic , and butyric acids a distinctly greater expansion is required to catch the natural nuclei than that required for the ionic nuclei produced by Rontgen rays . ( 7 ) As the expansion was increased the number of drops usually increased continuously with it so that the fog point was ill defined , except in the case of tertiary amyl alcohol . ( 8 ) Ethyl acetate , methyl butyrate , propyl acetate , acetic acid , and isoamyl alcohol were found to condense for a smaller expansion on the positive nucleus than on the negative . Water is the only known substance for which the negative ionic nucleus is more efficient than the positive . ( 9 ) On bubbling air through methyl , ethyl , and iso-amyl alcohols , ethyl acetate , propyl acetate , methyl butyrate , chloroform , and ethyl iodide they became negatively electrified . This was the sign of the electrification to be expected from Professor Thomson 's double layer theory of the relative -efficiency of ionic nuclei . Acetic acid was not in agreement with the theory for it became positively charged on bubbling .

rspa_1908_0075

0950-1207

The electrical qualities of porcelain, with special reference to dielectric losses.

221

242

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

H. F. Haworth, Ph. D., M. Sc., B. Eng., Assoc. M. I. E. E.|Professor W. E. Aryton, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1908.0075

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0075

10.1098/rspa.1908.0075

Electricity

Tables

Electricity

]\gt ; Qualities of Porcelain , uith special reference to Dietectric Losses . By H. F. HAWORTH , Ph.1 ) . , M.Sc . , B.Eng . , ] ( Communicated by Professor W. E. Ayrton , F.R.S. Reccived May 7 , \mdash ; Read June 4 , 1908 . ) The following research was undertaken to determine some of the electrical properties of porcelain , and their variations with respect to potential , temperature , and time . The electrical properties ated in this paper are as follows:\mdash ; . 1 . The of of a porcelain condenser . 2 . The of a porcelain condenser as a function of the potential . 3 . The lfluence of sudden cyclical of potential on the charge of a porcelain condenser . 4 . constant of porcelain as a function of the temperature , and its value . B. surements . 5 . The apparent conductivity of porcelain as a function of the potential . 6 . The ) conductivity of porcelain as a function of the time of electrification . 7 . The apparent conductivity of ) as a function of the temperature , and value . C. Didectric Loss 8 . Contact lnethod , variable frequency , and constant potelltial . 9 . Thermo-electric method : Constant frequency , potential . 10 . Thermo-electric method : Variable frequency , constant potential . 11 . Historical . 12 . Summary . porcelain was in the of discs , out . in and cm . , from the Fabrik Hermsdorf , . The iscs had a circular tinfoil electrode of . diameter xed 011 them on each side . .\mdash ; Current were taken with a Siemens anonlcter , the usual ilit of which was about tl11pere VOL. LXXXI . Dr. H. F. Hawortb . ay 7 , per deflection at 2 metres . The deflections were read by means of a telescope and scale , and be estinlated to 1/ 10 .\mdash ; For potentials up to 200 volts a battery of 100 accumnlatol'S was used . For potentials ) to volts a battery of 2500 small tors used . These cells were made sections of 50 in two rows of eacb , fixed into a paraffin wax base which rested on a ] plate backed with wood . Contact was made with mercury cups . 1 . The rate of charge of a conl ( enser . Two connccted in parallel used , and they were and dischar means of a affin nlerctly switch . To secure accuracy , and to avoid ) other tfects , the method was adopted:\mdash ; ( 1 ) plates were for then the galvanometer , the swing ( 2 ) They were then for , ( isch , and the noted . The plates were for a time to , reater than , the charge time . About 70 of these double were . of one and seconds . The of these resnlrs then culated , and from their difference the percentage ' of ( the time was incleased one to two The was also then on curve for th plates were then ) ' ! ) ) tlnoe in the same manner , then for three and fonr seconds , foul( six , etc. It was assunled in next , that potential charge curye for porcelain was a line , therefore timecharge curve may be continued , the three secon calculated for the o1iginal voltage . The curve was continued in this nlanler ) . Beyond 90 seconds a increase of the will noted , for may be due to a temperatule effect ; practically the is fully in one minute , if take the first galvanometer as a of the pacity . The results raphically represented in Curve 1 , unlel i in Table I. In the and 30 minute the ried S , it on acconnt of temperature so soul r re readings were , and tions in were reduced to per del o ) , the average result per cent. Electrical Qualities of Porcelain . Table I. so CURVE 1.\mdash ; Charge of a Porcelain Condenser as.'a Function of the Time of Charge . 2 . The charge of a porcelain condenser as a function of the potential . The two plates used in the previous experiment charged for half a minute , discharged for one minute , and the of the galyanometer and the potential were noted . Readings up to 200 volts were taken in steps of 20 volts , and 40 readings were taken at . Temperatures were noted at the beginning , middle , and end of each series , and a estimate of the percentage variation of per rrade was made ; it was about per cent. Up to 200 volts the points lie along a line , and any small variations from it followed the temperature variations . Dr. H. F. Haworth . [ May 7 , The potential charge cve was now constructed , using the high-tension up to volts . The results ) in Curve 2 , and from it will be seen that the is directly proportional to the charging potential . This agrees with J. Curie 's on crystals , he found that the charging current is exactly tional to ) potential when the potential changes are slow . It will be seen latel that this does not hold if the changes are rapid . 400 Izoo CURVE } Condenser . . The effect of sudden of on the of a porcelain was now Three plates cnclosed in a phospl ) oric acid as ( , for one minute in the usual manner . The tcred by ) roximRtely 4 each time b limits [ cievcral } , and the charge plotted ) ) in . The values are reater t ones , a small dielectric loss even very slow lates o field . point is dealt with 1norc fully ' ) \ldquo ; -k J. Curie , ' dc Docto ] at , ' June , 1888 . The El ectrical Quaiities of CURVE Curve for Porcelain Condenser , Potential varied cyclically . 4 . The variation of the dielectric constant with temperature was investigated in following manner:\mdash ; Three porcelain plates were placed in a copper vessel containing a drying agent . This copper vessel was heated by means of an oil bath , the oil of which was first heated to the required temperature by a Bunsen burner . The temperature was then main ( iained constant by means of all electric heater , which consisted of a framework of asbestos insulated iron wire wound on the \mdash ; er copper vessel . The heat ladiation from the apparatus was exactly balanced by the current sent through the resistance framework . The oil was ci1culated by means of a pump and stirrers worked by band . The temperature was measured by a thermometer resting on the porcelain . The porcelain was cred and in the usual mannel , and discharge being each of one minute 's duration , the potential being reversed each time to neutralise polarisation effects . The oinc and was continued until the alvanomeber swings and temperature were constant for at least one hour . The results of the experiment are given in II , and are hically shown in Curve 4 . Dr. H. F. Haworth . [ May 7 , Table II . 4.\mdash ; The Dielectric Constant of Porcelain as a Function of the Temperature . From the results it will be seen that the ) erature has a reat influence on che dielectric constant . At telnpent to C. increase of city is much smalier than at mpcraturcs . the capacity increases 54 per ccllt . , and } and increases 108 per cent. ) , a ninc1 times as great a rate of growth . From to the ctric ) is function of temperature , tion b of the . where dielectric constant at temperature dielectric c temperature . 1908 . ] The Electrical Qualities of Porcelain . From to 10 the equation of the curve is where dielectric constant at temperature and , From Table II , and the above equation , we find that the dielectric constant for this kind of porcelain at C. is B. Apparent By the apparent conductivity is meant the conductivity as expressed by the ratio of current to potential . 5 . The apparent conductivity of porcelain as a function of the potential . A porcelain plate was placed in an glass vessel containing a drying , and a current was sent it as well as through the galyanometer from the -tension battery . At the end of minutes the deflection was noted , and it the conductivity per centimetre cube was calculated . The potential was increased by steps of 110 volts to volts ; the current curves obtained were ncave towards the voltage axis , but they did not remain constant , they varied daily . The decreased greatly with increase of potential . On the with potentials the results obtained were widely different from those obtained with increasing potentials , and on putting the porcelain through a cycle of electrification the curve obtained for current with respect to the potential formed a closed curve as shown in Curve 5 . On putting the porcelain through a number of continuous ] of electrification the same curve was traced out each time , thus that a steady state had been reached . The porcelail ] , on having a otcntial innpressed on it , ates a back E.M.F. which varies for different cycles of electrilication . In other wordb the dielectric becomes polarised . If we consider the dielectric as being made up of electric doublets ( particles matter having electric poles ) , they are normally in a heteroeneous condition , but when an electrostatic field is impressed on the dielectric , the ) rticles tend to orientate with their electrical axes the lines of . The number which would do so would vary directly with the impressed voltage , and their electrostatic potentials would add to resist the flow of rent t dielectric . free poles of the ) ticles in contact with the . electrodes would constitute the charge . Dr. H. F. Haworth . [ May 7 , for , the tential being varied cyclically . On Curve 6 the is plotte } } lespect to the okntial . It ticed t with ] dielectric , the conductivity is fairly constant ) ) ( A to I ) on ( the potential the conductivity ) idly f to the ] ) tion of the ( to C ) , and fact the goes off to a ltegative infinity siml ) lncans that . of ) celain is greater than the implcssed cm on account of ) back , then the conductivity then eases l sl lie ( 1 ) to ) , a fairJy level value at the position of Dtaxinllll , and 011 the h. it a infinity again ( to ]ting a from positive infinity ) . A similar curve would be obfained if we plotted the of ainst ttetonlotive force . Current ( curves were ) lotted for cycles , and volts with sinnilar results . 1908 . ] The Electrical lities of Porcelain . CURVE G.\mdash ; Appaxent Volt ( Curve for Porcelain . The back 's for zero current , points where the curves cut the voltage axes , were as follows:\mdash ; curve and volts , , : It will be noticed that the positive values greater than the negative ones . The of these baclk .M.F. 's bear the following relationship to one another:\mdash ; The back . is not pp.tionate to the voltage applied . It would seem as if the number of doublets iuto line per unit fall of potential was decreasing , or in other words the meability of the dielectric decre ses with increase of cation , or the dielectlic tellds towards electrical tion . The currents voltage , i.e. the points where the cut the current axis , were as :\mdash ; volts curveaIld - volts , : , , 9.0 Dr. H. F. Haworth . [ May 7 , . The negative values are greater than the positive ones . The current due to the polarisation of the dielectric does not increase proportionately to the amplitude of the cycle but varies with the back E.M.F. The currents at volts were : and The apparent conductivity increases with decrease of negative values here are greater than the positive , the sum of these variations that the current curves are depressed htly into the . ative quadrants . 6 . The variation of the apparent uctivlty of porcelain with the time of electrification now rated . Fifteen plates , connected in parallel , were placed in a lass vessel containing a drying agent and a thermometer . The plates were placed in a on porcelain feet were connected in parallel with strips of tinfoil . The glass vesscl was paraffin lvax , and the connecting wires were out tubes filled with raffin 1 . CurIent as supplied by a batter ) of 100 cclls , the constar]t ( 200 ) throu hout the experiment . The rent cctivity plotted inst l time which it will be seen that the conductivity falls very rapidly the first 10 minutes , and then more gradnally for hour . After 18 the was considerably snlaller at tho ) hour , and C5 hours the conductivity an value . This was tbly a peratnre effect . Aftcr 60 hours 3 minutes odes -circuited a current } given in everse oction the ] ) ) urrent measured the cells tlot the , as galvanontetcr uited while this lace . current } minutc for over hours , and it fcll the manner the Gllt 1 ) th F. . fell . results arc1 in ; they the dielectric tinte to ] } ) nt that in so it stolcb ) trds be cycle is , the ) reelaiil d likc the current voltage ) of would altcr with the tinlt1 . the in vise I8 . ] The Electncal Qualities of Porcelain . CURVE 7.\mdash ; A. Conductivity of Porcelain as a Function of the Time of Electrification . B. Short Circuit Current from Porcelain . direction with increased time of the cycle on account of the lower conductivity due to the increase of polarisation with tinle . This point was investigated with the plates and -volt battery . The voltage was raised or lowered by steps of 40 ettC time . The time of the step in the first series was one minute , for the second sclies two minutes , for the third se1ies three minutes , series iive minutes , fifth series seven minutes . The curves flatten out and turn in a ockwise direction the of the cycle increases . The areas of the loops bear the following ratio to one another:\mdash ; : 2 : The maximum currents the ratio:\mdash ; : -( : : The apparent lctivity has with the increased tinle of tlJe cycle , thus viscosity in the 7 . The conductivity of porcelain as a function of th nperature . Fourteen porcelain plates were placed in a pile in the inner ) vessel used in the previous temperature experiment , with drying Dr. . Haworth . [ May 7 , . The heating arrangements were as before , but the oil was maintained at a temperature inclined propeller driven by a small motor . The plates were connected in parallel strips of tinfoil , and the terminals consisted of two mercury cups into rlass tubes which passed ( holes in cover of ) vessel . The mercury excluded air from the vessel , and contact was ] with the pol.celain ping ires into the mercul.y . was tested for by just the wires out of the mercury ( ( notin the . In all cases , however , the leakage was practically top and bottom porcelain plates had no electrodes and served as . The connections were as follows:\mdash ; H. ing battery . . Battery hing . F. reve1 switc . A B and ng By connecting A to current was sent ) ) celain , and by with C conductivity after ) electrification by switcb ]loti The was the1l ) , to get rid of polarisa ; hc ) ttery and , and the . At each nperitttue of the , in 1( when both ( temperature least one hour , the of these } txnd ctivit ) calculated . The heated live or taking the final it to electrical corresponding lesults of the ) eriment i given in II1 and Curve 8 . It seen th of luclivity with ature i , , . 08 . ] The Qualities of Porcelain . Table III and the above equation the specific conductiviCy of celain , calculated at C. , was mhos per centimetre cube . Table III . Specific resistance , Temperature , C. ohms per cm . 2 . 141.0 51.5 50.8 42.3 20 . 35.5 30 . 34 . 37 . 8.24 , , 6.25 , c 8.\mdash ; Apparent Conductivity of Porc Temperature , Specific resistance , ohms per cm.3 40 . 43 . 4.85 47 . 4 . 50 . 2.64 54 . 1.78 66 . 1.44 58 . 1.11 59 . 1.08 62 . 0.77 64 . 0.15 Dr. H. F. Haworth . [ May 7 , . 8 . The foregoing results show that there is a of energy in putting a porcelttin condenser a of ctrification , and it is desirable to find on what ctors this loss depellds and the laws connecting it with variations of voltage , frequetlcy , tcmperature . Another point which ] ( itself is : lJoes the ) acity o the condenser alter under if so , how ? To ' the } ) ence of the dielcctric loss on the frequency ol the cycle of electrification , the ) eriments were made : A porcelain plate was placed in a sealed lass V , with sulphuric acid as and was connected across secondary of a giving about 2000 volts . The current and voltage waves were then plotted with the Joubert contact method . The of the curre1lt wave then calculated for erent values of the time , and so the quantity electricity on the condenser was obtained for that time , The at this time WttS knowlI curve , and plotted ainst V. The resultant curve enclosed an arca similar to Curye 3 The area of this curve represents the required to put the condense1 a cycle of electrihcaCion at that frequency and voltage . A nunlber of these curves were ucted at various frequencies , and the results are given in results secm to show that the loss cycle is a constant quantity . Results , and 9 vory consideral ) from the average . to erl.ors of measurement , also the process of obtaining final loss rather a complicated one , and e1rors . . could easily creep in . Table I Cycles per cond . ] ) Temp , , whole plate ) . 130 2(i80 1SO 8 1$ II . 1908 . ] The Qnalities of To hese points further , the foJlowing method was adopted , which could be worked more rapidly , and by one person alone , whereas the previous method equired two observers . The porcelain was placed in a large lass case containing some strong huric acid . Pressure was supplied with a Ferranti transforrner , transfrom 150 to 40,000 volts . In series with the porcelain condenser was placed a condenser of large capacity with that of the porcelain , and a non-inductive resistance of 40,000 ohms . The current the porcelain was measured by the voltage across the resistance , and the voltage across the was measured by the same Grument ( an Ayrton ) erry Quarter Cylinder Electrometer ) placed across part of a non-inductive resistance , hich itself was placed across the primary of the transformer ( see diagram of connections ) . Connection to the bottom electrode of the porcelain was made through the brass case of the thermopile . The current passing had no effect on the thermopile . It was intended to measure the capacity of the porcelain by the pressnre across the condenser placed in series with it , according to the law , where small the capacity could be assumed to remain constant , but on connecting the condenser to the electrometer a snlall deflection was first obtained which rapidly grew larger until it was beyond the range of the electl'ometer . It was found that this deflection was due to polarisation , for , when a battery was placed in series with the ele , ctrometer , the deHection always increased when the pole of the battery was con nected with the earthed side of the condenser , thus thnt the current was through , or over , the porcelain from low to high tension side . It was that perhaps the ) rush discharge was effect , so an earthed guard was put round the bottom electrode , but the result was the same . This condenser was then dispensed with , and capacity calculations were made from the values of the current , voltage , and frequency . This was allowable as the E.M.F. wave was a pure Wave . A considerable alteration had to be made in the apparatus on account of the large quantities of ozone and oxides of nitrogen which were formed ) the , and which rendered the roonls very objectionable to work in . The polcelain plate was placed on one end of a thermopile ( used for tenlpera ( measurements ) , the whole in a raphic dish , and was covered with a bell-jar . Air was sucked into the apparatus two towers containing calcium chloride , and a wash-bottle containing huric acid ( see diagram of Dr. H. wortb . [ May 7 , ratus ) . The was sealed at , bottom with ordinary machine oil . The ozonised air led out a tower manganese to split the OIle a ottle c acid , to prevent tIty w ) ) into the ratus . air current was produced by an dinary pump , and the air was dried before ring the } ) paratus , in order to diminish the brush of Ci cctric lobs was measured ] ) the CIlCC of tcml ) which could ) ined ) centre of the surface of th above ) tcml ) eraturc . This teml ) creature difference ) a The Electrical Qualities of Porcelain . few degrees , it follows from Newton 's laws of cooling , that the heat lost is proportional to this difference ; and as the heat lost is equal to the heat gained , if the temperature is constant , a thermopile placed with one end in contact with the porcelain enerate an E.M.F. which is directly tional to the dielectric loss . This E.M.F. was measured by connecting the thermopile with a low resistance galvanometer through a reversing switch , and noting the direct and the reversed deflections to neutralise the effect of local E.M.F. 's , etc. The losses were first measured at a constant frequency of 50 per second , with pressures up to 38,000 volts ( R.M.S. ) . The results are graphically represented in Curve 9 . The equation to the curve is expressed by Loss per cycle Joule per cubic where is the B.M.S. radiant per centimetre . CURVE 9.\mdash ; Potential-Loss Curve for Porcelain . Frequency Constant Loss The losses were then detel.lnined at constant pressul.e ( 30,000 volts ) , and for frequencies between 108 and 200 . The points obtained lie practically on a straight line which does ) pass the ( Cve 10 ) , so we have the equation for the dielcctric loss as ectric 1imetre iiJne t VOL. LXXXI.\mdash ; A. Dr. H. F. Haworth . [ May where is the potentiaJ radien of cycles per second . . \mdash ; Frequency-Loss for elain . Constant B. Lobh constant is probably to the fact that porcelain is not a perfect insulator , and that a certain current would flow if a direct pressure 30,000 volts was applied to it , rise to an ordinary loss . We have here a striking si1nilarity between netic and dielectric losses . They each independent of the time in which the cycle is completed ( i4 we ( lect the due to the rfectio of the dielectric ) , and arc proportional to si1nilar powels of the amplitude of the cycle . May we not extend this similarly to the internal actions ? Let us the dielectric to consist of electric instead of netic doublets : these particlec would oscillate or evolve under the influence of an and energy would be absorbed in ovelconling their nloleculal friction . In 1861 , W. Siemcns ished a paper on the of the Leyden jar , pointed out that a condenser became heated on and . Many attcnll ) have been made to measure the loss of in dielectrics subjected to a field . Monatsl)'October , 1861 . 1908 . ] The Qualities of Porcelain . In 1890 , J. Swinburne suggested* that the loss was due to want of homogeneity in the dielectric , and imagined conducting channels to run across the dielectric , giving rise to a loss . This view has been accepted by many subsequent investigators . In 1891 , Major Cardew attempted to measure the power factor of a paraffined paper condenser ) the " " Three Voltmeter\ldquo ; method , but the results obtained are doubtful . In the same year Hutin and Leblanc , workin with paraffined paper condensers , also attributed the loss to heterogeneity of the dielectric , and came to the conclusion that they were dealing with tlJe case studied by Poisson of a perfect dielectric , containing many small spheres of conducting nlaterial . They destroyed the fibre of the paper by strongly heating , and in doing so the dielectric constant fell from 8 to . The condenser then stood 1000 volts per centimetre without heating , at higher pressures the temperature rose . Steinmetz , S experimenting on paraffined paper condensers , found the dielectric loss to vary as the square of the applied pressure . The pressures used varied between 80 and 320 volts at 170 ; at higher pressures he found that the loss increased at a higher power than the square of the applied pressure . Steinmetz pointed out the between the hysteresis loss in iron and dielectric loss , and so the name " " Dielectric Hysteresis\ldquo ; was loosely given to any kind of dielectric loss . makes a similar remark , and says that solid dielectrics present phenomena quite analogous to magnetic hysteresis , in consequence of which , at equal pressures , the charge in a condenser is smaller for increasing than decreasing pressures . Janet , in a later account , experimenting on a mica condenser , obtained a curve enclosing an area for the relation between and . analogous with a magnetic cycle in iron , but its form may be accounted for by hysteresis , or viscosity , or both . By a hysteretic loss we mean one which is independent of the time taken for the cycle , and this point has been overlooked by many experimenters . rees with Poisson in his case of a perfect dielectric containing conducting spheres , and deduces theoretically the existence of residual c and dielectric loss , and shows that the loss would with the results of 'Phys . Soc. ' vol. 11 , p. 49 . I. E. E. Proc May , 1891 . 'La re vol. 4 ] , p. 179 , ] , 1891 . S 'Electrical ' of New York , Malch 16 , 1892 . 'Comptes Rendus , ' Deceml ) , 1892 . Comptes Rendus , ' vol. 116 , p. , Februan , 1893 . 'La ectrique , ' vol. 46 , p. 402 , November , 1892 . Dr. H. F. Haworth . [ May 7 , Steinmetz and others . Hcss does not think that the result obtained by Steinmetz , for dielectrics , can be considered as analogous to his law for magnetic hysteresis , , because , if dielectric hysteresis existed , it would be entirely swamped by the loss due to the conducting bodies . Arnot*suspended hollow cylinders of various substances in a rotating electric field , and showed that the cylinders had a tendency to turn ; from this , Arnot calculated the energy expended in the dielectric , and called the ioss hysteretic , although he might just as easily have attributed it to viscosity . Bedell , Ballantyne and employed a method similar to the one described on p. 234 , and attributed the loss to hysteresis . and Morris , using very slow cycles of electrification , found the ialion in of a condenser for equal pressures , on decreasing the potential , to be less than one in eight thousand , and so concluded that the effects were due to viscosity rather than hysteresis . F. BeaulardS found that the energy dissipated in different dielectrics at different frequencies varied with the time of the cycle , and tended to vanish as the time of cycle increased . According to hinl , the loss was a viscous one . E. E. Northrup shows that the value of the specific inductive capacity of a dielectric is for a slowly field than for a rapidly varying field . Experiments of Blondlot and J. J. Tholnso show even greater changes . H. Pellat tried to show that the loss was due to dielectric olarisation , and that if a solid or liquid dielectric be suddenly placed in an electric field it polarises , the polarisation increasing with time , and tendin to a maximum . If the field ceases , risation diminishes to zero . W. suspended ellipsoids of ebonite and bifilarly etween the plntes of a Kohlrausch condensel found the loss from the of the ations . In the case of parnffin the was pptional to the square of field . Arnot found that varied as the of field . The methods have also been dopted to the losses in lectrics : ' Rendiconti . Accad . Lincei , ' ) ) ; 'The ician , , ) ) , , 189.3 ; 'La 4 ical P ' vol. 1 , ] , ' . 468 , . de A ust , ) ) . . and in Icctl itism , p. , etc. lnal . , ' vol. 18 , ) } . ) \ldquo ; . , 189 . 1908 . ] Tloe lities of Porcelain . Kleiner*used a thermo-couple embedded in the dielectric . BermischkeT used a bolometer to determine the rise in temperature in a paraffin wax plate , but failed to detect any , and concluded that dielectric hysteresis did not exist . He attributed the losses to ( 1 ) Joule effect , ( 2 ) residual charges ( viscosity ) , ( 3 ) mechanical lcsses due to yiblation condenser sheets . Rowland and used the split dynamometer method brought out by Professor Rowland ; they experimented on pa1affined paper condensers , and , found the loss to increase with the frequency of the cycle . In other experiments they found that the loss per cycle was independent of the time of the cycle . These results are opposite to those of Porter and Morl.is , and it seems not unlikely that , under certain conditions , viscosity may be the predominating feature of the dielectric , and , under other conditions , hysteresis . and Smith , S using a resonance method in conjunction with a wattmeter , found that the loss was proportional to the of the current , and hence the loss be attributed to the equivalent resistance of the condenser . The voltage varied to , and the condenser was of paraffined paper . Dr. P. Humman using the resonance wattmeter method with different kinds of cables , found that the loss was proportional to 1 . A porcelain condenser charges at a comparatively rate . This may account for the dielectric constant , as measured by alternating current , being smaller ( 718 at C. ) than that measured by continuous current ( 8 at 2 . For pressures up to 1200 volts the charge was directly proportional to the pressure , if the potential changes were made slow enough . 3 . If the potential changes were made rapidly , the was not quite proportional to the potential . Ihere was a certain dielectric loss . 4 . The dielectric constant , measured after one minute 's electrification varied with the temperature according to the laws : Between and C. , Between and 10 C. The ectric constant at was ( Curve 4 ) . 'Wied . Ann vol. 50 , p. 138 . Wiener Sitzber No. 102 , vol. . Mag vol. 45 , p. 66 , 1898 . S 'Phys . Review , ' vol. 8 , p. 4 , January , 1899 . 'Inaug . Diss Bonn , 1896 , Extract , " " El . Zeitschr 1898 , pp. 435\mdash ; 436 . Electrical Qualities of . The apparent conductivity of porcelain varies with the applied pressure and the duration of the application . The dielectric polarises , or generates a back , when a potential difference is applied to it ( Curves 5 and 7 ) . The conducting mechanism viscosity . 6 . apparent conductivity of porcelain , measured after one minute 's electrification , increases with the telnperature to the law:\mdash ; . urve 8 . The conductivity at C. is 0 mhos per centimetre cube . 7 . The dielectric loss varies as the -power of the voltage ( Curve 9 ) , and is independent of time of the . The dielectric loss at sures and fiequencies ) etel.nled hysteretic . At very slow frequencies the loss is nlainly loss , this slJows viscosity effects ; losses are swamped at by the dielectric hysteresis ( see Curve 10 ) . The dielectrlc consbant is not by , electrostatic , or by the frequency alternation of field , within the limits of the ) el.iment . The continuous Yent ecnls this were carried out at the Institut des technikums , , and 1 have to thank tisor Dr. H. ] . Wcber for his yaluable ] . The alternating current ere carried out ( the City and Guilds of tldon Centlal Teclmical ; and 1 indebted to ofessor W. Aylton , nd T. loan and advice . Kiilnes , , Lefe ( Nolthcute ( students of the Central ) the work required for

rspa_1908_0076

0950-1207

Note on a new sounding machine for use on lakes and rivers without a boat.

243

249

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

E. J. Garwood, M. A., Sec. Goel. Soc.|Professor T. G. Bonney, F. R. S.

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6.0.4

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10.1098/rspa.1908.0076

Measurement

Geography

Measurement

243 Note on a New Sounding Machine for use on Lakes and Rivers without a Boat . By E. J. Garwood , M.A. , Sec. Geol . Soc. ( Communicated by Professor T. G. Bonney , F.R.S. Received May 15 , \#151 ; Read June 4 , 1908 . ) 1 . Introduction . In the course of an investigation into the mode of origin of certain Alpine lakes in the Canton Ticino , it became obvious that no conclusive results could be arrived at so long as the subaqueous forms of these rock-basins remained unknown . In the admirable detailed map published by the Swiss Government , no attempt has been made to represent by soundings the storage capacity of these Alpine reservoirs , a fact somewhat astonishing , at first sight , when we consider the great value of water power to the inhabitants of the Republic . The omission , however , becomes more intelligible when the difficulties involved in obtaining the necessary soundings are realised . The majority of these lakes are situated in wild and uninhabited districts , where no boats are available , and though boats of the Berthon and Shellbend types have occasionally been employed in similar cases , their use is attended with many drawbacks , the chief of these being their instability and their liability to drift . The latter drawback renders them most unsuitable for work on mountain tarns where gusts and squalls are of constant occurrence . Under these circumstances it seemed desirable , if possible , to devise an instrument which would enable an observer to obtain an accurate bathymetrical chart of any mountain lake without being dependent upon a boat . With the assistance of a grant of \#163 ; 15 from the Government Grant Committee of this Society , which I here gratefully acknowledge , an experimental model was designed , which gave satisfactory results . The knowledge thus acquired was made use of in the construction of a second , more efficient instrument , with which a group of lakes in the Canton Ticino was successfully charted . The results of the investigation were published in the ' Quarterly Journal of the Geological Society ' ( vol. 62 , 1906 , p. 165 , Plates 7\#151 ; 21 ) . The instrument , which is here described for the first time , is the outcome of the experience thus gained , and in it are embodied alterations and additions suggested by practical experience acquired in working with the two previous models . Its chief advantages are:\#151 ; 244 Prof. E. J. Garwood . New Sounding Machine [ May 15 , ( 1 ) Its portability . It can easily be carried by one man even in mountain districts . ( 2 ) It can be used where no boats are available . ( 3 ) It is practically unaffected by any ordinary breeze , so that a line of soundings may be run between any two points in a nearly straight line from shore to shore . ( 4 ) Not only the depth of each sounding but the distance from the shore at which it is taken is automatically registered . 2 . General Description of the Instrument . The instrument consists essentially of two posts ( A and B ) erected on opposite sides of the lake or river , manipulated respectively by the observer and his assistant , who work gradually down from one end of the lake to the other . The posts are connected by a line , to the centre of which is attached a float carrying a pulley for the support of the plummet line . The ends of the connecting line are wound on two drums ( Y and Z ) fitted to the posts A and B. By means of these drums the float can be drawn backwards and forwards across the lake , and thus takes the place of a boat in the usual method of sounding . The post B , in charge of the assistant , carries nothing but this drum ( Z , fig. 2 ) , fitted with a stop-brake , and the duty of the assistant is merely to haul in and let out the float as directed . This is an important point in the construction of the machine , as it enables any boy or untrained assistant to be utilised for the purpose , all registering mechanism being confined to the post A. The post A ( fig. 1 ) is worked by the observer . It is provided with two drums ( X and Y ) accurately paired and placed on either side of the post . These are fitted to an axle which is common to both . The drum Y is firmly fixed to this axle and always revolves with it ; the drum X can also be arranged so \lt ; as to revolve with the axle by dropping the spring bolt ( a ) , it then revolves with the drum Y ; by raising the bolt ( a ) , however , the drum X is set free and can revolve independently on the axle . The line from the drum Y , as stated above , is attached to one end of the float , while the line from the drum X is the sounding line and travels through a counting machine W to the centre of the float , where it passes over the pulley to the plummet . The drum X is fitted with a check ( b ) , worked by a lever on the right-hand edge of the post.* This prevents the drum from racing when the plummet is running out , and can also be brought into action for the same purpose when the wheels are coupled and the float is being drawn to a new position . * Right and left hand from the point of view of an observer facing the counting machine . 1908 . ] for use on Lakes and Rivers without a Boat . SCALE 1:6.5 . FIG 1 Brace r Check Pulley ( k ) Clearing Pulley ( 1 ) Release Tever ( h ) Check Pulley ( k ) Adjusting Thumb Screw ( i ) Travelling Pulley ( e ) Brake ( c ) on Drum Y Drum X Guide Pulley ( f ) Tine to Plummet Driving Pulley ( g ) Counting Machine W Travelling Pulley ( e\gt ; .Spring Bolt ( a ) Tine to Float from Drum Y Check ( b ) on Drum X ----Spooling Arms ( d ) Point inserted in Ground . Fig. 1 . 246 Prof. E. J. Garwood . New Sounding Machine [ May loy The drum Y is fitted with a stop-brake worked by a sliding lever ( c ) on the-left-hand edge of the post.* This brake works on the toothed edge of a plate fixed to the inner side of the drum , and brings this drum instantaneously to-rest . By dropping the bolt ( a ) and thus coupling X and Y , the drum X is also rendered stationary when this brake is applied . The two lines are fed on to the drums by means of the spooling arms ( d ) , which are coupled and move together horizontally across the faces of the drums . These spooling arms are supplied to prevent the lines from piling . Should , however , piling take place , it will be forced to do so symmetrically on both drums , and the lines are thus kept equally taut . Without this- , device the plummet is liable to drag behind and become caught in shallow water . The free movement of the spooling arms is ensured by the travelling pulleys ( e , e ' ) . The line from the drum Y travels from the pulley e to the float . The sounding line from drum X , after leaving the travelling pulley ( r ) , . passes through the counting machine W and over the guide pulley ( / ) to the plummet . The Counting Machine W is driven by the plummet line , which passes round the large pulley ( g ) , forming the first counting disc and registering inches . Three other counting discs , geared to ( g ) , register feet , tens of feet , and hundreds of feet respectively . Each of the discs is engraved with a double series of numbers in red and black , registering in opposite directions^ by means of which the machine can be made to record either the amount of line let out or the amount drawn in . By loosening a thumb-screw , the lever ( h ) can be raised and the driving pulley { g ) and the sounding line disengaged from the remaining portion of the counting machine . The dials , recording feet , can then be rapidly returned to zero by the adjusting thumb-screw ( f ) , the plummet line meantime remaining at rest . The constant tension of the line on the driving pulley is secured by means of the spring roller clips ( k , k ' ) , while the line is prevented from running off the side of the driving pulley by the clearing pulley ( 7 ) , which ensures the line crossing freely , clear of the machine . The Float consists of an inflated air cushion of lifebuoy pattern . This-supports an aluminium platform , the centre of which is perforated for the passage of the plummet line , which runs over a pulley fixed to the platform at the margin of the perforation ( fig. 2 ) . When the lake is wide , it is sometimes convenient to add a small supplementary float to support the lines and to prevent them from sinking too far under water . * Eight and left hand from the point of view of an observer facing the counting machine . 1908 . ] for use on Lakes and Rivers without a Boat . 247 The Line actually used is a plaited waterproofed salmon line.* Stronger line or fine wire can be used for distances and depths greater than those usually met with in small Alpine lakes or ordinary rivers . Fig. 2.\#151 ; Showing Post B , Drum Z , and Float carrying Sounding Line . 3 . Method of using the Instrument . Starting with his assistant near one end of the lake , the observer erects the post A in a position suitable for taking a line of soundings across the lake . The assistant proceeds to a selected spot on the opposite shore , where he erects the post B , leaving with the observer the float , to which the end of his line is attached . He then winds this line taut , thus establishing direct communication between the opposite shores of the lake . The float can now be hauled across the lake and a line of soundings obtained at intervals between the two posts ( fig. 3 ) . The two drums X and Y on the observer 's post being coupled by means of the spring bolt ( a ) , and the counting machine being at zero , the assistant winds in his line until a given distance , say 25 feet , is registered by the red figures on the counting machine . This records the distance that the float has travelled out from the observer 's shore . The lever of the brake c is then raised , locking both drums securely . The spring bolt ( a ) is next drawn from * Supplied by Messrs. Carter and Co. , St. John Street , London , E.C. 248 Prof. E. J. Garwood . New Sounding Machine [ May 15 , its socket , allowing the drum X to revolve freely on the axle and the sounding line to run out . Fig. 3.\#151 ; Showing Method of Sounding . When the plummet reaches the bottom , the counting machine will register the depth of the sounding in addition to the 25 feet previously recorded on the instrument for the position of the float . The depth in feet , therefore , of any sounding , taken when the float is travelling from the observer to his assistant , is registered by the red figures , and is obtained by deducting the figure registered on the dial before the plummet is let down from the figure registered when the plummet has reached the bottom . Thus:\#151 ; Amount registered by red figures , plummet being at surface ... ... 25 ft. " " " bottom ... . . 45 " Depth of lake at 25 feet from observer 's shore = ( 45 \#151 ; 25 ft. ) = 20 ft. The sounding line is then wound in , when the red figures will again register 25 feet . The drums are then coupled again by dropping the bolt ( a ) , the brake b removed by lowering the lever ( c ) , and the float is hauled by the assistant to a new position and a second sounding taken . 1908 . ] for use on Lakes and Rivers without a Boat . 249 When the first line of soundings is completed and the float has reached the post B , the observer or his assistant moves further down the lake . The counting machine having been returned to zero , the observer proceeds to haul back the float to his side of the lake , taking soundings at intervals as before . The black , not the red , figures are now used . It must be remembered , however , in the case of this second series of soundings , that , since the plummet line as well as the float line is being hauled in by the observer , the figure representing the depth of the lake , at any sounding , will be deducted on the dial from the figure representing the distance from the shore for the position of that sounding ; for the plummet line , in running out , will move the registering dial in the opposite direction to that in which it is moved when the float is being hauled towards the observer . Thus:\#151 ; Amount registered by black figures representing distance from shore when plummet is at surface ... ... ... ... ... ... 25 ft. Ditto when plummet is at bottom ... ... ... ... ... ... ... 5 " Depth of lake at 25 ft. from assistant 's shore is ( 25 \#151 ; 5 ft. ) = 20 ft. The red figures can , of course , be ' used for taking the sounding if their position is noted each time . In practice , however , it is found to be more convenient to proceed as stated above .

rspa_1908_0077

0950-1207

The viscosity of ice.

250

259

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

R. M. Deeley, F. G. S.|Henry Woodward, LL. D., F. R. S., F. G. S.

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6.0.4

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10.1098/rspa.1908.0077

Tables

Measurement

Tables

]\gt ; Tlre Viscosity of Ice . . . ( Communicated by Henry , LL. D. , , F.G.S. Received Read June 4 , 1908 . ) Although the character of the motion of laciers is now well known , and the velocity of their motion has , in some cases , ) measured , calculations do not appear to have been made of the viscosity of either glacier or crystalline nor do there appear to } ) any published figures from which the viscosity be quite ccul ately ascertained . It is possible , , by estimating ' certain dimensions , to obtain results , although not strictly accurate , figures of the order of nitude . The property termed viscosity is here used as defined by tallow candle is much softer a f : but , if the candle and the stick of -wax are laid between supports , the .sealing-wax will , in a few weeks in summer , bend with its own weight , while the candle remains straight . The candle is , therefore , a soft solid , and the -wax a viscous liquid . A viscous body considered as one which manent and continuous of form under the action of a stress , however small . plastic body is which requires a definite and often stress to continuous of form . For ractical purposes , a bstance which continuous of form under very small stresses and yields at a rate to stress be as IGviou s the viscosity of ] uids , did not then ) them to any concrete case . now propose If a bed of acier were fairly and the ice the laws of iscous flow , then the vonld lnove f middle and slowly at the sides and bottonn . Tho rate of carefully uleasured ) placed ( line of stakes across a and found in the coulse ot a few honrs } bent into . We nu Cllenls vc is ictly parabolic in the case any to find such , the ] ) which laciers n ] ] sinuotls and have arities in Above sses form across the ice , into these vasses rock flaciel . falls . 'Theor of 'I . } . The Viscosity of Ice . of the ice surface , these dirt bands become visible lower down , the dirt bands are seen to stretch across the glacier in great parabolic curves . The downward movement of a ] acier is due to its weight and viscosity . In the case of a fluid of small viscosity , such as water , inertia efiects cause the stream to be swifter in some places than can be due to the slope there , and slower at other places . With a glacier , the viscosity of which is enornlous , the great viscosity enables it to transmit thrust to some considerable distance , and for this reason we get velocities at various points which are not wholly due to the effects of gravity at such points . The surface of olaciers also causes them to compression in many cases , and this again nplicates the question . Tyndall measured the rate of flow of a number of glaciers , the slopes of the upper surfaces of which can be approximately obtained . Their thicknesses , however , can only be estimated . This I have done by the valleys down which the glaciers move with other valle ) of somewhat similar width and length . I consider it probable that the slip at the bottom is about per cent. of the surface velocity , so the effective rence of velocity between top and bottom is 75 per cent. of the surface velocity . The rock dense and hard , the probability of the bolacier frozen to its bed does not seem boreat . The breadth of the glaciers being much in excess of thei1 thicknesses , and it being probable that the slip is much greater at the sides than at the bottom , the assumption has been in the calculations hat the glaciers are of infinite width . Table I are given both the calculated iscosities for a nnmbcr and the ures upon which the calculations are based . These fures will be subjected to criticism and modified ii more accurate inlates of the can be made . As an instance of the method adopted , the calculation for viscosity of the Great Aletsch glacier is given below : bodily force producing motion , downward component ravity ravity density Xradient dynes per cubic cenbinletle . By observation , maximum velocity is cm . per sec. and the depth ' is at the bottom of the glacier cm . The equation of , leads to , and , the viscosity of water only at C. Mr. R. M. Deeley . [ May 18 , The maximum shearing stress at the bottom of the glacier tending to drag the rocky surface along with it is total downward component of gravity , . per sq . ft. In many cases glaciers have in my opinion* frozen to beds , and have dragged along with them , and crumpled and contorted , the rocks over which they have passed . The shear at the bottom of the Great Aletsch glacier , to nearly tons per square foot , is the near the centre . This may be greatly exceeded at points where a rock projects above the general surface ; for owing to the very boreat viscosity of the ice , thrust can be transmitted very considerable distances . Although lacier grains are capal ) of deformed easily by a stress producing shear at angles to the optic axis , yet from the fact that these grains have their axes at all angles , the motion of the glacier must be partly due to some other assisting cause . This I have is the liquefaction and regelation which takes place when molecules pass from crystal to crystal . An ice crystal may evaporate more freely on one face than another , thus cansin a permanent and continuous ansfer of molecules from crystal to crystal . stntes that a bar of ice with }which he experimented decreased in width when the optic axis was vertical more rapidly than it decreased in depth . The effective viscosities of to in to these calculations from to . It is adnlitted that data t somewhat uncertain ; but as far as of lnovement , slope , and ickness are concerned , the cely b as will account for the whole of this diHerence . The most serious uncertainties are the extent to and the amount of ) ) onndaries may affect the results . Tn the case of the Great Aletsch the 1rity of the slope and the great of the ice stream seem to show is no rock of any depth below the strenm , the value of the viscosity obtained for it is robably the most reliable . the de and the Lower laciers are in smaller may be due to to thrust rnpid lnotion than is due the only . thehe two ice Lhe acier rains may also smaller , to of the ' the of ice falls , and this osity to be small . results are likely to ) cted by thrust , especially . ' Phil. , 1888 . \ldquo ; The Viscosity of Ice . towards the end , and a mean of the three viscosities obtained for this glacier may be considered to be fairly free from error . Table I.\mdash ; Viscosity of Glacier Ice . A viscosity of appears to be as near an estimate as can yet be made of the effective viscosity of a Swiss glacier . In winter the viscosity is probably double this figure to the lower temperature . J. C. McConnel* appears to have been the first to observe the exact conditions under which ice is capable of being deformed without fracture by stress . He showed that a crystal of ice can be sheared by very small stresses in a direction at right angles to the optic axis , and that the rate of shear becomes reater as the stress is increased . His two main conclusions are ( 1 ) that the friction between the particles of ice along the shear planes becomes greater as the temperature falls , ( 2 ) that when the molecules of ice slide over each other the cube of the friction varies as the square of the velocity . It must be remembered that McConnel died before his paper was quite finished , and that , therefore , his calculations were not completed , nor was his paper subjected to final correction . It will , consequently , not be out of place to reconsider his experimental results in detail . In Table II , I have set out a number of the experimental esults he 'Roy . Soc. Proc May , 1891 , p. 323 . , VOL. LXXXI.\mdash ; A. Mr. R. M. Deeley . [ May 18 , obtained with bars of ice loaded with various weights . Although in one place only he states the distance between the supports of the ice bars , it is clear that the distance was 51 mm. the used a solid iron frame placed in a small box to keep the temperature from varying rapidly , and to check evaporation . In no case is the full length of the ice bar given ; this I have assumed to be 60 mm. He states that during the eriments the bars lost by tion , and as he ives the rate of evaporation , I have calculated the size of the bar at each reading of deflection . This can readily be done , as gives the size of the . beforc and at the end of the experiment , and also gives the times when the were altered and the deHe tions were measured . In a few cases the figures he gives for the duration of the tests are htly in errol ; these have been rected . Table Ixperiments - by ) . , Shear F. , Viscosity , mm. mm. per cm.2 c.g.s. units . Time , Bending , Weight , ) , Shear F. , Viscosity , mm. kilos . mm. mm. per cm.2 c.g.s. units . Timc , Bending , ) , Shear F. , Viscosity , mm. kilos . mm. mm. per cm.2 c.g.s. units . Timc , Bending , mm. kilos . 0 . 0.089 0 . 0.032 0 . 0 . 0 . 0 . 3 . ! , 0 . Oh4 0 . 0 . 0 . 0.089 0 . 0.032 0 . 0 . 0 . 0 . 3 . ! , 0 . Oh4 0 . 0 . 0 . 0.089 0 . 0.032 0 . 0 . 0 . 0 . 3 . ! , 0 . Oh4 0 . 0 . 1.445 5 0 . 0 . 2 2 0 . 3 . ! , 0 . 2 . Oh4 3 ! 0 . 2 1.445 5 0 . 0 . 2 2 0 . 3 . ! , 0 . 2 . Oh4 3 ! 0 . 2 0 . ; 1.445 5 0 . 0 . 2 2 0 . 3 . ! , 0 . 2 . Oh4 3 ! 0 . 2 0 . ; 1.445 5 0 . 0 . 2 2 0 . 3 . ! , 0 . 2 . Oh4 3 ! 0 . 2 0 . ; 1459 ] 1 1:4.4 : ; 13.41 ' , 323 . of ic in 111 11 its suppol ts ith the optic Ulnes the ivcn 1 illt of it 1908 . ] Viscosity of lce . assumed that the is as shown by the full lines . This assumption much simplifies the calculations , and does not appear to me to introduce any serious error . When , as shown in fig. 2 , a mass of a viscous substance is distorted by the application of a stress to the plane , and the plane is fixed , the distortion is as shown by the dottedlines , and the stress at all planes between and parallel to the planes XX and is the same . Now , according to fig. 1 , the ice bar is distorted by shear in exactly the same way , and I have regar the weight on the centre of the bar as a stress parallel and coincident with the upper and lower faces of the bar . for distance between supports , total area of horizontal surtimetres . face , square centimetl'es . S deflection , centimetres . time , thickness , centimetres . load , dynes . The shear is S/ per hour ; the total force in the cross-section is , where is the area of the cross-section . This must be equal to , so that For the ninth test of Table II , so that and the shearing force In the last two columns of II given the to which the bars were subjected and the iscosities . . R. M. Deeley . [ May 18 , On Diagl.a I these viscosities are plotted , and tJainst each plotting is marked the shearing stress ( in dynes per square timeGre ) to which the ice was subjected . The equation to the curve on the is so is parabolic , where is the viscosity in dynes per square centimetre and is the temperature below zero ( considered positive ) . It will be lolice that out of tests , one of is stated by McConnel to be inaccurate , and two of which also appear unreliable , leaving 2 presumably accurate esults , 14 , or more than half , ve results within units with the . The want of exact eement w the curve seemb to be mainly due to the varying temperatures experienced during the continuance of expcriments . McConnel 's ) eriments show Chal the was taken off the ice , in addition to ) urely estic rise it lecovered slowly solle of the 1908 . ] The Viscosity of lce . the weight had produced . Many , if not all , soft solids do this . The recovery was very slow , and almost ceased after a time . It will be seen , on referring to Diagram I , that the experiments made with the small stresses ooive , in some slight degree , the ) reatest viscosities , but this is not true to anything like the extent McConnel thought . In this connection he states that when the is changed the alteration in the rate of depression is great out of all proportion , , the alteration in the rate of bendin from to when the weight is changed from to kilos . In this case , however , there was a change of temperature from C. to , and , as will be seen from the diagram , the change of temperature will account for almost the whole of the change of viscosity . He should have compared the case in which the temperature was with the one in which it was C. , and he would have found that , with stress . in the proportion of 1 to 9 , the rate of shear was very nearly proportional to the stress . found that continuous shear could not be produced in some samples of when very lightly stressed . It be that the small departure from the rate of shear being proportional to the stress , when the stress is small , is to some extent due to want of ularity in the structure of the ice tested , and may also be in some measure connected with the property ice possesses of slightly recovering its original form after distortion . There some uncertainty as to the actual behaviour of other viscous substances under stress , I made some experiments a bar of pitch . It was shaped by heating and pressing into a bar mm. long and 14 mm. square , and placed upon supports 117 mm. apart . The load at the centre of the bar was , partly due to the weight of the bar itself and the finger used to indicate the . After the application of the weight , the was allowed to bend until the reached the scale . The readings then taken are given in Table III . At 12.19 a veight of grammes was removed from the centre of the ) , which was then stressed only by the upon it and its own . After the lemoval of the weight , readings were taken for a time every seconds . On Diagram II some of the taken before and after the was removed are plotted . The shows that was an elastic unbending of the bar , follol ed a further , which ceased in about 4 minutes . The bar then again ) to yield viscously under its own weight . From this it } concluded that a viscous substance under stress requires time after a change in the nitude of the stress been made for the rate of shear to ) ecome proportional to the altered stress . AIso , that a The Viscosity of lce . viscous ( liquid ) substance may be elastic , , and may ) able to partly its shape after being deformed by viscous distortion . Table III.\mdash ; Sample of itch . , 1908 . Bar 100 mm. 14 mm. , 14 mm. decp . buppolts 117 mm. apart . 11.30 1.00 1.37 12.10 12.19 187 12.19 12.20 1.7:3 12.31 1 1 1 3 . 1.92 12.8 12.9 12.9 12.95 Off 13.0 the experiment } ) and experimental apparatus wele protected by a lass c dustel / ? . ? Since the above , my attention has called to the experimentl made by on several cous bstances , ) itch . Hc sCaC that " " it noticed that a ) movement ards recovery 011 removal of the forc of traction , which radually fell to zero time We may , I thin fairly conclude , from a consideration of fcConnel 's expelinlents and these ) described 011 pitch , ) the nature of shear ' Roy . Soc. Proc . p. 429 . Vortices Liquid . which can be produced in an ice-crystal at right angles to the optic axis very closely obeys the laws of viscous flow . If this view should ) sustained , it is not only true , as Professor H. A. Miers shows , that a liquid of low viscosity may have a crystalline structure , but also that , as in the case of crystalline ice , a solid may be liquid along one plane only . the equation to the curve on Diagram I , the viscosity of an icecrystal in a direction at right angles to the optic axis is about 2 at the freezing point . At this temperature the viscosity of a glacier is about , or 6250 times as great . The effective viscosity of a glacier is therefore due in a great measure to some other consideration . The optic axes of glacier grains are at all angles and they lock each other . I am much indebted to Mr. P. H. Parr for the assistance he has rendered in calculating the results from the Vortices / Liquid . By , O.M. , Pres. R.S. ( Received July 25 , 1908 . ) In a paper\ldquo ; on the Circulation of Air observed in Kundt 's Tubes , and on some Allied Acoustical Problems *I applied the equations of viscous incompressible fluid to show that the effect of the bottom of the vessel was to generate permanent vortices in the vibrating fluid . It was remarkable that the intensity of the vortical motion , when fully established , proved to be independent of the magnitude of the viscosity , so that the effects could not be eliminated by merely supposing the viscosity to become extremely small . The expression found for the vortices was simple . The horizontal component of the primary motion near the bottom being , the component yelocities of the vortical motion are , being measured ) wards from bottom , and the velocity of propagation of waves of the length in question . According to these 'Phil . TIans vol. 1 p. 1 , 1883 ; 'Scientific Papers , ' vol. 2 , p. 239 .

rspa_1908_0078

0950-1207

Vortices in oscillating liquid.

259

271

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

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

article

6.0.4

http://dx.doi.org/10.1098/rspa.1908.0078

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0078

10.1098/rspa.1908.0078

Fluid Dynamics

Tables

Fluid Dynamics

]\gt ; Vortices Liquid . which can be produced in an ice-crystal at right angles to the optic axis very closely obeys the laws of viscous flow . If this view should ) sustained , it is not only true , as Professor H. A. Miers shows , that a liquid of low viscosity may have a crystalline structure , but also that , as in the case of crystalline ice , a solid may be liquid along one plane only . the equation to the curve on Diagram I , the viscosity of an icecrystal in a direction at right angles to the optic axis is about 2 at the freezing point . At this temperature the viscosity of a glacier is about , or 6250 times as great . The effective viscosity of a glacier is therefore due in a great measure to some other consideration . The optic axes of glacier grains are at all angles and they lock each other . I am much indebted to Mr. P. H. Parr for the assistance he has rendered in calculating the results from the Vortices / Liquid . By , O.M. , Pres. R.S. ( Received July 25 , 1908 . ) In a paper\ldquo ; on the Circulation of Air observed in Kundt 's Tubes , and on some Allied Acoustical Problems *I applied the equations of viscous incompressible fluid to show that the effect of the bottom of the vessel was to generate permanent vortices in the vibrating fluid . It was remarkable that the intensity of the vortical motion , when fully established , proved to be independent of the magnitude of the viscosity , so that the effects could not be eliminated by merely supposing the viscosity to become extremely small . The expression found for the vortices was simple . The horizontal component of the primary motion near the bottom being , the component yelocities of the vortical motion are , being measured ) wards from bottom , and the velocity of propagation of waves of the length in question . According to these 'Phil . TIans vol. 1 p. 1 , 1883 ; 'Scientific Papers , ' vol. 2 , p. 239 . Lord Rayleigh . [ July 25 , expressions , the vortical motion is downwards over the places where has its eatest alternating values . In the case of water contained in a tank and vibrating in its simplest mode , the theoretical motion is downwards in the middle and upwards at the ends . To ) against misinterpretation , it may well to add that quite close to the bottom the motion , as calculated , is of a quite different character . In a recent paper , . Ayrton has examined , with much experimental skill , the iCeS arising water oscillates in a narrow tank , and has obtained results which differ somewhat widely from what are indicated in the aboye . Near the boCtonl , and especially when the depth is small , there are indeed vortices of this character ; but , , the most conspicuous feature consists of vortices revolving in the opposite direction , the water rising in the middle of the tank and falling at the ends . The first thought that occurred to me was that Mrs. Ayrton 's vortices might be due to defect of freedom in the surface , such as might ) Rupposed to arise from a greasy film extensions and contractions ; in some experiments that I tried , the vortical motion did not seem to ) much influenced by the surface , and the question was ested as to whether the free surface itself might not inate vortices in somewhat the same } ' as the bottom and more potently 011 account of the greater velocities of the motion there prevailing . I do not leulcml)er whether I had any clear view this question when I wrote the former paper . Vortices otherwise than at the ] ) ottom were nored , but I may not have intended to exclude their possibility . Tho consists mainly of ' nn ttelmpt to answer the question suggested . is limiled to the case of deep water , and eve then is rather complicated . If the calculations correct , we are to conclude that a free surface docs / generate ortices of this kind , at if .suppose the viscosity small and include only the square of the lnotion . hell are the ices , by . Ayrton , to be explained : might attribute thenn to of the taok , much ottom docs in my former } . In the latter the of the forces is near the parts luidw veen the middle of tank nd the ends , and to the fluid in the direction away from the place of . A like action at the of the tank would push the nei0 , and thus enerate revolvin in the observed direction . An objection to this lies in ) servalion by . Ayrton on water in " " On the Non-Periodic Rebidual Motion of WateI moving in ] StationaIy Waves ' oc , vol. 80 , p. 252 , 1908 . 1908 . ] Vortices in Liquid . tank with several subdivisions ( p. 255 ) . Since no solid walls are situated at the intermediate nodes , it may be thought that the action at the ends would be insufficient to establish the whole system of vortices . Probably this would be so . But another influence acting in the same direction may arise from the faces of the somewhat narrow tanks employed . It would seem that at the nodes , , the friction in up and down the faces have the effect as the up-and-down motion alon the solid walls which constitute the ends . But I must confess that some observations made with the lelp of Mrs. Sidgwick were not favourable to this view . The ends of the tank were eliminated by using the annular space between two cylinders , ( beakers ) , but the vortical motion did not seem to be diminished . The insertion of a strip of lass C held vertically across the annulus , and thus virtually one end , did not make much ] , if any , difference . This experiment seems to exclude the explanation depending upon the action of the , and that which would attribute the effect to the faccs is difficult to reconcile with the highly localised charactel of the effect , which at first seems to be limited to the immediate neighbourhood of ] ends . Can it be that the true explanation would require retention of terms of higher order than the of the motion ? I may mention that on more than one occasion I have witI ) esse the reversed movement described . Ayrton on p. 259 , " " as if a set of -ater springs had been wound up , and now to themselves I that the depends upon upon unequal densities in the fluid , the either to temperature or to variations in the amount of vder held in suspension . Another possible explanation would lie in the effect of surface contalnination . In the usual notation the equations of motion in two dinlcnsions are ( 1 ) , ( 2 ) Lord [ July 25 , where is measured vertically upwards , und is the kinematic viscosity . Since the fluid is supposed to be incompressible , ; ( 3 ) or what is equivalent , ( 4 ) the stream-fnncliou . In irtue of ( 4 ) , , have in ( 1 ) , ( 2 ) It may be vell to commence with the question 01 stationary aves , carl.ied to the second order of approximation , when viscosity is ected . If we eliminate from ( 1 ) , putting at the same , we find . ( 6 was to be expected from the eneral theory a fricfionless Huitl , solntion of ( 6 ) order of pproximation is . ( 7 We no assulne that the nloCion is periodic ith x\mdash ; proportional . to so as the Hrst ] ) tion is concern ed. Thus for imation we take , ( 8 the in hnissible , excluded ) the consideration that all motion must vanish when , inasmnch as the fluid infinitely deel ) . to ( 8 ) , ( 9 so . ( 11 ) In virtue , ( 7 ) , the tions of ) cssure ) . ' : si ( 12 ) 1908 . ] Vortices in Oscillating where denotes a function of which is arbitrary so far as the differential equations of pressure are concerned . The pressure at the surface is to be found from ( 12 ) by putting , where is the elevation of the surface at the point in question . The relation between and is thus required accurately to the second order of small quantities . The differential relation*is To the first order we have equal simply to the value of at the surface , so that ) the origin of in the undisturbed surface . value of may be used iu the small terms of ( 13 ) , and thus to a second where is an arbitrary function of of the second order of smitll quantities . We are now prepared to substitute for / 7 its value in ( 12 ) . In the principal term we must use the complete value of from ( 15 ) . fn the second term , already A as a factor , the first approximation for suffices , while in the third we may put . The third term thus becomes a function of only , and may be arded as cancelled by . We find . ( 16 ) In free vibrations the condition to be satisfied at the surface is . The annulment of the term in requires that and the same well-known relation suffices to annul term in surface condition is satisfied thought any addition to , if besides satisfying 17 ) we with - Thus , writing for obtain , as the complete value of . ( 18 ) We now proceed with the consideration of the problem when viscosity . Lamb 's ' Hydrodynamics , ' Lord Rayleigh . [ July 25 , is retained . Eliminating from ( 1 ) and ( 2 ) , we get , with use of and ( 5 ) , The terms on the hand of ( 19 ) are of the second order in the amplitude of vibration , and thus for the first approximation we have simply . ( 20 ) The solution of ( 20 ) may be Wl.itten , ( 21 ) where . ( 22 ) We now introduce the suppositions that in the first approximation are proportional to . and also to . The along is and the period is . The equations ( 20 ) now become by which and are to be determined as functions of . If we write we have , as the most ) solutionl of ) , ( 25 ) if the real part of is taken positive , the terms in and when t fluid is ted deep . our where A and now absolute real coml ) . We shall presently fin real . From ( 4 ) we now find , ( 27 ) ' ; and onlit terms of the second , we il of in like 1908 . ] Vortices in Liquid . Hence , ( 30 ) the expression to be integrated a perfect differential by ( 22 ) . Applying ( 30 ) to the present case , we find . ( 31 ) At the surface we are to suppose , and may be neglected in the term already multiplied by A. Thus at the surface . ( 32 ) Now that we have to reckon with viscosity , the stress conditions at the surface can no longer be expressed merely by . In the usual notation , applicable also in the theory of elastic solids , denote normal tractions across faces perpendicular to and respectively , while denotes the tangential traction which acts parallel to across the face perpendicular to , or the equal traction parallel to across the face perpendicular to The expressions for these tractions are* , ( 33 ) . ( 34 ) When viscosity was neglected , we were able to suppose that the surface of the fluid was entirely free from imposed force . Under such circumstances the vibrations of a viscous could not be maintained . If is to be real , some maintaining forces are necessary . We will suppose that these forces are exclusively normal in their character , and make ; for it is to be observed that in the present approximation a direction parallel to the surface may be identified with the horizontal . By ( 27 ) , ( 28 ) , ( 34 ) we find , making , ( 35 ) as the condition of no tangential force at the surface . Or , if we substitute for its value from ( 24 ) , ( 35 ) becomes . ( 36 ) For the normal traction at the surface we have from ( 33 ) , , ( 37 ) *Cf . Lamb 's 'Hydrodynamics , ' S 314 . Lord Ilayleigh . [ July 25 , and by ( 36 ) the expression for in ( 29 ) may be written These equations constitute the complete synlbolical solution of the problem of infinitely small stationary waves maiutained by purely normal surface pressures in a fluid of any degree of viscosity . * to pass to real quantities , it is simplest to , so that ( int . A is then given explicitly by ( 36 ) , and on substitution in ( 37 ) we ( jint . ( 40 ) The to real quantities is now only complicated by the telm in . If the viscosity be small , this term may be omitted , and we may take , ( 41 ) , the normal traction necessary to l1laintain vaves represented by . If , the part of in the same phase as disapl)ears , and simply . It is to ) remembered ) is a . If , as is usual in llydrodynalnics , use ) , see that the pressure has its maximum value when the is stest , as was to be expected . The accurate expression for the real of may , of course , be . If in ( 24 ) put then ) . ( 44 ) It is unnecessary to write down the actual of the real of ( 40 ) . Tn applications an of sufhceF ] . On account of the LllncbS of is very lar , with that is to sa the knChS ( the stratum ] which the motion can be time is the -length in tltc ' simply ( 4C ) , ' ' 1 , 332 . 1908 . ] Vortices in Liquid . It appears that the terms neglected in ( 40 ) when ( 41 ) is substituted are of the order In proceeding to a second approximation we have to calculate the terms of the second order forming the member of ( 19 ) , the values found in the first approximation . In these whence , the oinary part rejected , ( 4S ) . ( 49 Also , in real quantities by ( 27 ) , ( 28 ) , ( 36 ) , , ( 50 ) Pcos Hence \mdash ; By ( 19 ) to is elnl ) of . lt will be ) in the as { unctions of penden t tional in Lord Rayleigh . [ July 25 , of , and in addition we must include a " " complementary function\ldquo ; representing , so far as required , the complete integral of ( 53 ) whe the second member is made equnl to zero . This part contains the terms of the first approximation ( 26 ) , which now represent themselves ; and we must also be prepared to admit terms of the second order proportional to , and either independent of time or involving . In the former case the differential equation rednces to ' ( 54 ) as the ' solution applicable to deep water , ( 55 ) where and constants . A terln in would represent vortices ol the kind found in the former paper to from the action of the bottom ( when the liquid is not too deep ) ; and one of the principal objects of the present ation is to ascertain whether these terms occur as the result of the conditions operative at the free surface . It may be recalled that such vortices could not arise in an ideal frictionless fluid , nitude , when fully established , may independent of the amount of the fi.iction . In view of the complication of the it must suffice to limit the investigation to the case of viscosity , the question whether vortiees can be maintained the viscosity is reduced without On the right of ( 52 ) there nine terms , of which five are independent of . But they are not of equal importance . Since l ) is of the order , the term is the seyenth in . So far as this term is concerned , It is now convenient to to complex quantities , in ' as the ' of . Thus To the face condition , ) the evanescence of tangential fotce , shall require the expression of 1908 . Vortices in Oscillatinq- . Liquid . which , since is already involved as a factor , we may put . Thus rom which the imaginary part is to be re , iected . In tracing the value of ( 57 ) as diminishes , we get ultimately ( 58 ) . In this is of the order , and is of order , so that ( 58 ) is rder , becoming infinite in comparison with , as } without imit . We shall find , however , that infinite term is compensated ) mother , to be brought forward later . For our purpose we must retain all , which do not vanish with in comparison with . Hence , with cient approximation , which the second term , purely imaginary , is to be rejected . Thus real part of Referring to and regard to the orders of the various terms [ 1 respect of , we see that the only other term independent of which needs retained is the third in of arrangement . From this term we obtain [ 1 like manner , nd when rith sufficient approximation . In ( 61 ) , , so far as it need be retained , is a pure inary , and ccordingly there is no contribution from this source . We are left therefore with ( 59 ) as the complete contribution of the direct integral of ( 53 ) when , so far as the terms independent of are concerned . In a similar manner we may the in . We find for the eating term part of ; that , if we finally reject the inary part , VOL. LXXXI.\mdash ; A. Lord [ July 25 , when . And for the only there t which it is ecessary to retain , ( 7 , , . ( 63 ) We ve now sufficiently complete xplebsionS for so far as it results from the direct ) . But to we have to add terms arising fro1n the ) unctiol . In this there must , at any raCc , be included the terlns in found in ) first approximation . From ( 27 ) , ( 28 ) we ? is . and in this we are to substitute for value appropriate to the surface . In the hrst approximation terms containing / ' were ected , and surface condition . ( 65 ) This relation llust still hold , tcly at nny rate . it in the small of ( 64 ) , we in which we . in comparison with . Passing to real quantities , we find real value of from ( 3S ) , is , ( 66 ) so that this ( C4 ) beconnes . ( 67 ) for the ndcnt of we , ( 67 ) , ( 68 ) within braces ils may ) proved , crnls cillitc residue . Thns ishes w the lerms of concellled . terms in ( he lesb interest . We find , in the same , when is without limit of fit 1908 . ] Vortices in But we are not yet in a position to apply the condition which must be sittisfied at the surface , viz. , the tangential force shall there vanish ; for we nUSG l'enlember that the surface can no longer be treated as parallel to O. If be the angle which the surface point under consideration makes with , the of transformation are . For the present purpose may be regarded as a small quantity , equal to , whose square may be ected , and we may take . It is , and nob , which is to be made to vanish to the second order of the vibration . The expressions for , etc. , have already been give in ( 33 ) , ( 34 ) . Substituting the values of of the first approximation , we find , when is small , , ( 71 ) and . ( 72 ) It appears , then , that so as the terms dependent of concerned , there is no difference veen p and , and since we already seen that vanishes , it follows that the surface condition of no force is satisfied to a second approximation , without the addition of any further terms ( o5 ) , such as would represent permanent vortices . Accordingly , no such vortices exist . As terms find addition another term of the same form derived from and ( 72 ) . In a solution complete to the second order these terms would need to be compensated by the introduction of llew second-order terms in of the form ; ( 74 ) but it is scarcely necessary for our purpose to define them . Neithel does it seem worth while to express at ) the equation of pressure when the second-order terms are included . The particular case of viscosity already considered illustrates the procedure . Terms in the expression of the pressure are independent of are ) ondi c in not affecting the velocities .

rspa_1908_0079

0950-1207

On the accumulation of helium in geological time.

272

277

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.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1908.0079

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10.1098/rspa.1908.0079

Geography

Thermodynamics

Geography

272 On the Accumulation oj Helium in Geological Time . By the Hon. R. J. Strutt , F.RS . ( Received July 28 , 1908 . ) ( From Imperial College of Science , South Kensington . ) In a former paper* I gave an account of experiments on the presence of helium in a variety of the common minerals of the earth 's crust . The conclusion arrived at was that the quantity of helium is , in general , determined by the traces of radio-active elements present . The minerals investigated were mostly of palieozoic age , and little attention was paid to the effect of geological age on helium content . If , however , the accepted theory of the progressive accumulation of helium in minerals by radio-active change is correct , it is evident that geological age must be all-important . In the present paper , the subject is considered from that point of view . There is some difficulty in finding suitable material for comparing the helium content of minerals with their geological age . To make such a comparison advantageously , it is necessary to obtain minerals from a very great range of geological horizons , so that the oldest minerals considered shall be many times older than the youngest . Thus it becomes imperative to get material from the secondary and tertiary strata . Most of the constituents of these strata are unsuitable . For instance , derivative materials like clay and sand must be rejected , because they have presumably been accumulating helium long before they were laid down in their present stratigraphical position . The chemical precipitates like rocksalt and gypsum are so free from radio-active constituents that accurate measurements of the helium in them are very difficult ; while limestones are , in a lesser degree , open to the same objection . In view of these difficulties , I have been fortunate in discovering that phosphatic nodules ( the so-called coprolites ) and phosphatised bones are extremely rich in radio-active constituents , sometimes containing 50 times as much radium as the generality of rocks . These nodules and bones are found in a great variety of strata , from the pliocene downwards . The nodules frequently contain , or consist of , fossils characteristic of the stratum to which they belong , or of one very little earlier ; thus their age is well defined . The same remark applies still more to the mineralised bones . There is no reason to doubt that the radio-active material was introduced into the bones by infiltration at the time that they became phosphatised ; and from that epoch the accumulation of helium must be dated . * ' Roy . Soc. Proc. , ' A , vol. 80 , 1908 , p. 572 . On the Accumulation of Helium in Geological Time . 273 In these experiments I have extracted the helium by solution of the powdered substance in hydrochloric acid . The action takes place quite readily . The apparatus used is shown in the figure . To Pump s. for\ iloric The powdered mineral ( usually from .100 to 500 grammes ) is placed in the flask A , which is then sealed on to the rest of the apparatus . The system of tubes is evacuated through stopcock F , and washed out with a little oxygen to secure more perfect removal of air . Hydrochloric acid ( which has been well boiled , and closed up so as to cool in absence of air ) is then admitted through T. A violent effervescence of carbon dioxide follows . The gas is allowed to flow into the pump through F , by means of which the flow is regulated . On its way it traverses a bottle filled with soda lime , and in some cases a tube of hot copper oxide , followed by caustic potash . By these reagents the bulk of the carbon dioxide is absorbed , as are also small quantities of combustible gases which accompany it . A small residue , consisting chiefly of nitrogen , is collected through the pump . When the flask A is three-quarters full of acid , and the effervescence is nearly over , the stopcocks Hon. R. J. Strutt . [ July 28 , F and T are closed , and A heated to boiling . The gases expelled pass up into the top of B , while the lower portion is filled with steam , which condenses and runs back . When boiling has gone on long enough to ensilre complete expulsion of the dissolved gas , the heat is increased , so that the outflow of steam exceeds what B can condense . The gas then passes out at the lower end of C , where it is collected over mercury in D as shown . It is followed by steam , which condenses and forms pistons in C. By removing D at the right moment it is easy to make an exact separation of the gas from the condensed water which follows it . The gas collected in this way is added to that collected through the pump , and the inert constituents isolated by sparking with oxygen in the usual way . The gas was examined and measured substantially as described in the former paper . I have found that in practice it is much morfe difficult to avoid contamination with air when the material is dissolved in acid than when it is merely heated . Thus argon was usually conspicuous in the spectrum of the inert residue ; and on cooling the charcoal neon was sometimes visible , when it was not masked by a large excess of helium . Elaborate arrangements for boiling the acid in vacuo and admitting it without contact with the atmosphere would probably overcome this difficulty ; but it was not judged worth while to adopt them , as helium is readily isolated for measurement by the charcoal method . The great advantage of dissolving the material rather than merely heating it is in the certainty of extracting all the helium . In measuring quantities of helium less than a cubic millimetre , the method of sparking in a tube with sodium-potassium electrodes , followed by absorption with charcoal cooled in solid carbon dioxide , is inadequate . It is found that even with no helium present in the original gas the residue after this treatment is a fraction ( say 1 / 3 ) of a cubic mm. It would seem that hydrogen , which is almost always present in discharge tubes , is not perfectly absorbed by the sodium-potassium electrodes , but exerts a kind of vapour pressure . This hydrogen is not absorbed by charcoal at \#151 ; 80 ' C. By cooling the charcoal in liquid air , the residue ( in a blank experiment ) can be reduced below 1/ 100 cubic mm. It must he admitted that hydrogen was scarcely if at all visible in the spectrum of the discharge , when the tube had been run for some time . However , in spite of this , I think the above explanation of the residue is the most probable that can be suggested . When very small quantities of helium were to be measured , liquid air cooling was generally made use of . In cases where no liquid air was at hand , and when the experiment did not appear to be worth pursuing further , the quantity of helium was recorded as a maximum only . Badium was determined by the methods described in earlier papers . The 1908 . ] Accumulation of Helium in Geological Time . solution obtained in extracting helium was usually employed for the radium determination . The uranium oxide percentage was calculated from the radium observations , by standardisation with a uranium mineral . It will be observed that this method does not involve a knowledge of the ratio of uranium to radium in minerals , but only assumes its constancy . The results may be tabulated as follows :\#151 ; Material . Locality . Geological horizon . Helium , c.mm . per 100 grammes . U308 , grammes per 100 grammes . Helium , c.c. per gramme of u3o8 . hosphatised shark 's Florida Pliocene 0174 2 -48 x10 " ' 0 -0070 teeth hosphatised Cetacean Felixstowe Pliocene Red Crag 0-158 1 -55 x 1(P2 0 -0102 bones hosphatic nodules n 0-098 4 -78 x 10-3 0 -0205 a ) ) Cambridge Upper Greensand 3-03 1 -08 x10-2 0-281 J ) 3 ) Potton , Bedfordshire Lower Greensand 2T0 5-83xl0-3 0-360 hosphatised Saurian Ely Kimmeridge Clay \lt ; 0-365 3 -28 x 10-3 \lt ; 0 111 bones \lt ; 6-094 hosphatic nodules Knap well , Cambs . Base of Kimmeridge Clay Oxford Clay \lt ; 0-675 7 20 x10-3 hosphatised Saurian hAr\#187 ; pc Whittlesea \lt ; 0-51 9 -15 x 10-4 \lt ; 0-558 UvJJLLUo hosphatic bone frag- Lyme Regis Rhsetic bone bed \lt ; 0-22 2 -15 x 10-3 \lt ; 0 '102 ments taematite Frizington , by Carnforth , Cumberland Above carboniferous limestone 16 -5 1 -28 x 10-3 12-9 hosphatic nodules Kear Bala Bala beds 15 -3 3 -23 x lCT3 4-74 hosphatic limestone ... Chirbury , Shropshire Llandeilo limestone 5 -6 7 -90 x 10- " 7-10 hosphatic nodules Cailleach Head , Loch Broom Torrid on Sandstone 0-83 9 -9 x 10^ 0-84 It will be at once noticed that the order of stratigraphical position is not accurately followed . For example , the phosphatic nodules and bones from the Kimmeridge Clay do not show so high a helium ratio as those from the Lower or Upper Greensand , though they are geologically older than either . At the same time it will be noticed that helium ratios approaching 12 , such as are common in the mineral veins of carboniferous age in Cornwall , are not met with in the younger strata.* The facts are most easily explained by supposing that the retention of helium has been often if not always imperfect . One point remains to be referred to . If thorium were present in any of these materials we might expect it to have a disturbing influence , as an * Examples will be found in ' Roy . Soc. Proc. , ' A , vol. 80 , p. 573 . I have not reprinted the values here , as they were only obtained by the crude method of heating the minerals . This , however , suffices to give the order of magnitude . Hon. R. J. Strutt . [ July 28 , independent source of helium . The most searching experiments I have been able to make have only suggested a faint suspicion of its presence in the phosphatic nodules and bones . It can contribute nothing appreciable to their activity . The same applies to Cumberland haematite ; in this case the results were still more distinctly negative . I have included this mineral in the investigation as it is one of the few readily dissolved in hydrochloric acid . There is , of course , a very large field of research open in accurately determining the helium ratio for other minerals such as the metallic sulphides , but I have not yet had leisure to give any attention to them . Great interest will attach to determining the highest ratio to be found among minerals of Archaean age ; but here the presence of thorium enters as a complication . The chief interest of the present results is in their application to the measurement of geological time . For this application we require to know the rate at which helium is produced from 1 gramme of uranium with the equilibrium quantity of all the other products of the series . No direct measurements of this have yet been made ; 1 believe , however , that such measurements are quite feasible , and hope eventually to supply them . In the meantime it is interesting to calculate , as nearly as possible from indirect data , the time required for the accumulation of such quantities of helium as are found . Professor Rutherford has kindly communicated to me his latest estimate . It is that 316 cubic mm. of helium are produced per gramme of radium per annum . This is deduced on the following assumptions :\#151 ; ( 1 ) The number of helium atoms produced is equal to the number of a-particles emitted . ( 2 ) For every four a-particles emitted by radium with its immediate products , two are emitted by uranium , one by ionium , and one by polonium . I shall not enter on any discussion of the validity of these suppositions , beyond remarking that there are no definite grounds at present for deciding whether or not helium is liberated in the rayless changes . Taking the ratio of radium to uranium in minerals as 3*4 x 10~7 , we get for the annual helium production per gramme of uranium oxide , ( U3O8 ) , in \amp ; mineral , 943 x 10-8 c.c. Adopting this rate of growth provisionally , the following ages are obtained as a minimum for some of the materials examined:\#151 ; Years . Phosphatic nodules of the Crag ... ... ... ... ... ... ... 225,000 Phosphatic nodules of the Upper Greensand ... ... . . 3,080,000 Phosphatic nodules of the Lower Greensand ... ... . . 3,950,000 Haematite overlying carboniferous limestone ... . 141,000,000 1908 . ] Accumulation of Helium in Geological Time . 277 It must be emphatically repeated that these absolute values are provisional only . I hope that geologists and others will not regard the method as discredited if it should be necessary to alter them considerably , when the rate of growth of helium has been directly determined . The conclusions of this paper may be summarised as follows:\#151 ; 1 . Phosphatic nodules and phosphatised bones of all geological ages possess marked radio-activity , many times higher than that of rocks . This activity is due to products of the uranium series . . 2 . Helium has been detected in these materials , even when they are not of more than pliocene age . 3 . The ratio of helium to uranium oxide has been measured . This ratio does not strictly follow the order of superposition of the strata ; but high ratios are not met with in the younger deposits , whereas they are common in the older ones . It is conjectured that helium has been imperfectly retained , at all events in some cases . 4 . Provisional values are given for the time required to accumulate the quantity of helium now found in the nodules and other materials . In conclusion , I must record my best thanks to Professor Hughes and to Mr. J. J. H. Teall , who have most kindly supplied me with some of the materials used .

rspa_1908_0080

0950-1207

On helium in saline minerals, and its probable connection with potassium.

278

279

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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10.1098/rspa.1908.0080

Atomic Physics

Chemistry 2

Atomic Physics

278 On Helium in Saline Minerals , and its Probable Connection Potassium . By the Hon. R. J. Strutt , F.R.S. , Professor of Physics in the Imperial College of Science , South Kensington . ( Received July 31 , 1908 . ) In a former paper* I mentioned that saline minerals were often comparatively free from contamination with radio-active material of the uranium-radium series . Accordingly they afford special opportunities of testing whether or not helium is generated by the other elements present , namely , sodium , potassium , magnesium , calcium , sulphur , chlorine , oxygen , hydrogen . In this paper determinations are given of helium and radium in some of the saline minerals of Stassfurt . These minerals occur in strata of triassic age , though the age of some of them may be less , for there is evidence that secondary alterations have taken place in the salt deposits . Helium was liberated by solution of the mineral in water . The powdered substance was placed in a flask fitted up as shown in the preceding paper . The flask was exhausted , washed out with oxygen , again exhausted , and sealed off from the pump . Water , well boiled , and allowed to cool in a vacuum , was admitted through a tap . Heat was applied to promote solution , and when this was complete the gases set free were driven out by boiling and collected over mercury . Carbonic acid was removed by potash , and other constituents by sparking . The small residue was then examined as described in ' Roy . Soc. Proc. , ' A , vol. 80 , p. 592 , liquid air being generally used to cool the charcoal . When helium had been determined in this way , uranium was determined in the same solution , by the usual method of boiling out the radium emanation generated in a definite period . Previous to this determination the solution was acidified , to dissolve any slight sediment that remained and to prevent precipitation of radium as sulphate . The results were as follows :\#151 ; * ' Koy . Soc. Proc. , ' A , vol. 80 , p. 592 . On Helium in Saline Minera , etc. 279 Mineral . Composition . Helium , c.mm . per 100 grammes . Grammes uranium oxide ( U308 ) per 100 grammes . Helium , c.c. per gramme tj308 . Rock salt NaCl 0 -0233 7-1 x 10-6 . 3 3 Sylvine KC1 0 '55* 2 -15 x 10_G+ 256 Carnallite KMgcqeHoO 0 -151* 3 -23 x 10~6t 47 Kieserite MgS04H20 0 -0179 6 -47 x10~5 0-277 * These were repeatedly verified . In a specimen of carnallite purchased from another source , helium was scarcely detectible . This may have been due to the specimen having been allowed to deliquesce before it came into my hands . If so , it must have been dried again before I received it . f In these cases the amount of emanation was too small to be accurately determined . The values given are rough approximations only . The following were also examined qualitatively :\#151 ; Kainite ( MgS04KC13H20 ) . Krugite ( 4CaS04MgS04K2S042H20 ) . Astrakanite ( Na2(MgS04)24H20 ) . Langbeinite ( K2S042MgS04 ) . Polyhalite ( 2CaS04MgS04K2S04 + 2H20 ) . Schoenite ( K2Mg(S04)26H20 ) . Tachyhydrite ( CaMgCl6l2H20 ) . In none of them was the quantity of helium at all comparable with what was observed in carnallite or sylvine , though D3 could generally be seen . R*eturning to the quantitative experiments it is noticeable that very high ratios of helium to uranium oxide are met with in these two minerals . It seems altogether improbable that the minute traces of uranium and radium present can account for so much helium . On the other hand , the helium in rock salt is very much of the order to be expected from its geological age , if it originates from the uranium family of radio-active bodies . In view of Campbell and Wood 's observations on the radio-activity of potassium , * I am disposed to regard that element as the source . It is true that the other potash salts examined do not contain much helium , but , in view of the imperfect retention of the gas in some cases , such negative evidence has not much weight . The possibility of thorium as a source must not be overlooked . It would be very difficult to determine experimentally whether the small quantity requisite was present ; but in view of the freedom of sylvine from more common impurities I think it must be considered unlikely . * ' Carnb . Phil. Soc. Proc. , ' vol. 19 , p. 15 .

rspa_1908_0081

0950-1207

The rate of production of helium from radium.

280

286

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

Sir James Dewar, M. A., Sc. D., LL. D., F. R. S.

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10.1098/rspa.1908.0081

Thermodynamics

Atomic Physics

Thermodynamics

The Rate of Production of Helium from Radium . By Sir James Dewar , M.A. , Sc. D. , LL. D. , F.R.S. ( Received August 6 , 1908 . ) Some time ago I communicated a paper to the Society entitled " Note on the Use of the Radiometer in Observing Small Gas Pressures : Application to the Detection of the Gaseous Products produced by Radio-active Bodies."* In the course of the experiments recorded in that paper it was shown that a pressure of the fifty millionth of an atmosphere could easily be detected by radiometer motion , and that the helium produced by radio-active processes from some 10 milligrammes of bromide of radium could be definitely detected after a few hours . This led me to desire some direct measurements of the amount of helium produced by radium , and through the kindness of the Royal Society in allowing me the use of some radium chloride belonging to them I am able to give a condensed abstract of the experimental results so far obtained . The salt employed was the 70 milligrammes of radium chloride prepared by Dr. T. E. Thorpe , E.R.S. , for his determination of the atomic weight of radium , the preparation of which is fully described in 'Roy . Soc. Proc. , ' A , vol. 80 , p. 298 . The apparatus used for the measurements was a McLeod gauge in the construction of which no indiarubber joints were used ; the mercury reservoir being connected to an exhaust pump , while the elevation and lowering of the mercury was carried out by admitting and exhausting air in the reservoir . The air coming in contact with the mercury was purified by passage over stick-potash and phosphoric anhydride . Sealed on to the gauge was a long U-tube containing a \ gramme of cocoanut charcoal placed in a small enlargement at the bend , the whole being arranged for liquid air or other cooling for any desired length of time . The object of the use of this cooled charcoal is to take up and condense all adventitious gases , other than hydrogen or helium , which might arise from minute leakage or otherwise be generated in the apparatus . The radium chloride was contained in a small bottle standing in a cylindrical glass bulb connected by a T-joint to the U-tube . To the other arm of the T was sealed a bulb containing about 15 grammes of cocoanut charcoal for producing a high exhaustion in the apparatus when cooled to \#151 ; 190 ' C. The whole apparatus was well exhausted by mechanical * ' Eoy . Soc. Proc. , ' A , vol. 79 , p. 529 , 1907 . The Rate of Production of Helium from Radium . 281 means , all the glass tubes being heated as well as the charcoal receptacles and the radium chloride . On immersing the receptacle containing the 15 grammes charcoal in liquid air for some hours , while the \ gramme charcoal and the radium chloride were kept hot , an exhaust of 0*00015 mm. was obtained . This charcoal receptacle was now sealed off and the small \#163 ; gramme charcoal tube cooled in liquid air . In two hours an exhaust of 0*000054 mm. was reached . The volume of the gauge and apparatus being approximately 200 c.c. , a knowledge of the pressure in the apparatus gives by a simple calculation the actual volume of gas produced measured at atmospheric pressure and the temperature of the laboratory , and thus the rate of production of helium is obtained . This , referred to the weight of radium present , gives the increment in terms of cubic millimetres of gas per gramme of radium per day . During the first three days the growth of pressure was very small , amounting to about 0*3 cub. mm. per gramme of radium per day . This was , however , practically all produced in the first day . On then heating the radium the pressure was increased to an amount corresponding to an increment of 0*99 cub. mm. The laboratory having to be closed for a fortnight no observations were taken , and as no part of the apparatus was cooled the emanation had free play throughout . About the 350th hour after heating the radium salt the pressure had increased to a value exactly corresponding to the 0*99 cub. mm. increment observed after the first three days . This rate was , however , only kept up for the two succeeding days during which the radium was not heated . On heating the radium a further increase of pressure was obtained ( corresponding to a 1*1 cub. mm. increment measured from the start ) which largely disappeared on cooling the radium and did not reappear on presently heating the radium again . From this stage throughout the next 120 hours the pressure rapidly became less , despite the heating of the radium , which only temporarily and partially restored it ; and after 610 hours a lower pressure was recorded than that obtained immediately after the period of no observations , i.e. after 400 hours . * The charcoal was now heated to 450 ' C. by boiling sulphur . Then on again cooling it with liquid air the pressure was found to have been restored by an amount equal to one-third of that lost as stated above . This , however , quickly disappeared , and apart from fluctuations caused by heating , the radium remained during the next 300 hours at about the value observed just before heating the charcoal to 450 ' C. At this point the charcoal was again heated in boiling sulphur and the previous result was repeated . In the ensuing 150 hours , however , the pressure , after falling a little , remained fairly steady , and then showed 282 Sir James Dewar . [ Aug- 6 a definite and maintained increase for three days , not permanently affected by again heating the charcoal to 450 ' C. The quantity of permanent gas produced up to 1100 hours corresponded to an increment of 0*417 cub. mm. per gramme of radium per day taken over the whole period . At this point the radium was sealed off and the first experiment ended . The large increase over the period in which the charcoal and the radium were both at ordinary temperatures may find some explanation from the unchecked action of the emanation on the charcoal , organic matter and combined moisture possibly present on the walls of the glass tubes of the apparatus , in quantities though small yet large enough to produce the total amount of gas present which , as measured with charcoal at the ordinary temperature , corresponded to a pressure of 1\#151 ; 2 mm. It may be noted that on the supposition of this gas being largely due to a continuous air leak , the amount of uncondensed gases of the helium type thus introduced would be infinitesimal . Apart from the possible presence in the apparatus of organic material the radium itself might conceivably at the beginning have been contaminated with traces of organic matter , and a further experiment was decided on to which these objections could not be applied . In the second experiment the gauge as well as the connecting tubes were well cleaned out with nitric acid and all thoroughly dried . The radium , after the 1100 hours in which it was under high exhaustion and had been frequently heated , was certainly in a more satisfactory condition . Further , to prevent the unchecked action of the emanation throughout the apparatus , the little charcoal condenser was maintained at a degree or two below that of the boiling point of oxygen by the use of old liquid air for a period of about six weeks . A larger quantity of charcoal was used , viz. , 1 gramme , the more effectively to condense out extraneous gases while leaving any helium substantially unaffected . This charcoal had been treated with chlorine at a red heat and subsequently with hydrogen . Beyond this the conduct of the experiment followed the lines of the former one . The mercury pump exhaust was continued for several hours and was carried to 0*002 mm. The large charcoal bulb was then cooled for several hours in liquid air while heating the 1 gramme of charcoal and the radium salt . A pressure as low as 0*00005 mm. was thus obtained when the charcoal was sealed off . On now placing the U-tube containing . a small quantity of charcoal in liquid air the pressure registered was 0*000044 mm. Ihese conditions were maintained for five days , during which a steady 1908 . ] The Rate of Production of Helium from Radium . 283 growth of pressure was observed corresponding to an increment of approximately 0*3 cub. mm. per gramme of radium per day . The radium was then heated with a small Bunsen flame as before to a low red heat , when the pressure was increased by about 40 per cent. This increase showed no sign of disappearing , but during the next week a decided but somewhat irregular growth of pressure was recorded . The radium was again heated , when a further increase of pressure was observed . In the succeeding five days it remained steady , only to be again increased on heating the radium . This treatment was repeated in all 10 times at varying intervals during 1100 hours , and in each case the pressure rose on heating and remained fairly steady on standing . All the observations of the second set of experiments are graphically represented in fig. 1 . A mean line is drawn through the observations taken with the radium heated , giving a steadily maintained helium increment of approximately 0*37 of a cub. mm. per gramme of radium per day . In order to ascertain if any helium was occluded in the cooled charcoal and the surrounding glass , the latter was raised to a low red heat while the tube containing the radium chloride was temporarily cooled in liquid air , with the object of condensing out and localising the emanation coming from the heated charcoal and preventing its access to the gauge . The temperature was maintained for an hour , and then the charcoal was allowed to cool and finally replaced in the liquid air . The radium chloride was then allowed to warm up and was heated to near a low red for a short time . After these alternations no increase in pressure was observed , from which it may be inferred that the occlusion of the helium takes place mainly in that part of the apparatus where the radium chloride is situated . On two occasions the charcoal was cooled in liquid hydrogen , viz. , after 165 hours , and again after 650 hours . The proportionate reduction of pressure was the same in both cases , tending to show that the composition or nature of the gas remaining uncondensed by the liquid air remained the same throughout , although steadily increasing in quantity . In reference to this last point a separate experiment was made in which pure helium under a small tension , produced by heating 0*5 gramme uranite and passing the gas produced over 1 gramme charcoal cooled in liquid air , was subjected to the action of \ gramme of clean exhausted charcoal at the temperature of liquid air and liquid hydrogen respectively . The ratio of the two pressures so obtained was in close agreement with that observed in the radium experiment . A further test of the purity of the gas producing the permanent pressure observed in the radium experiment with the charcoal cooled in liquid air was made by simply cooling the bulb containing the radium in liquid ' Sir James Dewar . [ Aug. 6 , t f \ + \ \ \ 1 \ \ + \ * t \ \ + 1 ? 4 o b \ t \ \ \#163 ; 5 \#151 ; 8 w \ \ +- V Qj | X \lt ; c '\#165 ; sj ' ! Ql \ii \lj 'r-\#163 ; J. i ? 'l + \ \ + J x. J i - + sf \gt ; * \ + .2 ' ~ S , M i_ \#163 ; 2 - 1 # -"-a : . ... q . . $ - 1 a \ o et^ -I* : ? f \#166 ; T \ V \\#174 ; \ + Ji -S r-* r \ \ i 3 J . ^ \ \ \* ll \#163 ; % \#187 ; L 3 s- * \ \#174 ; + \ \ \amp ; \ , -\ i \ \ - C a 1 1 JfL \ \gt ; ft \ \ \ h d \#151 ; \#151 ; i L L C 5 u *5 . \ \ \ \lt ; \ + i\ v , \#151 ; \#163 ; \#163 ; vg \P QJ J5- i \#163 ; S r S V * A ' ' \ \ u o :o o 8 s : e c Z \lt ; i a c c \#163 ; J \#166 ; S 5 -5 \gt ; \ .f " + \ \ i J1 '2 3 i.f 4 ^ * \ cy xO d cy 1 D c f g - 8 rH O - ^X +\#166 ; \ *Vx = \#163 ; 5oS M PH \#165 ; X 4- \ \#174 ; N ' . \#165 ; \#166 ; i i \ \ \ * \ * X \#151 ; l t / X \#166 ; *\#166 ; ( x ' 'i . % S e\#163 ; * t g 8 f 1908 . ] The Rate of Production of Helium from Radium . 285 hydrogen , allowing the charcoal meanwhile to warm up to 0 ' C. If any hydrogen was present in the gas it is certain that there would be an increase of pressure recorded , since although hydrogen is partially absorbed by charcoal in liquid air yet it would not be reduced in pressure by cooling in liquid hydrogen . On allowing the charcoal therefore to warm up , any hydrogen expelled would remain and cause an increased pressure . Inasmuch as an increase was not recorded , it can be safely assumed that no hydrogen is present , and thus the gas pressure measured consists entirely of helium . A confirmation of this was made spectroscopically as follows:\#151 ; Two tinfoil electrodes were placed round the narrow capillary measuring tube of the gauge , near the closed end . These were about 3 cm . long and about li cm . apart and were wired on with thin copper wire . The gas was compressed into this capillary space , as in taking an ordinary measure to any pressure of the order of 2 or 3 mm. , while an induction discharge passed in the gas . The spectroscopic examination of this discharge revealed only the six principal helium lines , mercury , and a trace of the carbonic oxide spectrum . I have shown that the carbonic oxide spectrum always occurs in electrode-less tubes * I am not aware of any previous direct measurements of the rate of production of helium from radium , but in a paper on " Some Properties of Radium Emanation , " by A. J. Cameron and Sir William Ramsay , f the ratio of the amount of helium produced to that of the emanation was found to be 3T8 , and as the amount of the emanation found by them was about 1 cub. mm. per gramme of radium per day , the resulting helium according to this experiment ought to reach about 3 cub. mm. or at least eight times the rate of production found in the above experiments . I am at a loss to explain the origin of such grave discrepancies in the measured amount of the helium produced by radium.f On the other hand , Professor Rutherford , in his work entitled ' Radio-active Transformations/ 1906 , p. 186 , on the theoretical assumption that the a-particle is an atom of helium carrying twice the ionic charge , deduced from electrical measurements that the number of particles expelled per year per gramme of radium would reach 4 x 1018 , and as 1 c.c. of a gas at standard temperature and pressure contains 3*6 x 1019 molecules , the volume of helium produced per year would amount to 0T1 c.c. , which * See paper ( ' Roy . Soc. Proc./ vol. 64 , p. 237 ) " On the Application of Liquid Hydrogen to the Production of High Vacua ; together with their Spectroscopic Examination . " t ' Chem. Soc. Jour.,5 1907 , p. 1274 . X Professor Rutherford , in a paper , " Experiments with Radium Emanation,55 i Phil. Mag.,5 July , 1908 , shows this result is at least ten times too great , his value being of the order 0*11 cub. mm. of emanation per day , whereas from my experiments the rate of helium production is just three times this amount . VOL. LXXXI.\#151 ; A. U 286 Dr. Nicholson . Refection of Waves from a [ June 11 , is equivalent to about 0*3 of a cub. mm. per day . Considering I have found a rate of helium production of the order of 0*37 cub. mm. , the agreement between experiment and the theoretical prophecy of Rutherford is almost too wonderful , substantiating as it does the accuracy of the theory of radio-active changes he has done so much to initiate and develop . I have to express my obligations to Mr. Robert Lennox , F.C.S. , and Mr. W. J. Green , B.Sc. , for aid given in the conduct of these long and laborious experiments . On the Reflection of Waves from a Stratum of Gradually Varying Properties , with Application to Sound . By J. W. Nicholson , D.Sc . , B.A. , Isaac Newton Student , Scholar of Trinity College , Cambridge . ( Communicated by Professor J. Larmor , Sec. R.S. Received June 11 , \#151 ; Read June 25 , 1908 . ) In a variable medium , the velocity of propagation of a train of waves , and the wave-length at any point , are functions of the position of that point . The circumstances of such a propagation have only been worked out in detail in one particular case . Lord Rayleigh , * in connection with the transverse vibrations of a string of variable density , dealt very completely with the case in which the density is inversely proportional to the distance from a fixed point . In his original investigation-)* the results were applied to the corresponding optical problem , and a numerical example given . Although this is perhaps the only interesting case in which a simple exact solution appears possible , yet a close approximation may be made to the existing conditions , even in the general problem , when the waves are short in comparison with the other distances concerned . The development of such a theory , with an examination of some important cases , is the object of the present paper . Let V0 be the velocity of a plane wave-train at some point of a medium , which we may choose as origin , and suppose that the train is advancing along the direction x. * ' Theory of Sound , ' vol. 1 , S 148 . t 'Proc . Lond. Math. Soc. , ' vol. 11 , 1880 , pp. 51\#151 ; 56 ; 'Collected Papers , ' vol. 1 , pp. 460\#151 ; 465 .

rspa_1908_0082

0950-1207

On the reflection of waves from a stratum of gradually varying properties, with application to sound.

286

299

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

J. W. Nicholson, D. Sc., B. A.,|Professor J. Larmor, Sec. R. S.

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10.1098/rspa.1908.0082

Tables

Fluid Dynamics

Tables

]\gt ; . Nicholson . Reflect ' on of from [ June 11 is equivalent to about of a cub. mr per day . Considerin , I a rate of helium production of order of cub. mm. , the agreemen experiment and the theoretical of Rutherford is almost to wonderful , as it does the accuracy of the theory of radio-activ he has done so much to initiate and develop . I to express my to Mr. Robert Lennox , F.C.S. , an Air . W. J. Green , B.Sc. , for aid given in conduct of these long an laborious ) eriments . On the Reflection of from a Stratum of Properties , ? with to Soum J. W. NICHOLSON , ) , Isaac Newton Student , Scholar of Trinity College , ( Communicated by Professor J. Larmor , kScc . . Received June ll , \mdash ; Read , 1908 . In a variable medium , the velocity of ] } ) ation of a train of waves , an the at any are fnnctions of the position of that point . tances of such ation have only ) worked out in detail ir one particular case . in connection with the vibrations of a string of variable density , dealt very completely with the in which the density is inversely ) to the distance from fixec point . fiis original the results applied to optical , and example given . this rhaps th only case in which a simple exacl solution ) ) edrs possible , ) tion may be to existing , even in , when the ore short ill with the other rned . The of such a theoly , an { alnination of ) tant cases , is the object of prescnt Lct the velocity 01 a planc -train at some point of a medium , which 1nay choos as that train is 'Theory of Sound , ' ] . , S 148 . . Math. Soc vol. ] , 1880 , pp. ; 'Collected Papers , ' vol. 1 , 1908 . ] Stratum of Varying Properties . The velocity at the point defined by is taken as a function of only . In order that the results may not be restricted to any particular class of vibrations , let be the vector , of whatever character , whose propagation defines the vibration . In all } ) ortant cases , may be chosen such a vector that the surface conditions are ( i ) is continuous , ( ii ) is contin uous . equation of propagation yields for a simple wave-train , ( 1 ) where is the , which is a metion of If is the value of at the origin , we may assume a relation . ( 2 ) When is preponderant over , the approximate solution of the differential equation may be obtained by a method described by H. A. Webb , *after Horn , but employed earlier as a working method by Stokes and L. Lorenz . Write , ( 3 ) where and are functions of to be suitably chosen . If accents denote differentiations with respect to , we obtain coefficients of and separately to zero , since the terms are of different orders of nitude , we obtain , if A is an arbitrary constant , and if the first term proves negligible , as will appear in the cases treated , Thus the ooenelal solution , when the variable part of is small with , of the equation , ( 5 ) where represents , is obtained in the form . ( 6 ) We proceed to discuss the reflection backward of waves travelling in traversing a medium of this slowly character , and of extent large compared with the . Let the medium be unifortn from ' Roy . Soc. Proc vol. 74 , 1904 , p. ' . and Phys. Papers , ' vol. 2 , p. 334 . ( Euvres Scientifiques , ' vol. 1 , p. 436 et seq. Dr. Nicholson . of [ June 11 to , slowly from to , and again uniforn but differently so , from to , there being perfect material con tinuity and , and values of in the rGmG media and A into the atum is of type to which corresponds a refiect c wav from it , The factor , say , is included in K. In the intermediate variable stl.atntl , the complete direct and reflecte disturloance is brriven by ( 6 ) , in final form medium , where there ca be 110 ative wave , . , If is active index the terminal media in the case , then urface conditions at lead to , . If , where small pure } inaries of the ordel of a , then Thns , ( 10 which ] lives t amplitude and ) hasc of the eflected wave . At we which and are real . ( of the wave-length ) small conn ) Rred with that of the distanc this resnlt takes a simpler Write , ( 1 ] . so that antl is purely real . lf is the of intensities 01 the reflected incident waves , ; 908 . ] Stratum of Properties . lso the increase of phase in the reflection , measured at the front , is rhere . ( 13 ) Jigher nntions may be found desired ; the value the function reviously used be found to a order by writing , in the equation propagation , . . ( 14 ) of tl , The result may be tested by coml ) arison with Lord 's solution or a particular previously referred to , which is mathem tically exact . In that case where is the refractive index between the extreme media , which is to be much different from unity . Thus I , ( 15 ) while Lord Bayleigh 's result is that the reement is close even for only moderately large values of an Absorbing If the second medium have an absorbent effect , the differential equation relating to it has a term proportional to the velocity , and becomes , ( 16 ) where is the velocity of propagation , and is a certain constant whose value must be positive . A ative value would denote instability of the If ( has a time factor , and is the -length at the as before , , ( 17 ) and absorption may be accounted for by the function as complex . But the imaginary tion be essentially negative . If , therefore , the second medium be ) , and therefore , is complex , and we may write whel e and are positive . Cf . a discussion by Lord , of ' Tbeory of Reflection 1 Opaque Bodies , ' ' il . Mag vol. ] , p. 441 ; 'Collected ks , ' vol. 1 , 1 ) . 14 Dr. Nicholson . Jieflection of from [ June 11 Thus , in previous notation , cxp Even when is fairly small the function may be very large , the wave-length be small , and ately , in this case , The ratio of the intensities of the leflccled and inciclent waves becomes li . ( 18 A very moderate amount of bsorption is cient , in these to render the reflected wave practically independent of it , and to destro . entirely the periodic effects with ( thickness of ) , which obtain the absence of value of in ( 18 ) 1nay be called " " " " intensity . In order to obtain a ) of the validity of this reasoning , it sufficient to consider the case of variation of the medium , which will usually occur in practice . The ount of variation in the medium , this analysis can take accoun , nrust first be estimated . In obtaining ( 4 ) , was neglected , then became The ratio borlle to by the greatest term retained in the differentia equation is of order ; and for a law of variation given ) where is distance from the origin , this ) omes , or practically , on reduction , is th " " lneall\ldquo ; if is so reat that ) clror involved is not greatel than about 6 per cent. This may taken as an extrenle case in which the analysis is approximately correct . If is entirely due to , it ) itten --here is real positive , Thus if is the of ) btratnul , contains a factor -lxp value is ) ) ) in the evtreme case , where is the \ldquo ; leng ) . This is very even if is a . The result obtained for is therGfor justified under circumstances . 1908 . ] Stratum of Varyiny Properties . The formula for the transmitted wave discussed below indicates that in a case like the present the intensity of that wave contains a factor , or when the absorption is extreme . It therefore appears that the disappearance of the periodic effect with varying thickness of lnyer corresponds , in general , to an absorption is very complete in less than a ength . The analysis has been shown capable of taking account of this small thickness of provided the rate of change be not too rapid . For any wave-length there is a amount of change to which the method applies , iven by within an error of 6 per cent. A greater absorption requires a smaller mean wave-length . Tlbe ted Wave . In the more general case with previous notation , it may be readily shown that , ( 19 ) which determines the amplitude and phase of the tran mitted wave . When is real , we may , and also in comparison wibh uIlity . Thus and the incident wave , , leads to a transmitted undulation , . ( 20 ) When is complex of the form , and is positive , contains a factor , , making very small . Since this expression in the numerator of ( 19 ) will completely outweigh the smallness of the denominator , there is no appreciable transmitted wave . It is , in , wholly absorbed , in accordance with the character then possessed by the second medium . Discussion of the csults . everting to the case in is real , to which corresponds the formula ( 12 ) , we note that the intensity of leflection , for thickness of the layer , has maxima and minima fter the manner of Newton 's in optics . But since is essentially positive , olute extinction of the reflected waves is only possible when this quantity is zero , and therefore when The possible laws of slow variation to enable this to happen apart those of periodic character are contained in constant or , ( 21 ) Dr. Nicholson . Iteflection from [ June 11 , which lcads only to the case diseussed by . For all other laws , and minima of reffection occur the thickness of the layer varics . of phase in ( 13 ) is ) sured at the plane , where the waves enter the second mcdium . If the is unaltered , except by reversal , co whence ) on lting , where is constant and is index of refraction at a point . This equation caIl be by real values if does not exceed . ) When reflectiou is ttained , to complete but very gradual absorption in the second medium , the of phase must bc . This is a case in which absorption takes place almost entirely in a Reflection of The results have some ) upon the question of the action of a fog upon incident sound waves . The ations of Tyndall* and Henryt showed that sounds of dilferent their order of effectiveness , at a distance , in a remarkable manner . Henry certain conjectures as to the motion of the air , and regarded the consequent refraction as the causing the peculiarities ) distant sounds . Tyndall , however , whose view seems to be in with many of the obsel.vations on fogsignals , postulated the existence of . { Ioccnlent ition of the osphere in such cases , caused by unequal heatill or } the presence of an excess of lnoisture in certain parts . The views of Stokes and Hellry have been independently by who points out that , since ises sound by it to movcl below than above , any other catlbo such a differencc elocity of must also lift the a is in the tnlosphere . the results of 's balloon observations has the of tinle by quarter mile he been ) to vscend : feet . ' rnnh . , p. 18,3 . ' of U.S. trcl for ' lStokes , ' , p. 110 . . PIOC vol. , 1874 , ] ) . ) ' ' . 1908 . ] of dually VProperties . Although Peynolds has pointed out that some of Tyndall 's own obseryations ulay be explained by refraction , yet Lord has cited others appear explicable only by acoustic clouds . , the explanation by refraction of the increase in the of sound when the sky cloudy , or when evening.approaches , appears to of alternative . An atnlosphere with much aqueous vapour present a greatly power of , as well as of heat , and the removal of the sun 's eHccG therefore produce the acousti phenomenon in question . The above allow an estimate of the of { iciency of the cause rned by Tyndall . A portion of the numerator of the expression obtained for the reflected intensity is periodic , and depends both ) the period of the sound and the deglee of heterogeneity of the medium . For the present we are ecting the radiation of heat takes place dnring the of sound . changoe in does not appreciably modify the denominator of , but can cause a great alterstion in the numerator : and sounds whose periods are not far apart can thus exhibit , under certain circumstances , a fair amount of difference in etfectiveness . This is in accordance with observations . Since , moreover , is large compared with the part of , a fairly small amount of variation of the medium , not greatly and , may cause a more considerable change in which may ffice to change the of effectiveness of two sounds . A moder small in may cause to oscillate between the limits , so that the corresponding intensity of reflected sound oscillates between the limits , ( 23 ) which may differ fairly widely . This line of reasoning seems capable of many of the vagaries of sounds coming from a distance . In weather the atmosphere is more homogeneous than usual , and the backward is extremely snlall . The sounds then little tendency to vary their ordel effectiv eness , and are also effective at much reater dQtances than ordinalily . " " acoustic clouds\ldquo ; were farded by him ils mainly dne to the crlCG of of queous vapour in some of the sphele . , tloist . has a of heat than dry air , and the qncnt " " stifling\ldquo ; of sound very , although in air under ordinary conditions the effect is ) Tynd ( not give definite idea of the , nature of ctio of acoustic cloud , which may the ) poses of ilis t , by the of Sound , ' 1896 , Stakes , ' Phil. Mag ) , 18 ; Mntl ] . and ] } , 1 ) . 14 Dr. Nicholson . Reflection of from [ June 11 , sonlld , by it back to its . point . Probably the first ffect both play their ) ) arts . Moreover , as we have , the vard reflection when so1nd enters such a dissipative nnedium tends to lose its , and to be independent of the reflecting llediumvhen the dissipation exceeds a certain limit . The of Stokes that the of the ordinary equation of wave tion is to be ) by , where is the period of sound , is the radiation constant . * Since is snlall pared with , as proved by Stokes , and , it is to be replaced by . cahG , will Slll ) pose that is zero in air , and that the varial ) mediun of theory is the layer of transition between air and acoustic cloud . the transition to take place uniformly , we may replace by oneits tinal . Thus , is to bc lepl by . Now , the general effect of such complex value of has been already to ] ) tendency towards a certain " " " " reflection of the sound . The value of the lantity resent , bears to the value , when , the roximate ratio In ( the cllecC of ) that of the variation of is itself snlall , may ttlite . The ( the exponential therefore btcomc ) V. If this only , there is a reflection is almost limiting , since is ) , a value great the above theory non-periodic reHection to ) . In the absence of evidencet is for a eloud lpoSed 1 of vapour , it } ) ) ears that acoustic cloud act in lnannel , if the layer of th sulliciently In ( the ) ) wonld seem capable of nation 1 his . The of Civeness of sounds noticed 011 durin ) ) is change }coustio clo , the on may to found . Lord ointed o the scuce of an acoustic not inllncncc so of vely tion , as the ) of Cf . , ' of Sound , ' ol . 2 . I the 1908 . ] Stratum of dually Varying Properties . a , in the same manner as the proJonged sound given out by a siren . Moreover , the diffraction round obstacles may be less effective for sounds of short duration . These effects of the duration of the sound are , however , independent of the considerations treated at present . Upward of Sound in the The presence in the ) of a tempcrature gradient , and of a variation of density due to gravity , each cause the circumstances of propagation of sound to vary with the . When sound travels upward , each will cause a certain fraction to be reflected back to the . We may consider the effects separately , since both are small , and will first treat that of the temperature gradient . Let be the velocity at a height , and that at the earth . If , are the corresp d pressures and densities , then in convective equilibrium constant , and Since we deduce . ( 24 ) If is the period of the sound , and whele Hence , since at the surface , , the intensity ratio of sound reflected from the stratum of height , by the formula ( 12 ) , becomes Since is very small , we . nay write , retaining only its lowest powers , If is -length at the of the earth , there is extinction of reflected sound when , ( 26 ) where is an integer . For air under ordinary conditions we write per second , and Dr. Nicholson . flection of [ June 11 , whence we obtain , ( 27 ) . and are mcasured in feet . The total reflection due to the is thus very small , is a eliodic function of amplitude incleas slowly with in a linear manner . This discussion of case of convecti a general idea of the order of magnitude and mode of variaCion of the effect other distributions of temperature in the of of on lVith the tlsual notation , be ) ) , the equation of } ) ward agation of sound in atmosphore is where is displacement , and , by Boyle 's ] Thus . ( 28 ) ' is the at the SUl.face of the earth , where the velocity is , then or , ( 29 ) where . ( 30 ) The of the formula ( 6 ) is alJd the is or . Moleover , . is the ibility . Thus ( refole 1 the formula ( 12 ) the intensity of sound reflected from is . ( 31 ) undcl conditions , ) his small . 1908 . ] Stratum of radually Properties . the calculation , it appears that for sound whose wave-length , expressed in feet , is . ( 32 ) This effect is of the same character as that of the temperature gradient . For a given elfect of the variation of density is about 700 times as great as that of the temperature variation , provided that the ratio of height to wave-length is great . The type of analysis here employed is applicable to many other pbysical problems connected with short waVes , such , for examl ) , as that of short waves of transverse displacement in an infinite stretched string . TDIx.\mdash ; On Viscosity , onduction , and their Bffect on the Propagation of in a This appendix is an amplification of the previous discussion of . by moist . It was there tacitly assumed that sipation of sound took place merely by radiation of heat during its . This was based on the fact that radiation is the factor most liable to cause appreciable dissipation in sounds of any pitch whatever . Other factors capable of causing it for a smaller range of pitch are viscosity and conduction . If is the kinematic viscosity , and the thermometric conductivity , then the equation of ation of sound , when these dissipative encies alone act , , where . In C.G.S. units and thus cm . per second , and for a sound of frequency cm . It was shown above that the quantity of reflected sound in a val.iable medium , when radiation is present , bears to that when adiation is absent the ratio , or . Here is the quantity in the dissipation ralio due to radiation lone , which occurs in ordinary propagation in a uniform Kirchhoff , 'Pogg . Ann vol. 134 , p. 177 , 1868 ; Lord Ra leigh , ' of } edition , S , 'Wied . vol. 60 , p. 113 , 1896 . 298 Iieflection of ) from Stratum of roperties . Thns cm . and Thus if ( 1 bc not less than about 1/ 500 , radiation is the predominant factor in dissipation of sounds of low pitch , and , therefore , also in reflection the mediunl is not uniform . sound of very pitch , radiation is not so necessarily predominant . In the case of a soulld of frequency ( approx. ) . As to the value of , much ence of opinion exists . Wilmer Duff , * in a series of iments on the late of fall of intensity of sounds of frequency bout 7 , concluded that the great rate obtained could only be explained by to a value in ordinary air . parently valid reasons were for that atmospheric refraction and interllal reflection had not any ) eciable part in the rate of fall , for the conditions of the atr/ losphere and the circumstances of position appear to have widely . Morcover , wind was almost and the vertical tetnperature gradient , the other chief cause of refraction , must have been subject to variation , as obscrvations were taken at noon and after sunset . But Lord Rayleigh , in examinin , these results , concluded that the radiating power must be hundreds of times aller , and attributed Duff 's results to atmospheric refraction , or to some iCherCo nected cause . He suggested , as a possible cause , a delay in the equalisation of difTerent kinds of energy in a compressed not insensible in rison with a period of sound , and thus causi1lg dissipation . This cliticism was supI ) ted by an ument based on the theory of , and ) iment on the lines of that used by Clement Desormes in . The agreement of this experiment with to be and we must therefore ) is not of order unity for dinary air . This justifies the assumption made in a previous portion of this paper that ( ordiuaxy . very lloist the value of does not to been mined entally , and hnvG no irect of il , except ) it gteater than in ordinary . That its valuc ) ) in with that for dry air seems fnirly certain . ) eover , ) viscosity ) conductivity may be , nnd probably are , reater i lloist , thus lending support to the ument on ( 18 ) , adding their effects to those of ( which latter probably ntes , except for sounds of very pitch ) . ' Review , ' March , 'Phil . Mag vol. 47 , p. 308 , 1899 . 'Phil . ' vol. 4314 . 1899 . On the Nature of the in the Electric Spark . 299 Until the values of these quantities , and more especially of , are known for very moist air , the explanation iven 1 ) Tyndall of his own observations must be regarded as a very possible one , for the change of character of the reflection effect of ( 12 ) may readily occur in a sufficiently layer , if the three coefficients be at all appreciably modified by the ence of moisture . We may note that the effect of alone is independent of the pitch . On the of the in Electric Spark . By S. B. MILNEB , D.Sc . ( Lond. ) , Lecturer in Physics , the University of Qheflield . ( Communicated by Professor W. M. Hicks , F.R.S. Received February 10 , \mdash ; Read March 5 , 1908 . ) ( Abstract . ) The main subject of the wolk described in the present paper consists in the examination of the streamers in the inductive spark in the matic of the various metallic lines , It thus forms an extension of the research of Messrs. Schuster and Hemsalec which the examination of the streamers was restl.icted to the inductionless spark . The ) vations were taken by raphing the spectrum as } out by a rotating mirror , the slit of the spectroscope removed and the spark itself , so that each line of the spectrum a monochromatic image of the spark . In order to avoid the superposition of series of streamers which are for1ned in the out of each nlonochromntic , an arrangement of the prisms of the spectroscope used by which , while the images of the spark on the screen were vertical , out in a horizontal direction , the dispersion of the spectrunn was in a dilection to the horizontal . this arrangelnent the series of streamers corresponding to each metallic line becomes distinctly separated from the others . Photographs of the streamers in the spectra of the sparks fionl following metallic poles were taken , in each case with a number of diHelent inductances in series with the spark : aluIlIinium , antimony , bisnruth , cadmium , calcium , copper , lead , magnesium , mercury , nickel , } ) latinunt , 'Phil . Trans , vol. 193 , p. 189 ( 1900 ) .

rspa_1908_0083

0950-1207

On the nature of the streamers in the electric spark.

299

300

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

S. R. Milner, D. Sc. (Lond.)|W. M. Hicks, F. R. S.

abstract

6.0.4

http://dx.doi.org/10.1098/rspa.1908.0083

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0083

10.1098/rspa.1908.0083

Atomic Physics

Electricity

Atomic Physics

On the Nature of the Streamers in the Electric Spark . 299 Until the values of these quantities ( / z , v , q ) , and more especially of q , are known for very moist air , the explanation given by Tyndall of his own observations must be regarded as a very possible one , for the change of character of the reflection effect of ( 12 ) may readily occur in a sufficiently large layer , if the three coefficients ( / x , q ) be at all appreciably modified by the presence of moisture . We may note that the effect of q alone is independent of the pitch . On the Nature of the Streamers in the Electric Spark . By S. R. Milner , D.Sc . ( Bond . ) , Lecturer in Physics , the University of Sheffield . ( Communicated by Professor W. M. Hicks , F.R.S. Received February 10 , \#151 ; Read March 5 , 1908 . ) \#187 ; ( Abstract . ) The main subject of the work described in the present paper consists in the examination of the streamers in the inductive spark in the monochromatic lights of the various metallic lines . It thus forms an extension of the research of Messrs. Schuster and Hemsalech , * in wThich the examination of the streamers was restricted to the inductionless spark . The observations were taken by photographing the spectrum as drawn out by a rotating mirror , the slit of the spectroscope being removed and replaced by the spark itself , so that each line of the- spectrum formed a monochromatic image of the spark . In order to avoid the superposition of the series of streamers which are formed in the drawing out of each monochromatic image , an arrangement of the prisms of the spectroscope was used by which , while the images of the spark on the camera screen were vertical , and drawn out in a horizontal direction , the dispersion of the spectrum was in a direction of 45 ' to the horizontal . By this arrangement the series of streamers corresponding to each metallic line becomes distinctly separated from the others . Photographs of the streamers in the spectra of the sparks from the following metallic poles were taken , in each case with a number of different inductances in series with the ' spark : aluminium , antimony , bismuth , cadmium , calcium , copper , lead , magnesium , mercury , nickel , platinum , * ' Phil. Trans. , ' A , vol. 193 , p. 189 ( 1900 ) . 300 On the Nature of the Streamers in the Electric Spark . sodium , tin . The chief conclusions which are drawn from the research are as follows:\#151 ; ( 1 ) The streamers in the inductive spark consist of metallic vapour , the atoms of which are charged , and the motion of the vapour towards the centre of the spark gap is mainly due to the action of the electric force of the spark on the charged atoms . The chief evidence in support of this consists in a number of photographs in which the streamers move back again towards the poles as the oscillating electric field of the spark reverses its direction . ( 2 ) Very great differences were found in the appearances of the streamers which correspond to the different lines of the same metal . The streamers may be divided in this respect into three classes , between which there is in most sparks a sharp distinction:\#151 ; { a ) Blurred streamers , which are often partly masked by the whole spark gap being filled with their light . These invariably correspond to lines prominent in the arc . ( 6 ) Sharply-defined streamers , which appear throughout the whole time during which the electrical discharge lasts . These correspond to pure spark lines , i.e. , lines which are not present in the arc under ordinary conditions , ( c ) A third class of streamers show very brightly at the first oscillation , but fade away so rapidly that they appear for only one or two oscillations , even when the other lines , initially no brighter , show 10 or 12 . These lines are very sensitive to the influence of self-induction in the circuit ; they are very bright in the condensed spark without inductance , but disappear from the spectrum altogether when a moderate inductance is inserted . By studying the duration of the lines in the inductionless spark , the difference between the three classes of streamers is found to be solely a question of the duration of the luminosities of the metallic lines to which they correspond , the arc lives having a long , the spark lines a short , and the " condensed spark " lines a very short , duration . ( 3 ) No other difference than this one of the durations of the lines has been discovered in the character of the streamers . The photographs obtained show clearly that the velocities of the streamers corresponding to the different lines in the same spark are the same , in spite of the different character of the streamers .

rspa_1908_0084

0950-1207

Transparent silver and other metallic films.

301

310

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

Professor Thomas Turner, M. Sc.|Professor J. H. Poynting, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1908.0084

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10.1098/rspa.1908.0084

Optics

Thermodynamics

Optics

301 Transparent Silver and other Metallic By Professor Thomas Turner , M.Sc . , University of Birmingham . ( Communicated by Professor J. H. Pointing , F.R.S. Received May 9 , \#151 ; Read May 28 , 1908 . ) [ Plate 1 . ] It is well known that when thin leaves of gold or silver are mounted upon glass and heated to a temperature which is well below a red heat , a remarkable change of properties takes place , whereby the continuity of the metallic film is destroyed . The result is that white light is now freely transmitted , reflection is correspondingly diminished , while the electric resistivity is enormously increased . A simple method of illustrating this extraordinary change is to mount a .sheet of silver leaf between two clean lantern plates , clip them lightly together by means of wire paper fasteners or other suitable means , and then heat gradually to a temperature of not more than 500 ' C. This can be done conveniently by placing the plates on a thin fire-brick in a cold gas muffle , and then raising the temperature to the desired point . The gas should nowT be turned off , and the glass plates allowed to cool slowly , so as to avoid cracking . They can then be bound with strips like an ordinary lantern plate , and a permanent example of transparent silver is obtained . It will be found that such a plate transmits the light of the electric lantern almost as readily as ordinary glass , and does not produce any change of colour . The great transparency of the film may be shown by placing the plate upon printing or writing , and photographing the characters through the plate . Every detail of the characters can be reproduced with remarkable clearness . At first sight it is perhaps difficult to conceive that so distinct an impression could be -obtained through what was originally a perfectly opaque sheet of silver , and which has only been once heated to a moderate temperature . The properties of thin metallic films have already been studied by a number of observers and from several points of view . Thus Faraday , in his classical Bakerian Lecture , * dealt with finely-divided metals in connection with the undulatory theory of light . G. T. Beil by , starting from Faraday 's observations , studied the properties of annealed gold leaf , f and afterwards showed the bearing of such facts on the hard and soft states of metals , t while * ' Phil. Trans. , ' 1857 , p. 145 . + ' Roy . Soc. Proc. , ' 1903 , p. 226 . * * PhiL Mag. , ' 1904 , vol. 8 , p. 258 . VOL. LXXXI.\#151 ; A. X Prof. T. Turner . [ May 9 , Garnett has given at length the mathematical considerations arising out of the work of Faraday and Beilby.* Films of other metals have received attention , as in the work of Wood , f who deals with alkali metal films produced in vacuo , and Stone , J who describes the formation and properties of thin films of platinum . Another branch of the subject is that of finely-divided metals in solution or suspension ; on this there is a voluminous literature . In connection with a closely-allied branch of the subject , it may be recalled that Sir H. Davy , in 1813 , showed that the colours produced during the tempering of steel were due to oxidation , S while the author proved that the colours so obtained depend upon both time and temperature . It was also further suggested that the film of oxide so produced was transparent.il Transparent Gold.\#151 ; In Faraday 's experiments the gold leaf was usually mounted on a single sheet of glass . The alloy was 924 parts gold , 24 parts silver , and 12 parts copper ; it was beaten so that 278,000 sheets would be required to make a thickness of 1 inch . In this state it transmitted green light ; but it lost its green colour , and transmitted white light when heated in a bath of oil for a few hours to as high a temperature as the oil would bear . The same result was obtained though the supporting material was changed and the surroundiug medium replaced by air or by ; carbon dioxide . It was also found that gold leaf , rendered colourless by heating in a muffle , again transmitted green light after being burnished . In tests conducted by Mr. Dixon under the direction of the author , the gold leaf employed was 975 fine , and its thickness , as determined by weighing , was such as would require 303,000 sheets to make 1 inch . It was mounted between two microscopic slide glasses , and heated in a glass tube surrounded by an outer iron tube . The temperatures were determined by placing a thermo-electric couple in contact with the upper surface of the glass slide . Under these conditions it was found that gold leaf may be kept at a temperature of 500 ' C. for half an hour or more without undergoing any appreciable change other than that of annealing , which is an entirely different effect , and which , as observed by Beilby , occurs at about 275'.1 At 550 ' the green colour begins to fade in a few minutes in air , and still more rapidly in hydrogen . The nature of the change which occurs in the case of gold is made evident * ' Phil. Trans. , ' 1904 , p. 385 . t * Phil. Mag. , ' 1902 , vol. 3 , p. 397 . f ' Phys. Review , 'July , 1905 . S 'Thomson 's Annals , ' vol. 1 , p. 131 . II 'Phil . Soc. Birm . Proc. , ' vol. 6 ( 1889 ) , part 2 , p. 296 . IF ' Roy . Soc. Proc. , ' A , 1907 , vol. 79 , p. 467 . 1908 . ] Transparent Silver and other Metallic Films . 303 by the microphotograph , fig. 1 . In annealed gold leaf the structure is , as shown by Beilby , a crystalline network filled in with translucent amorphous metal . But the microphotograph of gold leaf , heated to 550 ' , shows noncrystalline dark parts where the gold has aggregated and white clear parts of plain glass . The gold itself is therefore opaque , instead of being translucent , and the white light passes through the intermediate clear spaces . In the case of a soft gold cornet from " parting , " the change on heating appears to be a gradual one , and not to present any breaks or sudden changes . Even at 100 ' the cornet shrinks and hardens somewhat , and this change increases up to 750 ' , by which point the metal has acquired a brilliant yellow lustre and a distinct granular structure when viewed under the microscope . No change has been observed in a cornet at about 550 ' which corresponds to the marked alteration which occurs in gold leaf at this temperature . Transparent Silver.\#151 ; Faraday 's observations with gold appear to have led him , and subsequent observers , to conclude that the change which takes place when silver is heated would be equally independent of the nature of the surrounding atmosphere . The nature of the gas in which silver is heated has , however , a profound influence on the result , and of this it is now proposed to furnish experimental evidence . Perhaps the simplest method of procedure is to introduce a sheet of silver foil into a dry test-tube , and to heat the tube till the glass just begins to soften . It will then be found that the silver leaf has shrunk considerably in size ; that it has become white and frosted in appearance , thus losing much of its metallic lustre ; and that it is now sufficiently transparent to allow of objects being readily seen through its texture . It will also be noted that the change is not confined to any one part of the metal , but that it takes place just as readily away from as near to the glass . But if the experiment be repeated with a tube which is filled with coal gas or with hydrogen , it will be seen that the silver retains its metallic lustre and opacity , and only decreases slightly in bulk . Starting from this simple observation , experiments have been made with the object of determining the temperature at which this remarkable change occurs and the conditions under which it takes place . The silver leaf used in these experiments was the purest commercially obtainable . It was found by cupellation assay to be 995T fine ; and when it was dissolved in nitric acid , and precipitated by hydrochloric acid , the solution gave but the faintest discoloration when tested with sulphuretted hydrogen or ammonium sulphide . Subsequent experiments appear to indicate that the only impurity present in appreciable quantity was a trace x 2 Prof. T. Turner . [ May 9 , of oily matter from the process of beating . Its thickness , as determined byi weighing , was such as would require 120,000 sheets to make an inch . In preliminary tests to determine the temperature at which the change from the opaque to the transparent state took place in air , sheets 4\#163 ; inches square ! were heated in a muffle . But in subsequent experiments , to ensure greater ! accuracy , the silver leaf was mounted between two ordinary microscope ! slides of glass 3 inches by 1 inch . In mounting silver thus between two ! sheets of glass , special difficulty is met with if the glass surfaces are perfectly ! smooth and true . The slightest sliding of one glass over the other during 3 mounting is then apt to produce innumerable cracks or fissures in the metal , \lt ; There is also the disadvantage that the air or other gas employed can only ] diffuse with extreme slowness . It is easier to work with at least one of the = slides of commoner glass , or , otherwise , after placing the silver on the lower ] side to sprinkle upon it a minute quantity of powdered glass , which has been previously passed through the 100 sieve . An air-space of something under ; one-hundredth of an inch in thickness is thus ensured , and experience has ; i proved this to be ample . The samples so mounted were then placed inside a small open cast-iron box , and were supported to allow of the introduction of a thermo-couple under the specimen and above , but near to the bottom of the box . The box was then placed in a cold muffle , and the temperature raised to the desired point , when the sample was removed and allowed to cool at once to the temperature of the air . One important incidental advantage in the use of microscope slide glasses is that the danger of cracking during heating and cooling is very slight , while with the larger glass plates disappointment from fracture during . cooling is not unusual . In these experiments no change was observed in the properties of the silver at temperatures below 200 ' C , but at 240 ' transparency commenced , and this was practically complete at about 390 ' . The change is a gradual one , and depends upon both time and temperature . A sample heated to 400 ' as rapidly as is safe on a glass slide , or , say , in about 10 minutes , is then quite transparent . To render this gradual change apparent , a series , of samples was arranged , and these were laid upon sensitised photographic plates . They were all exposed to the same standard light , and developed in exactly the same manner . A few of the results are given in fig. 2 , from which it will be seen that some light began to pass after the sample had been heated to 240 ' transparency increased at 260 ' ; became marked at 335 ' ; and was practically complete at 390 ' . In each case the temperature employed was written in ink on the back of the glass slide , and the clearness with which these figures s can be read is a simple measure of the relative transparency . 1908 . ] Transparent Silver and other Metallic Films . 305 Silver remains quite opaque , if heated in coal gas to about the same temperature as would render the metal quite transparent if heated in air ; and , even at 500 ' , no change is observed in an atmosphere of coal gas . Silver which has been made transparent by heating in air does not become opaque if heated in coal gas to 510 ' , though it is very slightly darkened in colour , and a transparent yellow stain is produced on parts of the glass . Very little effect is produced when silver is heated in charcoal powder for half an hour at 500 ' , while the metal may be heated in hydrogen to 400 ' without Sensible alteration . The structure of transparent silver , when viewed under the microscope , is seen in fig. 3 , which shows the appearance of silver leaf heated between glass slides for a few minutes to 390 ' . In this case the change has progressed to such an extent that it is practically complete . The magnification is the same as was employed for the specimens of gold , and on comparison it will be noted that the aggregations in the case of silver are much smaller than with gold , and the opacity of these separate particles is much less marked . In another series of experiments , silver leaves were heated in a porcelain boat in a combustion tube , in an atmosphere of oxygen which had been previously passed through potash and strong sulphuric acid . It was found that the silver became transparent at about the same temperature , and at least as readily as when heated in air . When still higher temperatures were employed , it was found that leaves of silver , if rolled up into small balls and heated in hydrogen to 750 ' , shrunk in size , and resembled in texture annealed cornets from gold assaying , the opacity and lustre being retained . But when heated in air to 750 ' the leaves crumbled down to a nearly white powder which occupied much less space than in the previous experiment . It would therefore appear that oxygen is necessary for the production of this remarkable change ; that the nitrogen of the atmosphere plays no part in the action ; and that the nature of the supporting material may be changed without affecting the result . When transparent silver is examined under the microscope , with moderately high magnification , it is found to have a somewhat arborescent form , and the separate granular masses appear to have some measure of transparency when viewed by transmitted light . This fact , together with what has been above stated , appeared to point to the formation of an oxide of silver which is transparent . Gravimetric experiments were therefore conducted in which carefully weighed quantities of silver leaf were heated in air or oxygen for various times and to gradually increasing temperatures . The conclusions arrived at were entirely negative . The weight taken was usually about 0T25 gramme ; sometimes a very slight loss was observed , followed by a Prof. T. Turner . [ May 9 , slight gain . But the maximum loss was never more than 1 milligramme , and the maximum gain was also never more than a milligramme . As the leaves were contained in a weighed porcelain boat , the differences observed were not much in excess of the experimental error , and the maximum gain in weight was not more than one-tenth of what would be required for the formation of silver oxide ( OAg2 ) . Evidence that at least much of the silver is still in the metallic state is afforded by the fact that with careful burnishing the lustre and opacity are restored over parts of the glass , while the white powder evolves copious brown fumes when treated with nitric acid . The method of experimenting was now changed , and four leaves of silver weighing about 0T25 gramme were placed in a glass tube and heated , vacuo , to 500 ' , and kept at that temperature for 10 minutes . The metal , on cooling , was unchanged in appearance and bulk . There was , in this case , a very slight depression of not more than 3 mm. observed on the gauge of the Sprengel pump , and a slight sublimate was obtained . Under the microscope this was seen to consist of minute oily globules , due apparently to a trace of fatty matter from the goldbeater 's skin . As the metal was unchanged when heated vacuo , oxygen was admitted to a pressure of 1/ 5 of an atmosphere , this corresponding with the amount of oxygen present in air . The metal was heated to 400 ' and maintained at this temperature for five minutes . On cooling it was found to be completely changed into a white more or less powdery material of much diminished bulk . The change took place in a similar manner when the pressure of oxygen was reduced to 1/ 25 of an atmosphere ; and also , though perhaps with less readiness and completeness , when the pressure of oxygen was only 15 mm. In each case the height of the mercury gauge was observed at the beginning of the experiment , and also at the end when the tube had again cooled down , and in no case was any appreciable alteration noticed in the volume of the oxygen . Whatever the exact nature of the change which takes place may be it is evident that though oxygen is necessary the metal does not increase in weight or the oxygen change in volume . In seeking for an explanation of an action of oxygen on silver , which does not lead to an increase of weight , reference may be made to some experiments of Plattner mentioned by Dr. Percy , * in which it was found that finely divided silver when heated to moderate redness in a stream of oxygen yielded a sublimate of metallic silver ; it was also shown that oxide of silver is decomposed if heated in oxygen . Dr. Percy carefully repeated Plattner 's experiments , but with negative results , so far as a sublimate of silver is * 4 Gold and Silver/ p. 18 . 1908 . ] Transparent Silver and other Metallic Films . 307 concerned . Probably in the absence of temperature measurements the conditions were not identical , as there is evidence of the volatility of silver at relatively low temperatures . Thus Professor Richards* states that silver shows signs of vaporisation when heated vacuo in quartz vessels to 680 ' C. In the author 's experiments on a number of occasions a minute sublimate was obtained when silver was heated in a combustion tube in a current of air or oxygen to somewhat above the point at which transparency is practically complete . This sublimate had every appearance of being white metallic crystals when viewed under the microscope , and a photograph of such a mirror at a magnification of about 120 diameters is given in fig. 4 . It appears probable , therefore , that at temperatures ranging from about 240 ' to 400 ' C. very finely divided silver combines with oxygen , but that the oxide so produced is again decomposed , the result being the production of metallic silver in a peculiar amorphous condition , in which it is transparent in moderate thicknesses . At the same time , there is sometimes a very minute , though appreciable , volatilisation of the metal , especially when it is heated to about 700 ' in a current of air . [ Added July 16.\#151 ; It may be added that transparency can only be produced with thin sheets of silver . The thinnest sheets obtained by rolling are about 1/ 2000 to 1/ 3000 inch in thickness . Tests made with sheets of silver about 1/ 2300 and 1/ 2800 inch in thickness have shown that no transparency is observed even after heating in air or oxygen to 500 ' for 24 hours . By beating such sheets , leaves of about 1/ 10000 inch in thickness are obtained ; but these , too , show no transparency on heating . Assuming the action to take place equally on each side of the leaf , it follows , therefore , that it does not penetrate to a depth of 1 / 20000 inch . In other words , it has been proved to occur , in the earlier experiments , through a thickness of about 4/ 1000000 inch ; it has also been shown not to take place through 50/ 1000000 inch . The intermediate thicknesses have yet to be examined . ] Transparent Copper.\#151 ; The examination of the effect of varying temperatures under different conditions upon other metals , in the form of thin leaf , was a natural result of the preceding observations . The first metal taken for this purpose was copper , which was obtained of a thickness of about 1/ 75000 inch . The metal was practically pure , as on analysis no trace of other metals could be observed in the necessarily moderate weights employed ; tested volumetrically against electrolytic copper it decolorised exactly the correct volume of standard solution of potassium cyanide . This copper leaf when heated between glass slides in coal gas , in hydrogen , or * 4 Electro-Chem . and Metal . , ' 1908 , p. 115 . Prof. T. Turner . [ May 9 " when embedded in fresh charcoal powder , retained its metallic lustre and opacity unimpaired . But when heated in air it gradually assumed the well-known succession of colours , including orange , red , purple , blue , and green . These colours repeated themselves in order several times , each time becoming less separate and distinct . On examining the specimen by transmitted light , as by holding it up by daylight to a window , it was found that in parts a remarkable transparency had been obtained . The first effect is the production of an emerald green colour of great transparency and brilliancy with further heating this passes into a light olive , then into a darker shade , and ultimately into a dark port wine colour . It is easy to obtain the whole of these transparent colours by heating the sample somewhat rapidly , when the coloured films will form round the outside of the sheet , while in the middle of the plate will be left a small island of untarnished copper . If the sample be now rapidly cooled and examined , it will be found that a brilliant transparent green band surrounds the unaltered metal , while the other shades tone off to a dark reddish transparent brown at the edges . A simple method of studying the nature of the change is to take a glass beaker about 6 inches high , and suspend vertically in the centre of this a leaf of copper between two glass slides . This will leave about 1| inches clear at the top and bottom . The beaker should be covered with a sheet of asbestos board , and surrounded with a thin sheet of asbestos , except for two holes , one on either side , to act as windows . On heating the beaker from below with a bunsen burner a temperature of about 185 ' should be obtained in the centre of the beaker ; the top of the slides will then be at about 160 ' and the bottom at about 215 ' . On maintaining the heat for about an hour it will be found that the lower half of the copper is now quite transparent , and transmits a light green or olive colour , while the upper part is almost unaffected and opaque . In the middle of the slide the opaque gradually passes into the transparent form . The effect produced when copper is heated in air or oxygen depends both upon time and temperature . Below about 160 ' the effect is very slight ; above 400 ' it is so rapid as to be scarcely under control . By careful heating between 200 ' and 250 ' any desired shade of surface coloration , or of transparency , may be obtained by suitably adjusting the time of exposure . The action in the case of copper appears to be quite different from that of silver . Both metals retain their lustre and opacity when heated in hydrogen , in coal gas , or in fresh charcoal powder . But when copper is heated in air there is a gradual increase of weight from the beginning of the action , and ultimately the weight of oxygen absorbed corresponds with that necessary to form the black oxide ( CuO ) . This oxide , though very dark in colour , Turner . Roy . Soc. Proc. , A. 81 , Plate 1 . Fig. 2 ( 1).\#151 ; Silver heated in air to 240 ' C. Fig. 2 ( 2).\#151 ; Silver heated in air to 260''C . Fig. 2 ( 3).\#151 ; Silver heated in air to 335 ' C. Fig. 2 ( 4).\#151 ; Silver heated in air to 390 ' C. Fig. 2 ( 5).\#151 ; Silver made transparent and reheated in coal gas to 510 ' C. Fig. 3.\#151 ; Transparent silver . 200 V. ( Transmitted light . ) Fig. 2 ( 6).\#151 ; Silver heated in charcoal powder . Fig. 4.\#151 ; Sublimate from heating silver in air . ( Mag. 120 diameters . ) 1908 . ] Transparent Silver and other Metallic Films . 309 transmits a deep olive colour when in sufficiently thin plates . The transparency of the copper is more marked during the early stages of the absorption of oxygen . When copper which has thus been made transparent is heated in coal gas or hydrogen , it becomes once more opaque and recovers its metallic lustre ; but the metal is full of minute cracks through which some white light passes and its reflecting power is considerably impaired . That the transparent film obtained on heating copper leaf in air still contains metallic copper can be proved in a very simple manner , namely , by the action of dilute nitric or sulphuric acid ( 5 to 10 per cent. ) upon the transparent coloured material . The acid causes the immediate separation of bright lustrous metallic copper . At the same time the yellow colour disappears from the film while the copper itself transmits white light . Aluminium.\#151 ; The thinnest sheet of aluminium which is commercially available is about 1 / 60000 inch in thickness , as determined by weighing several leaves . This may be heated between glass slides in air to any temperature up to 500 ' without showing any appreciable diminution of its opacity , and the surface oxidation is apparently slight , even at the higher limit , during one hour . Dutch Metal.\#151 ; Leaves of Dutch metal , of a thickness of 1/ 37000 inch , were heated to various temperatures , and for different periods in air between glass slides . Very beautiful surface colorations can be thus obtained , but no transparency was observed . With the higher temperatures , however , a certain amount of " skeletonizing , " due to the formation of cracks , was usually developed . From this result it is probable that zinc , like aluminium , does not become transparent when heated in oxygen . Sulphides.\#151 ; As sulphur produces coloured films on metals , it appeared probable that transparent intermediate products would be obtained by the action of sulphuretted hydrogen in sheet metals . Preliminary experiments in this direction have as yet yielded only negative results . Cause of Surface Colorations of Metals.\#151 ; The discovery of a transparent stage in the oxidation of copper affords strong support of the view that in all cases where a metal oxidises or tarnishes in such a manner as to produce spectrum colours , this is due to the formation of a transparent film . Gold and silver do not really become transparent , but only aggregate in such , a manner as to permit of the passage of light between the heaped tip particles ; hence there is no surface coloured film . Aluminium and zinc remain opaque ; hence again there can be no surface colorations as these metals oxidise . Copper , and , presumably , iron , yield transparent bodies during their oxidation , and hence produce films which are capable of giving the colours of the spectrum . \#166 ; 310 Mr. E. Cunningham . [ May 29 , The author has pleasure in acknowledging his indebtedness to Dr. T. J. Baker for information from which this research originated ; to Mr. O. F. Hudson for the preparation of the micro-photographs ; and to Mr. J. L. Dixon , Bowen Research Scholar in the Metallurgical Department of the University of Birmingham , for the care with which he has repeated and extended many of the earlier observations . The a-Functions , a Class of- Normal Functions occurring in Statistics . By E. Cunningham , M.A. , Fellow of St. John 's College , Cambridge , Lecturer in Applied Mathematics , University College , London . ( Communicated by Professor Karl Pearson , F.K.S. Received May 29 , \#151 ; Read June 25 , 1908 . ) I.\#151 ; Introductory . The present paper originated in an attempt to discover the significance of certain functions developed by Professor Karl Pearson in a memoir entitled " A Mathematical Theory of Random Migration , " and by him called co-functions . They belong to the category of normal functions , and are applied in the memoir named to obtain an expansion to represent a distriBu-tion symmetrical about a point in a plane . The distribution is not fixed but depends on a parameter a , the function being a function of \#151 ; r being the distance from the centre of the distribution . The fundamental differential equation is { d2/ dx2 + { x + x~l ) d 2 1 ) } = 0 . In the course of the present investigation it soon appeared that the same function led to solutions of the equation of conduction of heat in two dimensions for the case of symmetry round the origin , the time t taking the place of o-2 . In fact , it was found that if a solution of that equation is sought in the form f{t ) ( f\gt ; ( r2/ t ) , that solution is t~ ( n+1 ) ( r2/ R ) , being arbitrary . The function w2n is equal to e~r2/ 4\lt ; multiplied by a polynomial , and is therefore especially adapted to the solution of the problem of the cooling of an infinite sheet , the temperature at a great distance being always zero . The next step in the paper is to generalise the co-functions ; and all the solutions of the equation sj2u = du/ dt are found which are of the form f ( t)cf ) ( r2/ 1 ) \#169 ; , where \#169 ; is a function of the angular co-ordinates of the point

rspa_1908_0085

0950-1207

The \#x3C9;-functions, a class of normal functions occurring in statistics.

310

331

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

E. Cunningham, M. A.|Professor Karl Pearson, F. R. S.

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6.0.4

http://dx.doi.org/10.1098/rspa.1908.0085

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0085

10.1098/rspa.1908.0085

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Mathematics

]\gt ; Mr. E. Cunningham . The nctions , [ May 29 , The author has pleasure in his indebtedness to Dr. T. J. Baker information from which research inated ; to Mr. . F. Hudson for the preparation of the micro-photographs ; and to Mr. J. L. Dixon , Bowen Research Scholar in the Metallurgical Department of the University of crham , for the care with which he has repeated and extended many of the earlier observations . The unctions , ; of Normnl ctions occurring in Statistics . By , JM . A. , Fellow of St. John 's , Cambridge , Lecturer in Applied Mathematics , University , London . ( Communicated by Professol ' Pearson , . Received , \mdash ; Read Jull , 1908 . ) I. ltctor , The resent paper erinated in an to discover the ynificance of certain functions developed ] ) rofessor Karl Pearson in a memoir entitled " " of audom tion , \ldquo ; and by him called to the of normal functions , are applied in the memoir named to obtain an expansion to represent a distribution ical about a point in a plane . The distribution is not fixed but pends on a paralneter function being a function being distance the centre of distribution . The fundamental In the coul se of the ] ) ration it soon appeared that the same function led olutiollS of ) of conduction of heat in bions f. the of sylnnlctr round the , the time taking the place of Tn fact , it that if sohution of that equation is in follD is ) function nrultiplied ) a ) olynoUlial , is to sclution of the blenl of the of infinite , the a ( distance ) vays zero . in the to ; and all the of the equation fonnd which of the form is a lh ' co-ordinates the point 1908 . ] of occurring in Stafistics . 311 alone . The result is that , as in other problems , is a spherical harmonic , or circular function , in the case of three and two dimensions respectively , that is of the form , while satisfies the generalised equation , where or ) , if This equation is solved by the Laplace transformation , and the ] ution , , taken round a loop contour from infinity round , is denoted by . The asymptotic expansion of is which terminates if either , or is a positive integer . Thus the solutions of in the cases of one , two , and three dimensions respectively are , , being a spherical harmonic of order , which reduce for certain values of the constants to simple well-known ions , . :\mdash ; ( i ) To for , ( ii ) to for , ( iii ) to . The one-dimensional solution obtained is not new , it practically coincides with the function of the parabolic cylinder , or the functions considered by in connection with the conduction of heat , by Thiele and Charlier in reference to probability , and by Hermit The two-dimensional functions seem to be new , but they arc shown to be the equivalent in polar co-ordinates of the functions considered ) Hermit and the relations connecting the two types of function are It is shown in the paper that a.ny function of and can be anded in the form , whele and a proof of the ence and validity of the is iven in the case where is independent of , with all indication of the extension to the general case . Hence a series is obtained solution of the * Liouville , I and II . ' Reudus , ' vol. ) Mr. E. Cunningham . -Functions , [ May , which reduces for to a function iven all over the } ) viz. :\mdash ; , the coeHicient being obtained as above . This series is shown , by direct expansion , to be equivalent to Laplace 's definite integral solutio of the cooling of an infinite plate , Various other expansions are iven a to Neumann 's expansions of in a series of Bessel functions . The last part of the paper considers the equivalent functions in Cartesian co-ordinates , in terms of Hermite has expanded any function. . It is shown that an equivalent method of Hermite 's expansion is that of equating the successive moments of the series to those of the given , l'unction , with special reference to the best surface for a given frequency distri } ) ution in two dimensions . The series of approximations so obtained is compared with that of which is ultimately the same , and is shown to converge rapidly under the same conditions . An example is then given } coutour lines of a surface obtained by terms up to the fourth order . These contour lines show much similarity with those actually ) rved in statistical work , such as those given by Perozzo in his memoir . The possibility of a fairly close approximation to a iven distribution ) means of a knowledge of the product . moments up to the fourth order is thus blished . II.\mdash ; The 1 . \mdash ; In older to obtain the types of function suitable to the prol ) lelllS mentioned , the most creneral solution of the equation will be found in the form T. , where is a tiull of alone , lnction of , and of the ular inates . begin with , cases and t dimensions are considered in the , it becolJlcs If , and functions of and respectively , we have ' so that both sides lnnst be independent of and ' Camb . Phil. Trans tlsl , 1904 . 'Annali di Statistica , ' , 5 , 188.3 . 1908 . ] of Functions in Statistics . 313 Hence and ) where is any constant . Thus ( b ) \mdash ; The equation in polar co-ordinates is satisfies this equation , a function of only , and being independent of , the functions and satisfy a constant . Thus , and yain , putting , and , the same procedure as above gives and . ( 2 ) ( c ) Thrce Dimensions.\mdash ; Exactly similar procedure in this case leads to the conclusion that , if . Z. a function of and must be a spherical harmonic\mdash ; say of order must be , and that then satisfies the equation . ( 3 ) ( d ) .\mdash ; In this system of co-ordinates eneral solution is sinh , where satisfies the equation \amp ; . ( 4 ) The equations ( 1 ) to ( 4 ) can be brought under the same form . Putting in the four cases respectively , and also the equations become , using dashes to denote differential coefficients , , ( 6 ) , ( 7 ) . ( 8 ) as the standard form , the particular solution dealt with in this paper will be denoted by he corresponding solutions of ( 5 ) , ( 7 ) , and ( 8 ) are therefore Mr. E. Cunningham . The -Functions , [ May 29 , and the complete solutions of the original equations are ( 9 ) , ( 10 ) , ( ll ) , ( 12 ) The simplest solutions are given in the four cases as follows:\mdash ; ( i ) , ( ii ) , ( iii ) , ( iv ) 2 . of and Laplace transformation of the equation , we find that must tisfy the / ? while the must be such that the same at the miti to nd positive , this will be attained by a colltoul . of a leal axis from to then a circle of Iius ftlld a line the real axis to inhnity . A similar contour the point instead of 1 ) ) ill ) ) 1 and we have for the cxpression ( ) } The the lur ( 13 ) which if either or is a positive The portant c is that in . is a ) osil i : in that ( 14 ) , il this \ldquo ; ' omCb l. This es on is . 1908 . ] Class of Functions in tistics . 3 . jcting Successive lctions . eqnations\mdash ; Thus . ( 16 ) this twice and simplifying by means of the fundamental differential equation , we find . ( 17 ) ( b ) of \mdash ; Since the derivative of any solution of with respect to is also a solution , and since } , we deduce at once , after adjusting the numerical coefficients , the following relations in the cases of one , two , and three dimensions respectively , ( 10 ) , ( 11 ) ) ( 18 ) III.\mdash ; The } 1 . liestrictin the work in this section to functions arising in the one-dimensional case , which are briefly called the ] , it will be convenient to write for and for , and in place of From ( 18 ) we then have ' assuming that is an integer . If is an have , similarly , Thus in either Thus , as a function of is identified the function } . by Conl p Mr. . Cunningham . The -Functions , [ May 29 2 . s.\mdash ; The expansion is , which , if an odd and if is an even Hence , coefficient of in { and thereSore ( 22 and ( 23 the former mation being for even values of and the latter for odd , ether , ( 24 of Tl oing properties will now be applied to obtain an expansion of Laplace 's solution of the problem of the an finite l. We have , , for as as is a function when f to . . in , the subject of as above , we obtain 1908 . ] Class of Functions occurring in Statistics . 317 the following series to represent a the same equation reducing when , to : where In accordance with a remark made above , it may be noted that , when is real , is imaginary , so that the expansion is wholly real . A different method of establishing the same expansion is given below . IV.\mdash ; The cncral co-Function\mdash ; In fcgral Let The asymptotic expansion of the -function shows that the integration in regard to to the infinite upper limit is valid , and the older of integration may be inverted . Thus For every value of the subject of integration is zero to the second order at least when is infinite if is positive , and if ' is negatiye . positive for the sake of argument , , if , or if . Thus but . ( 27 ) , considel the moment VOL. LXXXI.\mdash ; A. Mr. E. Cunningham . The -Functions , [ May , if is a positive integer , is a polynomial subject of integration has no residue at ? . But if is zero a negative integer , the residue is Thus , ( 28 according as , or . In this is not necessarily an and are assumed to be integers . If these results , ( 26 ) and ( 27 ) , be applied in the one-dimensional cas considered above , assuming that , we obtain at one . Consequently , if and is a function satisfying , and reducin ] when to the iven function . Thus the expansion is obtained \ldquo ; nnctions ia to the special values of and suitable to the deyelopment lnnctions in plane , integer . is an relation ( 19 ) , we have . In particular , if we start the function independent of . put ? , so ticular set of functions ulay conveniently be called the -0i -fnnctions . If be , a p , so that is polynomial , . the functions found essed in terms of the fttives ol the with respect to , and Since ivatives of aIly solution of with respect tu co-ordinates ' : and are also solutions , we may expect all ] utious to expressible in ) of tho derivatives with respect to of the solution . 1908 . ] a of Normal ctions occurring Statistics . 319 The following equations may be shown to hold for the planar -functions , , and , therefore , being an , 0 ( 32 ) , we have and giving the values of in terms of and . Thus the connection is established between the planar -functions and Hermite 's functions , to which reference is made below . of Planar 1 . Suppose that a function of and may be expanded in the form where being a parameter . Then , the Fourier method for all values of , we have ' and In order to find the coefficients , we now use the rals developed above , and obtain , ( 33 ) with a similar expression for . Thus , in order to obtain the coefficient of , we make nse of the allied function , which bears to it the relation . The values of and to be taken do not appear , but it will be shown presently that takes all integer values and ? takes those values for which is zero 01 ' a positive . The expansion is therefore one in a series of polynomials . responding expansion in rtesian co-ordinates is iven by 'Comptes Rendus , ' vol. 68 . Mr. E. Cunningham . The -Functions , [ May 2 ! 2 . Th(siolb of the Dcfinite Integrat in \mdash ; An expa1 sion analogous to ( 26 ) will first be obtained . standing , as everywhere , , let ' stand for and for . Then , taking all valu ' and for which are both positive integers , ! . coefficient of ) in ; or , 'taking all half-integer values from to infinity . Again , taking the same range of values for Expanding the last expression by Taylor 's theorem , we have Thus , putting and This gives the proof of the relations given above ( 32 ) . and in ( 35 ) , that expression , where ( uv ) are Cartesian co-ordinates . Hence ' by , where . Now put and . Then the above becomes The sunmlalion oughout for all values of and such that and are ) ositive ihere thus correspond to terl in sulllmation an equal but opposite value of and , 1908 . ] a Class of Normal Functions occurring in Statistics . 321 jhese terms will only differ by being } to ering also that ? is an integer , . Hence . ( 36 ) This expansion is gestive of Neumann 's expansion in the theory of the 3essel metion . Another theorem is given below , which , in some respects , is nearer analogue . The development of the Laplace definite integral follows once from ( 36 ) and is identical with that in the last paragraph ( 33 ) . The nethod of this paragraph shows that the values of and ? are as there tated . 3 . The Expoension of in a of -Functions.\mdash ; As in the last section , ( the summation being taken for the same values of and as above ) \ldquo ; where the summation extends only to values of such that is a ositive i. Thus is expanded in a of -functions in the variable , and from this may be derived , by neans of relations ( 32 ) , the expansions of lsin , differentiations with to , and 4 . The ergence and Validity of the of a Function in a of -functions.\mdash ; The proof of the validity of expansions in a series of normal functions is always a difficult matter , and a general theorem to cover them has yet to be established . A discussion is here given of the expansion series of zonal -functions of a function symmetrical round a point , which seems capable of extension to the general -functions in a plane without much increase of difficulty , though with considerable addition to the analysis . The multiplication of different discussions for each particular set of normal Mr. E. Cunningham . The ctions , [ May 29 , functions seems undesirable , however , and the present investigation will therefore be limited to the single case of the functions . A erent method appears possible in the discussion of the validity of the processes in the development of the Laplace integral given above . In the , the basis of the work is the definite expression for the -function , The expansion to be justified is , where Consider the sum of of the sel.ies A necessary condition is at once obvious for the valiLlity of the processes involved . For , if is very large , since the -contour includes points for which real part of is negative , is not everywhele finite on that contoul But if be such that , no matter reat y may be , , where is some finite ative constant , we ma ] the -contour such that the real part of ? is always oo.reater than , and then the rations lequired are justified . Let Then , ? is finite , is , since tho ? -colltour includes no point at anishes for any value of contour . Also , by the condition to ) satisfied , the of from values of reater than finite nitude can bc tade c slnali as we ) lease by taking ] arge . Thus it to be ememljered that of the is sought when / tends uity , nd that since the contour encilcles the point the contours . have ) assumed such that does not vnnish for a ) of within these ) orcatel D 1908 . ] a Class ] Functions occurring in 323 than umity on the major portions of the con tours , so that the subject of therefore becomes indefinitely great as increases . Consider now the integral divide into two pol . Cions for which ? less than respectively , them and Let be the same integral with the limits and . ( say ) . Considel ' the latter part ; it is absolutely and uniformly and thelefore be written ( say ) . Within the contours considered there is no pair of points which . If the ? -contour be extended so as to include all the which yanishes for points on the 1-contour , we add to the contoul , but not , and this addition since the contour does not include the point , and since is positive . Thus the -contour in may be supposed extended so to include the point at which vanishes for of or Let the 1-contour be now specified more precisely as that part of a ol radius , with centre at , that lies on positive side uf straight line on the real part of ether with rt of line which lies within that circle . This contour is considered in , as follows : , the straight portion ; ) of the curved ljacent to and a small at the centre of the , the remainder . For values of on , the -contour , extended to include to a con tour just surrounding the complete -contour . For on and this contour is extended in the negative direction Mr. E. Cunningham . The -Functions , [ May 29 , to be a short distance on the negative side of . The -contouris considered in three portions similar to . : , the straight portion ; , the arcs contiguous to and subtending an angle at the middle point of , the remainder . Thus the whole of the double integral is divided into nine portions obtained by } one of the partial contours with one of the partial contouls Now remains always finite as and become , except for , a value which lies outside the under consideration . Thus and . Thus , if . Hence , if therefore , on the arc where , and this quantity tends to zero as diminishes , provided remains finite . On the arc , the expression certainly remains finite . On the straight takes its reatest yalue at the point where it adjoins , i.e. is finite on , but along a length of measured from the real axis it becomes comparable with with . with , where is large and finite . Similar considerations apply to the various portions of the -contour , and them together we that each of the portions of the double tends to zero as tends to infinity . Thus for all values of and also tcnds to zero as ) ecomes infinite , for any value of less than ) , in particular if Thus nd is lependent of the lower limit The , and -contours the same , this last will be unaltered if and be interchanged . Hence 1908 . ] of Normal Functions Statistics . 325 where where tends to zero as becomes large ; since , by reasoning similar to that used above , the double with the -contour extended to include the point vanishes as tends to infinity . Thus and Finally , thel.efore , , whatever the value of Apply now the same treatment to the integral , viz. :\mdash ; The coefficient of in the exponential in the second integral being now greater than that of , we carry out first the integration in regard to . The first part of is , as above , equal to . Thus In extending the -contour of this last integral , instead of the ? / , -contour as in , we add to it ; , as above , standing for a contour encircling , and not zero . As before , the extended integral is zero , and therefore the unextended integral equals . Thus for all values of We have . E. -Fnmctions , [ May 29 , and ; , therefore , finally and if the function is continuous , It will ) noticed that success of ) method depended on the s1ubject of in the a eoInetrical progression . If the general expansion for the unsymmetrical case is treated similarly , the subject of integration is a double progression and may be treated , but the analysis will not bc carried out th th 1 . was lneutined at the outset , the linear -functions have been nised for some time as suitable fnnctions purpose of a given frequency distributioJl to any degree of } ) proxinlation . The method commonly ) in fitting the coefficients is to make the btccesve Dloments of the equal to those of the iven distribution . * But it does not ) to ] ) been noticed that this nlethod i exactly equivalent to of ) the coefficients . , is { immediate the fact that the lnctioIt : is a ( . Thus the ) thod by luoments , comnlon]y as an artificial of obtiig a series to repl.esent a distl iution of a particular ) ' ) , is leally the and unique of by a of -fUnctions . anothcl thod of a series of successive approximations to a tril ) in the } ] if be developed , leads to series of -functions . The lelld the cociticicnls is that of the molnents , so tcly the series obtained by must ansio in -functions . lt vever , that , for statistical ( ions , of meant u by give . cit. . Phil. ) 1908 . ] Class of Norr Functions occurring Statistics . 327 more rapid approximation . The argument as to the nitudes of the coefficients , however , appears equally applicable to the present series . It is shown in the memoir quoted that the coefficients rapidly only if the standard deviation be small . Let this be assumed in the series , where . Then , if be the moment of the distribution , and , we have and in pal'ticular and hence , since is the standard deviation , is zero . ument , is of the order of magnitude itnd hence , by taking the above equations for different values of , we see that the coefficient is of the order \mdash ; the word order being used in the same sense as in the work cited . Thus the coefficients will diminish with about the same rapidity as the quantities , while the of the equations much pler . Pass now to the case of two dimensions . eference has been made to Hel.mite 's note on the expansion of a function in a series of the form , vilich l been shown to be equivalent to an expansion -functions . It is a problem of some importance to obtain a series to represent a distribution in correlated characteristics , such , for example , is considered by Perozzo in his memoir on the of wife The lines of equal by erozzo are far from being concentric ellipses , as they be if the frequency surface were a Gaussian normal surface . It is worth . whether a few terms of the expansion in -functions cau be made to an approximation that is tolerably near . The theol.etical possibility of repre- the distribution by a is not considered , the conditions of validity of the expansion are lnlost certainly satisfied . Hermit gives a method of obtaining the coefficients . Using the notation , ? and are both polynomials of degrees in and . If be exlJanded in the form , it is proved that 'Annali di bistica , ' 1883 . Mr. E. Cunningham . The -Functions , [ May 29 , where is a numerical constant depending on and alone . Now it will be much more convenient in practice to obtain the coefficients by means of the successive moments to the corresponding moments of the series . This is equivalent to Hermite 's process , a polynomial ; so that above is a linear function of the moments . Putting ? can be reduced by successive integrations by parts . If , we have whatever the values of and , and , similarly , the is zero if ? whatever the values of and . But if , and ! and if and and this last is zero if is an odd the notation , and , if we multiply the equation by , and integrate , we have there terms on the right , of which those { zero in which the sum of the subscripts of is odd . . the first fe equations , by choosing the origin at the mean of the distribution , and the constants so that the constants all become zero . By this means the normal face that best fits the distribution is obtained , viz. , But the fact the contour lines in the example quoted are by no means concentric ellipses with centre at the mean shows that the fit is not yet sufficiently good . The next approximation to the distribution is 1908 . ] Class of Functions occurring in tistics . 3 The equations the coefficients of the fourth order terms are : , etc. Thus in terms of the moments the coefficients are quickly obtained , and 's argument as to the rapidity of approximation applies equally well here if the standard deviations are sufficiently small . But the labour of obtaining the moments is very great , and a suitable example for testing the closeness of approximation is not available . What will be done here , therefore , is to show more or less generally how , in a simple case , contour lines can be obtained which are approximately of the type found in the example given above ( see diagrams , Perozzo , loc. 2 . An of Contour Lincs Two uensions.\mdash ; The example chosen here is that of . and it will be assumed that there is symmetry about the line The most general first correction is , where , , . In ular , if , and is negative , vanishes on the straight line , and the ellipse ; on the positive side of it is positive outside the ellipse , and }ative inside , and vice on the negative side of Thus the effect of the correction , while not altering the mean or second moments , is to introduce skewness about , the maximm ordinate being displaced in the negative direction along . Outside the ellipse the surface is depressed on the ative side of , and raised on the positive side . The zero-line of is . shown in the figure ( curve A ) for The contour lines on the poSiGiyG part of the surface will now be oval curves . ounding the point of maximum ordinate with their reatest width parallel to , and crowding closely together in the neighbourhood of the zero curve . These have not been shown in the figure to plication . variation in their form could be produced by introducing a term , but the effect of skewness is again the most noticeable . Consider now a fourth order correction , which for the end in view has been conveniently taken to be The which this is is drawn in the figure ( curve B ) , and ortions of the plane are indicated in which it is positive and ative respectively . Thus the effect of this COl.rection on the contour lines in the hbourhood of the maximum ordinate is to contract them in the direction The , and to in direction . A sel.ies of contoul lines is drawn for ; so ) the lines shown are curves of equa ] frequency for the function The curves arc distinctly similar in ) to Perozzo 's , though no attempt ] been made at exactly what the coefficients should be . Probably a better nation would be found with a rather largel coefficient for the order corrcctio1l , as skewness is not so marked it should be . Li of A\mdash ; the B\mdash ; the cve tectic R Similar curves can clearly be obtained there is correlation to be taken into account . For by making the change of variable is turned into a normal surface with correlation , while are linear functions of and Eutectic Research . No. 1.\mdash ; The Alloys of Lead and Tin . By WALTER , B.C.E. , with . A. TUCKEr , . ( Communicated Dr. R. T. Glazcbrook , . Received June , 1908 . ( From Ph atory . ) ( Abstract . ) Attempts to prepare pure eutectic alloys of known constitution led to the discovery of discrepancies between the authors ' experiments and the data on lead-tin alloys published by Roberts-Austen . A complete redeCel'mination of the equilibria of the lead-tin system was therefore undertaken , by both pyrometric microscopical methods . -curves of the taken by both inyerse-rate and differential methods are given ; these , with microscopic data , lead to the equilibrium diagram shown in the . This diHers pcipally from that given by in eutectic point is placed at a concentration of 63 per cent. of tin instead of 69 , that the eutectic line towards the lead end of the series terminates at a concentration close to 16 per cent. of tin , and that a series of transformations the line ) have been found in the solid alloys near the lead end of the series . The discrepancies of these results , as regards the eutectic composition , arise from the more delicate lnethod employed in the presentl.esearch . While alloys within cent. on either side of the true eutectic composition show no detectable diffelence in or -point , the presence of small amounts of excess of either constituent can be detected by the microscope , and in this manner the composition of the pure eutectic has been ascel.tained . As solnbility of tin in solid lead , it was found that the of the eutectic arrest-point in alloys containing less than 16 per cent. of tin -Austen , ' Fifth Report to Rese rell Committee of the Institutio of Mechanicnl iueers , '1897 .

rspa_1908_0086

0950-1207

Eutectic research. No. 1.\#x2014;The alloys of lead and tin.

331

334

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

Walter Rosenhain, B. A., B. C. E.|P. A. Tucker|Dr. R. T. Glazebrook, F. R. S.

abstract

6.0.4

http://dx.doi.org/10.1098/rspa.1908.0086

en

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0086

10.1098/rspa.1908.0086

Chemistry 2

Measurement

Chemistry

Eu tecticResearch . e 1 Similar curves can clearly be obtained where there is correlation to be taken into account . For by making the change of variable 7 } \#151 ; a(\amp ; '-*- if ) , \#163 ; + V = / 3 -f ( .\#171 ; -'+\#187 ; /2 ) is turned into a normal surface with correlation , while c/ dx and 3/ 3y are linear functions of 3/ 3\#163 ; and 3/ 3 rj . Eutectic Research . No. 1.\#151 ; The Alloys of Lead and Tin . By Walter Bosenhain , B.A. , B.C.F. , with P. A. Tucker . ( Communicated by Dr. B. T. Glazebrook , F.B.S. Beceived June 17 , \#151 ; Bead June 25 , 1908 . ) ( From the National Physical Laboratory . ) ( Abstract . ) Attempts to prepare pure eutectic alloys of known constitution led to the discovery of discrepancies between the authors ' experiments and the data on lead-tin alloys published by Boberts-Austen . A complete redetermination of the equilibria of the lead-tin system was therefore undertaken , by both pyrometrie and microscopical methods . Cooling-curves of the alloys taken by both inverse-rate and differential methods are given ; these , together with the microscopic data , lead to the equilibrium diagram shown in the figure . This differs principally from that given by Boberts-Austen , * in that the eutectic point is placed at a concentration of 63 per cent , of tin instead of 69 , that the eutectic line towards the lead end of the series terminates at a concentration close to 16 per cent , of tin , and that a series of transformations ( along the line EFG ) have been found in the solid alloys near the lead end of the series . The discrepancies of these results , as regards the eutectic composition , arise from the more delicate method employed in the present research . While alloys within 1 per cent , on either side of the true eutectic composition show no detectable difference in freezing- or melting-point , the presence of small amounts of excess of either constituent can be detected by the microscope , and in this manner the composition of the pure eutectic has been ascertained . As regards the solubility of tin in solid lead , it was found that the occurrence of the eutectic arrest-point in alloys containing less than 16 per cent , of tin * Roberts-Austen , 1 Fifth Report to the Alloys Research Committee of the Institutio of Mechanical Engineers , ' 1897\#187 ; Messrs. W. Rosenhain and P. A. Tucker . [ June 17 , depended upon the rate of cooling ; by maintaining alloys at a temperature of 175 ' C. for periods up to six weeks , approximately complete equilibrium conditions can be attained , and the study of the cooling-curves and micro* \gt ; S + . .8 31908 . ] Eutectic Research . structure of such alloys has led to the conclusions embodied in the diagram . These conclusions are much strengthened by the fact that the authors have succeeded in preparing alloys very rich in lead for microscopic examination by polishing with levigated oxide of chromium . The transformation in the solid alloys along the line of the diagram has also been studied by means of cooling-curves of alloys , both when cooled direct from fusion and after prolonged heating at 175 ' C. ; a rough quantitative interpretation of the indications of these cooling-curves is given on the lines laid down in a recent paper on this subject.* The changes in i micro-structure associated with this transformation have also been studied , and for this purpose specimens of the alloys , after prolonged heating , were I quenched in liquid air from a temperature just above that of the transformation , and their structure was compared with that of specimens quenched in liquid air from temperatures just below the transformation point and also with others cooled very gradually to the ordinary temperature . The i conclusion arrived at is that the transformation involves the rejection of tin i from the solid solution of tin in lead . The evidence does not support the view * that the formation of a definite compound is involved , but indicates that the change takes place in the solid solution of tin in lead which passes from one [ modification ( / 3 ) to another ( a ) on cooling . The reversal of this change is ' very gradual when the alloy is heated above the transformation temperature . In the case of alloys containing less than 16 per cent , of tin , the transformation occurs at lower temperatures in the alloys containing least tin ; thus while the 16-per-cent , alloy undergoes the change on cooling to 159 ' C. , the alloy with 8 per cent , of tin passes through the change only I when cooled to 72 ' C. For still lower concentrations of tin the change could e not be observed , even when cooling-curves down to the temperature of liquid i air were taken , thus proving that the change in question is not simply due to j allotropy in lead , but that the presence of tin is essential to its occurrence . * A further curious feature in connection with this change is that the lead-rich [ constituent of the eutectic does not take part in the transformation , land must therefore be regarded as retaining the / ? condition in the meta-s stable form . The non-transmission of the reaction from the free lead-rich [ constituent to that forming part of the eutectic is readily explained from I the micro-structure of the alloys , which always show the crystallites of this I constituent surrounded-by a sheath of pure tin , thus separating it mechanically I from the lead-rich constituent of the eutectic . The chemical composition and constitution of the eutectic is deduced from H * Rosenhain , ' Observations on Recalescence Curves , ' Physical Society of London , I January 24 , 1908 . VOL. LXXXI.\#151 ; A. Z Eutectic Research . the equilibrium diagram , and its density as determined by the authors is compared with that of its two constituent phases ; there is a discrepancyi which is ascribed to the persistence of meta-stable in the eutectic ; this difference of density , as found from the density of the eutectic , and as determined directly , amounts to 0'08 , which is too large a difference to be ascribed to experimental error . The volume composition of the eutectic is calculated and found to be T8 volumes of tin to 1 volume of the lead-rich ft body ; this indicates the great extent to which the tin is the predominating constituent of the eutectic . The structure of numerous examples of the lead-tin eutectic is described and illustrated by a number of photo-micrographs ; the eutectic is found to consist of regions or grains , in each of which there is a systematic orientation of the laminations produced by layers of the two constituents . Study of typical examples under oblique illumination and low magnification leads to the view that these grains are true spherulitic crystals , crystals having a regular radiating structure , and it is suggested that this structure is due to the manner in which the predominating constituent has crystallised , leaving the other constituent to fill up the interstices between the radiating dendrites formed by the first . The microscopic features , at all events , preclude the view that the eutectic is an indiscriminate mixture of separate minute crystals of each of the two phases . Finally , the authors describe some eutectic and other lead-tin alloys prepared by compression of powders of the constituent metals , and give photo-micrographs proving that the original particles persist unchanged in alloys prepared in this way , i.e. that there is no real flow or diffusion , at all events in the relatively short time for which these alloys have so far been under observation , even at temperatures up to the melting-point of the eutectic . The authors express their indebtedness to Dr. R T. Glazebrook , F.RS . , and to members of the staff of the laboratory in connection with the work described in the paper .

rspa_1908_0087

0950-1207

The spectrum of scandium and its relation to solar spectra.

335

336

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

A. Fowler, A. R. C. S., F. R. A. S.|Sir William Crookes, D. Sc., F. R. S.

abstract

6.0.4

http://dx.doi.org/10.1098/rspa.1908.0087

en

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0087

10.1098/rspa.1908.0087

Atomic Physics

Biochemistry

Atomic Physics

335 The Spectrum of Scandium and its Relation to Solar Spectra . By A. Fowler , A.R.C.S. , F.R.A.S. , Assistant . Professor of Physics , Imperial College of Science and Technology , South Kensington . ( Communicated by Sir William Crookes , D.Sc . , F.R.S. Received June 23 , \#151 ; Read June 25 , 1908 . ) ( Abstract . ) The greater part of this investigation of the spectrum of scandium under different experimental conditions has been based on purified scandia , generously placed at the authors disposal by Sir William Crookes . The principal results are as follows :\#151 ; 1 . The arc spectrum of scandium consists of two distinct sets of lines , , which behave very differently in solar spectra . Each set includes both strong , and faint lines . 2 . Lines belonging to one set correspond with the enhanced lines of other elements , notwithstanding that they appear strongly in the ordinary arc spectrum\#151 ; * ( ? ) These lines are very feeble or missing from the arc-flame spectrum , and are strengthened in passing to the arc , the arc in hydrogen , or the spark . ( ? ) They occur as relatively strong lines in the Fraunhofer spectrum . ( c ) They are weakened in the sun-spot spectrum . ( d ) They occur as high-level lines in the chromosphere . 3 . The remaining lines show a great contrast when compared with the first group\#151 ; ( a ) They are relatively strong lines in the arc-flame . ( \amp ; ) They are very feebly represented in the Fraunhofer spectrum . ( c ) The stronger lines are prominent in the sun-spot spectrum . ( d ) They have not been recorded in the spectrum of the chromosphere . 4 . The special development of the enhanced lines in the Fraunhofer spectrum , together with their presence in the upper chromosphere , indicates that the greater part of the scandium absorption in the solar spectrum originates at a higher level than that at which the greater part of the iron absorption is produced . 5 . The discussion of scandium lines indicates that while in the case of some elements solar identifications are to be based chiefly on arc lines , in z 2 336 Vapour-pressure and Osmotic Pressure of a Volatile Solute . others it is the enhanced lines which may be expected to show the most important coincidences . 6 . The flutings which occur in the arc and arc-flame do not appear when the arc is passed in an atmosphere of hydrogen . As suggested by Thalen , they are probably due to oxide of scandium . Tables are given , which show the lines of the arc spectrum from 3930 to 6580 , the positions of the oxide flutings , and comparisons of the principal lines of the two classes with the sun , sun-spots , and chromosphere . On the Vapour-pressure and Osmotic Pressure of a Volatile Solute . By H. L. Callendar , M.A. , F.R.S. , Professor of Physics at the Imperial College of Science and Technology . ( Received June 17 , \#151 ; Read June 25 , 1908 . ) It follows by a method given in a recent paper by the author that if the osmotic membrane be assumed to be impermeable to the solute , the formula for the change of vapour-pressure of a volatile solute with hydrostatic pressure , and also the formula for the osmotic pressure which is deduced from it , must be the same as the formula for a non-volatile solute , and should not contain any terms depending on the vapour-pressure of the solute , except in so far as it may affect the hydrostatic pressure of the solution . If , on the other hand , an osmotic membrane is regarded as a vapour-sieve , permeable to the vapour of the solution but not to the liquid phase , the equation takes a different form , depending on the concentration of the constituents in the vapour-phase . If ch C2 , etc. , be the concentrations of the constituents in grammes per gramme of the vapour , and if Ui , U2 , etc. , be the specific volumes of the constituents in the solution , the change of total vapour-pressure dp of the solution for a change of hydrostatic pressure dP is given by the relation , 2cU dP = v dp , where v is the specific volume of the whole vapour-phase . If only one constituent is volatile , this relation reduces to the form U dV = v dp for that 'Constituent .

rspa_1908_0088

0950-1207

On the vapour-pressure and osmotic pressure of a volatile solute.

336

336

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

H. L. Callendar, M. A., F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1908.0088

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10.1098/rspa.1908.0088

Biochemistry

Atomic Physics

Biochemistry

336 Vapour-pressure and Osmotic Pressure of a Volatile Solute . others it is the enhanced lines which may be expected to show the most important coincidences . 6 . The flutings which occur in the arc and arc-flame do not appear when the arc is passed in an atmosphere of hydrogen . As suggested by Thalen , they are probably due to oxide of scandium . Tables are given.which show the lines of the arc spectrum from 3930 to 6580 , the positions of the oxide flutings , and comparisons of the principal lines of the two classes with the sun , sun-spots , and chromosphere . On the Vapour-pressure and Osmotic Pressure of a Volatile Solute . By H. L. Callendar , M.A. , F.R.S. , Professor of Physics at the Imperial College of Science and Technology . ( Received June 17 , \#151 ; Read June 25 , 1908 . ) It follows by a method given in a recent pape* by the author that if the osmotic membrane be assumed to be impermeable to the solute , the formula for the change of vapour-pressure of a volatile solute with hydrostatic pressure , and also the formula for the osmotic pressure which is deduced from it , must be the same as the formula for a non-volatile solute , and should not contain any terms depending on the vapour-pressure of the solute , except in so far as it may affect the hydrostatic pressure of the solution . If , on the other hand , an osmotic membrane is regarded as a vapour-sieve , permeable to the vapour of the solution but not to the liquid phase , the equation takes a different form , depending on the concentration of the constituents in the vapour-phase . If ch c2 , etc. , be the concentrations of the constituents in grammes per gramme of the vapour , and if Ui , U2 , etc. , be the specific volumes of the constituents in the solution , the change of total vapour-pressure dp of the solution for a change of hydrostatic pressure dT is given by the relation , 2cU dV = v dp , where v is the specific volume of the whole vapour-phase . If only one constituent is volatile , this relation reduces to the form U rfP = v dp for that constituent .

rspa_1908_0089

0950-1207

The emission and transmission of R\#xF6;ntgen rays.

337

338

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

G. W. C. Kaye, B. A. (Cantab.), B. Sc. (Lond.), A. R. C. Sc.,|Professor J. J. Thomson, F. R. S.

abstract

6.0.4

http://dx.doi.org/10.1098/rspa.1908.0089

en

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0089

10.1098/rspa.1908.0089

Atomic Physics

Optics

Atomic Physics

The Emission and Transmission of Rontgen Rays . By G. W. C. Kaye , B.A. ( Cantab . ) , B.Sc. ( Lond. ) , A.R.C.Sc . , Trinity College , Cambridge . ( Communicated by Professor J. J. Thomson , F.R.S. Received June 17 , \#151 ; Read June 25 , 1908 . ) ( Abstract . ) A Rontgen ray tube was designed with an anticathode which consisted of a ' number of elements mounted on a small car . By means of an external magnet the car could be moved , and any element desired brought under the beam of cathode rays . The Rontgen rays produced ( by a coil discharge ) passed out through a thin aluminium window , and their intensity was measured by an ionisation method . Some twenty elements were used as anticathodes , and the effects upon their radiations of a number of different metal screens were investigated . The results of the work give rise to the following conclusions:\#151 ; 1 . The relative intensities of the radiations as they issue from the window of the tube , unobstructed by any screen , do not follow the order of the atomic weights of the anticathodes . The order shows agreement with that given by Stark for the relative numbers of cathode rays returned by metallic reflectors . The intensities indicate a grouping of the elements which agrees with , and in features is similar to , that arrived at by Barkla and Sadler from a consideration of the secondary Rontgen rays . 2 . Over a certain region , when screen and radiator are of the same metal , selective transmission of the radiation is manifested , that is , the radiation from the metal is augmented relative to the radiations from other anticathodes . The effect is also present to a less extent when radiator and screen have closely adjoining atomic weights . 3 . This augmentation , when radiator and screen are alike , is most pronounced in the case of the metals of the chromium-zinc group . It is least marked for a substance of low atomic weight such as aluminium , which of the metals tried can be regarded as the most suitable for screens to measure ray intensities . 4 . Generally speaking , the lower the atomic weight of a metal in a group the softer is the radiation for which it shows special transparency . 5 . If the different radiations are cut down by aluminium screens of increasing thickness , the intensities reach ultimate relative values which are not altered by a further increase in the thickness of the screen . These intensities when plotted against the atomic weights of the radiators yield , 338 The Emission and Transmission of Rays . Toughly speaking , a straight line . The relative values of the heavy-atom metals increase somewhat with a rise in potential on the tube . There is reason to believe that screens of other metals would eventually yield much the same sort of curve , modified slightly in the neighbourhood of the atomic weight of the radiator . 6 . When screen and radiator are alike , the absorption per unit mass of unit area of the screen ( X/ p ) is relatively low . One of the consequences of this is that the shape of Benoist 's " transparency " curve , besides depending on the range and degree of absorption , is largely dependent on the material of the anticathode . Bor example , the curve is much straighter for a radiator of aluminium than for one of platinum working under the same conditions . With an anticathode belonging to the chromium-zinc group the . transparency curve has to be modified by the addition of a sharp maximum in the neighbourhood of the radiator . Barkla and Sadler have obtained a similar result in the case of secondary Bontgen rays . 7 . The question of the atomic weight of nickel is gone into , and an explanation put forward to account for the anomalous results obtained with the secondary radiation from this element . 8 . The curve of transmission in which the thickness of screen is plotted as abscissa against the logarithm of the intensity consists , in general , of three parts when radiator and screen are of the same metal . First with thin screens there is a relatively steep portion , which for thicker screens is followed by a straight-line region ; this again is ultimately succeeded by one in which the slope gradually diminishes with the thickness of the screen . Corresponding to the straight-line portion of the curve there is , of course , an exponential absorption . The extent of this region diminishes with the potential on the tube . The preliminary steepness is attributed to secondary radiation ; the extent of the steepening for each metal agrees with that obtained by McClelland working with the / 3-rays of radium . The ultimate flattening of the curve is probably due both to scattering and to the presence of hard primary rays . This latter region may not be detectable if the potential on the tube is not too high ; the absorption curve then indicates homogeneity throughout its length . 9 . When screen and radiator have very different atomic weights , the region of exponential absorption does not appear . The early portion of the logarithmic curve is steepened by secondary radiation , but throughout the whole region the transmission is one in which the coefficient of absorption steadily diminishes as the thickness of screen increases . This result is brought about in the early stages chiefly by scattering , and in the later stages by the heterogeneity of the primary beam of rays .

rspa_1908_0090

0950-1207

The boiling-point of sulphur on the constant-pressure air thermometer.

339

362

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

N. Eumorfopoulos, B.Sc.,| Professor H. L. Callendar, F. R. S.

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http://dx.doi.org/10.1098/rspa.1908.0090

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10.1098/rspa.1908.0090

Thermodynamics

Tables

Thermodynamics

339 The Boiling-point of Sulphur on the Constant-pressure Air Thermometer . By 1ST . Eumoefopoulos , B.Sc. , Assistant in the Department of Physics , University College , London . ( Communicated by Professor H. L. Callendar , F.R.S. Received June 19 , \#151 ; Read June 25 , 1908 . ) The following experiments were undertaken at the suggestion of Professor Callendar , with a view to the redetermination of the boiling-point of sulphur ( S.B.P. ) on the scale of the constant-pressure air thermometer . The experiments unfortunately have not led to a result that can be regarded as final , owing to the uncertainty in the expansion of the glass , but it has been thought desirable to publish the results.* The air thermometer was made of Jena glass , 16 III , and is in construction substantially the same as that described by Callendar.f Fig. 1 will make clear the form of the apparatus , and is drawn roughly to scale . A f m *458 A lii Scale . Fig. 1 . * All measurements of length are given in centimetres , and all measurements of volume in gi'ammes of mercury at 0 ' C. t H. L. Callendar , ' Roy . Soc. Proc. , ' vol. 50 , p. 247 ; ' Ency . Brit. , ' " Thermometry . " Mr. N. Eumorfopoulos . The Boiling-point of [ June 19 , T is the bulb to be heated , and is connected by capillary tubes on the one side to a tap A , and on the other to a second bulb E and by M to the gauges , which will be described shortly ; E itself is connected to an inlet for mercury at L and an outlet at K. The reservoir H is convenient in setting up the apparatus , but is not used in the actual experiments . There is a small air-trap at G , in case air is accidentally introduced in manipulation through K or L. This part of the apparatus which contains the bulb T may be termed the thermometric side ( T side ) . Alongside the above , and quite close to it , is an exactly similar system of tubes , except that the bulb T is missing , so that the capillary tube passes straight across from D to B ( instead of down to C ) , and thence to a stopcock alongside A. This second system can be called the compensation side ( C side ) , and contains a bulb similar to , and alongside , E. The two systems are connected together by the gauges , which are represented in fig. 2 . NOP is a mercury gauge for the rough adjustment of the pressure , while NQP is an oil gauge for the fine adjustment . 0 and Q are three-way stopcocks . It should be added that the plane of fig. 2 is at right angles to that of fig. 1 . In an actual experiment the air in T is limited in the direction of A by a thread of mercury which occupies part of the horizontal tube , in the direction of the gauges by the mercury and oil they contain , while E , which is always immersed in ice along with the corresponding bulb on the C side , contains a variable amount of mercury ; the latter occupies also the capillary tubes to the outlets at H , K , and L. It is by varying the amount of mercury in E that the pressure on the T side is always adjusted to a certain standard , this standard being the pressure of the air on the C side in the bulb corresponding to E. It is thus unnecessary to read the barometer for this purpose . The mass of air on the C side is made as nearly as possible equal to that on the T side . If now the capillary tubes on the two sides are of the same temperature and volume at corresponding points , they exactly compensate M ' AA 0 1908 . ] Sulphur on the Constant-pressure Air Thermometer . 341 one another , as will be shown later . As , however , it is impossible to make the volumes absolutely equal , a rough measurement of the temperature is all that is necessary . It will be noted that there is either mercury or oil at all the stopcocks . they are thus not assumed to be gas-tight . The diameter of all the connecting tubes is approximately 0T , except that of the oil-gauge , which is 0-2 . The latter was read by means of a microscope containing in the eye-piece a scale divided to OOl ; differences of pressure were thus read to 0-001 cm . of oil such as is used in a Fleuss pump . The weighings were made to the nearest milligramme . In order to ensure the delivery of mercury being accurate to this , the open end of each delivery tube was slightly constricted , the tube cut off at 45 ' to the axis at the narrowest part , and the end ground . The concordance of the results obtained when determining the expansion of the glass indicates that the delivery of mercury is probably accurate to 1 milligramme ( 1 in 360,000 on the F.I. ) . It has already been stated that the oil in the oil gauge was that used in a Fleuss pump . The fact that it can be so used indicates that its vapour-pressure must be very low . For additional security a flask containing a sample of this oil was heated to 100 ' C. and kept evacuated for some time to remove any lower boiling substance that might be present . In this operation it was found that the oil dissolves a very small , though appreciable , quantity of air . The density of this sample was determined at 10 ' C. and at 20 ' C. Development of Formula . In the course of an experiment the two bulbs E are always kept at 0 ' C. , or T0 absolute . The bulb T is heated to any required temperature T. No change whatever is made on the C side , but on the T side mercury is added or removed , until the pressures on the two sides are as nearly as possible equal , any residual difference being read on the oil gauge by the microscope already referred to . C side.\#151 ; Let the volume of gas in the bulb E = S , this at temperature T0 ( absolute ) , " " connecting tubes = v , " " 0 " , i S . vmE then \#151 ; + ~ =--- , io 0 V where m = mass of gas and p its pressure , E being the usual gas constant . T side.\#151 ; Let the volume of gas in the bulb T = V at temperature T ( absolute ) , n j\gt ; E \#151 ; Q " To , , " connecting tubes " 6 . , 342 Mr. N. Eumorfopoulos . The Boiling-point [ June 19 , Let the mass of the gas = m + and its pressure = -f then V v + 8vQ m + 8 m \#151 ; fl + p \ m T 6 To approximately , as 8m and 8p are very small quantities 8m_8p V Subtracting the former expression from the latter , we get Y T S \#151 ; Q E j mE r , 8v \#151 ; \#151 ; -t + - 8m--T8p\#151 ; \#151 ; . T0 p p2 6 When obtaining the freezing-point of water ( W.F.P. ) , the bulb T is surrounded by ice . Let us call the corresponding quantities 8p0 , 8v0 , \amp ; o ( note that the latter is not 0 ' C. ) . Then , as p remains practically constant , Yo To So \#151 ; Qo . II c- mE o m---+- \#151 ; To V V p p We thus obtain the following equation : Y_V0 Q-Qo To To S \#151 ; So mE/ rv j x 8vo 8v 1r-+-r\#171 ; p.-\amp ; )+-s~ eo e . It will be noticed that the term involving 8m has disappeared from this equation . It is necessary , however , that 8m should be small , otherwise the compensation will be inaccurate . Multiply throughout by p , the density of mercury at 0 ' C. , so as to convert volumes into weights of mercury ; we thus get , with an easily understood notation , W T Wo To w ps-s , }p+^^ Bp)+ip_p_epy to t0 p V Writing this equation , for shortness , in the form + A+B + C T T0 T0+ + + ' we have finally t _ ( W\#151 ; W0 ) + m\#151 ; ( A + B-t-C)T0 To Wo-m + ( A+B + C)T0 * where t = T \#151 ; T0 , and is the temperature on the scale of this gas thermometer . To obtain the coefficient of expansion of the gas , or its reciprocal To , after observing the W.F.P. , the bulb T is surrounded with steam , thus giving the boiling-point of water ( W.B.P. ) . t is thus approximately 100 , while the right-hand side of the equation contains known quantities . We can hence calculate T0 . In obtaining the S.B.P. the converse of this process is gone through , T0 being now known , while t is calculated . The volumes of the connecting tubes , etc. , were obtained by finding the quantity of mercury required to fill them . When the weight exceeded a few 1908 . ] Sulphur on the Constant-pressure Air Thermometer . 343 grammes , weighings were made in both pans , and a buoyancy correction applied . The following remarks will indicate the corrections that have been applied to the various terms of the above equation:\#151 ; ( i ) W0.\#151 ; This depends slightly on the height to which the ice is piled , as the two sets of tubes do not exactly compensate one another . ( ii ) W.\#151 ; Besides the correction mentioned in ( i ) , allowance has to be made for the expansion of the glass . This will be discussed later . There may be a small pressure correction to apply to W0 and W owing to variations of the external pressure . This , however , never amounts to more than 2 or 3 milligrammes . ( iii ) w.\#151 ; The weight of the mercury in E causes this bulb to expand . As , therefore , mercury is removed , the bulb contracts . The correction due to this pressure effect amounts to 4 milligrammes for the W.B.P. , and to 8 for the S.B.P. There is no external pressure correction , as this effect is compensated . ( iv ) A.\#151 ; As the two air-traps G ( of fig. 1 ) are not exactly of the same volume , S may on this account differ from S0 . This correction is , however , quite small , a change of temperature of 10 ' being equivalent to 6 milligrammes . ( v ) B.\#151 ; This does not call for any remark . ( vi ) C.\#151 ; This term depends on imperfect compensation of the tubes connecting together the various parts of the apparatus . The temperature was read at three points : one thermometer was placed just above BD ( of fig. 1 ) , another just above this at the bend , and a third between N and P ( of fig. 2 ) . The reason for this distribution is obvious . The first thermometer would be considerably affected by the heating of T , the second to a much smaller extent , and the third scarcely at all . Screens were , of course , placed at suitable points to minimise these corrections . The ends of the mercury threads at A ( of fig. 1 ) were read , also the positions of the mercury and oil in the gauges , and the corresponding influence on Sv allowed for . amounts to about 05 gramme , this being almost entirely due to the difference in volume of the junctions at N and P ( of fig. 2 ) . As these parts are at a considerable distance from T , the correction involved lias little uncertainty attached to it . This list of corrections is formidable only in appearance . The corrections are very small . Tables are easily calculated , and the working out of a result involves only a few minutes ' work . Sensitiveness of the Oil-gauge . With the apparatus as used the following table gives the approximate values of the sensitiveness of the gauge:\#151 ; 344 Mr. N. Eumorfopoulos . The Boiling-point of [ June 19 , At 0 ' C. a change of pressure of 0'001 cm . of oil corresponds to a change of temperature of 0a00032 . " 100 ' C. a change of pressure of O'OOl cm . of oil corresponds to a change of temperature of 0o,00060 . " 445 ' C. a change of pressure of OOOl cm . of oil corresponds to a change of temperature of 0o,00220 . " 1000 ' C. a change of pressure of O'OOl cm . of oil corresponds to a change of temperature of 0''0070 . In other words , the sensitiveness diminishes with increase of temperature . This , however , is of no practical importance . The accuracy with which a temperature can be measured cannot be greater than the accuracy with which the fundamental interval has been determined . Thus , at 1000 ' C. the sensitiveness need only be 1/ 10 of that at 100 ' C. , and this is nearly fulfilled , as the above table shows . When , in addition , one takes into account the difficulty of maintaining these high temperatures constant , it would appear that the sensitiveness is all that is necessary . As regards the uniformity of the results , I think separate measurements of the coefficient of expansion should not differ from the mean by more than some 20 units , if the coefficient is expressed by six significant figures . This point will be again referred to when discussing the second series of experiments . Pressure Coefficient of the Bulbs . These are required , but only roughly , for some of the measurements . Thus , in finding the volume of the bulb T by filling it with mercury , the pressure of the latter produces an appreciable expansion of the bulb . This , of course , has to be allowed for . Again , in calibrating the apparatus ( in finding the volume of the capillary tubes ) it was necessary to have occasionally the bulbs full of mercury . It was therefore essential to allow for the changes of pressure produced by running out the liquid . Finally , in the ordinary use of the thermometer , a small correction is required , as has already been explained . The pressure coefficient was determined by filling the bulb in question with mercury , and increasing or diminishing the internal pressure . The compressibility of the mercury has , of course , to be allowed for . The constancy of the coefficient obtained with both small and large changes of pressure affords a very good test of the presence or absence of small air bubbles . The pressure coefficient for the two bulbs E was determined at 0 ' C. , 1908 . ] Sulphur on the Constant-pressure Air Thermometer . 345 while for the bulb T it was determined at 0 ' , 100 ' , and 184 ' with the following results:\#151 ; An external pressure of 1 cm . produces at\#151 ; 0 ' C. a change of volume of 0-00095 gramme . 100 ' C. " " 0-00099 184 ' C. " " 0-00106 Volume of the Before any experiments were made the bulb T was heated for many hours in sulphur vapour to anneal it . This produces an unknown change of volume . In general , therefore , the volume was determined at the end of each series by filling with mercury at 0 ' C. Each determination of the S.B.P. involves , however , a small change of the volume . It was noticed , in fact , that more mercury is run out of the bulb E in heating up T from the W.F.P. than has to be reintroduced in cooling down . This difference has been taken as a measure of the change of volume . The justification for this lies in the fact that it leads to nearly consistent values for the coefficient of expansion , although a total change of volume amounting to nearly 1 in 1000 has to be allowed for in the second series . There is , however , another method by which the volume of the bulb T can be measured . Suppose all the bulbs are in ice , while both bulbs E are full of mercury . Now run out from the bulb E on the C side a weight of mercury somewhat greater than the approximately known capacity of the bulb T , allowing dry air to take its place . From the bulb E on the T side run out the estimated difference of these two volumes , allowing air to take its place , the pressures on the two sides being equal . This can be tested with the oil-gauge . The C side now contains a known quantity of air . Now turning off the stopcocks to*prevent the entry of any further quantity of air , run out from the bulbs E mercury so as to diminish the pressure on both sides . From a knowledge of the weights of this mercury , and the observation on the oil-gauge of any residual difference of pressure , it is evident that by an application of Boyle 's law a value can be obtained for the volume of T. Any deviation of the gas from Boyle 's law is , to all intents and purposes , compensated for . It must be remarked , however , that for a good determination by this method a much more accurate knowledge of the volume and temperature of the capillary tubes must be obtained than is required in the ordinary use of the thermometer . It is , perhaps , due to this that the results to be given immediately are not more closely concordant ; unfortunately , owing to an accident to the bulb at the end of the experiment , the volume could not be checked by the weight method . Mr. N. Eumorfopoulos . The Boiling-point of [ June 19 , The following are the results obtained :\#151 ; First Measurement , filling with mercury\#151 ; January 11 , 1900 ... ... ... . 1276'015^ " 11 " ... ... . 1276-016 Mean , 1276-017 . " 26 " ... ... . 1276-020 J Second Measurement , filling with mercury ( after a further heating in sulphur vapour)\#151 ; March 19 , 1900 1274-828^ " 24 , " 1274-831 l Mean , 1274-824 . " 30 " 1274-813 J Third Measurement , filling with mercury\#151 ; July 13 , 1901 ... ... ... . 1273-912 . The substantial accuracy of this was confirmed a few days later by a rough measurement , which gave 1273*90 ( not carried out in ice ) . After this the bulb was heated for some 15 hours to a temperature of 600 ' to 700 ' C. Fourth Measurement . Boyle 's law experiment\#151 ; June 24 , 1903 ... ... . . 1260-882 " ) " 25 " ... ... ... 1260-831 | " 25 " ... ... ... 1261-054 [ -Mean , 1260-980 . " 25 " ... ... ... 1261-035 j " 26 " ... ... ... 1261-099J It is possible that the above table represents the concordance that one is able to get . On the other hand , there seems to be a sudden change after the second measurement , and in this connection it should be noted that an error in a weighing would entail an error in all the subsequent estimations of the volume of the bulb . It would have been better to have used throughout for each side a single vessel containing mercury from which to run back into E , or viceversd ; this would limit the error caused by an erroneous weighing to the one experiment , but a loss of mercury by careless manipulation , if of unknown weight , would still affect all the subsequent determinations of the volume of the bulb . As regards the uncertainty introduced by an error in the volume of the bulb , calculation shows that a positive error of 1 in 10,000 in W0 produces a negative error of 50 units in the coefficient of expansion ( with six significant figures ) and a negative error of 0'"055 in S.B.P. Fifth Measurement , filling with mercury ( fresh bulb)\#151 ; July 11 , 1906 ... ... . . 1265*391 . 1908 . ] Sulphur on the Constant-pressure Air Thermometer . 347 Coefficient of Expansion of Bulb . The important question of the expansion of the bulb made of Jena glass , 16 III , must now be dealt with , and it will be found necessary to discuss the results in some detail . The expansion of unit volume for any temperature t , measured on the constant-pressure scale , will be expressed in the form [ a + b{t\#151 ; 100 ) ] t. The measurements were carried out by filling the bulb and the capillary tubes that lead to it with mercury and heating the bulb . The corresponding tubes on the C side were also filled , so as to compensate for the exposed stem of the thermometer . The calculations have been made , using the two available values for the absolute coefficient of expansion of mercury , viz. , that due to Iiegnault as recalculated by Brooch , * and that due to Chappuis.f First Series of Experiments.\#151 ; After the observation in ice , the bulb T was heated up to W.B.P. in a double-jacketed apparatus of the ordinary form . After a small correction due to imperfect compensation of the capillary tubes , we get for the quantity of mercury driven out the following values:\#151 ; Date . Temperature . Observed weight . Calculated weight . 1900 . January 8 100 -165 19 -857 19 -856 " 8 100 -165 19 -858 19 -856 " 8 100 -168 19 *858 19 -856 " 25 100 -331 19 -883 19 -888 The two first values , marked for the same temperature , represent the mercury removed on heating up to W.B.P. , and introduced on cooling down again to W.F.P. This was frequently done , and will not be again referred to . The last column is calculated by taking a = 23974 x 10-9 , from Regnault 's value for the expansion of mercury , or a \#151 ; 24361 x 10-9 " Chappuis ' " " " A set of values was also taken at intermediate temperatures , the bulb T being heated in a large water bath kept vigorously stirred . At the higher * ' T. et M. , ' vol. 2 ( 1883 ) . t ' T. et M. , ' vol. 13 ( 1907 ) . A small slip has occurred here in calculating the cubical from the linear coefficient of expansion of glass , so that the term in C1 for mercury should , be O'OOO 000 002 847 , instead of O'OOO 000 002 951 . It is this corrected value that has been used . " 348 Mr. N. Eumorfopoulos . The Boiling-point of [ June 19 , temperatures the water was covered with a layer of oil to prevent cooling by evaporation . When the desired temperature was nearly reached , the flame was turned a little lower , so as to get a very flat maximum temperature , time readings being alternately taken of the weight and of a platinum thermometer . The indications of the latter were converted to the constant-pressure scale by assuming 444-53 as the S.B.P. at normal pressure . This perhaps , is slightly inconsistent , as the results of this paper lead to a lower value . It was , however , deemed inadvisable to make a change at this point . Now the expansion of mercury is given on the constant-volume scale . It becomes , therefore , necessary to allow for this small difference between the two scales . This has been done in accordance with D. Berthelot's* formula . Correcting as before for a small want of compensation in the exposed stem , we get the following table :\#151 ; Temperatu : re on the\#151 ; Weight of mercury . Date . Platinum scale . Constant-pressure scale . Constant-volume scale . Normal scale . 1900 . January 20 19 -717 19 -478 19 -470 19 -465 3-931 ) ) 9 20 -613 20 -366 20 -358 20 -353 4-130 } ) 10 26 -944 26 -647 26 -637 26 -632 5 -372 33 22 31 -001 30 -678 30 -669 30 -663 6-169 33 9 40-404 40-040 40 -029 40 -022 8-053 33 10 45 -353 44 -979 44 -968 44 -961 9-021 33 22 47 -943 47 -566 47 -555 47 -548 9-531 33 24 73 -896 73 -605 73 -597 73 -593 14 -667 1 In calculating the mean value of b from the above data , I have omitted the second and fifth values , which give abnormally high values of These two weights ( the two experiments were carried out on the same day ) are not independent of one another , as the second weight was obtained by adding to the first the mercury driven out in heating up from 20 ' to 40 ' . It is hence thought probable that some error has crept into the first value . It will , in fact , be seen from the next table that a diminution of both weights by , say , 30 milligrammes would bring both into line . The above experiments lead to the following value for b:\#151 ; b = 10"55 x 10-9 ( Begnault 's mercury formula ) , b = 19-70 x 10-9 ( Chappuis ' " " ) . * 'T . et M. , ' vol. 13 ( 1907 ) . 1908 . ] Sulphur on the Constant-pressure Air Thermometer . 349 The second and fifth columns of the following table have been calculated , using the following formulae for the expansion :\#151 ; { 23974 + 10-55 ( *-100 ) } x 10"9 , ( i ) ( 24361 + 19-70 ( *-100 ) } x lO"9 . ( ii ) Weight of Mercury driven out . Calculated\#151 ; Observed . Regnault . Chappuis . Formula ( i ) . Formula ( iii ) . Formula ( ii ) . j Formula ( iv ) . Formula ( v ) . 3-931 3-928 3-918 3-932 3-943 3-916 4-130 4 -106 4-096 4 110 4-121 4-093 5-372 5-365 5 -353 5 -369 5 -382 5-349 6-169 6-171 6-158 6 -175 6-190 6 153 8-053 8 -038 8-023 8-039 8 -056 8 -015 9-021 9-019 9-005 9-020 9-038 8 -996 9-531 9-533 9-519 9 -533 9-551 9-508 14 -667 14 -669 14 -667 14 -665 14 -684 14 -651 The third , fifth , and sixth columns will be explained later . Second Series of Experiments . After this , the bulb was heated up for a long time in sulphur vapour . The volume diminished , as already explained , and later the following experiments , were carried out:\#151 ; Date . ! Temperature . Observed weight . Calculated weight . 1900 . March 19 99 -399 19 -702 19 -702 " 19 99 -399 19 -702 19 -702 " 20 99 -738 19 -766 19 -768 " 30 100-115 19 -841 19 -841 The last column is calculated by assuming for the expansion of the bulb\#151 ; a \#151 ; 23868 x 10-9 ( from Begnault 's mercury ) , a = 24254 x 10~9 ( " Chappuis ' " ) . It will be noticed that heating has diminished the value of a. This has been noticed by other observers . VOL. lxxxi.\#151 ; a. 2 A 350 Mr. N. Eumorfopoulos . The Boiling-point of [ June 19 , To obtain a better value for b , it was determined to heat the bulb to a higher temperature , and the vapour of boiling aniline seemed the most convenient for the purpose . The aniline was boiled in a beaker about 40 cm . high and 9 cm . diameter . The bulb , with the platinum thermometer in contact with it , was surrounded by a copper cylinder to stop radiation and prevent cooling by convection currents . This was also aided by placing two horizontal tin-plates , one immediately over the copper cylinder and the other a few centimetres above this . These plates were of nearly the same diameter as the beaker , and had five holes punched in them to allow the various tubes and platinum thermometer to pass through . A small asbestos umbrella was placed on the stem of the weight and of the platinum thermometer to prevent the condensed aniline trickling down the bulb . In addition , two or three layers of asbestos paper were wrapped round the beaker . Three experiments were carried out , between each of which the bulb was emptied and refilled:\#151 ; Date . Temperature on the\#151 ; Weight of mercury . Platinum scale . Constant-pressure scale . Constant-volume scale . Normal scale . 1900 . March 28 181 *227 183-450 183 -490 183 -522 35 -935 \#187 ; 23 181 -563 183 -798 183 -838 183 -870 36 -003 " 23 181 -563 183 -798 183 -838 183 -870 36 -015 " 29 181 -661 183 -901 183 -941 183 -973 36 -022 " 29 181 -661 183 -901 183 -941 183 -973 36 -022 The mean values of b calculated from these experiments are : b \#151 ; 4-20 x 1CT9 ( from Regnault 's formula ) , b = 23'47 x 10-9 ( " Chappuis ' " ) . We hence have the two following formulae : { 23868-f- 4-20 ( \#163 ; \#151 ; 100 ) } x 10-9 , ( iii ) { 24254 +23-47 ( \#163 ; -100 ) } x 10"9 , ( iv ) while , to show the change introduced by a variation of b , the following formula has also been used : { 24254 +10 ( \#163 ; \#151 ; 100 ) } x 19"9 . ( v ) Columns corresponding to these formulae have already been given in connection with the experiments between 0 ' and 100 ' . The following table gives the corresponding calculations for the aniline values : 1908 . ] Sulphur on the Constant-pressure Air Thermometer . 351 Weight of Mercury dri ven out . Calculated . Observed . JJegnault . ; Chappuis . Formula ( i ) . Formula ( iii ) . Formula ( ii ) . 1 Formula ( iv ) . Formula ( v ) . 35 -935 35 *789 35 *938 35 -986 35 *938 36 *201 36 *003 35 *856 36 -004 36 -054 36 -005 36 -269 36 -015 35 -856 36 -004 36 -054 36 -005 36 *269 36 -022 35 *874 36 *024 36 *074 36 *025 36 *290 36 -022 35 *874 36 -024 36 -074 36 -025 36 -290 It will be noticed that Regnault 's value for mercury makes diminish with rise of temperature , while Chappuis ' shows an increase . It is true that Chappuis carried out experiments only between 0 ' and 100 ' C. As , however , his formula contains the same number of terms as Regnault 's , it seems reasonable to extrapolate it . We have evidence from other observers that b diminishes with temperature . Kamerlingh Chines , * from experiments on the same kind of glass between \#151 ; 182 ' and 100 ' , is quite sure of the fact . Experiments at the Reichsanstaltf between \#151 ; 190 ' and 500 ' indicate this as a general law for all substances tried , such as glass , porcelain , metals , and alloys , the only exception being brass . ETo experiments , however , are given for this particular kind of glass between these temperatures . Chappuis ' values for mercury were obtained by a weight thermometer method in a tube of verve dur , the linear expansion of which was measured directly between two marks made on the tube itself . These marks were not , unfortunately , on the neutral fibres . But apart from this , when one takes into consideration the method by which the ends of a tube are sealed off so as to form a bulb , and the change in the coefficient of expansion that must result from this , it seems unjustifiable to calculate the cubical from the linear coefficient , unless the tube has been very thoroughly annealed . This does not appear to have been done ; at all events , no mention is made of it . The value of the mean cubical coefficient of expansion obtained was ( 21696 +16*490 x 10"9 . This is in good agreement with a value obtained by Harker and Chappuis , J ( 21801 +15*5360 x 10-9 , * 'Comm . Phys. Lab . Leiden , ' No. 956 . t 'Ann . der . Phys. , ' 4 . F. , vol. 6 ( 1901 ) , p. 36 , and vol. 22 ( 1907 ) , p. 631 . f 'Phil . Trans. , ' A , vol. 194 ( 1900 ) , p. 74 . 352 Mr. N. Eumorfopoulos . The Boiling-point of [ June 19 , which is , presumably , an independent measurement . On the other hand , the second term does not agree with a value obtained for the same kind of glass at the Reiehsanstalt : * ( 22252 +10*830 x 10"9 . Experiments between 0 ' and 100 ' on Jena glass , 16 III , carried out at the Reichsanstalt , give for the mean coefficient , { 24238 + 10-71 ( \#163 ; -100 ) } x 10~9 . \t is here on the normal scale , but for this purpose the difference can be neglected . ] The expansion was observed on the neutral fibres , but the glass had not been annealed , except that it was slightly softened with a Bunsen burner to straighten it . It will be noticed that the " term is in excellent agreement with the value ( 10-55 ) deduced from my experiments with Regnault 's values . This agreement has led me to prefer the latter observer 's values for mercury , especially as use has to be made of the 184 ' value ; a fair conclusion seems to be that the question of the true coefficient of expansion of mercury must still be regarded as an open one . In calculating , therefore , the S.B.P. , the following formula has been used:\#151 ; { 23868 + 4-20 ( if\#151 ; 100 ) } x 10~9 , where t is expressed on the constant-pressure scale ; but it is useless to disguise the fact that it leaves the trlie value of the S.B.P. still uncertain . To change b from , say , 5 to 20 will raise the temperature by about 1'-41 , and to change a from 23,868 to 24,254 will raise the temperature by a further 0'-06 . Recovery of Zero . It was interesting to see if any recovery of zero could be observed after the aniline points . Two sets of observations were taken ; readings at the W.F.P. could only be taken about three quarters of an hour after the aniline point . Readings of the mercury on both sides are observed , and it is to the difference of the readings that attention must be paid , so as to eliminate emergent stem errors . * 'Wise . Abh . Reichs . , ' vol. 2 , p. 129 . 1908 . ] Sulphur on the Constant-pressure Air Thermometer . 353 March 27 , 1900.\#151 ; Put out flame ( heating the aniline ) at 12.15 P.M. , cooled bulb rapidly , first with hot , then cold , water . Started piling the ice at 12.40 p.m. 12.55 p.m. readings \#166 ; \lt ; '"T side ... ... 915 ' 1 LC \#187 ; ... ... 9-43 1.15 " " \ fT jj . \#187 ; i ... . 914 Lc jj . . . ... . 9-42 2.30 " " 4 fT ) ) . * 1 ... . 912 Lc ... . 9-41 4.45 * fT \gt ; ) . . ... . 912 The second set is as follows:\#151 ; March 29 , 1900.\#151 ; Put out flame at 3.40 p.m. Began adding ice at 4.10 p.m. 4.30 p.m. readings fT side . . ... . 10-05 Lc " ... . 10-06 4.50 " ... . 10-05 March 30 , 1900.\#151 ; Lc " . . ... . 10-06 11.50 A.M. " ... . 10-06 Lc " . . ... . 10-06 In the latter case in the course of 20 hours a contraction of the bulb equivalent to 0'005 was observed . As , however , readings were only taken to 0*01 , it is possible that even this is mere error of observation . When dealing with the determination of the S.B.P. , some evidence will be given indicating an appreciable change in the course of a day . The Resistance Measurements . As the S.B.P. was observed directly on the air thermometer , and not through the intermediary of the platinum thermometer , the latter was only used in obtaining the expansion of the glass , where the accuracy of the readings is of less importance . It , therefore , seems unnecessary to enter into any long description here . It may briefly be stated that the box used was one made by the Cambridge Instrument Co. , and is similar to one already described by Dr. Chree.* The coils were all replaced by silver-soldered manganin coils annealed for about 10 hours at 140 ' C. Three extra coils were added , as the thermometer used had a resistance at 0 ' C. of about 10 ohms . The calibrated bridge wire was shunted , so that 40 cm . * ' Roy . Soc. Rroc . , ' vol. 67 , p. 6 . Mr. N. Eumorfopoulos . The Boiling-point of [ June 19 , were equivalent to OT ohm . The resistances were occasionally tested against each other . In making the measurements the galvanometer circuit is kept closed , while the slider is shifted , until no deflection is observed on reversing the key in the battery circuit . Such a point could always be obtained . To eliminate heating effects , this balancing point was obtained first with one cell , then with two in series . The heating effect in the second case was assumed to be four times that in the first . As the latter never amounted to more than 0o-025 , and later with a more sensitive galvanometer was much less , there is little uncertainty in the correction for the purpose required . Leakage in the thermometer was frequently tested for . The Barometers . It is , of course , necessary to read the barometer for calculating the W.B.P. and the S.B.P. Originally , a Hick 's barometer constructed on Fortin 's principle was used . This bears a Kew certificate , dated December , 1873 , giving the correction as -t-0'005 . The vernier reads to O'Ol , but was estimated to 0'003 . Later , a barometer was constructed , the design of which is due to Professor Callendar . The object is to get the whole barometer immersed in water , so as to ensure a true temperature correction . Fig. 3 will make clear its construction . A and B are two platinum-iridium needles , about 7*8 cm . long , fused in the glass . Their difference of length was determined after fusion , but before this part was joined on to the barometer , so that it was not necessary to make the observations through the glass . The distance apart is about 76 cm . C is a small air-trap ; D serves for evacuation , and is afterwards fused off . The tube E communicates by rubber and glass tubes with a vessel F containing mercury , and a graduated oil manometer G open to the atmosphere at H. The barometer and rubber tube are surrounded by a wide tube full of water , the temperature being read on two thermometers . F is surrounded by cottonwool to prevent any rapid change of temperature ; an obvious arrangement permits the pressure in F to be varied . The quantity of mercury in AB is adjusted , so that when one surface touches the lower point of A the other should be practically touching B. The process of reading the barometer consists , then , in bringing the surface of the mercury first into contact with A , then with B , and reading the manometer on each occasion . If , for this small adjustment , we can assume the tube at A to have the same diameter as the tube at B , the arithmetic mean of* the two manometer readings will give accurately the difference between the barometric pressure and that due to a column of mercury equal in height to the distance between the lower points 1908 . ] Sulphur on the Constant-pressure Air Thermometer . 355 of the needles . An electrical arrangement for the contact was first tried , but very soon the contact at B became very bad , and an optical adjustment was adopted in its place . This barometer was found to work very well , but in the course of a few years the mercury and glass at B became dirty , partly no doubt due to water vapour passing through the rubber tube.* Fig. 3 . As the needles at A and B project above the tube , it is possible at any moment to verify the distance between them . This was done several times * Compare Rayleigh , ' Coll. Pap . , ' vol. 4 , p. 42 . 356 Mr. N. Eumorfopoulos . The Boiling-point oj [ June 19 , with a cathetometer , the scale of which was compared with an invar scale procured later:\#151 ; Length at 11 ' C. April , 1901 ... ... ... ... ... 76-348 October , 1901 76-345 December , 1901 ... ... ... ... . 76'344 After the invar scale was procured , the length was compared directly with this :\#151 ; May , 1902 ... ... ... . . 76-3462 December , 1906 ... ... 76-3445 The invar scale was standardised once at Sevres , and once at Teddington a few years later . To obtain the coefficient of linear expansion , advantage was taken of a change of temperature in May , 1902:\#151 ; May 7 , 8 , and 9 , 1902 ... ... . . 76-3462 at 11 ' C. May 27 and 28 , 1902 ... ... ... . 76-3524 at 19'*3 C. This is the length between the upper points , which were adjusted so as to be vertically one over the other . To obtain the distance between the lower points , three small corrections must be applied , one for the difference in length between the two needles , and the other two for the want of verticality of each needle . The Hicks barometer was compared with this later one , and the correction for the former found to be + 0*007 . As the vernier only reads to 0*01 , the agreement with the value given by the Kew certificate ( + 0*005 ) was considered satisfactory . A small correction , due to a difference in height between the reservoir of the barometer and the bulb of the air thermometer , was applied to the barometer readings . Further , in calculating the pressure due to a given column of mercury , \lt ; 7 in the laboratory was taken as equal to 1 00058 ^45 , on addition to the above barometer , a compensated barometer was used , the construction of which will be seen from fig. 4 ( Callendar 's Patent , No. 10,456 , 1891 ) . The tube AB contains dry air up to a level E. The annular space between AB and CD , and the tubes to the levels E and F , contain Fleuss pump oil . The tube F is open to the atmosphere . The tubes G and H , which are finally sealed off , are convenient for filling the apparatus . The assumption is made that the air in AB is at the same temperature as the oil in CD . Knowing the coefficient of expansion of the oil , the volumes of AB , CD and the tubes are calculated , so that a change of temperature only of the atmosphere should make no difference in the level of the oil in E , while a change of pressure as 1908.J Sulphur on the Constant-pressure Air Thermometer . 357 measured on a mercury barometer should be magnified 10 times on the tube E , which is accordingly graduated to read changes of pressure . If the volumes of the bulbs are not quite in the right ratio , small pieces of glass rod Asbestos Scale Fig. 5 . Fig. 4 . can be introduced through G or H to correct this . In practice , the standard barometer was read once during the day , and the changes of pressure in the course of a day read on the compensated barometer . A considerable saving in time was thus effected . Course of the Experiments . Only three temperatures were observed on the thermometer , viz. , W.F.P. , W.B.P. , and S.B.P. For the W.F.P. the ice was obtained in -^-cwt . blocks , washed with distilled water , and crushed very fine . The interstices were filled up with distilled water , or water from melted ice . Although the purity was occasionally tested with silver nitrate , this was , unfortunately , not done as a matter of routine . The W.B.P. apparatus was of the ordinary double-jacketed form . The lid of this was perforated for the various tubes , and leakage of steam Mr. N. Eumorfopoulos . The Boiling-'point of [ June 19 prevented by plugging with asbestos made into a pulp by moistening with a little water . No manometer was attached to this , as a similar hypsometer , but taller , and of smaller cross-sectional area , showed a practically negligible difference of pressure . The values of the WJB . P. are taken from Harker and Chappuis ' paper . The S.B.P. apparatus is shown in fig. 5 with the air thermometer in position ( the tubes on the C side are omitted ) . The latter was sometimes accompanied by a platinum thermometer . To prevent radiation , the bulb was surrounded by a tinplate screen of the usual type ( not shown ) , while above this two horizontal plates were placed ( also not shown ) , almost closing the cross-section . These plates were , however , a source of much trouble . It was practically impossible to put them in place without scraping the sides of the glass tubes . This , after a time , always resulted in scratching , and later cracking , the tubes , and so putting an end to the experiments . Dr. Harker informs me that the prolonged action of sulphur vapour on the French verre dur is to make it very brittle . This can easily be shown not to be a mere temperature effect . The accidents may , of course , have been due to this . In reducing the S.B.P. to normal pressure , the correction has been taken equal to 0'88/ t ; no correction has been made for the pressure due to the sulphur vapour . Some experiments were made to test the agreement of the S.B.P. obtained in a large and small iron boiler of the same type . The same platinum thermometer was immersed to the same height in both:\#151 ; Small Boiler . Diameter , 3*7 . July 16 , 1903\#151 ; No vertical screen , two horizontal discs. . pt . = 419*691 at 75*176 = 420*328 " 76 July 17 , 1903\#151 ; A vertical screen " " ... . pt . = 419*923 " 74*960 = 420*726 " 76 Larger Boiler . Diameter , 7*6 . July 17 , 1903\#151 ; No vertical screen , two horizontal discs . pt . = 419*548 = 420*351 July 20 , 1903\#151 ; A vertical screen " " ... ... pt . = 420*861 = 420*764 July 20 , 1903Two vertical screens " " ... ... pt . = 420*916 = 420*770 " 74*960 " 76 " 76*125 " 76 " 76*189 " 76 1908 . ] Sulphur on the Constant-pressure Air Thermometer . 359 ' The Experiments . The bulbs and tubes were cleaned first with hot nitric acid , then hot potassium hydrate , then again nitric acid , and finally the whole apparatus was several times completely filled with distilled water . In the final drying , the bulbs C and E were at 100 ' C. , while T was in sulphur vapour , and the whole apparatus repeatedly evacuated with a Fleuss pump . The thermometer was allowed to cool full of air at atmospheric pressure , and when cool it was finally evacuated and filled with air at 0 ' C. The air was purified bypassing through a tube containing potassium hydrate , then sulphuric acid , and . finally phosphorus pentoxide . March 9 , 1900 March 13 , 1900 March 14 , 1900 March 15 , 1900 March 16 , 1900 March 17 , 1900 W.F.P. , W.B.P. j W.F.P. | W.B.P. J W.F.P. , W.B.P. J S.B.P. First Set . 0 -003 671 25 0 -003 671 18 0 -003 671 53 0-003 671 63 Diminution in volume of | bulb \#151 ; 0 -610 gr. [ *443 '47* at 76 . W.F.P. , VO-003 671 15 J \#166 ; W.B.P. J S.B.P. T Diminution in volume = 0 -246 . \gt ; 442 -481 at 74 -865 = 443 -480 at 76. . W.B.P. , Y 0-003 671 11J W.F.P.J Mean coefficient ... ... ... ... ... . 0 '003 671 31 Final volume of bulb ... ... ... ... . 1274 '824 Pressure ... ... ... ... ... ... ... ... 76 *7 * In this my first experiment with the large sulphur boiler , the evolution of vapour was so great that I turned the flame low\#151 ; too low , in fact . The above temperature is obtained through the intermediary of the platinum thermometer which was alongside. . The highest actual temperature measured wTas 443*495 . The barometer on that day was 77*4 . 360 Mr. N. Eumorfopoulos . The Boiling-point of [ June 19 , Second Set . June 25 , 1901 ... ... W.F.P. , \gt ; 0'003 669 86 W.B.P. -1 June 26 , 1901 ... ... W.B.P. , [ -0 '003 670 42 W.F.P. ^ \lt ; 10-003 670 33 June 27 , 1901 ... ... W.B.P. j 1 1 W.F.P. 1 lo -003 | 669 85 10-003 669 64 June 28 , 1901 ... ... W.B.P. J [ L 0 '003 669 74 W.F.P. L 0-003 669 57 W.B.P. - 1 [ 0-003 669 63 W.F.P. J 1 July 1 , 1901 ... . . S.B.P. 1 Change of volume = 0 '632 July 2,1901 ... ... W.B.P. 10-003 670 37 W.F.P. J July 3 , 1901 ... . . S.B.P. 1 { r 442 -834 at 75 -239 = 443 *504 at 76 . Change of volume = 0 '226 W.F.P. July 4 , 1901 ... . S.B.P. . " | Change of volume = 0 -148 W.B.P. July 5 , 1901 ... ... W.F.P. 1 443 -134 at 75 *472 = 443 -599 at 76 . * 443 -909 at 76 '209 - 443 '725 at 76 . j-0'003 671 15 j-0-003 670 28 lo -003 670 05 W.F.P.J July 8 , 1901 ... S.B.P. J Change of volume = 0 '181 j\#187 ; 444 '130 at 76 '480 = 443 '708 at 76 . W.F.P. . July 9 , 1901 . . W.B.P.W.F.P. .0-003 670 08 \#166 ; 0 '003 670 65 J Mean coefficient ... ... ... ... . 0 '003 670 12 Final volume of bulb ... ... ... 1273 '912 Pressure ... ... ... ... ... ... ... 75 '3 If the total changes of volume given above are added on to this finali volume , it will make the initial volume greater than the final volume of the j 1908 . ] Sulphur on the Constant-pressure Air Thermometer . 361 first set . This , of course , is not impossible , as the bulb had a long time in which to recover . But the first set of coefficients is distinctly lower than the rest ; it thus appears that the change of volume deduced is too large . Now , as regards other variations observed in the coefficients . The second and third are both calculated from the same W.F.P. It is possible that the ice was not quite pure in this case , as the variation seems to exceed the experimental error . On July 4 , when a W.B.P. was taken immediately after a S.B.P. , this coefficient comes out very large . The same effect will be noticed again in the fourth set . On July 8 , a W.F.P. is taken just after a S.B.P. , and the corresponding coefficient is smaller than the succeeding one , though the difference here is small . It is as if the bulb gets larger again ; the effect may , of course , be due to something occurring in the gas . It should not be difficult to decide between the two explanations . June 26 , 1903 June 29 , 1903 July 1 , 1903 . July 2 , 1903 July 3 , 1903 In this case the volume was determined by the use of Boyle 's law ; it has not , therefore , the same claim to accuracy as in the other cases . Third Set . W.F.P. 1 L 0-003 671 55 W.B.P. i 1 10-003 671 26 W.F.P. : J 10-003 670 91 W.B.P. J S.B.P. Change of volume = 0 '147 W.F.P. W.B.P. S.B.P. 0 -003 671 22 444 -201 at 76 611 = 443 -842 at 76 . 443 -920* at 76 -170 = 443 -770 at 76 . Mean coefficient ... ... ... ... ... ... 0 *003 671 23 Initial volume of bulb ... ... ... ... 1260 '980 Pressure ... ... ... ... . . ; ... ... ... . . 76'0 * This is deduced from the preceding W.F.P. , the experiments having come to a. conclusion at this point , owing to an accident . \#166 ; 362 The Boiling-point of Sulphur . jo-003 671 06 J Fourth Set . June 21 , 1906 ... . . S.B.P. Change of volume = 0 '174 444 afc 7g .739 = 443 .52g afc ^ June 22 , 1906 ... . . W.B.P. W.F.P. June 27 , 1906 ... . . S.B.P. " j Change of volume = 0 -012 ! 443 . m ^ ^ .g43 = 443 .61Q ftt ^ W B P ) 0-003 671 76 J June 28 , 1906 ... . . W.F.P. I I 0 -003 670 18 W.B.P. J S.B.P. I Change of volume = 0 *080 }\gt ; 443 *140 at 75 *490 = 443 '589 at 76 . June 29 , 1906 ... . . W.F.P. J Mean coefficient ... ... ... ... 0 #003 670 62 Final volume ... ... ... ... ... . 1265 *391 Pressure ... ... ... ... ... ... . . 76 '2 The mean coefficient is that derived from the first and last ; the second has been omitted for reasons that have already been referred to . If the mean o : the three had been taken , the S.B.P. would be lower by 0'06 . On June 27 after the W.B.P. , an attempt had been made to obtain a W.F.P. Owing t( want of time , it was considered unsatisfactory and cancelled the same evening If any reliance can be placed on the observation , there was a diminution o : pressure by the next day of 0'002 cm . mercury , and the W.B.P. was taker before this ; it is obvious , then , what a serious error must arise owing to the ' uncertainty as to the behaviour of the glass . Eleven values of the S.B.P. have thus been obtained , the lowest of which is 443-47 , and the highest 443-84 . The mean is 443-62 ; while , if we miss out the third set as being less reliable , the mean is 443-58 . In conclusion , I must express my indebtedness to Professor Callendar for constant help during the progress of the experiments ; I have also to thank Dr. C. E. Guillaume for advice in procuring and standardising the invar scale .

rspa_1908_0091

0950-1207

Note on the boiling-point of sulphur.

363

366

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

H. L. Callendar, M. A., F. R. S.

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10.1098/rspa.1908.0091

Thermodynamics

Tables

Thermodynamics

363 Note on the Boiling-point of Sulphur . By H. L. Callendar , M.A. , E.R.S. , Professor of Physics at the Imperial College of Science and Technology . ( Received June 19 , \#151 ; Read June 25 , 1908 . ) As I have been partly to blame for the delay in the publication of the observations described in the preceding paper by Mr. N. Eumorfopoulos , it seems tight that I should make a brief statement , by way of apology , with regard to the object of the work and the causes which have led to the delay . The determination of the boiling-point of sulphur by Mr. E. H. Griffiths and myself in 1890* was made with the same air thermometer as that employed in my original experiments of 1887 , f and gave the same value for the difference-coefficient of the platinum thermometer . The result depended , however , on the scale of the constant-pressure air thermometer , and the correction for the expansion of the bulb was deduced from observations of the linear expansion over the range 0 ' to 500 ' C. of a piece of glass tube from which the bulb was made . Some uncertainty was introduced also by changes in the volume of the bulb at a temperature of 450 ' C. Shortly afterwards I succeeded in devising a much more delicate type of gas thermometer , J with compensated connecting tubes , and independent of barometric measurements , the bulb of which could be used as a mercury weight thermometer in determining the expansion correction . In the hope of obtaining a more accurate verification of the boiling-point of sulphur , as well as of the difference-formula for the platinum scale between 0 ' and 450 ' C. , I undertook a series of observations in 1893 in conjunction with Mr. E. H. Griffiths and Mr. G. M. Clarke , employing two gas thermometers precisely similar to that described by Mr. Eumorfopoulos , except that they were made of English lead glass . One of these thermometers was filled with air and the other with hydrogen in the first instance . At a later stage both were filled with nitrogen , because it was found that hydrogen reduced the lead glass at high temperatures , and there was some reason to suspect action .of oxygen on the mercury . The English lead glass , when it had once been annealed in sulphur vapour , proved remarkably free from changes of volume , and there was no difficulty in determining its expansion in terms of mercury between 0'and 100 ' C. , with * ' Phil. Trans. , ' A , 1891 . t 'Phil . Trans. , ' A , 1887 . J ' Roy . Soc. Proc. , ' vol. 50 , p. 247 . Prof. H. L. Callendar . [ June 19 , an accuracy of the order of 1 or 2 milligrammes of mercury in 1300 grammes corresponding to an error of about 1/ 2000 degree of temperature , but it was found that the results could not be brought into satisfactory agreement with Eegnault 's formula , or with the previous determination by the linear expansion method . Assuming Eegnault 's formula for the absolute expansion of mercury , V/ V0 = 1 + 0-00017901* + 0-000,000,0252*2 , the expansion of the lead glass bulbs could be approximately represented by the formula Y / V0 = 1 + 0-00002242* + 0-000,000,0240*2 , which may also be written ( adopting the form employed by Eumorfopoulos ) V/ V0 = 1 +{0-00002482+ 0-000,000,0240 ( *-100)}* . The expansion did not appear to follow accurately a parabolic law , but if a parabolic formula were assumed for mercury , the b term , or the coefficient of *2 , came out nearly the same as for mercury . The observations could be almost equally well represented by assuming the expansion of both mercury and glass to be uniform between 0 ' and 100 ' C. , an assumption which also appeared to represent Eegnault 's observations on mercury over this range within the limits of experimental error . The effect of the b term on the temperatures deduced by gas thermometer is about 130 times as great at 445 ' C. as at 50 ' C. , amounting , if b = 24 x 10~9 , to 2'-64 at the S.B.P. , and to 0o,020 at 50 ' C. Since the expansion did not appear to follow accurately a parabolic formula , it seemed useless to attempt an extrapolation . It appeared probable that the b term for mercury was not constant , as in Eegnault 's formula , but increased with rise of temperature ; and that it would be necessary to make a redetermination of the absolute expansion of mercury , and also to employ the weight thermometer method at much higher temperatures than 100 ' C. , if any certain result were to be obtained by this method . I accordingly designed a multiple manometer for the absolute expansion of mercury , in which the expansion to be measured was increased to about eight times that obtained by Eegnault ; and I hoped , by employing platinum thermometers and other refinements not available in his time , to be able to secure a much higher order of accuracy in this fundamental determination . At this point the work was interrupted by my appointment as Professor of Physics at McGill College , Montreal , in October , 1893 , and I was unable to resume it until my return to University College in 1898 . Meanwhile the Kew Committee and the International Bureau of Sevres , recognising the importance of the work , had collaborated in arranging a redetermination of the boiling-point of sulphur and of the scale of the 1908 . ] Note on the Boiling-point of Sulphur . f platinum thermometer , which was undertaken by Messrs. Chappuis and Harker.* The results of their work with a constant-volume nitrogen thermometer led to a somewhat higher value , namely 4450,26 C. , of the S.B.P. than the value 444a53 C. obtained with the constant-pressure air thermometer . The difference between these two values was too great to be explained by the difference between the scales of the constant-volume and constant-pressure thermometer , which probably amounts to only 0'*3 at this point.f But as I pointed out at the time , ^ the uncertainty of the expansion correction was sufficient to account for a much larger discrepancy . The \#166 ; results of Messrs. Chappuis and Harker depended on the extrapolation of a formula for the linear expansion obtained from observations over the range 0 ' to 80 ' C. , which gave a comparatively high value for the coefficient b. They subsequently adopted a different formula for the expansion , which had the effect of reducing their result to 444'*77 C. on the constant-volume scale , which is in practically perfect agreement with 444'-53 on the constant-pressure scale . Having regard to the excellence of this agreement it might have appeared superfluous to proceed further . But the uncertainty of inferring the cubical from the linear expansion still remained , and it was desirable to obtain a more accurate verification of the scale of the platinum thermometer at ordinary temperatures for the reduction of experiments on the variation of specific heat . My original gas thermometer had been broken on the way out to Canada , and again on the way back . I therefore had another constructed of Jena glass to fit the same stand , hoping that the new glass would prove less troublesome in respect of change of volume . At the same time I proceeded with the construction of the apparatus already designed for the absolute expansion of mercury . This was nearly finished , and several determinations of the S.B.P. had already been made by Mr. Eumorfopoulos , when I had to leave University College in April , 1902 . After several fruitless efforts to find a place to set up the apparatus at the Boyal College of Science , I had finally to await the completion of the new buildings , then in course of erection . I was able to proceed with the erection of the apparatus at the end of last year , and some preliminary experiments which promise well have already been made with it . The apparatus seems likely to realise the same order of accuracy in the absolute expansions of mercury as in the weight-thermometer tests of the bulb . It was designed with that intention , but , until it was set up and tested , it was difficult to foresee * \#163 ; Phil. Trans. , ' A. vol. 94 , p. 74 . t ' Callendar , ' Phil. Mag. , ' 1903 , p. 93 . X ' Phil. Mag. , ' December , 1899 , p. 544* VOL. LXXXI.\#151 ; A. 366 Note on the Boiling-point of Sulphur . whether effects of lag and viscosity might not be serious in so great a length of tubing . It will be seen from the experimental results given by Mr. Eumorfopoulos in the preceding paper that the hopes which I had formed of Jena glass were far from realised . The continual changes of volume of the bulb were among the chief difficulties encountered , and are doubtless indirectly responsible for the apparent variations in the coefficient of expansion observed , which considerably exceed the limit of accuracy of reading . An alternative method of treating the observations , which I adopted in the experiments of 1890 , would be to calculate the changes of volume by assuming a constant value of the coefficient . This would tend to eliminate the accumulation of accidental errors in a long series of weighings . In spite of the changes of the bulb , and of other possible sources of error , it is obvious that the results obtained by Mr. Eumorfopoulos are entitled to great weight , and will lead to a more certain value of the S.B.P. when the expansion of mercury has been more accurately determined . Publication has been delayed from time to time in the hope that these difficulties might be surmounted , but as it now appears certain that glass is an unsuitable material for accurate work of this nature , it would be useless to delay any longer . The description of the method and apparatus employed , which has not been previously published , although the apparatus has been in existence for so many years , may prove serviceable to others engaged in similar work . That the final result given , namely , 443''58 C. for the S.B.P. , should be nearly 1 ' lower than \#171 ; the value previously admitted may appear surprising . But it must not be forgotten that , if Chappuis ' formula for the expansion of mercury had been adopted , the result would have been 445a8 C. approximately , or more than a degree higher than the old value . This illustrates the necessity for a redetermination of the expansion of mercury . At the same time it must be admitted that Regnault 's formula is more likely to be right at the higher temperatures , and that the old value of the S.B.P. is likely to be too high in consequence of the probable error involved in deducing the cubical coefficient from the linear expansion of a tube .

rspa_1908_0092

0950-1207

On optical dispersion formul\#xE6;.

367

377

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

Richard C. Maclaurin, M. A., Sc. D., LL. D., |Professor J. Larmor, Sec. R. S.

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6.0.4

http://dx.doi.org/10.1098/rspa.1908.0092

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10.1098/rspa.1908.0092

Tables

Atomic Physics

Tables

367 On Optical Dispersion Formulae . By Richard C. Maclaurin , M.A. , Sc. D. , LL. D. , Professor of Mathematical Physics , Columbia University in the City of New York . ( Communicated by Professor J. Larmor , Sec. RS . Received July 2 , 1908 . ) In the half century that elapsed from the time when Cauchy published his memoirs on dispersion , the only measurements of refractive indices that were available for the test of any theory were confined to the neighbourhood of the visible spectrum . They extended from somewhat beyond 02 / a to about 08 / a , i.e. over a range of two octaves . In this range the variation of refractive index for most substances is small , and it is not surprising that , by a proper adjustment of constants , a variety of different formulae may be made to fit the experimental facts . More recently , however , the range of observations has been immensely extended , so that we now have a large number of determinations of refractive indices for various wave-lengths extending from less than 0'2/ a to 22'3/ a. With a knowledge extending over this range of about seven octaves , there is more hope of testing the merits of different dispersion formulae . Accordingly , when , in 1879 , Mouton made the first considerable extension in the direction of great wave-lengths , he found that , with the same number of constants , the formula of Briot represented the facts much better than did the older one of Cauchy , and the isame result was reached by Langley in 1884 and 1886 . The still more ^extended observations of Paschen , Rubens , E. F. Nichols , and A. Trowbridge , published at various dates from 1892 to 1897 , have shown that Sellmeier 's ( formula* \#151 ; K + Ci/ ( A2\#151 ; Xj8 ) + ... is the only one of those that have been tried that is in thorough accord with the observed values of the refractive indices over the whole range of the '/ experiments . It must , however , be admitted that there are various doubts and difficulties ( connected with the development of this formula from a sound dynamical / basis in any of the various forms of its presentation , whether we follow / directly the arguments of Sellmeier , Ketteler , Helmholtz , or Kelvin , or / express their ideas in the language of electron theory as Drude and others / have done . But apart from difficulties as to the exact character of the reaction between ether and matter , and doubts as to the validity of certain * Usually quoted now as the " Ketteler-Helmholtz formula . " Prof. P. C. Maclaurin . [ July 2 , dynamical principles employed in its evolution , the Sellmeier formula is open to two serious objections . ( 1 ) When the wave-length is indefinitely increased , the formula gives n2 = K , so that , on the electromagnetic theory of light , IC should be the dielectric constant of the medium . The values of K , determined by the Sellmeier formula from the observations of refractive indices by Eubens and Nichols , are 6'09 , 4*58 , 5T8 , and 4*55 for fluorite , quartz , rocksg.lt , and sylvin respectively , and the slightly different observations of the other physicists mentioned above make scarcely any appreciable change in the estimate of K. Thus Langley finds K = 5T747 for rocksalt , while Eubens and Trowbridge find K = 5T79 . Unfortunately there is not the same agreement amongst different direct determinations of the dielectric constant . Tor fluorite the constant is 6*8 , 6'7 , or 6'9 , according to Curie , Eomich and Nowak , or Starke ; while for quartz these observers find 4*55 , 4*6 , and 4*73 respectively . Lor rocksalt Curie gets 5*85 , Thwing 5*81 , and Starke 6*29 ; and the last named observer gives 4*94 as the dielectric constant of sylvin . Taking the mean of these for the different substances , we find 6*8 , 4*63 , 5*98 , and 4*94 , as compared with 6*09 , 4*58 , 5*18 , and 4*55 of the dispersion formula . It will be noted that the differences are in all cases in the same direction , and , except in the case of quartz , are considerable , being more than 10 per cent , of the quantity considered . ( 2 ) A more serious discrepancy reveals itself on comparing the calculated values of X2 and the observed positions of the absorption bands of different substances . According to the theory , the absorption band should be found very near to X2 , although not absolutely coincident with it . The values of X2 , calculated from the formula to fit in with the experimental determinations of refractive indices by Nichols , Eubens , and Paschen for rocksalt , sylvin , and fluorite are 56*12 , 67*21 , and 35*47 respectively , whereas the absorption bands were found at 51*2 , 61*1 , and 23*7 . Here , again , the differences are in all cases in the same direction , and are of an order of magnitude altogether beyond the limits of experimental error . The difference is greatest for fluorite , where it amounts to nearly 12/ 4 , but the smallest difference , about 5 / t for rocksalt , is at least five times too great to be ascribed to errors in the experiments . It must be borne in mind that the formula involves not X2 but its square , so that the observed and computed values that are to be compared are 2621 , 3733 , and 562 , with 3149 , 4517 , and 1258 respectively for the three substances mentioned . The substitution of the former for the latter numbers in the formula will make a very great change indeed , and throw the observed and computed values of the refractive indices into hopeless disagreement . 1908 . ] On Optical Dispersion Formula . If we are to retain the Sellmeier formula , only two methods of escape from these difficulties seem possible . One is to ascribe the discrepancies to experimental errors . This is , however , quite out of the question as regards the position of the absorption bands , and there is still less hope of reconciliation from the very slight differences in the measurements of the refractive indices . The greatest differences found in the refractive indices of rocksalt are those between the measurements of Langley , on the one hand , and Rubens , Nichols and Trowbridge on the other . The consequent changes in the estimates of K and A22 from the Sellmeier formula , are , however , very slight , for , while .Rubens gets K = 5*179 and A22=3149*3 , Langley has K=5*175 and A22=3145'7 . The other mode of escape that has been suggested is to ascribe the discrepancy between the observed and calculated values of A2 to the influence of absorption bands in the unexplored regions . The Sellmeier formula contains a term c"/ ( A2\#151 ; \n2 ) , corresponding to each absorption band , and one or more of these terms may be neglected in estimating the refractive index in any region , on the supposition that A2\#151 ; An2 is very large , which means , of course , that the region is far removed from the absorption bands in question . However , there is no evidence of the existence of any absorption band in a position that would enable us to bridge the gulf between theory and experiment for either rocksalt or sylvin.* In the case of fluorite , there is a well-marked band in the neighbourhood of 24 and strong absorption for a considerable distance beyond , but not reaching nearly so far as 35'47 The only one of the substances mentioned for which an absorption band has been found in a region that should affect the calculated refractive index is quartz . This has an absorption band at 12'5 which was not considered in the calculations quoted above . Quartz , however , is the substance in which the agreement between Sellmeier 's formula and the observed values of the dielectric constant and the position of the other absorption bands is most satisfactory . * Quite recently Paschen has made another interesting contribution to the discussion of dispersion formulae . In the ' Annalen der Physik ' ( 1908 , p. 120 ) he deals with rocksalt and sylvin on the basis of Sellmeier 's formula . By assuming that there are three absorption bands\#151 ; one in the infra-red and two in the ultra-violet\#151 ; he has seven constants at his disposal , and obtains a close agreement between theory and observation as far as the dispersion is concerned . However , the difficulties as to the values of the constants in the formula do not seem to be removed . The dielectric constant is still too low , viz. , 3'87 , instead of 4'94 , for sylvin , and 5*68 , instead ot 5*98 , for rocksalt ( taking the mean of the observations quoted above ) . The absorption bands of rocksalt are placed at 0T2 / x , 0T6 / x , and 60 / x , and those of sylvin at 0T1 / x , 0T6 / x , and 57 / x. Lyman has experimented with wave-lengths much less than 0T6 / x without finding any absorption bands , and the most accurate observers of the bands in the infra-red agree in placing them a long way from 60 / x and 57 / a. Prof. K. C. Maclaurin . [ July 2 , It seems then worth while inquiring whether there is not some other dispersion formula that will agree satisfactorily with the observed values of the refractive indices and be free from the difficulties in which Sellmeier 's formula is involved . In order to make clear the meaning of the symbols , it may be well to sketch the process by which the formula that we propose to test may be derived . Let \#163 ; , rj , \#163 ; denote the components of the displacement in an ether that resists rotations only . If , for convenience , we take the density of this ether to be unity , the torque F necessary to produce a rotation / is F = c2f and the work required to do this is \c2p . Here is a coefficient of elasticity and c is the velocity of a wave in the ether . If there be electrons present , these will be disturbed so as to produce and equilibrate a new averaged rotational strain f. The total rotation in the elastic ether is thus / -+./ , say / , while the torque is Fi = c2f . The quantity f will , on the usual hypothesis of very small displacements , be proportional to / so that we may write/ = l)/ l c2 where n is some constant . We thus have Fi = \#151 ; / i , where / = n2f . The r work absorbed in producing the total rotation / , for the compound medium made up of ether and electrons , will be A \#151 ; A2 . Thus the c of free ether is n2 replaced by c/ nfor the compound medium and n represents the refractive index . If we employ the language of electrodynamics , F is to be identified with the electromotive force and the velocity ( \#163 ; rj \#163 ; ) with the magnetic induction . In estimating the actual local electromotive force effective in straining any molecule P it is convenient , as in the theory of attractions , to consider separately the influence of the electrons within the region adjacent to P and that of the external field beyond this . What exactly the contribution of adjacent molecules is will depend on the character of the inter-molecular forces and the configuration around each molecule ; but in any case it must be proportional to / , and it will be compensated locally by static reaction on the adjacent molecules . Hence the actual electromotive force around the molecule is F ' = c2 ( / +/ ' \#151 ; \#171 ; i/ 7 ) = mf where m = ( 1\#151 ; a{)c2and a = ai/ ( l\#151 ; ai ) . We thus have ( n2\#151 ; l)/ ( n2+a ) = ? n/ 7/ F7 , so that the refractive index ( n ) depends on the relation between/ 7 and the torque F7 that produces it . To find the relation between / ' and F7 we have to consider the effect on the molecule of the alternating field of force due to the impinging wave of light . 1908 . ] On Optical Dispersion Formula . This is the well-known problem of determining the oscillations forced on a vibrating system in steady motion by a given periodic force . The principle of least action lends itself most readily to such a discussion and enables us to arrive at the form of the relation sought for without any special hypothesis as to the character of the steady motion of the electrons , or as to the nature of the intermolecular forces . If p/ 'Zjr be the frequency of the impinging wave and A the corresponding wave-length , we are thus led to the formula* ft2-1 =73fL= Al + a2 , Awe n2 + a F ' p2\#151 ; p\2 \#151 ; _ BjX2 B2A2 B"A2 A2 - Ap5 A2 - A22 A2 -Xn2 ' where Pi/ Ztt , . . . Pn/ Z-rr are the frequencies of the free vibrations within the molecule . For indefinitely long waves we have = K , so that |=l = B1 + B , + ... + Bw Jv-f a whence , by subtraction , ft2 \#151 ; 1_K \#151 ; 1 , Cl \#166 ; _____C2____ . n2 + a K + a X2\#151 ; Ax^A2\#151 ; X22 ' A2-Are2 ' This formula should give the refractive indices for all the different wavelengths for which the medium is transparent . The formula will be modified in the same way as that of Sellmeier in the neighbourhood of an absorption band . If anything occurs to put f out of phase with / , then , . . . will be complex and there will be general absorption of the metallic type . It has been remarked that the value of the constant a depends on the influence of the electrons in the immediate vicinity of the point where the disturbance is considered . In the present state of our ignorance as to the arrangement and mutual influence of the molecules the value of this constant cannot be accurately determined from theory . In the case of a liquid or gas we might expect the average effect to be that of a uniform distribution and under these circumstances Larmorf has given reasons for expecting the constant a to have the value 2 . If = 2 we have the expression ( n2 \#151 ; l)/ ( n2+ 2 ) , which is what occurs in Lorentz 's original paper$ connecting refractive index ( and dispersion ) with density . The experiments there discussed , and the more recent estimates of the refractive indices of liquids and gases agree , on the whole , fairly closely with Lorentz 's * Cf . Larmor , ' Phil. Trans. , ' 1897 , A , p. 236 , for an investigation in detail . What is here denoted by a is Larmor 's 47r/ X\#151 ; 1 . t Loc . cit. , p. 233 . f H. A. Lorentz , 'Ann . der Physik u. Chemie , ' 1879 , vol. 9 , p. 641 . Prof. R. C. Maclaurin . [ July 2 , theoretical formula . With these considerations before us it would seem natural to inquire whether the formula \#163 ; lrl = K=I+__\#163 ; !_ + +-J=_ v ? + 2 K + 2 X2-X,2 X2-X"2 will apply to solids as well as liquids . However , on attempting this on the basis of the experiments referred to below , we are met with the same difficulties that confronted us when considering Sellmeier 's formula . A fair agreement between theory and observation can be obtained as far as the dispersion is concerned , but the constants are unsatisfactory . Thus in the case of rocksalt , if we take any probable value of the dielectric constant , the formula predicts an absorption band in the neighbourhood of 46 and this is as much below the mark as that given by Sellmeier 's formula is above it . We shall therefore retain the constant a in our formula and endeavour to determine its value for different substances from the experimental evidence that is available . The substance best adapted for the test of any such formula is rocksalt . Its refractive indices are known to a high degree of accuracy over a very large range , within which there are only two free periods as compared with four in the case of quartz . The addition of a free period increases the number of unknown constants , and makes it more difficult to determine any of them accurately . Amongst the most careful determinations of the dispersion of rocksalt we have the observations of Langley* from 0486 to 4T23 of Rubensf from 0'434 / / , to 5'746 / x , of PaschenJ from 2'8 to 9'76 of RubensS from 0434 / xto 8-95 / x , of Rubens and Mchols|| from 0434 fx to 22*3 / x , and of Rubens and Trowbridge IF from 9'88 \x to 17'87 On the whole there is excellent agreement between these various observers , the differences in the estimates of the refractive indices being rarely more than 3 or 4 in the fifth significant figure . Langley gives the indices to seven significant figures , and his results are admirably self-consistent . Unfortunately , however , they are almost uniformly higher than those of the other observers , so that it is useless at present to include more than five figures in calculating the values of n from our formula . The influence of small differences in the fifth significant figure * 'American Journal of Science , ' 1886 , vol. 32 , p. 98 , and 'Annals of Astrophysical Observatory of Smithsonian Institution , ' 1900 , vol. 1 , p. 261 . t 'Ann . der Physik u. Chemie , ' 1892 , vol. 45 , p. 254 . % Ibid. , 1894 , vol. 53 , p. 340 . S Ibid. , 1894 , vol. 53 , p. 278 ; and 1895 , vol. 54 , p. 482 . || Ibid. , 1897 , vol. 60 , p. 454 ; and 'Physical Review , ' 1897 , vol. 5 , p. 162 . IF Ibid. , 1897 , vol. 60 , p. 733 ; and corrections in vol. 61 , p. 224 . 1908 . ] On Optical Dispersion Formula . on the estimated values of the constants will , however , as has been indicated already , be very slight , and it is almost immaterial which set of observations we use as the basis of our computation . If we take Langley 's figures , our problem is to determine the six constants lv , a , \i2 , X22 , cj , and c2 , from the formula ? i2\#151 ; 1 _ K \#151 ; 1 Ci c2 r ? + a K-fa X2\#151 ; X12 X2\#151 ; X22 ' so as to get the best possible agreement with over 50 observations of the refractive index ( n ) for different wave-lengths . To pick out six different observations and solve the corresponding set of six equations for the unknown constants would be possible but very laborious . After the eliminations were performed the resulting equations , of whatever degree , would have numerical coefficients , and so could be solved ; but the process of elimination would be very troublesome . In practice it is more feasible to begin by trial and error , and to proceed by successive approximations . It soon becomes evident that the constant e\ is small , and that for large values of X the term ^i/ ( X2\#151 ; X12 ) is almost negligible compared with t'2/ ( X2\#151 ; X22 ) . Thus for the longer wave-lengths we have the simpler formula n2\#151 ; 1 _ K \#151 ; 1 c2 11 ? +a K + a X2\#151 ; X22 ' Setting out , then , with any arbitrary values of a and K , we can determine the other constants to fit in with the experimental results , and proceed with this process until a set of values is reached that gives a close agreement throughout the whole range . Once such an agreement has been reached , we may reduce the equations for the small differences in the constants to a linear form by the process usual in such problems , and , if required , can determine the probable error of the various estimates . It might seem at first that with so many constants at our disposal it would be possible to vary their values considerably without producing an appreciable change in the calculated values of the refractive indices . It will be found , however , on trial that the observations are sufficient to confine the constants within narrow ranges , and , amongst other things , that a slight diminution of the constant a would make X12 negative , which is , of course , impossible . The process of trial and error described above leads to the following values of the constants :\#151 ; Xj2 = 0-0160074 , X22 = 2632-14 , ci = 0-00191605 , C*2i \#151 ; 683-816 , a = 5-51 , K = 5-9 , Xi = 0-12652 , x2 = 51-3 . Prof. P. C. Maclaurin . [ July 2 , Calculating the refractive indices from the formula with these constants , we get the following table , which also gives a comparison with Langley 's observations . The numbers obtained from theory and observation are identical except in the cases marked with an asterisk:\#151 ; A. n ( theory ) . n(observation ) . X. n ( theory ) . n ( observation ) , 0-4861 m 1 -5533 1 -5533 0 -9916 n 1 -5323 1 -5323 0 -4920 1 -5526 1 -5526 1 -0084 1 -5321 1 -5321 0-4937 1 -5525 1 -5525 1 -0368 1 -5317 1 -5317 0 -4983 1 -5519 1 -5519 1 -0540 1 -5315 1 5315 0 -5173 1 -5500 1 -5500 1 -0810 1 -5312 1 -5312 0 -5184 1 -5499 1 -5499 1 -1058 1 -5310 1-5310 0 -5273 1 -5491 1 -5491 1 -1420 1 -53069 1 -53063* 0 -5372 1 -5482 1 -5482 1 -1780 1 -5303 1 -5303 0 -5530 1 -5469 1 -5469 1 -2016 1 -53018 1 -53014* 0 -5660 1 -54586 1 -5458* 1 -2604 1 -5297 1 -5297 0 -5710 1 -5455 1 -5455 1 -3126 1 -5294 1 -5294 0 -5758 1 -5452 1*5452 1 -4874 1 -5285 1 -5285 0 -5786 1 -5450 1 -5450 1 -5552 1 -52820 1 -52814* 0 -5860 1 -5445 1 -5445 1 -6368 1 -5278 1 -5278 0 -5893 1 -5443 1 -5443 1 -6848 1 -52770 1 -52764* 0 -61.05 1 -5430 1 -5430 1 -7670 1 -5274 1 -5274 0 -6400 1 -5414 1 -5414 2 -0736 1 -5265 1 -5265 0 -6563 1 -5406 1 -5406 2 -1824 1 -5263 1 -5262* 0 -6874 1 -5393 1 -5393 2 -2464 1 -5261 1 -5261 0 -7190 1 -53814 1 -53815* 2 -3560 1 -5258 1 -5258 0 -7604 1 -5368 1 -5368 3 -1104 1 -5241 1 -5240* 0 -7992 1 -5358 1 -5358 3 -2736 1 -5237 1 -5237 0 -8424 1 -5348 1 -5348 3 -3696 1 -5235 1 -5235 0 -8835 1 -5340 1 -5340 3 -6288 1 -5229 1 -5229 0 -9033 1 -5336 1 -5336 3 -8192 1 -5224 1 -5224 0 -9724 1 -5325 1 -5325 4 -1230 1 -5216 1 -5216 The differences between theory and observation being so slight , and in every case less than those between the different observers , it was not thought necessary to proceed to any closer approximation by modifications of the constants . We must now inquire how the refractive indices obtained from our formula with these constants agree with the observations of Eubens and others in the region beyond 4-123 ya. The results are set out in the following table:\#151 ; X. n ( theory ) . n ( observation ) . Difference . 4 " 65 u 1 -5200 1 -5197 + 0-0003 5 -22 ' 1 -5183 1 -5180 + 0 -0003 5 -79 1 -5155 1 -5159 -0-0004 6-78 1 -5123 1 -5121 + 0 -0002 7 -22 1 -5103 1 -5102 + 0-0001 7-59 1 -5086 1 -5085 + 0-0001 8-04 1 -5063 1 -5064 -o-oooi 8-67 1 -5030 1 -5030 0 9-95 1 -4952 1 -4951 + 0-0001 11 -88 1 -4809 1 -4805 + 0-0004 13 -96 1 -4625 1 -4627 -0 -0002 15 -89 1 -4415 1 -4410 + 0-0005 17 -93 1 -4152 1 -4148 + 0-0004 20 -57 1 -3736 1 -3735 + 0 -0001 22 -3 1 -3407 1 -3403 + 0 -0004 1908 . ] On Optical Dispersion It will be seen that the agreement is very close throughout , the differences being nearly all of the order of experimental error . In considering the slight differences that do exist , we must bear in mind two facts . ( 1 ) The formula , with the constants adopted , gives values of n for the larger wave-lengths that are on the average slightly in excess of those observed . This is what is to be expected from the fact that the constants were chosen to fit in with Langley 's observations , and in the range common to all observers Langley 's results are almost uniformly slightly higher than those of the others . ( 2 ) For the larger wave-lengths an error in the estimate of X affects the refractive index more than in the case of short waves . Thus in the neighbourhood of 18 an error of one-sixth of 1 per cent , in the estimate of the wave-length would account for a difference of more than ( \gt ; 0004 in the value of the refractive index . Such a mistake in the estimate of the wave-length is not beyond the limits of experimental error in this region.* The value of Xi adopted to fit in with Langley 's observations of the refractive indices is Xi = 0T2652 / x. If we had used the observations of Kubens instead of those of Langley we should have found a slightly lower value of Xi . We should thus expect an absorption band in the neighbourhood of 0T2 fji . Lyman , in his examination of rocksalt , used wave-lengths as short as 0T25 fx . He did not find an absorption band , but he discovered marked absorption for the shorter wave-lengths , indicating that he was on the confines of a band.f It thus appears that the formula n2-l_K-l c2 n2 + a K -f \amp ; ~X2\#151 ; Xi2 ~X2\#151 ; X22 is in thorough accord with experimental knowledge on the optical properties of rocksalt . It agrees with experiment in indicating absorption bands in the neighbourhood of 0T2 / x , and of 5T3 / x ; it suggests a dielectric constant of 5-9 , which is very near the mean of the best experimental measurements of that constant ; and it assigns values to the indices of refraction agreeing within the limits of experimental error with 70 observations extending over nearly six octaves . Next to rocksalt , the substance for which the existing data are best adapted for the test of a dispersion formula such as that here discussed is fluorite . Its refractive indices have been carefully determined from 0T98 fx * See Rubens and Nichols , ' Physical Review , ' 1897 , vol. 5 , pp. 102 and 161 ; and ' Ann. der Phys. u. Chemie , ' 1897 , vol. 60 , pp. 426 and 453 . t ' Astrophysical Journal , ' Jan. , 1907 , pp. 51 and 52 . Prof. P. C. Maclaurin . [ July 2 , to 8-95 yu\gt ; by Rubens and Snow , * from 01856 to 91291 by Sarasin , Carvallo and Paschen , f from 0 2 fx to 234 / x by Simon , f and from 076 / x to 3'4 fx by Langley . S Taking the numbers as set out by Paschen as the basis of our calculations , we get the following approximate values of the constants in the dispersion formula : \#151 ; a = 1'04 , K = 6-8 , Xi2 = 0-00716764 , X22 = 576-353 , Xi = 0-0846618 , X2 = 24-0074 Ci = 0-001303 , c2 = 231-856 . The corresponding values of the refractive indices for different wavelengths are set out below , with a comparison between theory and observation . * * * S A. n ( experiment ) . n ( theory ) . Difference . 0-1856 1 -5094 1 -50945 + 0 -00005 0 -19881 1 -4963 1 -4962 -0 -oooi 0 -20243 1 -4933 1 -4932 -o-oooi 0 -20610 1 -4904 1 -4904 0 0 -20988 1 -4876 1 -4875 -0 -0001 0 -21441 1 -4846 1 -4845 -o-oooi O -22645 1 -4776 1 -4775 -o-oooi 0 -23125 1 -4752 1 -4751 -0 -oooi 0 -25713 1 -4648 1 -4647 -o-oooi O -27467 1 -4596 1 -4596 0 O -32525 1 -4499 1 -4498 -0-0001 0 -34015 1 -4477 1 -4477 0 0 -34655 1 -4470 1 -4469 -o-oooi 0 -36009 1 -4454 1 -4454 0 0 -39685 1 -4421 1 -4419 -0 -0002 0 -48607 1 -4371 1 -4371 0 O -58932 1 -4339 1 -4339 0 0 -65618 1 -4326 1 -4327 + o -oooi 0 -68671 1 -4320 1 -4320 0 0 -71836 1 -4316 1 -4317 + o -oooi 0 -76040 1 -4310 1 -4311 + 0 -oooi 0 -8840 1 -4298 1 -4299 + 0 -oooi 1 -1786 1 -4279 1 -4280 + 0-0001 1 -3756 1 -4269 1 -4270 + o -oooi 1 -4733 1 -4264 1 -4265 + 0-0001 1 -5715 1 -4260 1 -4261 + 0 -0001 1 -7680 1 -4251 1 -4251 0 1 9153 1 -4244 1 -4244 0 1 -9644 1 -4241 1 -4241 0 2 -0626 1 -4236 1 -4237 + 0-0001 2 -1608 1 -4231 1 -4231 0 2 -3573 1 -4220 1 -4220 0 2 -5537 1 -4209 1 -4209 0 2 -6519 1 -4202 1 -4202 0 * 'Ann . der Phys. u. Chem. , ' 1894 , vol. 53 , p. 273 ; 1892 , vol. 45 , p. 254 ; 1892 , vol. 46 , p. 529 . t Ibid. , 1894 , vol. 53 , p. 328 ; 1895 , vol. 56 , pp. 765 and 821 . I Ibid. , vol. 53 , p. 553 . S 'Annals of Astr . Obs. , ' vol. 1 , p. 221 ; see also Maidens , 'Ann . der Pliys.,5 vol. 6 , 1901 , p. 619 . 1908 . ] On Optical Dispersion Formulae . X. n ( experiment ) . n ( theory ) . Difference . 2 -9466 1 -4183 1 -4183 0 3 -2413 1 -4161 1 -4161 0 3 -5359 1 -4138 1 -4138 0 3 -8306 1 -4112 1 -4112 0 4 -1252 1 -4085 1 -4085 0 4 -7146 1 -4024 1 -4023 -0 -0001 5 -3036 1 -3953 1 -3952 -0 -oooi 5 -8932 1 -3872 1 -3871 -0-0001 6 -4825 1 -3782 1 *3781 -o-oooi 7 -0718 1 -3680 1 -3680 0 7 -6612 1 -3568 1 -3568 0 8 -2505 1 *3444 1 -3444 0 8 -8398 1 -3308 1 -3308 0 9 -4291 1 -3161 1 -3161 0 It will be seen that the agreement is very close throughout . It could probably be improved by a slight modification of the constants in the dispersion formula ; but it is needless to do this until there is a closer agreement between different observers as to the values of the refractive indices . The value assigned to the dielectric constant is the mean of the best direct determinations of that quantity , and the prediction as to the positions of the absorption bands is as near the mark as could be desired .

rspa_1908_0093

0950-1207

The effect of pressure upon Arc spectra. no. 2.\#x2014; copper, \#x3BB; 4000\#x2014; \#x3BB; 4600.

378

380

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

W. Geoffrey Duffield, D. Sc.|Professor E. Rutherford, F. R. S.

abstract

6.0.4

http://dx.doi.org/10.1098/rspa.1908.0093

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0093

10.1098/rspa.1908.0093

Atomic Physics

Thermodynamics

Atomic Physics

378 The Effect of Pressure upon Arc Spectra . No. 2.\#151 ; \ 4000\#151 ; \ 4600 . By W. Geoffrey Duffield , D.Sc . ( Communicated by Professor E. Rutherford , F.R.S. Received September 1 , 1908 . ) ( Abstract . ) A direct current arc from 100-volt mains was formed between copper rods within a pressure cylinder designed by Professor J. E. Petavel , E.R.S. The light passed through a glass window , and , after reflection from two mirrors , was focussed upon the slit of the large Rowland grating spectroscope in the Physical Laboratories of the Manchester University . The apparatus and method of using it have been described in a previous paper.* The spectrum of the copper arc in air has been photographed in the region X \#151 ; 4000 to X = 4600 A.U. at the following pressures : 5 , 10 , .15 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , 100,125 , f 150 , f 203f atmospheres ( excess above 1 atmosphere ) . I. Broadening . Within the region XX 4000\#151 ; 4600 :\#151 ; 1 . All lines are broader under high pressures than under atmospheric pressure . 2 . The broadening increases with the pressure ; it has not been determined if the increase is continuous and linear with the pressure . 3 . The broadening of all lines is unsymmetrical , being greater on the red side . 4 . The amount of broadening is different for different lines . 5 . Two types of broadening have been observed : some lines at first become faint and hazy , almost resembling bands , and are completely dissipated under higher pressures ( series lines ) ; others , though much broadened , remain well-defined lines ( non-series lines ) . 6 . No simple relation has been found between the width of a line under pressure and its original intensity . 7 . The intensity curves of the sharp lines under pressure are steeper towards the violet than are those of the nebulous lines . The sharp and nebulous lines retain their characteristic " hard " and " soft " appearances throughout . * Duffield , ' Phil. Trans. , ' A , vol. 208 , p. Ill ( 1908 ) . t Added October 19 , 1908.\#151 ; G. D. The Effect of Pressure upon Arc Spectra . 8 . The nebulous and sharp non-series lines broaden to about the same extent ; for the well-defined lines , the width may be as great as 12 A.U. aj ; 203 atmospheres.* 9 . The broadening at first appears to increase more rapidly than the displacement , making measurements at low pressures less accurate than those at high pressures . II . Displacement . Within the region Xk 4000\#151 ; 4600 :\#151 ; I 1 . Under pressure , the most intense portion of every line is displaced from the position it occupies at a pressure of 1 atmosphere . 2 . The displacement is in the direction of greater wave-length . 3 . The displacement is real , and not due to unsymmetrical broadening , i.e. % the line is broadened about a displaced position . 4 . The displacement of each line is , within the limits of accuracy of the-experiments , continuous and linear with the pressure . 5 . The rates of increase of the displacement with the pressure are different for different lines . 6 . The lines belonging to the first and second subordinate series have greater-displacements than the non-series lines . Their great width precludes accurate measurement . 7 . The displacements of non-series lines are functions of their wavelengths . The evidence indicates that they vary with a power of theyatter , . at least as great as the third and possibly as great as the sixth . 8 . There is some reason to believe that there are two values for the displacement of a line at one and the same pressure . 9 . The mean displacement of the non-series lines is 12'2-thousandths of an , A.U. per atmosphere . The largest displacement measured is a little more than 2 A.U. at 203 atmospheres.* III . j Rever None of the copper lines within this region showed any signs of reversal under pressure . IY . Relative Intensities . Within the region W 4000\#151 ; 4600:\#151 ; 1 . Changes in relative intensities of lines occur under pressure . 2 . Those belonging to either the first or second subordinate series vanish at * Added October 19 , 1908 , \#151 ; G. D. The Effect of Pressure upon Arc Spectra . about 40 atmospheres and do not reappear as the pressure is increased { obliterated lines ) . 3 . Members of the first sub-series become at low pressures faint and hazy , almost resembling bands , and are at higher pressures dissipated . There is , however , always a marked cloudiness in the neighbourhood of their original position . 4 . Members of the second sub-series gradually diminish in intensity without abnormal widening . No cloudiness is distinguishable near their original position . 5 . Of the non-series lines , those that are nebulous are strengthened relatively to those that are sharp . 6 . Lines strengthened under pressure do not correspond with those given .by other workers as " enhanced " lines . Y. Brightness of the Arc. The brightness of the copper arc increases enormously with the pressure of the surrounding air . i

rspa_1908_0094

0950-1207

The action of chlorine upon urea whereby a dichloro urea is produced.

381

388

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

Frederick Daniel Chattaway, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1908.0094

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10.1098/rspa.1908.0094

Chemistry 2

Biochemistry

Chemistry

381 The Action of Chlorine upon Urea a Dichloro Urea is produced . By Frederick Daniel Ciiattaway , F.R.S. ( Received June 10 , \#151 ; Read June 25 , 1908 . ) Although a few of the more familiar substances containing halogen attached to nitrogen , as , for example , nitrogen chloride , have been known for a long period , it is only within the last 10 years that such compounds have been systematically studied . They form , however , a group of extraordinary interest and play an all important part in many complex reactions ; to illustrate this it is only necessary to refer to the substitution of halogen in anilides and to the well-known method for obtaining amines from amides . I have shown in a series of investigations that hydrogen attached to nitrogen in compounds of the most varied characters may be replaced with ease by chlorine or bromine if suitable conditions are observed and it may be said , speaking generally , that this can always be done , although the nitrogen halogen derivatives produced may react or undergo isomeric change so readily that they can only with difficulty be isolated . All compounds in which halogen is directly attached to trivalent nitrogen can take part in certain well-defined reactions characteristic of the linkage . One of the most striking of these group reactions is that with hydriodic acid , whereby at the ordinary temperature the halogen is replaced by hydrogen and iodine is liberated quantitatively . This reaction , which may be expressed by the general equation :nx+2HI = :nh+hx+i2 affords an easy method of analysing these compounds . Such a nitrogen halogen derivative is formed as an intermediate product in a reaction with urea , the course of which has never hitherto been explained although it has received an unusual amount of attention on account of its furnishing a ready method of estimating the quantity of this substance present in a liquid . When urea is added to a solution of an alkaline hypochlorite or hypo-bromite it is at once decomposed , nitrogen and carbon dioxide being set free ; if an excess of alkali is used the carbon dioxide is fixed and the nitrogen , which alone escapes , should thus afford a measure of the amount of urea . The reaction is generally represented by the equation:\#151 ; CO(NH2)2 + 3NaOBr = C02 + N2 + 3NaBr + 2H20 , 2 c VOL. LXXXI.\#151 ; A. Dr. F. D. Chattaway . Action of Chlorine [ June 10 , which throws no light upon its nature ; indeed it obscures it , as it makes it appear to be a case of oxidation . It does not even express quantitatively what takes place , for all chemists who have investigated the decomposition shave noted that the amount of nitrogen liberated is invariably less than that -contained in the urea used . When the operations are carried out under specified conditions this loss of nitrogen , which may amount to as much as half of the total , is very constant and so can be allowed for by adding a -definite fraction of the whole to the gas actually measured . The method can thus be made to give results sufficiently accurate for clinical purposes and since it is easy to carry out it has received very general application . It is not known what becomes of the nitrogen which does not appear as gas , for all the suggestions that have been made hitherto wholly fail to account for more than a small fraction of the quantity that disappears . If urea be added instead of to an alkaline solution of a hypochlorite to one acidified by acetic acid , that is to a solution of hypochlorous acid no gas is evolved , nor is any gas liberated if chlorine itself is passed into a solution of urea in acetic acid . Action , however , takes place in each case and a nitrogen chloride is produced ; for although the hypochlorous acid or chlorine disappears , the resulting solution liberates iodine in large quantity from hydriodic acid . The isolation of the substance produced from such a solution is not practicable , since the method of extraction by chloroform which often serves for the separation of substituted nitrogen chlorides cannot be used , as the ehloro urea formed is easily soluble in water but almost insoluble in chloroform . It is , however , less soluble in water than urea itself and crystallises out in a pure condition when chlorine in excess is passed rapidly through a cooled sufficiently strong aqueous solution of urea . The action \#166 ; which takes place is represented by the equation C0\lt ; nh ! +2C12= C0\lt ; NHC1+2HC1\gt ; two only of the four hydrogen atoms of the urea being replaced by chlorine . This dichloro derivative appears to be the only stable nitrogen chloride which urea is capable of forming . The crystals which separate from the solution of urea have this composition from the first and chlorine seems to .have no further substituting action upon them . Dichloro urea , having regard to its mode of formation , as well as to the structure of urea itself , has most probably the constitution represented by N Cl the formula OIC^ X*\lt ; C1 which explains its formation and such of its reactions as have yet been studied . 1908 . ] upon Urea whereby a Dichloro Urea is produced . 383 If this constitution be granted it seems probable that the reaction between urea and chlorine takes place in two stages and that the amino groups are substituted successively , but the monochloro derivative does not crystallise out , possibly owing to its solubility being not far removed from that of urea itself . Either of two causes may prevent the formation of a ter- or tetra-chloro derivative ; the hydrochloric acid which is formed in the reaction may prevent that addition of chlorine to the nitrogen which must precede furthur substitution , or the more highly substituted urea may be hydrolysed so easily that it breaks up as soon as it is formed . Dichloro urea is so much more easily hydrolysed than urea itself that the latter is the more probable cause . Although two molecules of hydrogen chloride are formed when urea is substituted by chlorine , very little heat is developed , dichloro urea must therefore be an endothermic compound and might be expected to be highly explosive . When heated , however , it does not explode itself but decomposes with liberation of nitrogen chloride which , if heated a few degrees above the temperature at which it is set free , may detonate with great violence . Dichloro urea gives all the characteristic reactions of a typical nitrogen chloride ; for instance , it liberates iodine from hydriodic acid , chlorine from hydrochloric acid , and reacts with alcohol , forming ethyl hypochlorite , urea being in each case re-formed . It is distinguished from most other substituted nitrogen chlorides by the readiness with which it is hydrolysed in presence of water , nitrogen chloride , carbon dioxide , a little nitrogen and ammonium chloride being formed . If the compound is dissolved in water or kept in a moist atmosphere , this hydrolysis takes place slowly at the ordinary temperature and becomes very rapid at about 30 ' C. It is probable that in this reaction a mono-substituted ammonia is first produced thus:\#151 ; C0\lt ; \#153 ; a+2H ' ' = CO\lt ; oh+2NH2C1 ; but if so it apparently can only exist momentarily , as nitrogen chloride is at once liberated . The formation of the end products of the reaction can be explained by assuming that this monochloro ammonia at once breaks up into ammonia and nitrogen chloride , 3NH2C1 = 2NH3 + NCI3 , which then to some extent react , forming nitrogen and hydrogen chloride , the latter at once combining with the free ammonia and allowing the remaining 2 c 2 Dr. F. D. Chattaway . Action of Chlorine [ June 10 , nitrogen chloride to escape , as this does not react with ammonium chloride . Both acids and alkalis accelerate the rate of hydrolysis and also alter the nature of the end products by hindering or furthering the secondary reaction between the ammonia and the nitrogen chloride . In presence of dilute acids the ammonia is at once fixed and the reaction between it and the nitrogen chloride with its accompanying liberation of nitrogen is prevented , all the chlorine contained in the dichloro urea is therefore liberated as nitrogen chloride . In presence of alkalis , on the other hand , the reaction between the ammonia and the nitrogen chloride goes on to completion , since the hydrochloric acid formed in it is at once fixed ; no nitrogen chloride , therefore , is set free , since twice as much ammonia is formed as is required to decompose it . The reaction between dichloro urea and a solution of caustic potash is instantaneous : nitrogen is liberated with violent effervescence , the excess of ammonia and the alkaline carbonate formed remaining dissolved in the liquid . The action , which is quantitative , is expressed by the equation 3CO\lt ; k ! c1+12K'II = 3K2C03 + 2NH3 + 6KC1 + 2N2 + 6H20 . The behaviour of dichloro urea with alkalis affords an explanation of the course of the reaction which occurs when urea is decomposed either by an excess of alkaline hypochlorite or hypobromite . The urea is , without doubt , converted into dichloro or dibromo urea , * which is at once hydrolysed in the manner above described . In presence of the excess of hypochlorite or hypobromite , the mono-substituted ammonia formed in the hydrolysis may be further substituted to a greater or less extent , nitrogen being evolved quantitatively only when this takes place under such conditions that the amount of hydrogen attached to nitrogen in the reacting system is always sufficient to react completely with the chlorine attached to nitrogen . Preparation of Dichloro TJrea.\#151 ; The preparation of dichloro urea should be carried out at a low temperature and as rapidly as possible , since , in presence of the hydrochloric acid formed at the same time , hydrolysis so readily occurs and so much nitrogen chloride is produced that if it is carried out at the ordinary temperature , or its duration is unnecessarily prolonged , a poor yield is obtained . It is best , therefore , to work with small quantities , to cool thoroughly , and to pass the chlorine as rapidly as possible . * It is possible that in absence of free acid , and in presence of excess of hypochlorite or hypobromite , a tri- or tetra- substitution product may be produced , the formation and decomposition of which can be formulated easily , but this does not affect the essential character of the reaction , which is one of halogen substitution followed by hydrolysis of the substituted urea and interaction between the resulting compounds . 1908 . ] upon Urea whereby a Dichloro Urea is produced . 385 The following procedure gives a good result:\#151 ; Dissolve 20 grammes of urea in 40 c.c. of water and cool to about \#151 ; 10 ' C. in a mixture of alcohol and crushed ice.* Pass in as rapidly as practicable a stream of chlorine made by dropping strong hydrochloric acid upon bleaching powder . So little heat is evolved in the reaction that with proper cooling the temperature never rises above zero , however rapid the stream of chlorine . Nitrogen chloride is produced from the first and can be recognised by its characteristic smell , but it remains in solution , the liquid , owing to its presence , becoming bright yellowT in colour . After passing the chlorine for a considerable time , white crystals make their appearance , at first usually on the surface of the liquid ; these increase in amount till the whole becomes a pulp of thin colourless plates . When these no longer appear to increase in amount , filter off , separating the acid mother liquor as completely as possible ; wash once or twice with a little water and when as much of the latter as possible has been removed wash the crystals several times with dry chloroform . Dichloro urea is not appreciably soluble in cold chloroform and a good deal of adhering moisture is thus got rid of . Press finally between filter paper , spread out in a thin layer on a clock glass , and free from the last traces of water by exposing for about half an hour over phosphoric oxide in a vacuum . A further crop of crystals can be obtained by again passing chlorine through the cooled mother liquor and this can be repeated as long as any separate . Nothing besides dichloro urea and th products of its hydrolysis are formed in the reaction ; if the acid mother liquor is evaporated down , carbon dioxide is given off and nitrogen chloride escapes in quantity ; later , as the liquid becomes concentrated , hydrogen chloride is expelled , and finally ammonium chloride is left . Although the final result of the action which takes place is the substitution of two atoms of hydrogen by two atoms of chlorine , as in other similar cases , this is without doubt effected by the addition of four atoms of chlorine to the nitrogen followed by the elimination of two molecules of hydrogen chloride . The yield of dichloro urea is not very large , so much being hydrolysed during the process : in a well conducted experiment it reaches about 25 per cent , of the theoretical , the weight of pure dry product obtained amounting as a rule to rather more than half the weight of the urea used . The loss , although largely due to the hydrolysis of the compound , is much increased by the * It is not absolutely necessary to use a freezing mixture , the temperature , owing to the urea dissolving , falls at once to below zero , and if the flask in which the operation is carried out is cooled by tap-water , a moderate amount of the compound can be obtained , but the yield is much better at a lower temperature . 386 Dr. F. D. Chattaway . Action of Chlorine [ June 10 , circumstance that dichloro urea is very soluble in water and consequently a considerable amount does not crystallise out from the mother liquor . Dichloro urea reacts with an aqueous solution of hydriodic acid in the way characteristic of nitrogen chlorides ; urea is reformed and iodine quantitatively liberated . It was analysed by taking advantage of this reaction : a known weight was added to an excess of a solution of potassium iodide made acid by acetic acid and the iodine liberated estimated by a standard solution of sodium thiosulphate . 0*5112 gramme liberated iodine = 158*6 c.c. N/ 10 I. Cl , as ! NCI = 54*99 per cent. CON2H2CI2 requires Cl , as ! NC1 = 54*96 per cent. Dichloro urea cannot be kept for any length of time without change . When damp it hydrolyses exactly as when dissolved in water . To obtain it pure , therefore , it must be dried very rapidly over phosphoric oxide in a vacuum . When only freed from adhering water as far as possible by a pump , it is slowly hydrolysed by the retained moisture even though placed in a desiccator over strong sulphuric acid , and this often occurs to such an extent that the mass becomes quite yellow from the nitrogen chloride mechanically retained by the crystals . To show the amount of hydrolysis which takes place under these conditions a quantity of the pure substance freed from all but adhering water thus tvas kept over strong sulphuric acid , and analysed from time to time , the nitrogen chloride formed being allowed occasionally to escape . In two days the percentage of chlorine as : NCI had fallen to 43*79 and in seven days to 13*33 . Even when dried and kept over phosphoric oxide it slowly decomposes , nitrogen chloride being evolved . A quantity of the pure dry compound thus preserved in a vacuum over phosphoric oxide was analysed at intervals ; after 12 hours the percentage of Cl as I NCI had fallen to 54*67 , after two days to 52*97 , and after nine days to 47*87 per cent. When an aqueous solution is kept at the ordinary temperature the dichloro urea is slowly hydrolysed ; carbon dioxide , a little nitrogen and nitrogen chloride escape and ammonium chloride remains in solution . Hydrolysis by water takes many days to complete unless the aqueous solution is warmed , when it is much more rapid ; at about 20 ' bubbles of gas are freely evolved and rapid effervescence sets in at about 40 ' , the nitrogen chloride escaping without explosion . Dichloro urea prepared as described above is a soft , white , crystalline powder with a pearly lustre . Under the microscope it is seen to consist of thin transparent plates somewhat irregular in shape . It can be recrystallised 1908 . ] upon Urea whereby a DichUrea is produced . 387 from water , in which it is easily soluble and from which it separates in similar but larger plates , by cooling an aqueous solution saturated at about . 15 ' C. though with some loss owing to hydrolysis . Its aqueous solution is at first colourless but becomes yellow as hydrolysis proceeds , owing to the liberation of yellow nitrogen chloride which remains dissolved in the water . It is easily soluble in alcohol and ether , very slightly soluble in chloroform and insoluble in petroleum ether . When its alcoholic solution is heated it reacts in the way characteristic of nitrogen chlorides , urea is reformed and ethyl hypochlorite is produced , the latter very easily breaking down into aldehyde and hydrogen chloride . Its behaviour with acids is complicated by the circumstance that it is so readily hydrolysed ; for example , when it is added to strong hydrochloric acid though chlorine is rapidly given off the amount of urea reformed is not very large . When placed in cold strong sulphuric acid it is hydrolysed and nitrogen chloride is liberated . The latter decomposes into its elements if the liquid be heated , its characteristic smell disappearing and being replaced by that of chlorine . Dichloro urea is a compound of a marked acid character , it has an acid taste recalling that of hypochlorous acid and its aqueous solution strongly reddens litmus paper , which only becomes bleached after the lapse of some minutes . It acts very corrosively upon the skin , staining it yellow and destroying the tissues . When heated , dichloro urea melts with decomposition at about 83 ' , nitrogen chloride being liberated . Although the substance appears not itself to explode , if the temperature of the bath in which the melting point is being taken is allowed to rise at all rapidly a few degrees above this point , the nitrogen chloride set free in the melting point tube may explode with considerable violence . It can be decomposed without danger by throwing it into a porcelain dish heated to 100 ' on a water bath in quantities of not more than about half a gramme at a time . The white compound fuses and gives off nitrogen chloride as a yellow vapour which escapes quietly unless , through too large a quantity of material having been decomposed at once , some of the vapour is mechanically retained as bubbles in the semi-fused residue and thus becomes heated to the temperature at which it explodes . Hydrogen chloride is not set free when dichloro urea is thus decomposed by heat . When an aqueous solution of the compound is added to a solution of caustic soda , vigorous effervescence , due to escape of nitrogen , occurs . The liquid remaining contains ammonia and potassium carbonate , the volume of carbon dioxide liberated when this is treated with an acid being to the volume of Mr. A. Mallock . O Instability of [ June 25 , nitrogen previously liberated in the ratio of 3 to 2 . One-third of the nitrogen contained in the dichloro urea used is found as ammonia . The investigation of dichloro urea , which is an extremely reactive body and promises to be of considerable use in organic synthesis , is being continued . The thanks of the author are due to Dr. Baker for allowing him to use the Christ Church Laboratory , where this work has been carried out . Note on the Instability of Tubes subjected to End . and on the Folds in a Flexible Material . By A. Mallock , F.R.S. ( Received and read June 25 , 1908 . ) When a straight rod is subjected to end compression it is stable for small lateral displacements unless the compressing force exceeds a definite limit depending on the elastic constants of the material of the rod and its length and cross section dimensions . If this limit is exceeded , the rod is unstable and the least departure from straightness grows under the action of the force , the axis of the rod then taking the form of one of the well-known elastic curves ; and this is the only form which a solid rod can take in the circumstances . With tubes and plates , however , the case is different , for with the tube the ratio of the thickness of the walls to the diameter of the tube has to be considered as well as the ratio of the diameter to the length . Thus a tube whose length is insufficient to produce instability involving a bending of the axis may become unstable by the crumpling up of the walls , the axis itself remaining straight . In plates something of the same kind may take place . The edges of a rectangular plate may be constrained to remain straight and parallel to one another , but if pressure is applied to two opposite edges instability will ensue if it exceeds a critical value . In the case of solid rods the governing condition is the constancy ( to the first order ) of the length of the axis ; with tubes and plates it is the constancy to the same order of the area of the mid-wall surface . Considering the case of tubes in rather more detail , take the axis of the tube as z and let its unstrained radius be r0 .

rspa_1908_0095

0950-1207

Note on the instability of tubes subjected to end pressure, and on the folds in a flexible material.

388

393

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

A. Mallock, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1908.0095

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0095

10.1098/rspa.1908.0095

Measurement

Fluid Dynamics

Measurement

388 Mr. A. Mallock . O Instability of [ June 25 , nitrogen previously liberated in the ratio of 3 to 2 . One-third of the nitrogen contained in the dichloro urea used is found as ammonia . The investigation of dichloro urea , which is an extremely reactive body and promises to be of considerable use in organic synthesis , is being continued . The thanks of the author are due to Dr. Baker for allowing him to use the Christ Church Laboratory , where this work has been carried out . Note on the Instability of Tubes subjected to End . and on the Folds in a Flexible Material . By A. Mallock , F.R.S. ( Received and read June 25 , 1908 . ) When a straight rod is subjected to end compression it is stable for small lateral displacements unless the compressing force exceeds a definite limit depending on the elastic constants of the material of the rod and its length and cross section dimensions . If this limit is exceeded , the rod is unstable and the least departure from straightness grows under the action of the force , the axis of the rod then taking the form of one of the well-known elastic curves ; and this is the only form which a solid rod can take in the circumstances . With tubes and plates , however , the case is different , for with the tube the ratio of the thickness of the walls to the diameter of the tube has to be considered as well as the ratio of the diameter to the length . Thus a tube whose length is insufficient to produce instability involving a bending of the axis may become unstable by the crumpling up of the walls , the axis itself remaining straight . In plates something of the same kind may take place . The edges of a rectangular plate may be constrained to remain straight and parallel to one another , but if pressure is applied to two opposite edges instability will ensue if it exceeds a critical value . In the case of solid rods the governing condition is the constancy ( to the first order ) of the length of the axis ; with tubes and plates it is the constancy to the same order of the area of the mid-wall surface . Considering the case of tubes in rather more detail , take the axis of the tube as z and let its unstrained radius be r0 . 1908 . ] Tubes subjected to End , etc. Under end compression the surface may become unstable by deformation into any of the cylindrical harmonics of the type r \#151 ; r0 + a cos n cos \#151 ; z , A , where 6 is the angle which r makes with a fixed diameter of the tube and \ the length of the fold parallel to the axis . The order of the harmonic which will naturally be assumed by the deformed tube depends on the ratio ( h/ r ) of the thickness of the walls to the diameter and will be such that the potential energy of the combined bending and shearing involved may be a ' maximum . I will not in this note work out individual cases , but it will be seen that the smaller the ratio h/ the higher will be the order of the harmonic , because , since the shear becomes relatively more important as diminishes , must also diminish to fulfil the condition of maximum potential energy.* If the crushing is continued until the tube is greatly reduced in length the folds are seen to develop into the symmetrical shapes shown in the photographs ( figs. 1 , 2 , 3 ) , for which n = 1 , 2 , and 3 respectively . For 1 the folds Fig. 1 . Fig. 2 . Fig. 3 . are circular in plan and independent of 0 ; when = 2 the plan of the folds is a square , and when n \#151 ; 3 the plan is hexagonal . It may he noticed that the instability always shows itself first at one end , and that since the reaction against end pressure decreases as the deformation goes on , each fold is completed in succession , the next not becoming marked until the reaction is increased by the previous fold resting against the last hut one . * It often happens that owing to the constraint applied by the surfaces between which the tube is crushed , the fold first foi'med is of the first order , even when the ratio of thickness to diameter is such that a higher order is the natural one . 390 Mr. A. Mallock . On Instability of [ June 25 , The crushing force requisite therefore undergoes periodic variations , being a maximum at the beginning of the formation of a new fold and a minimum when the fold is nearly completed . If we examine the completed folds on the assumption that the extension of any element of the surface is small compared to the depth of the fold , it will be seen that the side of each fold ( AB ) , see fig. 4 ( for which = 3 ) , at the Fig. 5 . Fig. 4 . re-entrant angle has a length 27 rr/ n.Also that the least distance ( OC ) of the fold from the centre is \#151 ; cos \#151 ; and the maximum distance ( OB ) is \#151 ; sin \#151 ; , n n n n The length of each fold as it would appear on the undeformed tube is therefore 27rr ( 1\#151 ; cos -)w sin\#151 ; . Thus for = 2 , rr ; and for 3 . n n \ = 27rr/ 3v/ 3 . The formulae do not apply when for in this case the assumption that the extension is small compared to the depth of the fold is untenable . But with n = 2 and n = 3 I find by trial that the number of folds formed from a given length of tube corresponds very fairly with the supposition that the extension is small . In fig. 5 the vertical and horizontal lines are the nodal lines of the harmonic cos 3 6cos of 3 z on a cylindrical surface ; the spiral lines ultimately become the salient angles of the folds , and the dotted lines indicate the locus of points of no compression or extension when the tube is completely crushed . The potential due to small deformations of either the tubular or the completely crushed surface can be calculated by the use of recognised Tubes subjected to End , etc. 1908 . ] functions , but the intermediate stages , where the local extension or compression of the mid-wall surface is not a small quantity , present a far more difficult problem , the solution of which would probably require the investigation of functions of a new class . The problem is , in fact , merely a particular case of the general theory of the form of the folds of drapery , that is of the surfaces into which a plane can be deformed if its material can be stretched by an amount which is finite but small compared to the depth of the folds . As a simple example , consider the case of a circular cone ( fig. 6 ) . Let this Fig. 6 . Fig. 7 . be intersected by a similar cone , the axes of both being in the same plane , and intersecting at equal distances from their apices . The curve of the intersection of the surfaces is a conic whose plane bisects the angle between the axes . Now let that part of one of the cones outside the curve of intersection be removed ; the remaining surface is of exactly the same area as the original cone and could have been formed from it by bending without any stretching of the mid-surface . Such a partly inverted cone is typical of the fold in a flexible and inextensible surface , and it remains to be seen what form the angle of the fold would take if the material resisted bending . In this case there cannot be an abrupt change in the direction of the surface in passing from the original cone to the part inverted , and what in the perfectly thin and flexible material was a sharp crease becomes , in virtue of the stiffness , a rounded curve , EFG . If AB , AC , fig. 7 , are two of the generating lines of the cone , a small distance on either side of that passing through the vertex of the conic , the effect of resistance to bending will be to increase the distance of the surface from the axis of the original cone from E to F and to diminish the distance Mr. A Mallock . On the Instability of [ June 25 of the surface from the axis of the inverted cone from F to G. Hence there will be circumferential extension of the material from E to F and circumferential compression from F to G. The distorted generating lines will therefore take some such shape as is indicated by the dotted lines in fig. 7 . In the undistorted cones the principal radii of curvature at the vertex of the conic are , for the original cone , \#151 ; co and AF tan a and for the inverted surface -f oo and \#151 ; AF tan\#171 ; . By a general theorem relating to the curvature of surfaces ( the measure of curvature being ( RiR2)-1 , where RiR2 is the product of the principal radii of the surface ) , no stretching of the surface is involved by any changes in the principal radii of curvature which satisfy the condition ItiR2 = constant . In the neighbourhood of the vertex of the conic the resistance to bending makes both the principal radii of curvature finite , hence ( RiR2)-1 is finite ( instead of zero as on the undistorted surfaces ) , and if s be any small area on the distorted surface , the amount of stretching due to the resistance to bending is ( 1 \#151 ; cos #)/ ( l-f cos 0)* where 0 is the average angle which the edge of the distorted area makes with the original surface . Where , as at AH , the generating lines cut the conic very obliquely , only one of the principal radii of curvature is appreciably affected , and the resistance to bending has hardly any effect in altering the area of the surface . Thus absence of perfect flexibility causes a general rounding off of the sharp crease which forms the conic on the undistorted surface , a rounding off which is more and more marked as the distance from the vertex increases , and in addition to this , a knuckle-like prominence is produced in the neighbourhood of the vertex itself . As a second example of simple folds , it may be seen at once that any rectangular plane surface can be folded without stretching into a series of cones such as are shown in photographs Nos. 8 and 9 . In No. 9 the radius of curvature has the same sign in all the cones , but in No. 8 the curvature is alternately positive and negative . In both , when seen in plan , the average direction of the edges at right angles to the axes of the cones is parallel to direction of the corresponding edges of the plane before folding . When viewed in elevation , however ( figs. 8a and 9a ) , it will be noticed that the free edges of the folds appear to be at right angles to the original plane in No. 8 , where the curvature is alternately positive and negative , but at right angles to the slant side of the cones in No. 9.f * The stretching is not uniform over the area , but increases from 0 to a maximum at the boundary . t It should be stated that the edges do not really lie in a plane , but the departure from a plane is of a very small order . 1908 . ] Tubes subjected to End , etc. If , then , any number of equal rectangular sheets are folded as in fig. 8 , they may be joined at the free edges of the folds without stretching and the average surface of the joined sheets will be a plane . Sheets folded as in No. 9 may also have the free edges of their folds joined , but each sheet will now make an angle with the adjacent one equal to twice the angle which the slant side of the cones makes with the plane from which they were formed . Sheets thus joined are shown in the photograph ( fig. 10 ) and in plan in fig. 10a . Fig. 10 . Fig. 10a . Thus the cones of the combination of folded planes will all touch a cylinder , and the character of the surface of the combination will be analogous to , but not identical with , the intermediate stages of crushing of a tube by end pressure .

rspa_1908_0096

0950-1207

Note on horizontal receivers and transmitters in wireless telegraphy.

394

397

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

Prof. H. M. Macdonald, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1908.0096

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10.1098/rspa.1908.0096

Fluid Dynamics

Tables

Fluid Dynamics

]\gt ; S94 Note on Horizontal Receivers nsmitters iWireless By Prof. H. M. MACDONALD , ( Rcgistered July 18 , having been received by the Secretary at Cambridge , May 12 , \mdash ; Read November 19 , 1908 . ) In a communication published in the ' Proceedings , '* Mr. Marconi given the results observed when a straight horizontal conductor is sub . stituted for the usual vertical conductor employed as a transmitter 01 receiver at a wireless telegraph station . object of the following note is to consider the theory of such an arrangement , or at any rate one aspect of it . The receiver , as being the more important , will be considered first . earth Let AL ' represent the horizontal receiver , of a end A connected to a spark-gap or other wave detector . The osciilations in AB can be represented by a distribu tion of oscillators along AB , and , if denotes the current strengtl ] at any point of AB , it must satisfy the conditions at , the free end and at , since the electric force perpendicular to AB at A must vanish . If the dislance of AB from the earth is not too small , the effect 04 the oscillations belonging to the in the earth of AB on those in AH may be ected , the radiation from the free end will be approximately sylnmetlical with respect to AB , and the oscillations in AB are then approxilnately tlJe same if formed part of a sclli-infinite conductol in a system of oscillations is being free and first node from the free end ; che -length of these oscillations is very ) oximately five times the length of AB , ctnd therefore the receiver is of cienC ) is one-fifth of the of nsmitted w , a result observed ) When the distance of AB fi earth is snlall that the effcet of the oscillations in the of in the earth on the oscillations in ) is not ible , the ladiatio1 ] -f , Malch , lncdonald , ' Electric aves , . X. . Soc. Proc. , , vol. 7 p. Horizontal Receivers Transmitters . rom the free end will not be symmetrical with respect to AB , but may be ( aken as approximately symmetrical with respect to some through 3 an angle with BA ; the wave-length of the oscillations in AB is herefore equal to the wave-length of the oscillations in a bent conductor oiuing ; that is greater than five times the of AB , and , therefore , this case the receiving conductor has its maximum efficiency when its ength is what less than one-fifth of the length of tlje transmitted wave , result also obseryed by Marconi . * To examine the effect of the orientation the receiver , consider a straight conductol BAB ' twice the of AB fig. 2 ) and its in the horizontal plane , A and their niddle points respectively . earth FIG. 2 . When electric oscillations are being maintained in BB ' with the correset in , A and are nodes , hence , if a wave-detector is placed effect will be observed in it due to its own oscillations , and herefore the potential difference at , due to the forced oscillations in the ceceiver when the receiver AB is in the position fig. 1 is equal and opposite any instant to the potential difference at when the receiver is in the position which results from turning it through two right-angles ound C Now , the total effect at is made up of two parts , one due to the action of the ancing waves , the other due to the oscillations in the receiver . If in fig. 1 the advancing waves be supposed to be from left to right , the oscillations in the receiyer may be regarded as the resultant of two sets of progressive waves , one travelling from to A and the other from A to ; and , since the oscillations in the receiver are maintained by the advancing waves , the set of ressive waves in the receiyer travelling from to A must be in the snme phase as the advancing waves at A. Further , since the electric force perpendicular to AB at A vanishes , the electl'ic distribution on AC has at any instant the opposite sign to that on AB , and therefore the potential diffel'ence at due to the oscillations in the receiver is at each instant in the opposite phase to the potential difference due to the direct action of the advancing waves . Hence , if denote the maximum potential difference at due to the direct action of the waves , and the maximum potential difference due to the oscillations in the Prof H. cdonald . lIay 1 recciver , the diflercnce at at nny instant is AB is two ) , the es stil left to , the set of ) ssivec , ayes in elling to A ) in opposite to the wavCf , since the tions in the are , as waves , and therefore ) ntial difference at due to oscillations the receiver is in ] case the same as that to the action of the and instant Hence the total effect at is eater wheIl the free eIJd f is dire the tIlSInittcr L il is ) ctly t it . In the ) ) the ) has ) ssumed to ) placed wave onts . is in the plane of the fronts of the ions lvil be set up BB ' ; and , therefore , when ] an the tion of the waves , the of the in betweell and the alue ] ) ) ndinr ) to . Hence , AB all angle with direction in waves dvaneing , the ential rencc at is ) where , and depends } . If , then , a curve lepresent the potential iHeren in terms of the orientation the er , it will of the form ) , with uneqnal ) loop ] ) further fionl the txansnlilter , its radius ) eing When the horizontal conductol is usetl as \ldquo ; its effect is ma two sets of ations , one oscillations in condnctol eltlanating from the free end , other At a distance the eHect of the is as that oscillator its inlage in the ] ) ) ; hence , such that is vertical and is the tion oi AB , the vertical distance due to this set is The due to the secol ) is only face is from ) the lre und proximately the op posite on 1908 . ] Transmitters Wireless proceeding from . Hence the square of the amplitude of the vertical force at a distance is where is the angle the direction of the receiver makes with AB , and for a given value of this gives a figure 8 curve , with unequal loops to represent the intensity of the transmitted waves . [ A 31.\mdash ; The essential feature of the various systems of directed wireless rraphy is the ence of two sets of waves differing in phase and proceeding from sources at a distance apart . ement consists of three vertical , each 20 metres , placed at the corners of an equilateral triangle whose side is 30 metres . The waves from one of these differs in phase by from the waves from the other two . For the best effect the perpendicular of the is a of a wave-length , as then the waves in one direction are in the same phase , while those proceeding in the opposite direction are in opposite phases . For this , that is , or approximately five times the height of the antenna , , with theory . Artom 's arrangement consists of two equal antennae , each inclined at an angle of to the horizontal , the oscillations in them in phase by . The antennae are bent through an of at the ends above the horizontal , and led to conductors ; the waves that interfere are those radiated from the bends , and the wave-length for the freatest effect be greater than five times the length of the straight part of an antenI ) , the radiation from the bend not ; symmetrical with respect to the antenna . For complete interference , that is , with the waves in one direction in the same phase , and the waves in the other direction in opposite , the distance between the two ends is a quarter of a wave-length ; hence , if is the of the straight part of each of them , , that is In arran ement the two sources are the and the free end of the horizontal conductor , whose distance apart is approximately onefifth of a ) , while oscillations differ in phase approximately , the waves at the bend differing in phase by . It should be observed that in Braun 's and Artom 's arrangement the amplitudes of the two component sets of waves are for all distances in the same constant while in Marconi 's angement the atnplitudes are in a ratio distance . ] ' Drahtl . Tele vol. 1 . Lincei , , vol. 1 p. 692 , 1906 . VOL. LXXXI.\mdash ; A.

rspa_1908_0097

0950-1207

The propagation of groups of waves in dispersive media, with application to waves on water produced by a travelling disturbance.

398

430

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. J. Larmor, Sec. R. S.

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6.0.4

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10.1098/rspa.1908.0097

Tables

Fluid Dynamics

Tables

]\gt ; The ofGroups of in , with Application to produced by T. H. HAVELOCK , M.A. , D.Sc . , ellow of St. 's College , Lecturer in Applied natics , College , Newcastle-on-Tyne . ( Communicated by Prof. J. Larmor , Sec. R. . Received August 26 , \mdash ; Read November 19 , 1908 . ) CONTENTS . SECTION PAGE 1 . Introduction 398 2 . Definition of Simple Group 399 3 . The Fourier Integral rega1ded as a Collection Groups 400 Damped nonic W 401 ( b ) InterI U Simple Wave-train 402 4 . Features or the ralS I 403 5 . Line Displacement ) ) Water 404 6 . Initial Displacement of Finite readth 406 7 . Limited Train of Oscillations 407 8 . Initial ilse on Deep 410 9 . Moving Line Impulse on ) Water 411 10 . Surface WnveH 413 11 . Water Waves due to Gravity and Capillarity 416 12 . Surface Waves in Two Dimensions 415 13 . Point Impulse Travelling over Deep Water 417 ( a ) The TrRnsyerse Svsteln 418 The ) Wave System 420 ( c ) The Line of 421 14 . Point Impulse for ) 15 . Impulse Moving on Water of Finite Depth 426 S1 . nction . The object of paper is to strate the my features of ) xation i. In the case of surface waves on deep watel renlal k earlier ators c the difficul proble ] of the ] ! of all itrary initial disturl ) ance as expl e a Fourier integral , developed subse ation of a single elelnent of their an train of rnlonic waves . point of view on ] is consists of a return to ourier i the elenlenr , of disturbance is not a ) harmonic ) , an of siInple } ains c a ivel possible to select from l of Groups of in , etc. 399 he few simple groups that are important , and hence to isolate the chief features , if , in the phenomena . In certain of the following sections well-known results nppear ; the aim las eeIl to develop these from the present point of view , and so illustrate he dependence of the phenomena npo11 the character of the velocity function . the other sections it is hoped that ress has been made in theory the ation of an arbitrary initial ( roup of waves , and also of the haracter of the wave pattern from a point ulse t on he surface . S2 . of Sintpfc We have to consider the translnission of disturbances in a for which the velocity of ation of eneons simple ] ) wave- , rains is a deiinite fmlction of the . The kinematically rroup of waves is composed of only two simple trains , of by an infinitesimal amount then with the usual ve have for the ined effect , ( 1 ) where . ( 2 ) The ession ( may be regarded as at any instant a , whose amplitude varies slowly with to the , lirst cosine factor . Thus it does not lepresent a which oves forward ; but it has a certain periodic , for the at ttny given instant is repeated after equal intel v of time , acedo 1 ) forward equal distances . The ratio of these quantities , namely , is called the group-velocity . It has also the , : in the ( hbourhood of an observer travelling with velocity the disturl ) ance continues to be approxi1nately a train of simple waves of The most feneral simple , or elementary , may be defined in the ving manner . Let the central be a sinlplc harmonic of , and let the other be similar whose a ) litude , length , and velocity differ but slightly fiotl the central ) ' ; then , similar approximation , have Dr. T. H. Havelock . T'he of [ Aug. 26 The of values of infinitesimal , roup as a whole may written , in the previous case , in ( 4 is a slowly ; and the -velocity is iven by . The group , to an observer travelling with velocity , appears as consistin of roximately simple of . The sinrple roup is , in fac ated as an nately homogelleons simple wave-train ; the impo ] tance of t , he yroul)-velocity lies in the fact that any departure fro1 eneity on a nple wave-train , due to local variation of amplitude phase , is ated with ] the velocity U. . Intcgral ' as a Collcction of An disturbance CftIl , in , be analysed by Fourier 's metho into a collection of simple wave-trains ran over possible values of thus after a time the disturbance ) iven by an expression of the typ , ( 6 where is a given function of The method adopted with is based on Lord treat meant of the case , in -ich the amplitude factol is a constant , so that solution of } is lcted tesent the subseque1l effect of an initial disturbance which is inhnitelv intense , and concentl'ated il a line the origin ; Lord Kelvin 's process boives an approximat suitable times and ) laccs such that is , and argument may be stated in the following llanner:\mdash ; In the dispersive medium the -trains included in each element of the varying } ) ] destructive , except when -hey in the same and so cnlnulativ ' the time under consideration , when the meant of the is stntionary in vadue . each as regards period , in the integral . represents a which cept around a point which itsel Now if we this ethod to the more . W. Tholnson , ' Boy . Soc. Proc vol. 42 , p. 80 . 1908 . ] Groups of , etc. expression for the total urbance , attending only to its prominent features and , the rest , provided we aSSUUle the of the amplitude factor to be gradual . On this hypothesis the resulting expression contains ] amplitude of the component trtIins simply as a factor ; and in this way the trains for which it is a maxinlnm show predominantly in the formula , which exhibits the nlain features of the disturbance as they arise from place to place though cunlulation of synchronous component trains . The ument shows that in some respects the integral ( 6 ) may be more conveniently arded ns a collection of travelling instead of sinple wave-trains ; when ( is a slowly function , the ) will be simple groups of the type ( 3 ) . The limitations within which this is the case will appear from the subsequent nalysis ; one method of procedure would be boraphical : to take a graph of the fluctuating factor and see that the other factor , which is taken constant , does not vary much within the range that is important for the In the cases we shall examine , the effect is due to a limited initiaI disturbance , and the salient features are due to the circumstance that has well-defined maxima ; thus the prominent part of the effect can be expressed in the form of simple groups belonging to the neighbourhood of the maxima . Before considel.ing in detail special cases with assigned forms of the velocity function , two illustrations of interest may be mentioned . ( a ) harlit \mdash ; If is a function satisfying the conditions for the Fourier transformation , we have For an even function of this ives , where . ( 7 ) let ) an fun ction of ( / , defined for all values , and such that it is equal to for positive ; ) we find ( 8 ) Consider this function the initial value of a disturbance occurs in a dispelsive lnedium ; then the value of at can be ressed , in eneral , by ( 9 ) . T. H. Hayelock . of [ Aug. 26 , are constants which need not be specified further in the connection . These ] are of type and represent infinite in the ) ( sitive and aCiv ecctions respectively . We see ( S ) that when is small , the amplitnde factor consists practically of single well-defined ) in the of the value . Hence , the coefficient is sJllall , -trains in question may considered as in the form of a roup of uIlchanging waves this specified structure . example serves to illustrate the ) ation of a very train harnlonic }aves s ) . as they travel to a small danlpi coefficient , and is of interest in connection with Lord ayleigh 's enera proof that -velocity is the vclocit with which energy is A small coefficient is introduced by him , so tha the transmitted is ined b the dissipated ; the argumen which of loses its neaning if is actually , shows that when ifished indefinitely the rate of transmission of approaches as limiting . SimilarJy , the Fourier transformation is inapplicabl when is aetnally zero , lnfer from the above analysis that when is dJle as a simple group of definite structure . ( b ) cider an disturbanc defined by , . Then disturbance is prcssio of the form ( 9 ) , in which , so the initial ) ance to an infinite with narrow that t of factor is the to in of the vadue . We infer from that a } ) is intell.upte i , s kin ) equivalent to a ) of , of lcfillite stluclre valne of the length . Lord , ' . lslath . Soc vol. 9 , p. 24 ( 1908 . ] of in Dispersire , etc. S4 . 's of the The inteoralso we have to consider in such problems are of the type . ( 11 ) All such integrals we can treat in the sa1ne manner , adopting the method employed ) Lord Kelvin for the particular case referred to above ( S.3 ) . This method consists in supposing that is , so that the cosine factor is a rapidly quantity compared with the first factor ; thus , as in the Fresnel discussion of the diffraction of light waves , Che prominent part of the of the integral is contained within a small of , for which is stationary in value , so that the elements are then cumulative . In other words , we select from ( 11 ) the roup or roups of terms round values ? of which make . ( 12 ) In such a roup of terms we may . Then if we write for , the contribution of the group to the value of ( 11 ) by , ( 13 ) where the limits of the integral may be in eneral extended , as in diffraction theory , , provided does not coincide with either limit of the integral ( 11 ) , and also proyided that is not zero . Thus we have , from ( 13 ) , / ? This is the sum of the contributions of the constituents of each around a central value iveu by ( 12 ) , provided the value comes within the of values of in the . If is ative , corresponding result may written We write down for reference the similar pair of results for a group of terms from the . ( 16 ) Dr. T. H. Havelock . The gation of [ Aug. 26 , Tf is positive , / ? ; and if is ative , . ( 18 ) The chief form in which such trals occur is , where . ( 19 ) The principal groups are iven by the values such that , or U. ( 20 ) The value of the can written down from one of the previous forms ; if is ative , should . ( 21 ) As an illustrative example we may supposc a disturbance to be iven at time by expression* . ( 22 ) When is , the elementary iven by ( 22 ) reinforce each other ] for the groups beriven by valnes for which the oument of the cosine is stationary , so that . ( 23 ) This equation ( 23 ) defines a velocity such that to an observer from the igin and with velocity complex disttlrbance has the earance of simple waves of 1-ength . Or , we ma } ' regard ( 23 ) as the predominant value of at any position and tinle in terms of and features of the bance depend on the form ] of the velocity ; we proceed to consider some ) ecial forms . S 5 . Iinp ) on cp consider surface waves on lited sleet of water , the only odily forees ) those travity . , and the bo vertically . Let be the tion of slllfnce waves of snlall nnplitude with parallel crests and to the -planc . It be shown that for an initial displace*Lord Kelvin , loc. cit. 1908 . ] Groups of in Disper . Media , etc. meant iven by without initial velocity , the surface fornl at any subsequent time is iven by where . ( Let be any even function of which can be analysed by Fourier 's integral theorem . Then , to an initial surface displacement ) , without innitial velocity , there is a surface form given at any subsequent time by where If we suppose the initial elevation to be limited practically to a line through the and assume that , so that , we can use , as an illustration of the procedure , the form We select from these integrals the groups which give the chief ular features at large distances from the original disturbance . This cumulative group from the first integral is iven for a ooiven position and tinle by the value of for which is stationary , where , so th ; and , similarly , from the second by Thus there groups of waves proceeding in the two directions from the ; for positive we need only consider the first in second redominant } at a point at time is iven by this predominant group by means of ) ression ( , we tain the known result . At a given position , far from the source for the train to taken Dr. T. H. Havelock . Propagation of [ Aug. 26 as unliJuited , this indicates oscillations succeeding each other with frequency and amplitude ; if we follow a of waves with value of varies scly as , or inversely as ( root of ) S 6 . of If 1 is the } } ithin which the placement is ensible , ious results hold ' s1uall ; fn1ther , as Cauchy showed , nlnst ) sDlall if the function of is to be taken as constanl Prof. has ) nate equations for the surface form du to linnited initial ) accnlents not confilled to an 1larrow strip . From the present point of view , such lesults can be recovere simply by from the integl.flls the nore impol troups of waves . Lct the initial ) ) given ) , ( 30 where be supposed small . Then Hence from the surface form is . ( 31 For oints at some distance the in }hich the bance valic3 with the cosine term thus we consider the rals as ) up of sinlple roups . For ositive we need only considel the The vadue of is thus connected with and by the sam equation ) as ) efore . Since ater al1lplitudes are associated with the of . the reatel . values of , it is clea that , at a ) ticular point , dies its maximunl at up to it . ( the ) resuJts the as . The call be deduc.ed . The cosine } aries aled titor s may the llaximum considi the latter alone ; it is easily this occurs whelt , ' Pro Loud . , , p. ( 1904 ) . W. , : . Lond. Math. Soc vol. 20 , 1 ) . 22 ( lb88 ) . 1908 . ] xroups of in Media , etc. Thus the maximum is out with uniform velocity ; and we see that in its hbourhood the predominant is Let the initial displacement have a constant value A oyer of breadth , and be zero at all other points ; then we have Hence the surface elevation is . ( 33 ) With the same umenl as before , we consider the value of at a point as due to the important of a succession of ) groups , one , , for which the ument is so ) } ) oneIlts reinl.orce over a considerab ] oi can down , from the revious results , an expression for this group which and at least in the vicinity of the ) of the ance . We , ( 34 ) corresponding to 1'urnside 's result in the ) already cited . Here have a of nlaxima given those of , that is , at times ) CJiven by , where ) ) . period of the gloup that is thus cumulative is different for different localities , and for ent tiIIles at the saute locality : ) the accumulation is prominent only for tinles and ) lnaximunl value to the amplitude , which has been raphed for the next example in fig. 1 . The maxima here diminish continually in alue , and are ated each with unil.orm velocity , namely , the roll )-velocity to the predominant wave-lel } in the hbourhood . S 7 . Train of Simplc Another interesting example is the case of an illitial displacement of a limited of simple harnlonic oscillations . If is synlmelical with respect to the o zero except wavewithin which it is A , we have ( 35 ) Hence , , have the surface elevation , of which wo write down Dr. T. H. Havelock . agation of [ Aug. 26 , only the necessary for in the direction of positive , is , If is very , the main fcattl . C consists of the component waves round : but in eneral it ; to noticed that a series of ) sidiary ponents a whose effects ] ) . of fnitnde to be . But the component are ctlllulalie only of and such ) which is the to ument of the cosine ; thus the linent effect at time , of ] of alncter be ties where the value , or , else , a to one of ) iary naxima . Th result may be in the manner as before , we find can prominent eferl e to , which this in olves , ) the nlaxilna of the amplitude function . ( 38 ) The ornl of this function is shown by 1 ; it is ) tained 1 ) the Ctlrv is roportional to , and , \ldquo ; to 1 COll.esponds to equal The lepresents the of the disttl.bance at a given point ith the the local ions of last cosine factor in ( 37 ) ; it sh tion ccment C . complete of } ) of } istu rrlce 1 as sipl ) with V. But his of tions of with in of of in of the the wave-velocity of dis1908 . ] Groups of in Dispersire , etc. turbance if it were unlimited . the of the roup we have also a series of roups , following each other much more quickly and with their and velocities less separated out than in the front of the roup . Hence the disturbance in the rear , especially at tances from the origin not reat , may be expected to consist of small , more FIG. 1 . ular , motion from the superposition of this latter system of roups , thus there will be a more distinctive rear of disturbance with velocity . These inferences may be compared with some results iven i Lord Kclvin 's later ) from a solution of the equations for an elevation in the form of a single crest , the results were phically so as to show in a series of ures the ation of Dr. T. H. Havelock . Propagation of [ Aug. 26 , an disturbance five Cl.ests and four hollows of approximately sinusoidal shape ; the ] remarks are made :Immediately aftel the water is left free , the disturbance itself into two groups of waves , seen in directions from the middle line of the d. The pelceptible fronts of two groups extend rightwards and vards from the end of the initial group far beyond the hypothetical onls , ) to tl.avel at ] the wave-velocity , which to the dynamics of ) , in their important and interesting consideration of the work required to feed a uniform procession of waves)vould the actual frollts if the free roups remained uniform . How is from ealised is illustrated by the diagrams of which show a reat extension in each tlirection far beyond distances travelled at the ' ' there is this reat extension of the fi om the middle , we the two groups , after from tence in middle , their ears 1 ( space ) thel1t of water not ) disturbed , but very minute wavelets in ll1lll)cr following slower and in the of 'roup . The ) rear avels at a speed closely to the ( half -velocity . ' . . . . Thus ) perfi ont travels at actually than the -velocity , and this ) ) ) GCOlles 1 inlportant relatively to the whole with th advance uf tinle extract will selve to sis the of definition and ns of wold ( orroup . A sinlple gloup , of ucture , -ith it a definite elocity d ) only on the wave-length , but not so ttll limited displacement . In various cases we foumd it convenient to analyse such into roups , each definite velocity ; ill special cas may be equivalent practically to one S8 . the is , but that } ) lied 1 it . iven b ical distribution of , suitable ysis , initial elevation , the cl ation at Stlb t is by Lold , ' Phil. , vol. 13 , p. . 1908 . ] Groups of in , etc. If we assume equal to 1 , so that it is confined to an indefinitely narro strip of i1npulse ( cf. S5 ) , we obtain the result corresponding to ( 29 ) for nitial displacement by that expression the value of ; thus we find . ( 41 ) For comparison with the previous results , suppose that Then we find the surface form as of roups , each of them umulative and so prominent only in a ) ited region , iven by ( 42 ) For a given place the maxima are given by , that is , by . Thus the maximuun moves with velocity , and consists of neal . lie imple waves of wave-length with the result in S for an initial displacement of the same character , see that the is pro- pagated outwards with slower elocity , the wave-length at maximum being one-half the value in the former case . S9 . npnlso on De Suppose that the line impulse of the previous section is over the surface of deep water at angles to its length with unifornl velocity ; started at some infinitely renlote . Then we may regard the effect at as the summation of the effects due to all the consecutive elements of impulse , and we can obtain an expression by modifying ( 40 ) and integrating with respect to the time . We measure from a fixed origin which the line i1npulse at zero time ; then we substitute for and for in ( 40 ) , and integrate with respect to for all the time the impulse has ) . Thus we obtain - Dr. T. H. Havelock . The of [ Aug. 26 where , and anCe in advance of the present positio : of the nlse . We proceed to 110W the portant regular features the distllbance ) resented b these lViCh the notation of ( 19 ) thd ) ve the first integral . , . Hence ] value of , which corresponds to a stationar is ivcn by Thus the first in ( 43 ) gives ? We choose the of oscillations by the condition , Now must be positive to conle within of the integral ( 45 ) hence if is positive we no ibution towards a ] disturbance . If is ative obtain a series of ways which we can from ( 45 ) . have , when Hence , expression ( 18 ) , we ) the value of the chief roup from ( 45 ) namely , ' hich holds when is the second in ( 43 ) , easily see by the principal ( roup hat must ) ative : must be ative and between ero and ) llumelically . Thell the group in , we have to lltmerictlly . Hence is no resulting roup of vaves in th and second integral contributes to the disturbance . then the result in front of the travellinoopulse is disturbance , whilc in rear there is of ortional to ( 4C ) , with ) to the 1908 . ] Groups of in Disf'ersiue Media , etc. The same method can be used for waves on water of depth , due to a travelling impulse system . For in the integrals we should have . ( 47 ) The group with respect to would give a term proportional to , ( 48 ) where has the value given by . ( 49 ) We then select the , roup with pect to by . ( 50 ) we find this leads , or . ( 51 ) Since ninishes continually from 1 to as increases from to , there is only a real solution of when is less . In this case we have regular waves of length suitable to velocity ] in the rear of the impulse ; when is reater than the llaximtll1l wave-velocity there is no wave form . S10 . In order to illustrate the of element of the expression as a limited travelling group of undulations , consider another fornl of velocity function . If waves are ated over the surface of a liquid of density under the action of the surface tension , it can shown that the velocity of simple waves of is . Hence in this case the group-velocity is ; thus the -velocity is greater than the wave-velocity , and shall see this affects some of the results . ( a ) Initial ) / /tvccn considel the same problem as in S7 we have Phil. . ) . VOL. LXXXI.\mdash ; A. ) I Dr. T. H. Havelock . The Propagation of [ Aug. 26 , The predominant value of , for criven place , is given by The roups , with approximately constant amplitude , are iven by . At a iven place the maxima of ftlnplitude are those of Fig. 2 represents the curve ( 57 ' where is proportional to the time and equal to 1 corresponds to equal to Comparing this with S 7 we draw the inference that in this case the perceptible front of the is ltore clearly lnarked than the rear and advances with the half-wave-velocity onding to , in agreement with simple observation . lime line i1npulse at rest leads to . Consequently a moving line impulse will 908 . ] Groups of in Dispersive Media , etc. Then we choose so that , or value ivin a ular wave pattern is the poSitiye root , for positive . Hence in this case have a ular train of waves of suitable to he velocity in of the . pressure system , with no regular attern in the rear . S11 . Waicr Waves to Gravity and If we take account of ravity and the surface tension , we have the elocity function Hence . ( 60 ) We have not here a simple ratio , independent of . The velocity a minimum for a certain value , equal to , and for this value I is equal to \mdash ; as in fact follows from the definition of U. For less than ultimately to ; while for is reater than and approaches as a limit If we consider a travelling line impulse , whole problem of the roups is contained in the equations . ( 61 ) Hence ' where the positive sign is taken for positive ( in advance of the impulse ) , the negative sign for ative ( in the rear ) . Thus there is no wave attern unless is greater than the minimum wave-velocity ; and if so here are regular trains both in advance and in the rear , the smaller engths in advance . With the ratio large , the results approximate very small waves in front and waves in the rear with equal to S 12 . Surface Waves in Dimensions . Suppose that the initial data instead of being symmetrical about a bransverse line are symmetrical around the Cyin . Let the axes of Dr. T. H. Havelock . of [ Aug. 26 , \ldquo ; be in the undisturbed surface and axis of vertically upwards ; we write for . Then , esponding to , the surface elevation ! due to an in itial displacement , set free without initial velocity , giyen by where For an initial point-elevation we may take for simplicity equal ; then we have . ( 64 For deep water separate a real group from the first with respect to , around the valne of by This is replaced by the Considering now the raltge f , we can ( select the ) oscillations from ; it occurs at to zero , so we one-half result iven by the ession ( obtain the known result ( 66 ) , for an initial ) oillt impnlsc have , instead of ( 04 ) , the { si in to the . ( 6S ) 1908 . ] Gronps of , etc. S 13 . Point Impulse over Let the impulse be . along Ox with constant velocity ; let P ) be position at time , A at any ) revious time , and suppose the system to lave beeu for an indefinitely time . We have OA ; OB ; Then in ( 67 ) we have to for for , and raCe with respect to from to ; we obtain . ( 69 ) With , we select the group around the value of by . ( 70 ) By the formula ( 17 ) we find . ( 71 ) from this the chief ronp which occurs near equal to zero , } find Finally we choose the chief groups of terms in from the condition ; ( 73 ) Dr. T. H. Havelock . The Propc(gation of [ Aug. that is , from or We have then different cases to consider according to the llatule of ives a ition of the moving impulse , tinc eviously , for which the Hent out reinforce each other th at time ( i ) In the where 9 , both roots are thus position is non-existent , and there is no principal in th . Hence all wave pattern is contained within tw straight lines from the point pulse , each with the line otion an , or approximately ( ii ) When 9 are two different real roots for . Thus have two chief groups in , corresponding to two regula wave systems super on each other . At any point within the two bounding radii the disturbance consists two parts : one part sent out from A at time previously , where OA and ; ( 76 and another part sent out from at time before , where OB and . ( 77 We he1l two vave systelIls , which llay be called the nsverse waves and { shall them separately . ( a ) sc er ( ? the larger value of in ) we find ( 78 ) 1908 . ] Groups of es Dispersive , etc. Further , when is zero , we have . ( 79 ) the formula ( 17 ) we obtain the particular group of erms from the integral ( 72 ) as , ( 80 ) in which the special value of nrust be substituted . this expression we ) tain . ( 81 ) This represents a systenl of transverse waves ] with the impulse ; the amplitude for a given azimuth diminishes as On the central line , where is zero , this reduces to , ( 82 ) to simple line waves of length suitable to velocity on deep water , but with the amplitude factor Following the crest of a nsverse wave we have ( 83 ) where is a positive . The crests cut the axis in points given by , ( 84 ) and cut the radial given by ) , in the points . ( 85 ) Considel the variation of anlplitude a crest ; substitute for from ( S3 ) in ( 82 ) and obtain . ( 86 ) This becomes infinite at the outer boundary , when is ) nately ; this is due to failure of the nethod of approximation snd we shall consider it later . For the present the following table of values and curve show that the proxinlation holds np to angles very near the limit . Dr. T. H. Havelock . The Propagation of Table I. relative amplitude , ( the at different azimuths . 1 ( b ) root iven ( 77 ) , we obtaill the systcn of need ] the of ladiclc in order to rite d the corresponding results in this case . ests of the waves are given by Wllen zcro ; the clcsts the oint of ; . ( 8S ) 1908 . ] Groups of Waves in , etc. The law of amplitude the same crest is given by ( 89 ) In this case , for the same reason as for the transverse , the ression f ' the ) littlde tends to infinite . at the onter of each crest ; we shall find an in the next ) . But ( 89 ) becomes infinitely large for small values of . From ( 88 ) we see that also becolnes snlall , so that the approximation furthcr , we should expect the cxpression to become infinite ' the impulse account of its special character . sho how the infinity disappeal if we remove this cause . Consider , as an ) , a finite impulse , of constant intensity over a circular area of radius lotlnd the , and of value outside circle . Then , as see from ( 63 ) , we shall have the paule expressions as before , a factor iven by ) . in the final onp for the ( system we Hence the additional factor due to is proportional to ( 90 ) When approaches zero , ) argument of the Bessel 's fullction increases inde fitely and } may use the asymptotic expausion : then is to . ( 91 ) If now we uJultiply ( 89 ) by ) ) we obtain a limiting vaiue of the amplitude of the ( system neftr the axis ; it ) ) to and the infinity neal ' the axis httS disappeared . ( c ) Tha of \mdash ; We shall consider the infinity hich occurs at the outer of the two wave systems , is ) . At Dr. T. H. Havelock . The of [ Aug. 26 , the lines of constant ) in the two wave ) atterns cross at an seen to ) ivcn by . ( 92 ) As either ] ) the two waves ultimately have the same direction , they will have the } when they meet ; ( ' norn ) elevation is the outer ries , two systcnls tIlitc in lines of cusps . As see from , the two points coincide f'or on line of cusl ) ; and it is on ccount this fact ) vious aoxin ations fail for both systems . in fact a root of the ttion for findiIlg the chief of integral . Consider the { . , ( 93 ) is such Following the previous method , we have and rovided f is not small , we rite the value of the ooroup for the ( louble root ils si ( 94 ) Now ot the line of cusps the ecolnes find that : ; / . we FIcltcc , . these values , . ( 96 ) 1908 . ] of in We notice first the difference of phase of between this and the expressions for the parate systems where they cut the outer boundaries , this is to the of phase an optical ray in passing a focus . We saw that the separate transverse and ying crests towards points of equal on the outer boundaries given by but with the result iven in ( 96 ) we see the actual crests on the line of cusps are given by The amplitude of the cusped waves diminishes at a slower rate than the transverse waves , so that their size becomes nor marked the lear of the disturbance . amplitude of successive crests is iven by ( 96 ) and ( 97 ) as The amplitude of successive crests of the transverse waves where they cut the axi are iven by ( 82 ) and ( 84 ) , and we find Taking the ratio of these two quantities we have an expression for the magnitude of the crests at the cusps compared with the transverse crests on the axis ; approximately ( 100 ) The following table and curve show how the successive crests at the axis and outer line diminish , and exhibit their relative for erent values of On August 3 , 188 Lord Kelviu delivered it " " On Ship Waves \ldquo ; before the Institution of Mechanical Engineels at Edinburgh , in which he to have shown a model to scale of the theoretical wave pattern produced by ship . Only a diagram of the crest curves has been published ( ' Popular Lectures , ' vol. .3 , p. 482 ) ; form of the crests agrees with that deduced above , except of course near the disturbance or the radial boundaries . It has , in fact , been verified that on substituting his expreqsions for / ? in ternls of a parameter in the present equations , the latter are satisfied identically . The law of amplitude along the waves is not stated by Lord Kelvin Prof. ) conjectures , his result seems to have been obtained by ] ) lication of the idea of gloupvelocity Lamb , mics , . Dr. T. H. Havelock . The Propagation of Table II . 85 65 / / Consider a point innpulse with clocity c over the surface of lnediunl for hich respectively the and wave-velocity for a value of Let disturbance fi om ) ) } the 1bourhood of a ( A contbine so as to ) rodtlce at I ' at lnent the inlpulse is at . Theu of the ) ossible persistent wave1 systelns is contained in the equations ; ( 101 ) is , in wave ) nltent dends npotl the ctcr of the positive roots of these and such valne of defines wave system 1908 . ] Groups of Waves in Dispersive Media , etc. with wave front through at right , to , and each system can be expressed in the with and as functions of and Suppose the lnedium is such that the group-velocity bears a constant ratio to the wave-velocity , that is , suppose where / is independent of Then the equations ( 102 ) and(103 ) Iead to a quadratic for Hence we have the roots We shall examine some special cases . \mdash ; There are two positive values of , which are real , ed Thus there are two wave systems , transverse and divero i , with a line of cusps corresponding to the double roots , and the whole wave pattern is included within an which increases with The previous section on deep-water waves is the case zero . ( b ) . This is a critical case , coincidence of wave-velocity with group-velocity , and consequently no dispersion . ( c ) . This is the case of capillary surface waves . We see that there is only one positive root of the quadratic , and it is real for all values of the root is . ( 108 ) There is only one vave system , but it extetlds ovel the whole surface ; along the line of motion is zero in the rear , while in advance of the impulse it is of value suitable to simple waves moving with velocity ( d ) . This holds for flexural waves on a plate ; tlrere is one sysCcnl of waves extending over the surface , to the root The crests , and other lines of equal phase , are iven by the CUl.ves constant . ( e ) relation between and is . T. H. Havelock . Propagation of [ Aug. 26 , not constant ratio in this case ; we had in S11 the expressions for the two yelocities as functions of . It can be shown that in certain cases the equations for cu to four possible roots , yivino . four wave-branches the point . S15 . Point ) moving on Water of Finit With the same problem we now , if the water is of depth . ( 109 ) If we varies between and 1 , being dependent upon the value of . We use the notation ( 110 ) Then and are monotonic functions of with the following limiting values : ; ? ; ? ; ; The two equations for , and become , ( 111 ) . ( 112 ) these we obtain ; . ( 114 ) the last two we have the values of as , ( 115 ) 01 . ( 116 ) We have cases to consider as or \mdash ; Front ( 114 ) sce the equal values of cn , 1908 . ] Groups of Waves in Dispersire , etc. defining the lines of cusps within which the vave pattern lies , are iven by such values of that . ( 117 ) the value of can only lie between 1 and ; hence can only lie between and or between and . The smaller value is the for deep water , when is considered zero for all values of We see from and ( 116 ) that the equal values of occur when , or when greatest possible yalue of is 2 ; hence we have the limitation . Only in this case is there a double vave system a line of cusps . As decreases to 1 , that is as the velocity approaches the critical value , and at line of cusps both approach their value 1 ; and at the same time the cusp widens out , a angle . Further , along the axis we have Hence on the axis the transyerse waves are the simple waves travelling with velocity on water of depth . As decreases to 1 , the wave-length increases indefinitely ; , and consequently , approach unity on the axis . Now if is 1 , the group-velocity equals the wave-velocity and the medium is non-dispersive . Thus at the critical velocity , equal to we have a source emitting disturbances and travelling at the rate of propagation of the disturbances ; we see that the whole effect is practicaIly concentrated into a line through the source at right angles to the direction of motion . This agrees with observations of ship waves when approaching shallow water at the critical velocity . * ( b ) \mdash ; We may now have the greatest value , unity , of ; it is easily seen that for less values of and the values of given by ( 113 ) become smaller . At the outer limit we have . ( 118 ) Consequently the wave pattern is contained within two lines making with the axis an which as increases . * Trans. Inst. Nav . Arch vol. 47 , p. 353 ( 1905 ) . also the motion of an electron with the velocity of radiation . Dr. T. H. Havelock . The Propagation of [ Aug. 26 , ther , sincu values iven 1 ) we sc hele arc no cusps , for the left-band side cannot be greater than 2 . values of in ( 115 ) and ( 1 ] b ) correspond to the transverse and ( ( waves respectively . If we ) ) titnte ( in equations ( 111 ) and ( 112 ) we find ] are satisfied idelltically ; hence there is always a system . . hand , if we substitute ( 115 ) we find we llllst lave , the ible value of the side unity . Hence there can be a tranhversc wave } ' steIl only so long as is greater ; when exceeds ransycrsc1 isapl ) At otltel line ivcn by the ) nter ] front of the wave stem . 1Ve that the there }ronts ( lines of equal phase ) are now concave to , instead } ) convcx } tvhcn . There is no definite iIlllel limit to system ; as is , the tvave fronts become more the , and the , as the is increased , the ninishes , and the tlar are a from the centre of ance . ( Ill ) the culve in fig. 8 show how the the velocity is abed n to and beyond the critical Table III . , :al . : ; : ; 0.55 0.7 $0 1$ D8 . ] Groups of in , etc. VOL. LXXXI.\mdash ; A. able I FIG. 9 . Rev. F. J. Jervis-Smith . -eneration of [ Sept. 9 With the help of these results , sketches are given in fig. 9 to represen the in the wave pattern , as the critical velocity is approached an passed . the Generation of a Glow in moving Field , and the Action of agnetic Field on the Glow so ; the Residual being Oxygen , Hydrogen , Air.\mdash ; Part 3 . By JOHN . ( Oxon ) , Eeceived September 9 , \mdash ; Read November 5 , 1908 . ) ( 1 ) A silica bulb , similar to those employed in the experiments describe at p. 214 , ' . Soc. Proc , vol. 81 , was rotated four to five revolution second ; degree of exhaustion was similar to that reached in th former experiments , the residual gas being oxygen . The inductor wa valley , until the bulb bolowed ; then slowly through piece of damped thread , until the entirely died out ; the graduate electroscope the slow establishing th field , the brilliant glow was at once restored . This phenomeno : could be repeated at any time with celtainty . In some experiments th south pole was effective , the north pole not so . This was probably connecte with the that the north pole defiected the glow away from the stem the bulb , which was the axis oi rotation , and thus in contact with outsld ( 2 ) A silica bulb , the residual gas . air , when reate glowed ; but the netic effect as less mnrked than when was residual ( 3 ) A bulb of glass was next rotated ; the inductor being char as il the former experiment ; the wos much less than when a silica bull was used . The glow as deflected ) the field , not increased . Even the inductol ' } charged to 3000 volts the glow feeble . ( 4 ) In order to discover how the residual gas in the exhausted bull alfccted phenomena , I detern ined to contrast the effects il bilica ) ) wheu neon or wcle residual ooases in the ) ) bir Willianl amsay very kindly offered to repare me a bulb , in the residual neon .

rspa_1908_0098

0950-1207

On the generation of a luminous glow in an exhausted receive moving near an electrostatic field, and the action of magnetic field on the glow so produced; the residual gase being oxygen, hydrogen, neon, air.- Part 3.

430

433

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

Frederick John Jervis-Smith, M. A. (Oxon), F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1908.0098

en

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0098

10.1098/rspa.1908.0098

Electricity

Thermodynamics

Electricity

430 Rev. F. J. Jervis-Smitb . Generation of a [ Sept. 9 , With the help of these results , sketches are given in fig. 9 to represent the change in the wave pattern , as the critical velocity is approached and passed . On the Generation of a Luminous Glow in an Exhausted Receiver moving near an Electrostatic , and the Action of a Magnetic Field on the Glow so produced ; the Residual Gases being Oxygen , Hydrogen , Neon , and Air.\#151 ; Part 3 . By Frederick John Jervis-Smith , M.A. ( Oxon ) , F.B.S. ( Received September 9 , \#151 ; Read November 5 , 1908 . ) ( 1 ) A silica bulb , similar to those employed in the experiments described at p. 214 , * Roy . Soc. Proc./ A , vol. 81 , was rotated four to five revolutions per second ; the degree of exhaustion was similar to that reached in the former experiments , the residual gas being oxygen . The inductor was charged gradually , until the bulb glowed ; then slowly discharged through a piece of damped thread , until the glow entirely died out ; the graduated electroscope being observed during the slow discharge . On establishing the magnetic field , the brilliant glow was at once restored . This phenomenon could be repeated at any time with certainty . In some experiments the south pole was effective , the north pole not so . This was probably connected with the fact that the north pole deflected the glow away from the stem of the bulb , which was the axis of rotation , and thus in contact with outside bodies . ( 2 ) A silica bulb , the residual gas being air , when similarly treated , glowed ; but the magnetic effect was less marked than when oxygen was the residual gas . ( 3 ) A bulb of glass was next rotated ; the inductor being charged as in the former experiment ; the glow was very much less than when a silica bulb was used . The glow was deflected by the magnetic field , but not appreciably increased . Even when the inductor was charged to 3000 volts the glow was feeble . ( 4 ) In order to discover how far the residual gas in the exhausted bulb affected the phenomena , I determined to contrast the effects produced in silica bulbs when neon or oxygen were the residual gases in the bulbs . Sir William Ramsay very kindly offered to prepare me a bulb , in which the residual gas was neon . 1908 . ] Luminous Glow in an Exhausted etc. Neon Bulb tested for After-glow . ( 5 ) A silica bulb was exhausted , the residual gas being neon , and placed between disc and point electrodes of an induction coil , and subjected to a discharge similar in all respects to that used in the experiment in which the residual gas was oxygen . No after-glow was produced , as was the case when either air or oxygen was the residual gas . ( 6 ) The neon bulb , while subjected to the discharge , was filled with a reddish glow , which changed its shape with a change of distance of the pointed electrode . In the figure ( fig. 1 ) the dotted curves show roughly the shape of a section through a cap of glow , and the numbers refer to the relative positions of the pointed electrode and the pairs of curve-shaped caps of glow . When the electrode was within 5 mm. of the surface of the bulb , the radius of the cap of glow became small and brilliant exactly opposite the electrode . But as the point was moved away the radius of curvature of the cap became greater . The neon bulb was next mounted in the rotation apparatus in an electrostatic field , and when treated in exactly the same manner as the oxygen glow-bulbs it gave but little glow , but what it gave was of a reddish colour ; also the neon glow was but feebly affected by the magnetic field . Hydrogen Oxygen ( 7 ) A silica glow-bulb , the residual gas being air , was rotated , as in the previous experiments.* The inductor was charged to 800 volts , and placed at such a distance from the bulb that it did not show any glow . Then on establishing a magnetic field , in which the bulb rotated , it glowed brightly , the glow being either to the right or left hand , according to the polarity of the magnet.f The glow varied with the strength of the magnetic field . The phenomenon is very remarkable , but at present sufficient evidence has not been obtained to suggest an explanation . The effect was not altered * ' Roy . Soc. Proc. , ' p. 216 , A , vol. 80 . t Loc cit. 432 Rev. F. J. Jervis-Smitb . Generation of a [ Sept. 9 , when a sheet of non-magnetic material was interposed between the bulb and the magnet . ( 8 ) Glass bulb , residual gas hydrogen . A glass bulb in which the residual gas was hydrogen was rotated in the same manner as the glow-bulbs already described . Since hydrogen passes through silica at a high temperature , a glass bulb was used , so that the exhaustion might not be affected by the process of sealing-off the tube of the bulb . The position of maximum glow in the case of glow-bulbs in which hydrogen-and Oxygen are the residual gases is shown at G in figs. 2 and 3 , in which D is the inductor charged negative , and S the south pole of magnet . ( 9 ) The effect of a magnetic field on the generation of electricity , by friction of a silica glow-bulb against a camel-hair brush , or the finger . A silica glow-bulb B , fig. 4 ( the residual gas being air ) , was rotated 30 times FlCr 4per second , between the poles of a large electro-magnet , of the type used in diamagnetic experiments . The pole pieces , N , S , were flat , and the field between them practically straight ( 6 cm . ) . The revolving bulb was in contact with a stiff camel-hair brush C , the length of the flexible hair being about 5 mm. This brush was held by a metal arm midway between the poles of the electromagnet . The pressure of the brush on the bulb was so adjusted that not the slightest glow was visible ; but the instant the magnetic field was established the bulb glowed brightly , and ceased to glow the instant the magnetic field was removed by opening the magnetising circuit . The experiment was repeated , at short intervals , by me and my assistant , during one and a-half hours , when the same phenomena exactly repeated themselves . The intensity of the magnetic field was about 1050 to 3000 c.g.s. units , by the Kelvin long coil ballistic method . The glow was produced , in a slight degree , by a lower intensity of magnetic field . The same effects were produced by using a finger as a rubber , instead of the brush . It was noticed that flashes of light passed through the tubular stems of the glow-bulbs , to a conductor touching their ends ; this appears to indicate that the matter within the bulb is electrically charged , as well as the surface of the bulb . 1908 . ] Luminous Glow in an Exhausted , etc. 433 ( 10 ) The effect of a magnetic field on a glow-bulb after the rubber had been removed . A silica glow-bulb was rotated , as in section ( 9 ) . The camel-hair rubber , after being in contact with the bulb , was removed , and no glow was visible ; but on establishing the magnetic field ( about 800 c.g.s. units intensity ) , the bulb instantly glowed brightly , the glow lasting in some cases eight minutes before it died out . ( 1.1 ) When pointed pole pieces were used on either side of the rotating bulb , a bright equatorial band about 5 mm. wide of greenish glow was generated , the rest of the glow in the bulb being reduced in intensity . ( 12 ) None of the effects described in sections ( 9 ) , ( 10 ) , ( 11 ) could be produced in an unexhausted bulb . ( 13 ) The experiments described in this paper illustrate the profound change which takes place in the behaviour of a moving static induction of electricity when the bulb in which it occurs is in a magnetic field , and show how the action of the magnetic field on the electric motion in the residual gas is modified by the nature of the gas employed . In the case of hydrogen , the maximum glow is approximately situated , in the bulb , at an angle of 45 ' from the maximum glow when oxygen is the residual gas . When air , oxygen , or neon are the residual gases , the positions of the glow with respect to the magnet pole are similar .

rspa_1908_0099

0950-1207

On the osmotic pressures of aqueous solutions of calcium ferrocyanide. Part. I\#x2015;Concentrated solutions.

434

434

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

The Earl of Berkeley, F. R. S.|E. G. J. Hartley, B. A. (Oxon)|C. V. Burton, D. Sc. (Lond.)

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http://dx.doi.org/10.1098/rspa.1908.0099

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10.1098/rspa.1908.0099

Biochemistry

Thermodynamics

Biochemistry

434 On the Osmotic Pressures of Aqueous Solutions of Calcium Ferrocyanide . Part I.\#151 ; Concentrated Solutions . By the Earl of Berkeley , E.R.S. ; E. G. J. Hartley , B.A. ( Oxon ) ; and C. V. Burton , D.Sc . ( Lond. ) . ( Received July 4 , \#151 ; Read November 5 , 1908 . ) ( Abstract . ) The principal aim of this paper was to test the nearness of possible approach to complete osmotic efficiency for strong solutions . To this end the experimental verification of the exact physical equation given by A. W. Porter* was undertaken , a membrane having been constructed which could withstand osmotic pressures of calcium ferrocyanide up to 150 atmospheres without any sensible percolation of the solution . It was found , notwithstanding many precautions , that the formula would not verify within about 3 per cent. But further consideration showed that this formula must refer to osmotic pressures in vacuo , whereas the experiments were necessarily conducted in air at atmospheric pressure . Reconstructing the argument in terms of ideal osmotic partitions impermeable to air but permeable to the solution , the equation was modified so as to apply strictly to the quantities involved in the experimental determinations , which required the addition of the atmospheric pressure to the limits in the first and third of the integrals concerned in it . The final results are given in the following table :\#151 ; I. W eiglit concentration . II . " Unmodified " equation . hi . " Modified " equation . IV . Observed equilibrium pr . 49 -966 135 '04 atmos . 131 -45 atmos . 130 '66 atmos . 47 -219 116 -05 112 -96 " 112 -84 " 42 -889 88 -99 86 -61 " 87 -09 " 39 -503 72-54 jy 70 -61 " 70 -84 " 31 -388 42 -38 yy 41 -24 " 41 -22 " From the concordance of these numbers , it may fairly be deduced that the membrane establishes , unambiguously , even with concentrated solutions , the full theoretical osmotic pressures , for the thermodynamic relations , at these high pressures , are completely verified . * 'Roy . Soc. Proc. , ' A , vol. 79 , 1907 , p. 519 .

rspa_1908_0100

0950-1207

On anomalies in the intensity diffracted spectra.

435

439

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

H. C. Pocklington, M. A., D. Sc., F. R. S.

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6.0.4

http://dx.doi.org/10.1098/rspa.1908.0100

en

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0100

10.1098/rspa.1908.0100

Fluid Dynamics

Tables

Fluid Dynamics

]\gt ; On in the Intensity in By H. C. POCKLINGTON , M.A. , D.Sc . , F.E.S. ( Received August 31 , \mdash ; Read December 10 , 1908 . ) Professor Wood* has found that the spectra of an incandescent lamp formed by a rating can have bright and dark lines in them . These occur at the same place in each order of spectrum , and move through the spectrum when the inclination of the grating altered . The phenomenon has been investigated by Eayleigh , who discusses the case of diffraction by a grooved reflecting surface . On account of the analytical difficulties he uses approximations . In the present paper a theoretical grating is discussed , the phenomena of which can be ated accurately , an advantage that is , however , coupled with the drawback that we cannot feel certain how far the phenomena with those of the ordinary metallic reflection grating . A theorem that gives the sum of certain infinite series in a finite form , and transforms others into new series , is found in S5 . 2 . Let the grating consist of an infinite number of very thin rods of specific inductive capacity unity , each electrified to a line density and capable of oscillating , lying at equal distances parallel to each other in a plane . We take the axis of one of the rods , that of in the plane of the , and that of perpendicular to that plane . Let the incident waves be pagated in a direction parallel to the plane of and making an angle with the axis of , and let the electric force be . The displacement of a rod is , where A is complex , unless the phase of the displacement of the rod is the same as that of the wave incident on it . Since the diffracted waves depend only on the motion of the rods , and are given by a formula without peculiarities , the features that characterise these waves will depend only on the behaviour of the quantity A. 3 . We first consider the case where the electric vibration in the incident waves is parallel to the rods . The rods here vibrate . The forces acting on one of them are : , a force of restitution partly of mechanical origin and partly due to the repulsions of the other rods , say , , a force of * R. W. Wood , ' Phil. Mag Ser. 6 , vol. 4 , 1902 , p. 396 . Lord Rayleigh , ' Boy . Soc. Proc , vol. 79 , 1907 , p. 399 . Dr. H. C. Pocklington . On Anornalies in the [ Aug. 31 , electrical origin due to the rod itself and in phase with the motion , which produces an apparent increase in the inertia of the rod ; , a similar force in quadrature with the motion ; iv , another force , due to the action of all the other rods . The work done by the third force is equal to the energy radiated by an isolated rod , and hence the force is easily shown to be of the form , where is a constant . 4 . In order to find the value of the last force , we must find the field due to the rods . Now , the components of the electric force at due to an oscillating charge at are where the distance of from . On integrating with respect to , we find that X , , and the first term of vanish , and we have , or if where is that second solution of Bessel 's equation , the graph of which at infinity consists of waves of the same amplitude as those of the Bessel 's function , but in quadrature with them . Hence the mechanica ] force exerted on the rod by the other rods is ( , since 5 . Consider the expression Its limit when is . ( A ) in the limit , vanishes unless is a nultiple of say and its integral with respect to from a value slightly less Co one htly gxtel . than one of the critical values is . Hence the ies also is ( B ) , ' unctions , ' 230 , Ex. 18 . 1908 . ] Intensity in Diffracted where only positive values of the argument are to be taken . The function need not be continuous . The value at any point of discontinuity is to be taken to be the mean of the values on either side , and is to be replaced* by . If vanishes mess lies between certain limits , we may reduce the integral to one taken between these li1nits , and in the Series take only those terms the arguments of which lie between these limits . 6 . Putting , In the case of the functions , take the integral in the firsb instance from to . Then , but where we may add or take away any finite number of terms at the end of the series . Hence , making , our sum is now the force due to the incident waves to the sum of the other forces and the reversed acceleration multiplied by the mass , we have where is the mass per unit length of a rod . Cf . Dirichlet 's investigation of 's Selies . If we ke , we get a theorelu in Elliptic Function. . Dr. H. C. Pocklingtoll . On in the [ Aug. 31 , The summations are in case for integral values of . In the first case such values are to be taken as make the neither negative nor greater than . In the second case the are not to be less than pa , the in is to from 1 to and each is to be considered as one term ( this the omission of one or two of the three terms from some of the at the crinning of the series ) . 7 . Now let increase a value . ( 2 ) The first becomes infinite when is infinitesimally greater than this value , and the second becomes infinite when is infinitesimally less than it . In either case A vanishes . Hence each of the spectra composing the diffracted will have a dark line for any such value of , if is large , so that the natural period of a rod is small , there will a value of , rather less than that which makes the second infinite , for which the real of the coefficient of A vanishes . In this case the value of A will be exceptionally . We have , in fact , a case of resonance . Hence in each spectrum will be a line near to the dark one and on the red side of it . 8 . We must now consider the case where the electric force in the incident waves is perpendicular to the rods . irst let the rods be capable of vibration only in own plane . The electric force due to a rod is now This is to be multiplied by and sullmed for all values of by . Now if is any 's function of zero order , is equal to by finite quantity ( for the case / is exclnded ) . Hence the seaies in question converges and is finite for all values of . Hencc there are no ularities of the kind that discussed in 9 . lct the lods bc ) of vibration only at to their lane , incident as ) efore . The force due to a rod is now is we the force in question 1 that in S 8 from found in S 6 . force ) ives rise to no ularities , and those that the latter risc1 to already been discussed . There is , however , one 1908 . ] Intensity in Diffracted feature , for the left-hand side of equation ( 1 ) now is , with the result that there are no diffracted waves if Finally , let the rods be free to } ) rats in any direction . If the force of restitution is opposite to the displacement the liffracted wave is the sum of those found in SS 8 , 9 , and no new singularities occur . If the force of restitution is a linear vector function of the displacement the same result seems to hold , but there may be a acted wave in the case of perpendicular incidence . 10 . We must next consider the effect of change in the angle of incidence of the . As increases one of the values of given by ( 2 ) increases and the other decreases ; hence one set of dark lines moves towards the blue end of the spectrum and the other towards the red , in each case accompanied more or less closely by the corresponding bright lines . 11 . We cannot obtain mechanical systems that have frequencies comparable with that of light . However , when a conducting rod is placed in an electric field perpendicular to it , a displacement of electricity occurs in it which makes it behave in much the same way as if it were a cvidly electrified displaced bodily , and the frequency will be comparable with that of if the diameter of the rod is comparable with the wave-length of light . The damping due to radiation is also high , and therefore in the case of a wire grating exposed to waves in which the electric force is perpendicular to the wires , we should expect to find the dark lines but not the bright ones . The kind of grating that seems most favourable to the production of the latter is one in which the are narrow cracks , such as a diamond makes in glass when used to " " cut\ldquo ; it . Possibly , however , the cracks in a made in the would be so narrow that there would be no appreciable reflection at them , even at very oblique incidences .

rspa_1908_0101

0950-1207

On the refraction and dispersion of krypton and xenon and their relation to those of helium and argon.

440

448

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

C. Cuthbeetson|M. Cuthbeetson|Prof. F. T. Trouton, F. R. S.

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Tables

Atomic Physics

Tables

]\gt ; On the action ersion of lKrypton and Xenon Relation to cf Helium Argon . By C. TSON , of London University , University College ; and M. CUTJIBERTSON . ( Commumicated by Prof. F. T. Tronton , .S . Received , \mdash ; Read Noveml ) , 1908 . ) By the kindness of Sir William Ramsay and Prof. . B. foore , we been enabled to measure the refractive indices of krypton and xenon with much larger quantities of these gases than were available at the time of their first isolation . The method of preparation of the rases will be given by Prof. Loore in a paper about to be presc ted to the Chemical Society . The procedure followed in determining the indices is described in a paper lately ublished by the Royal need be on recapitulated . Jamin 's refractometer was used , and the source of crht was , for the efraction , a Bastian mercury lalnp , and for the dispersio1l , ernst lamp in conjunction with a fixed-deviation spectroscope . In the dispersion , one of the two tubes was filled with the gas in question , and the other with air at such a pressure that the optical of path of the rays were approximately equal . The then Conti ] from to , and ) the position of the centre of a iven bright band was obsel.ved in a telescope fitted lvith a lnicrometer eyepiece . The on the same scale ] ) veell the cclltres of two ad , acent bright bands of known wave-length ( generally ) as also noted . These observations constituted the point of departure . The pressure of the in then altered till convenient number of bands of wavelength 6500 ( usually had passed in one ; and , , the pressure of air in the other tube was altered till same number of bands ) assed in the contrary direction . of the was then the first ] to the second , and the movelnent of the of the balld under was noted . Supl ) that nlovement is divisions of the llicromefel , and distance between the centres of two adjacent is divisions . Let be llullber of of -length and epass , the number of bands of -length ) which vould have been ) erved with of this -length if the of " " the ) } ) of ) , Sulphur ; phorn , by tsoll n. P. letlf , ' ol . 80 , 1 ) . 411 , On the Refraction and Dispersion of Krypton , on , etc. 441 the air alone had been changed , and the corresponding number if the pressure of the gas alone had been Then what is observed is that the relative path retardation which may be written where is the path retardation for any wave-length . And since is in each case proportional to , this equation becomes The first on the left is the dispersive power of air , which is known , and since is observed , the dispersive power of the gas can be calculated . Krypton.\mdash ; About 100 . of gas at normal temperature and pressure were employed . The refractive index for the mercury green ray was determined six times , each determination being the mean of two of 100 bands , in one of which pressure was and in the other , so as to eliminate the effect of a drift of zero . The following are the values obtained :\mdash ; No. of experiment . Mean of l , 2 , 3 , 5 , and6 The divergence in the fourth experiment was accounted for , and it may be ected . The othe1s to one part in a thousand , and their mean may be accepted . The dispersion was calculated from seven experiments:\mdash ; . of Excess of power of Kr expcriment . over that of dry air . lIean. . 442 . Cuthbertson and Mrs. Cuthbertson . On the [ Sept. 28 , The dispersive power of air has been fated several times , but , unfortunately , the r ] are not very concordant . following table shows the principal deternlinations , the difference of refractivity between and the fraction expressing ] dispersive power calculated for these limits . Table I. The ures of Mascart , Scheel , and Perreau , are so alike hat the probably lies near them , and we select those of Scheel . According to him , the dispersive power of air between the lilnits an is ; and this , added to the excess of the dispersive of krypton over air gives If the dispersion of krypton is expressed in the form we have , therefore , And from the refractivity ior we have JIence . It be remelnbcled figures ' the ature { pressure , without allowance for the fact that the ( is . In mitking ison for an equal nulnl)er of , in stead of an equad , the value of must bc doublec In foul eriments , were taken of the of the . The shows the results:\mdash ; 1908 . ] Refraction and Dispersion of Krypton , Xenon , etc. 443 Table II . Dispersive power . to to to . Excess of krypton over Air ( Schcel ) ) Krypton ( calculated ) It will be observed that the values of calculated from the two sets of ures agree well . Xenon.\mdash ; About 120 . of this gas were employed . The table shows the results of four determinations of the efractive index for the boreen cury.line : No. of experiment . Mean The dispersion was calculated from eight experiments . No. of Excess of dispersive power experiment . over dry air . Mean Add dispersive power of air From these ures we find the refractive index of xenon doubled ( X ) is expressed by the formula With regard to the accuracy of these results , it is only necessary to ) serve briefly that it depends on four principal factors:\mdash ; ( 1 ) The purity of the gas , which is dealt with in Prof. Moore 's , to which reference has been made . 444 . Cuthbertson and Mrs. Cuthbertson . On the [ Sept. 28 , ( 2 ) The ness of the assumed value for the dispersion of air : shown above , this is probably trustworthy within 2 or 3 per cent. ( 3 ) Tho experimental errors , which can ) judged from the ures given We think that they do not amount to much more than in the case of air . ( 4 ) The adequacy of CauclIy 's formula : the figures given for the intermediate values of the dispersion of krypton show that the degree of accuracy attained was not sufficient to test this point . Relative of the Inert Gases . \mdash ; The index of helium has recently been determined by four sets ol observers . Their results are as follows , and are for Table III.\mdash ; Refraction and Dispersion of Helium . . Observers . W. Burton , ' Roy . Soc. Proc , vol. 80 , 1908 , p. 390 . Kurt . JIerrmann , ' Ber . . Deu . Phys. gosell 1908 , part 5 . K. Scheel and Schmidt , Cuthbcrtson and Mctcalfe , ' Roy . Soc. Proc , vol. 80 , 1908 , p. 411 The first last sets of figures agree very well ; the others do not . We select those of Mr. Burton comparison with our results . \mdash ; We regret that we have not been able to obtain a sufficient quantity of pure neon to enable us to measure its dispersion . The only value with which we are acquainted is that of 1'amsay and Travers for white light ; , while , for has also redetermined the index of for valuc . On several occasions it has been shown how closely the efractivities of these approach to the ratios of 1 , 2 , 8 , 12 , and 20 . We are now able to Jltl ) the values for infinite as calculated from Cauchy 's , and that the coincidence is still more stl.iking . The original of anlbay a Travers ttrc shown in colunlll 2 . They are for white 1908 . ] and oersion of 445 light . In columns 5 , 6 , and 7 the figures for neon are the old for white light multiplied by two . elative Pefractivities of the Inerb Gases for infinite Wavelengths . 1 . 2 . 3 . 4 . 6 . and Divergence gence Col. cent. from Col. ( 1ivid ) Col. 3 , ( molecular ) . . ( atomic ) . ' cent. . Col. 3 . reviQed val , Helium . . ) NeonArgon . ndard pton . . 425 Xenon . . 689 Dispcrsi be of the In his paper , cited above , Mr. Burton compares the owers of helium and with hydrogen , and points out that when they are expressed in the form the values of are in the ratios of 1 , 3 , and 2 respectively . It is now possible to extend this comparison to krypton and xenon . The following figures show that the coincidence fails in these cases . If the value of for helium be taken as 1 and that for , the values for krypton and xenon are.not in the ratios of simple integers . It Qhould also be that Mascart 's value of for , adopted by rton for comparison , is not supported by the eterminations o other Helium . . Argon . . . 997 ) Krypton . . X enon. . . . ] S45 Another relation between the refraction and dispel.sion can , } , be deduced . The shows the valnes of ) the refractivities for infinite wave-lengths iven in Table A very good staaight line can be drawn the heJium , krypton , and xenon , and is not far off . , instead of 's value for for helium , we take Cuthbeltson and the position of is innproved . Burton states that his il Sir lVilliam Famsay and obtained frolll fessrs . Tyrer give its density . If it contained any utlt the value of , while the valuc of ''would scarcely be -k Iascart 's value is frolll KetteleI 's ) fi , from Perreau , from Schee ] ) . VOL. LXXXI.\mdash ; A. ) and Mrs. Cuthbertson . the [ Sept. 28 , The dots for X , Kr , He ) closer to line . that , even for air , values of have varied so widely as from ( Mascart ) ( Kayser and , it may fairly be that within the limits of experimental error , in the inert ases , is linear function of the refractivity for infinite It is unfortullate that , at , we are unable to compare with these results the dispersions of any other series of more than two elements . The dispel.sions of selenium tellurium and of al.senic have been roughly nneasured , but not with cicnt accuracy to justify their use . But in htcr 1ncmbers of the series to they ivcly belong the dispersions have been ) served with somelv greater accuracy , though experimental qtill leave to ) found ) , . 13 ' ' . So 80 , 1908 . 1908 . ] Refraction Dispersion of Krypton , Xenon , etc. 447 and for phosphorus ( Cuthbertson and Metcalfe ) Similarly , the for ( Mascart ) are , and for sulphur ( Cuthbertson and Metcalfe ) If we assume that in each group , where and ( / are constants for the group , the values of and calculated from these figules Inert ( calculated from and X ) Oxygen and sulphur . . . 2 . Nitrogen and phosphoru . . These numbers do not show any obvious relation , and more is required the law cau be traced further . Thus , for example , the value of air cannot be deduced from the nitrogell : and oxygen here fronn observel . S of reputation . Mascart found ogen the values , and in diH'erent parts of the spectrum , and pointed out his values of nitrogen and could not be reconciled with his for air , and that more accurate determinations were required . It should , however , be remarked that , though the values of . helium , krypton , and xenon obtained by us were calculated with reference to air , the linear relation which we find would not be affected by any change in the number adopted for the dispersion of , which would increase or diminish all alike . A error would affect their relation to Mr. 's values ; but a large error is not to be feared . In the diagram , the position of mercury is icated , and it is plain that though it resembles the inert gases in monatomic in the gaseous state , it does not fall into line with them in regard to the relation between refrnctive and dispersive power . It remains to consider the physical meaning of the from experiments . On comparing Cauchy 's formula with the theoretical expression , [ Oct. ,3 , ( ption that the latter only one , for which is with If all inert ases it would follow that the square of the of the vibration the dispersion is equal to a constant plus a tcrm to the refractivity for infinite wave-length . We pleasure in expressing thanks to Sir William and of . . Moore for the loan of the yases ; to Prof. Trouton Prof. Porter , and the staff of the Physical tory of University College London , for much assistance and advice ; to the Society for a rant in aid of these iments . ote By LoRlJ I by aves advance inally tend tlpon holl that the slol ) ) steeper and steeper onditions , there formed what is be } called akers 1 beacl ] of actcr , lout is tidal ) ores tions some iven j ' . etica . ' clll ctll opposite llotiol . then to ocit ) \ldquo ; [ ' velocity . 1 . ilic 1 . .

rspa_1908_0102

0950-1207

Note on tidal bores.

448

449

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

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

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Tables

Fluid Dynamics

Tables

]\gt ; Lord [ Oct. ,3 , ( iStltlption that the latter only one term , for which is , we If all ) inert ases it vould follow that the square of the of th vibration the dispersion is equal to a constant plus a term to the refractivity for intinite wave-length . WG have great pleasure in thanks to Sir William and . Moore the loan of the ases ; to Prof. Trouton Prof. orter , and the staff of the Physical tory of University much assistance and advice ; and to the Society for a grant in aid of these IGlI , I yhcu nxves adyance ally u tend holl the steeper and steeper Ultimat , conditions , there fornled what is be called npon beach are of orcs { ptions some these iven j . ctica . ' clll rely to of tht [ . . 1908 . ] on places where these velocities and depths are reckoned are supposed to be situated on the two sides of the bore and at such distances from it that the motions are there sensibly uniform . The ) roblem being taken as in dimensions , two relations may at once be formulated connecting the depths and velocities . By consel . Vation of matter ' continuity we lJave ( 1 ) Aud since the } pre ac the two sections ) ) , , the equation of momentum is ( 2 ) whence ) ) . ( 3 ) The luSb of enelgy per time the is hus ( 4 ) That there should be a loss of constl no difficulty , at least in the presence of viscosity ; bnt the of a of energy shows that the motions here contenlplated ca1mot be reversed . In order to recur to the natUl'al condition of where the shallow is at rest , we have to superpose the velocity , taken atively upon the above motion . The velocity of the bore is then and that of the the bore . If is relatively small , is reater t The .just used is very similar to that ) by Stokes*and by to sound waves of expansion one dimension . The matter is discussed in ' Theory of Sound , 5253 , it is that the discontinuous solution , obtained from the ation of mass and momentunl , violates the condition of energy . When his was pointed out to tokes ] Kelvin and by myself , he abandoned his solution , which is , however , maintained by a competent Gel.man authority . S It is clear , at least , that when the motion is such as to involve of the solution ) nnot 1 ) } . The opposite case stands a different and to of he of discontinuity . Even Chen shoulcl lu facc thu iled by the develo } ) meant of . Ill case of liquid , heat is of little consequence , and since the motion is not entirely in one dimellsion , we escape the necessity of dealing with a single plane of discontinuity . 'Phil . vol. , p. 349 , 1848 . ' Abh vol. 8 , 1860 . Stokes , ' Math. ttnd Phys. ) ' vol. 2 , p. Private correspondence .

rspa_1908_0103

0950-1207

On a method of comparing mutual inductance and resistance by the help of two-phase alternating currents.

450

452

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

Albert Campbell, B. A.|R. T. Glazebrook, F. R. S.

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10.1098/rspa.1908.0103

Electricity

Tables

Electricity

]\gt ; Method of and Resistance by the Help of Two-phase By ALBECRT by R. T. zebrook , F.R.S. Received September 22 , \mdash ; Read November 5 , 1908 . ) ( From the National Physical ) ( 1 ) Introd2 A standard mutual inductance , after the design recently described by the writer , now been constructed at the National Physical Laboratol.y . As the details of its construction will be published later , it is sufficient here to mention that its value calculated from the dimensions is millihenries . It forms an extremely accurate standard , against which both mutual and self inductances can be readily tested . In addition to this , it a means of values of resistance coils in absolute measure , and thus evaluating the ohm . can be done in an indirect way by finding the capacity of a condenser in terms of resistance and time by Maxwell 's Conlmutator Method , in terms of esistance and mutual inductance by Heydweiller 's modification of rey 's method . The comparison of resistance with mutual inductanee can , however , bc made nply and directly by the use of two-phase euls in the method which I proceed to descl.ibe . 1 shall first take the ideal simple case , nd afterwards notice some of the difficulties that may arise in practice . ( 2 ) of the Mcthod . lu let be the mutual inductance ( a small fraction of it being Ijubtable ) and the esistance ; and let A and pt be currents in quadrntule , from a two-phase lternator device . Let a vibraCion gel ' to frequency ) . When the alvanometer shows no deflection , the electromotive introduced into its circuit is zero every instant , and hence so that 1 ) 'lioy . ) . , lJOi . ' On This condition gives a direct comparison between and , when and are known . By observing the speed of the alternator , is found ; while the ratio of A to is obtained by means of the electrostatic voltmeter , which is put alternately across the equal resistances and , or by a differential electrodynamometer . In practice A is made very nearly equal to B. FIG. I. The condition of balance is arrived at by , or ' until galvanometer deflection becomes zero , accurate quadrature by adjusting the self inductance . For , if millihenries and ohms , the necessary frequency is about 80 cycles per second . The chief difficulties at first sight would be in obtaining alternating current of absolutely pure sine wave-form ; but the necessity for this is obviated by the use of the tuned to resonance with the fundamental in the wave-form , and thus ignoring the harmonics in comparison with the fundamentals AI and . This is found to be the case experimentally , for a sharply defined balance was obtained when a suitable alternator was used ; and the mathematical estigation of the more case substantiated this result . If necessnry , the harmonics 1 be still further obliterated electrical tuning with inductance and capacity in the alvanometer circuit . The effects of a small amount of self inductance in the resistance and of distributed capacity in the secondary coil have been theoretically investigated ; it has been found that the former is practically negligible , and that , if the latter is not quite negligible , the proper correction can easily be found . ( 3 ) A few preliminary xpcrinlents 1 been made to test the working of . The easurement of made with a scale electro . talic voltuleter which yave about 2 mm. for a difference of 1 in 10,000 her could no obtained by an electro . dynamometer two anlic ) llloving coils ; this would allow , made . Errors would ) by int , two circuits of the instrument mean esult . In the inlents already lllade , the fiequeney was steady at a ] ) telv correct , and varied the addition small accurately calibl.ated variable mutual inductance with a range two or three thousandths of M. The results obtained have ) encouraging appear to indicate thal the is fiusceptible of ) accuracy . It ma be of interest tc deterlnination obtained with an inductor alternator ol Jlely i. wave-form errors only 3 per cent. ; while with a . he frcm the nominal values was within the li mits of } tal error , which were of the order ol 1 in 1000 . This last is only the result of preliminary trial ; in ) ultimate experiments ) a ]theh ) order .

rspa_1908_0104

0950-1207

The occlusion of the residual gas and the fluorescence of the glass walls of crookes tubes.

453

459

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

Alan A. Campbell Swinton.|Sir William Crookes, F. R. S.

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10.1098/rspa.1908.0104

Thermodynamics

Optics

Thermodynamics

453 The Occlusion of the Residual Gas and the Fluorescence of the Glass Walls of Crookes Tubes . By Alan A. Campbell Swinton . , ( Communicated by Sir William Crookes , F.R.S. Received October 5 , \#151 ; Read November 12 , 1908 . ) : In a previous paper on the first part of this subject , * the writer has* described experiments indicating that the occlusion of the gas is due , at any rate in some instances , to the gas being mechanically driven into the glass , in which it forms bubbles on the glass being heated strongly . Since this paper was published , several comments on the writer 's conclusions have appeared , and these have led to the writer making further experimental investigations which it is one of the purposes of this paper to describe . In a lecture on March 16 , 1907 , at the Royal Institution , f Prof. J. J. Thomson suggested an explanation of the considerable depth from the inner surface of the glass at which the bubbles occur . This depth , as measured by the writer , amounts in some cases to more than one-tenth of a millimetre , which is a considerably greater distance than cathode rays are found to penetrate through aluminium . Prof. J. J. Thomson pointed out that both glass , and silica have been shown to be permeable to hydrogen and helium at high temperatures , so that the effect in question might arise from the cathode ray bombardment raising the temperature of the surface of the glass sufficiently to permit of these gases penetrating by ordinary diffusion . Again , in a paper entitled " The Formation of Gas Bubbles in the Walls of Heated Discharge Tubes , " read before the German Physical Society on June 28 , 1907 , + Mr. Robert Pohl disputes the contention of the writer that the gas is driven mechanically into the glass , and maintains that the formation of the bubbles is entirely due to the presence of films of aluminium disintegrated from the electrodes and to chemical action connected with the oxidation of this aluminium when the glass is heated in a flame . Finally , Mr. Frederick Soddy and Mr. Thomas D. Mackenzie , in their paper on " The Electric Discharge in Monatomic Gases , " read before the Royal Society , November 7 , 1907 , S from experiments made on argon , neon , and * " The Occlusion of the Residual Gas by the Glass Walls of Vacuum Tubes , " 4 Roy . Soc. Proc.f A , vol. 79 , pp. 134\#151 ; 137 . t See 4 Engineering,5 March 22 , 1907 , p. 387 . f 'Berichte der Deutschen Physikalichen Gesellschaft,5 pp. 306\#151 ; 314 . S ' Boy . Soc. Proc.,5 A , vol. 80 , pp. 92\#151 ; 109 . VOL. LXXXI.\#151 ; A. 2 H 454 Mr. Swinton . Occlusion of Residual Gas and [ Oct. 5 , helium spectrum tubes , seem to have come to the conclusion that the gas which causes the bubbles is not the residual gas in the tube , but is gas generated by chemical decomposition of the glass under the influence of local heating produced by the discharge , which heating in the case of their particular tubes was probably very considerable . First of all , to deal with Mr. Eobert Pohl 's conclusions , as the writer 's previous experiments did not at all bear these out , it was decided to make a crucial experiment in which there would be no possibility of the presence of any aluminium within the tube . For this purpose a vacuum tube was constructed as shown in fig. 1 , the electrodes consisting of two caps of tinfoil , A and B , pasted on the outside of the tube . The tube was pumped up to a vacuum at which it gave green fluorescence . Alternating current at about 7000 volts was employed , this giving a current of 1 to 2 milliamperes , which was found to be as much as the tube would stand without getting warm . After sparking for 7J hours the tube was broken up , when it was found that on portions of the glass being strongly heated in a blowpipe flame they immediately became filled with large numbers of very small bubbles . These bubbles were on the average about half the diameter of those observed by the writer in his previous experiments with tubes containing internal electrodes , and were also much nearer the surface of the glass , the depth being only about 0*025 mm. as against the 0*122 mm. measured in the case of the previous experiments . Therse variations are no doubt due to the fact that with tubes with external electrodes only very weak electrical discharges can be obtained , and the bombardment consequently is much less violent . These experiments , which were repeated several times with different tubes , .always with similar results , appear entirely to dispose of Mr. Pohl 's contention that the presence of a film of aluminium , or for that matter of any other metal , on the inside surface of the tube is in any way requisite for the production of the bubbles . Furthermore , it was found that boiling the glass of these tubes with external electrodes in strong nitric acid , prior to heating in the flame , did not prevent the formation of the bubbles except in one case in which , after sparking for a number of hours , the interior surface of the tube was found to Fig. 1 . 1908 . ] Fluorescence of Glass Walls of Crookes Tubes . be covered with a brown film which was dissolved away by the boiling nitric acid , after which process no bubbles could be obtained in the glass . The writer is indebted to Mr. J. Thomas , of Faraday House , for making an analysis of this brown deposit , from which it appears that it consisted of carbon , due , as the writer has since ascertained , to volatile portions of the grease used in a stopcock on the pipe employed for exhausting the tube . It would appear , therefore , that when there is a sufficient deposit of this nature the occlusion takes place in the deposit and not in the glass as it does when no deposit is present . Next , experiments were made with a view to ascertaining whether under the bombardment the gas is driven into the glass to as great a depth as that .at which the bubbles appear on subsequent heating . In all cases , whether internal or external electrodes were employed , it was found that grinding away the interior surface of the glass to a sufficient extent prevented any formation of bubbles on subsequent heating , and by just grinding to the extent necessary for this purpose and measuring the thickness of the glass before and after grinding , it was possible to estimate the distance which the gas had travelled into the glass under the bombardment , prior to the heating of the glass in the flame . In specimens of glass from different tubes this distance was found to vary from 0*0025 mm. with external electrodes to as much as 0*015 mm. with internal electrodes , the differences being no doubt due to the varying velocities of the cathode rays , but in all cases this distance was found to be considerably less\#151 ; usually in the ratio of about 1 to 10\#151 ; than the distances between the surface of the glass and the centres of the bubbles produced by heating in the flame . From this it would appear that the gas travels considerably further into the glass when the latter is strongly heated . As difficulties were met with in making accurate measurements owing to the curvature and irregular thickness of the glass of the tubes , in some of the experiments a piece of flat microscope cover glass , laid inside the tube in a position where the bombardment would reach it , was employed instead of the walls of the tube itself . As regards the penetration of the gas and the production of bubbles , this cover glass was found to behave exactly like the glass of the tube . It was also found that the depth of the bubbles in the glass could be very easily determined by examining the glass edgewise in a microscope . Observations made in this way showed that the bubbles , though in one layer , are usually at by no means a uniform depth . Experiments were also made to ascertain what is the maximum distance that cathode rays will penetrate aluminium . For this purpose a small fluorescent screen of Willemite was placed behind a patchwork screen of 2 h 2 456 Mr. Swinton . Occlusion of Residual Gas and [ Oct. 5 , aluminium foil , the four patches into which the latter was divided being composed of two , three , four , and five thicknesses respectively of aluminium 0*0028 mm. in thickness . The whole was placed in a tube opposite a flat cathode , so that the rays could only reach the Willemite after passing through the aluminium . With this arrangement it was found that the five thicknesses of foil gave about the limit through which the cathode rays would pass , at any rate sufficiently to cause fluorescence , the amount of fluorescence obtained through the five thicknesses being exceedingly feeble , and only visible at all with cathode rays of a very active description . From this it appears that the maximum thickness of aluminium through which cathode rays can ordinarily be made to pass in any quantity is about 0*014 mm. , which , as the density of aluminium is 2*7 and that of glass about 2*47 , agrees very fairly closely with the figure of 0*015 mm. , which , as mentioned above , was found to be the maximum distance that the gas penetrated into the glass before heating sufficiently to form bubbles on subsequent heating in the flame . It should be mentioned that in the experiments already alluded to on the tubes with external electrodes , the electric discharges passing through the tubes were so weak that the heating of the glass was very slight , the temperature of no portion of the exterior of the tubes exceeding that of the surrounding atmosphere by more than a very few degrees . Even after allowing for the fact that the instantaneous temperature of the interior of the tubes during each discharge would be higher than the mean temperature of the exterior , it does not seem possible that the temperature can have been sufficiently raised either to allow of the gas passing into the glass by ordinary diffusion , as suggested by Prof. J. J. Thomson , or to have caused the gas to be evolved inside the glass by chemical decomposition due to heat as put forward by Mr. Soddy and Mr. Mackenzie . Furthermore , neither of these explanations seems really necessary , for , as has been shown , the gas in the first instance travels into the glass only about the same distance that cathode rays can be made to pass through aluminium , and it is therefore reasonable to suppose that the gas may be driven in mechanically . Diffusion , however , probably plays an important part in the final result , taking place at the later stage when the glass is softened in the flame . Under its influence , and also , perhaps , under that of surface tension , the gas then travels much further into the glass and forms bubbles at the moment of solidification , in much the same way that air dissolved in water forms bubbles when the water is frozen into ice . No doubt where there is considerable deposit on the glass of aluminium from the electrodes , of platinum or of other material employed from the anti1908 . ] Fluorescence of Glass Walls of Crookes Tubes . 457 cathode , or of carbon as above instanced , the occlusion may take place largely in such deposit , but otherwise the above experiments seem to bear out the writer 's original conclusion that the occlusion is due to the gas being mechanically driven into the glass itself . Experiments were also made in order to discover whether the penetration of the gas into the glass has any bearing on the fatigue of the latter in respect to fluorescence , discovered by Sir William Crookes nearly thirty years ago.* In many cases this fatigue , according to the writer 's observations , is due to deposits of aluminium or other electrode matter or of carbon on the glass , barely noticeable deposits having a marked effect in this respect . In other cases , however , fatigue shows itself where the most careful examination can find no evidence of such deposits , or after they have been removed , and where the cause of the fatigue must therefore be sought elsewhere . In order to investigate the matter , a strip of glass was mounted in a tube opposite to a flat aluminium cathode , with a screen consisting of a strip of sheet iron considerably narrower than the strip of glass placed between the cathode and the glass , so as to shield a central zone of the latter from the bombardment . The iron screen was hinged at the end where it was supported , so that by means of a magnet it could be moved out of the way so as to allow the whole of the glass strip to be uniformly bombarded when required . The tube was exhausted to a state in which the glass fluoresced brightly , and with the iron screen in position to shield part of the glass strip , the latter was subjected to vigorous bombardment for some seven hours . At the end of this period the bombarded glass showed very considerable fatigue , and when the iron screen was moved so as to allow the cathode rays to strike the whole surface , fluoresced much less brightly than the portion that had been shielded . Furthermore , the fatigue of the glass was found to be permanent to the extent that it had not perceptibly diminished after a rest of some sixteen hours . The glass strip was next removed from the tube , and after its thickness had been carefully measured with a microscope a layer of wedge section of part of the bombarded surface was removed by grinding . On replacing the strip in the tube , and again subjecting the whole of it to bombardment , it was found that part of the strip where most glass had been ground off now showed no signs of fatigue , and fluoresced as brightly as the portion that had been screened from the initial bombardment , while those parts off which only little glass had been ground , or none ground off at all , still * ' Phil. Trans.*5 1879 , part 2 , p. 645 . 458 Mr. Swinton . Occlusion of Residual Gas and [ Oct. 5 " showed the fatigue , there being a well-defined line of demarcation between the fatigued and non-fatigued portions . On again removing the glass from the tube and measuring in the microscope its thickness at this line of demarcation , and comparing the figure with that of the original thickness of the glass , it was found that the thickness of the glass that had been removed at this point was 0*017 mm. , this being the amount of glass that had to be ground off in order to do away with the fatigue . The experiment was repeated several times with both longer and shorter periods of bombardment , but always with similar results , the measurements varying but little . Also it was found to make little difference whether a separate piece of glass mounted in the tube , or a bombarded portion of the walls of the tube itself , were employed for the experiment . As will be observed , the figure of 0*017 mm. approximates very closely to the 0*015 mm. , which , in tubes with internal electrodes , was the distance that the gas was found to be driven into the glass by the bombardment in quantities sufficient to form bubbles-on subsequent heating . Furthermore , experiments showed that glass which had been well bombarded by cathode rays so as to be greatly fatigued , and off a portion of which a layer had been ground of just sufficient thickness to restore the fluorescence of that part to the original brilliancy when tested under further-bombardment , evolved bubbles under subsequent heating in a blowpipe flame only in those parts which had not been ground down sufficiently to remove the fatigue , the line of demarcation between those portions of the glass that gave and did not give bubbles on heating being very nearly though not quite identical with that between the portions that did and did not show fatigue . In each case the want of identity between these lines of demarcation showed that a slightly greater thickness of glass must be removed to do away with fatigue than is sufficient to prevent the formation of bubbles . This seems natural , as fluorescence under cathode ray bombardment is a surface effect , and it does not therefore signify so far as it is-concerned whether the layer permeated by the gas is thick or thin ; whereas for bubbles to be formed on heating , the gas must probably be located in the glass at not less than some definite minimum mean depth , at less than which the gas merely escapes when the glass is heated . . From the above it would appear , in some cases at all events , that the fatigue of the glass is intimately connected with , and is perhaps the direct result of , the penetration of the gas , for , as should be pointed out , the thickness of the layer of fatigued glass is quite considerable , and much greater than that of any surface deposits of carbon or of aluminium which , as already mentioned , have also the effect of diminishing the brightness of 1908 . ] Fluorescence of Glass Walls of Crookes Tubes . 459 the fluorescence , and are , partially at any rate , in some cases the cause of fatigue . The further suggestion that the fatigue may be due to the actual presence of the gas in the glass may help to explain the permanent nature of the-fatigue where there is no carbon , aluminium or other deposit , for , as-mentioned in his previous paper referred to above , the writer obtained bubbles in portions of the walls of a tube due to gas which had been1 imprisoned in the glass for some nine years . That the fatigue is very permanent is further borne out by the fact that the writer finds that the ' glass of a Crookes tube containing a hinged aluminium cross , of the usual description for showing this fatigue phenomenon , which has been lying unused since the year 1898 , is still sufficiently fatigued by the bombardment it received ten years ago to show quite distinctly the usual appearance of a bright fluorescent image of the cross on a less bright background when the glass is uniformly bombarded , though no signs of any discoloi'ation due to deposition of carbon or of aluminium or of other effect on the glass are visible by ordinary light . Though some portion of the fatigue effect is permanent , the remainder , which as a rule is the larger part , is but temporary . This may be due to the gradual escape of such portion of the gas as has been driven into the glass only such a very short distance that the latter is unable permanently to retain it . The writer is again indebted to Mr. J. C. M. Stanton and Mr. R. C. Pierce for their assistance in carrying out the experiments .

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Note on two recently compiled calendars of papers of the period 1606\#x2014;1806 in the archives of the Royal Society.

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

A. H. Church, D. Sc., F. R. S.

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http://dx.doi.org/10.1098/rspa.1908.0105

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10.1098/rspa.1908.0105

Biography

Reporting

Biography

460 Note on Two recently compiled Calendars of Papers of the Period 1606\#151 ; 1806 in the Archives of the Royal Society . By A. H. Chuech , I).Sc . , F.R.S. ( Received October 26 , \#151 ; Read November 5 , 1908 . ) The second section of Chapter XYI of the Statutes of the Royal Society 'commences with these words : " A catalogue of the manuscripts in the archives shall be available for reference at the rooms of the Society . " Now a catalogue assigning a single number and title to a whole volume or collection of more or less independent documents does not afford much help to the inquirer . However , one detailed catalogue , dealing , item by item , with a large part of the correspondence of the Society , down to the year 1740 , was compiled by Mr. W. E. Shuckard , the Librarian , and published in 1840 . The arrangement adopted in cataloguing the documents preserved in the 48 " Letter-Books " of this series , was alphabetical for authors , and \#166 ; chronological in the sequence of the contributions of each writer . Parallel with these " Letter-Books , " there exists a set of guard-books , 39 in number , filled mainly with early classified MS . papers of the period 1606\#151 ; 1741 . These documents , about 2500 in number , the production of some 800 authors , were catalogued in 1907 , a manuscript Calendar being compiled , together with an Introduction and Index Nominum , both since printed . The titles and numbers attached to the several guard-books of this series are here given : it should be noted that the documents had been arranged mainly in accordance with their subjects , but in a few instances by authorship . There has been given to this set the designation\#151 ; CLASSIFIED PAPERS . VOLUME i. Arithmetic , Algebra , Geometry , Trigonometry . ii . Surveying , Opticks , Perspective , Sculpture , Painting , Music , Meclianicks . iii ( 1 ) and iii ( 2 ) . Mechanicks , Trades . iv ( 1 ) and iv ( 2 ) . Physiology , Meteorology , Pneumaticks . v. Journals of the Weather . vi . Staticks , Hydrostaticks , Hydrmdicks , Hydrology . vii ( 1 ) and vii ( 2 ) . Architecture , Shipbuilding , Geography , Navigation , Voyages , Travels . viii ( 1 ) and viii ( 2 ) . Astronomy . ix ( 1 ) and ix ( 2 ) . Mineralogy , Magneticks . x ( 1 ) , x ( 2 ) and x ( 3 ) . Botany and Agriculture . xi ( 1 ) and xi ( 2 ) . Pharmacy and Chemistry . xii ( 1 ) and xii ( 2 ) . Anatomy and Surgery , xiii . Monsters ; Longevity . Calendars of Papers of the Period 1606\#151 ; 1806 . 461 VOLUME xiv ( 1 ) and xiv ( 2 ) . Physic . xv ( 1 ) and xv ( 2 ) . Zoology . xvi . Gramar , Chronology , History , and Antiquities . xvii . Miscellaneous Papers . xviii ( 1 ) and xviii ( 2 ) . Experiments of Papin , Hawksbee , and Desaguliers . xix . Inquiries and Answers . xx . Dr. Hook 's Papers . xxi . Halley 's Papers . xxii ( 1 ) and xxii ( 2 ) . Accounts of Books . xxiii ( 1 ) and xxiii ( 2 ) . Inoculations . xxiv . Papers by Collins , Oldenburg and Hook , xxv . Political : Trade . Although some notion of the character and range of these " Classified Papers " may be formed from the titles given to the several books , yet a reference to the MS . Calendar will be required should exact details of any particular paper be wanted . Here the printed Index of Authors ' names will be found useful . Still there are many papers which , being anonymous , cannot be reached in this way . In this connection may be mentioned two long lists of manuscripts in various libraries ; these lists are Nos. 32 and 33 in vol. xvii . Of authors ' names in the Index which afford no clue to the subjects of their papers are those of a number of persons concerned in the farming of sea-coals and the trade therein , both at Newcastle , and in Scotland . These papers are Nos. 29 to 55 in vol. xxv , and belong to the period 1610\#151 ; 1633 . They , and many others dated long before the foundation of the Royal Society , scarcely belong to the Archives , but are interesting in themselves and afford material useful in tracing the antecedents , the scope , and the development of the Society . It is scarcely necessary to state that the majority of the documents preserved in this set of guard-books consists of papers communicated to the Society . Of these a good many were never published in the ' Philosophical Transactions ; ' In the printed pamphlet which was distributed last year to the Fellows , some further particulars concerning the Classified Papers are given . Attention may now be drawn to a third set of guard-books containing both letters and papers , and forming a continuation of both the earlier sets , that is , of the " Letter-Books " and of the " Classified Papers . " The 127 volumes of this third set begin in the year 1741 and close in 1806 . Their contents are arranged chronologically , but there are a few gaps in the sequence , while some documents have been misplaced , In the earlier papers the form of a letter was generally adopted\#151 ; even at the end of . the period it was not unusual . 462 Prof. A. H. Church . Calendars Papers of the [ Oct. 26 While the bulk of these guard-books is made up of papers and memoirs yet letters to and from the officers of the Society , as well as reports from special committees , are not infrequent . Some of the acknowledgments sent by foreign members on election into the body are fortunately preserved . Among these may be cited the letters of Pierre de Vigny , Carolus Linnams , the Abbe Jean Jacques Barthdlemy , le Comte de Saluces , Jean Bernard M.D. , and Michel Adanson ; such letters , though read at the meetings , were not printed . Indeed the student of the documents , over 3650 in number preserved in this long series of guard-books , cannot but feel a special interest in those letters and papers which did not appear in the \#163 ; Philosophical Transactions . ' Some of these have been noted in the printed pamphlet which has been prepared to accompany and explain the MS , Calendar of this collection , while four unpublished letters , one each from Benjamin Franklin , Carolus Linnaeus , Captain James Cook , and John Hunter , have been printed in full , as typical examples . Most of these " Letters and Papers , " being signed holographs mainly of notable peisons , afford abundant material for the study of handwriting . But the collection is much more than a collection of autographs , for it contains the original announcements of most of the great discoveries in natural knowledge by which the latter part of the eighteenth century was marked in Great Britain , nor are noteworthy contributions from foreign philosophers wanting . Many original illustrations , including some excellent water-colour drawings ( such as those by the Rev. John Lightfoot and Edward Edwards , A.R.A. ) , are here preserved . As a matter of minor interest , mention may be made of the time armorial seals attached to a number of the letters ; these are noted in the MS . Calendar . Throughout these guard-books occur the original MSS . of many of the Croonian and Bakerian Lectures . Unpublished discourses of the former series include some by James Douglas , John Hunter , Samuel Foart Simmons , Edward Whitaker Grey , Sir Gilbert Blane , Sir Wm. Blizard , Mathew Baillie , Sir Everard Home , John Abernethy , and John Pearson . There are unprmted Bakerian Lectures by Peter Woulfe , Tiberius Cavallo , and Samuel Vince . The compiler of the MS . Calendar , and of the printed pamphlet already mentioned , has met with many difficulties in his task . The names of authors are not always legible in the original manuscripts ; frequently , Christian names being omitted , they had to be sought elsewhere . Moreover , in a few cases where names were apparently identical , there might be indications that they belonged to two individuals , not one ; mistakes in the opposite sense may also have occurred . But the value of an Index Nominum warranted the 1908 . ] Period1606\#151 ; 1806 in Arch of the Royal Society . 463 devotion of much time and trouble to rendering it more useful than it could have proved had no errors been corrected and no deficiencies supplied from sources outside the " Letters and Papers " themselves . The construction and the mode of using the printed Index may now be briefly described . The 127 guard-hooks wrere taken in groups of ten , or Decades , a fresh numeration of the documents being commenced with each Decade . Thus , Decade I includes guard-books 1 to 10a ; Decade II , 10b to 20 ; Decade III , 21 to 30 , and Decade XII the guard-books 111 to 119 . As , however , there are irregularities in the original numbering of the books , some of the Decades have to comprise supplementary volumes and appendices . Two figures are attached to each document in the Index ; the first , a Roman numeral , refers to the Decade , the second , an Arabic numeral , points to the particular paper in that Decade . As an example , we turn to the Index , and find , under Jenner , Edward , M.D. , the figures IX 37 . On referring to the MS . Calendar , and to the section dealing with Decade IX , we read , under Dr. Jenner 's name , that the document No. 37 is entitled " Of the Cuckoo " ; that it is a signed holograph of 32 pages , dated : Berkley , Feb. 20 , 1787 . Further , we note that it is endorsed " cancelled at the desire of the Author , C. B. , Sec. R.S. " The paper itself will be found in one of the guard-books labelled " Decade IX , Nos. 23 to 49 . " There is no need to ascertain the old number attached to the guard-book in question ( it is 82 ) , as the new label on the volume gives all necessary information ; a mark in blue pencil , on the first guard to which the document is pasted , indicates its number in the Decade . Letters and Papers . The approximate dates covered by the several Decades , with the number of calendared documents in each Decade , are shown in this conspectus:\#151 ; Decades . Dates . Documents . I. October 1741 to October 1746 ... ... ... ... 480 II . December 1749 " March 1755 ... ... ... ... 586 III . March 1755 " March 1760 ... ... ... ... 426 IY . March 1760 " November 1767 ... ... ... ... 415 Y. January 1768 " December 1772 ... ... ... ... 330 YI . November 1773 " December 1777 ... ... ... ... 260 YII . January 1778 " June 1782 ... ... ... ... 272 YIII . November 1782 " June 1786 ... ... ... ... 190 IX . June 1786 " January 1792 ... ... ... ... 221 X. February 1792 " March 1796 ... ... ... ... 150 XT . June 1796 " December 1801 ... ... ... ... 175 XII . December 1801 " June 1806 ... ... ... ... 146 It will be seen that there are now at the disposal of Fellows of the Society two newly-compiled Calendars of papers in the Archives , with corresponding Prof. J. S. Townsend . [ Nov. 3 , printed Indexes of some 2150 Authors . These cover a period of 200 years , deal with more than 6150 documents preserved in 166 guard-books , the contents of which were , until now , very little known , and , though accessible , were scarcely available for purposes of study . The Charges on Ions in Gases , and the Effect of Water Vapour on the Motion of Negative Ions . By Prof. John S. Townsend , F.R.S. ( Received November 3 , \#151 ; Read November 12 , 1908 . ) 1 . In a paper published in the ' Proceedings of the Royal Society , ' vol. 80 , p. 207 , January , 1908 , a method was given for comparing the charges on ions in liquids and gases . The first set of experiments gave results in accordance with the theory , and it was found that the charge on a positive ion in a gas was double that of a negative ion , the latter being equal to the charge on a monovalent ion in a liquid electrolyte . The ratio of the charges obtained was 2*4-r-l-23 . The ions were produced by secondary Rontgen rays emitted by a brass surface , and further experiments have shown that positive ions with double or single atomic* charges may be produced , the number of either kind depending on the nature of the secondary rays , which is determined by the state of the metallic surface from which they originate . In all cases the negative ions have a single atomic charge . Another difference between the positive and negative ions has also been found . It will be seen from the experiments to be described that the motion of a negative ion in an electric field is influenced to a great extent by the presence of water vapour in very small quantities , there being no corresponding effect with positive ions . 2 . In the first set . of experiments that were made no particular attention was paid to the state of the surface at which the secondary rays were produced , and when the air-tight cover was taken off the apparatus it was found that this surface was very much tarnished . The surface was carefully cleaned with the intention of getting a sufficient number of ions generated in the gas * For simplicity the charge on a monatomic ion in a liquid electrolyte may be termed the atomic charge . Denoting its value in electrostatic units by e , then No = 1'225 x 1010 , N being the number of molecules in a cubic centimetre of a gas at 760 mm. pressure and temperature 15 ' C.

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The charges on ions in gases, and the effect of water vapour on the motion of negative ions.

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471

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

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

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http://dx.doi.org/10.1098/rspa.1908.0106

en

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0106

10.1098/rspa.1908.0106

Tables

Electricity

Tables

]\gt ; Prof J. S. Townsend . [ Nov. 3 , printed Indexes of some 2150 Authors . These cover a period of 200 years , deal more than 6150 documents preserved in 166 guard-books , the contents of which were , until now , very little known , and , accessible , were scarcely available for purposes of study . The in Gases , the Effect of Vapour Motion oj ' Ions . By Prof. JOHN S. Received vember Read ovember 1 1 . In a paper published in the of the loyal Society , ' vol. p. 207 , January , 1908 , a method was given for comparing the on ions in liquids and gases . The first set of experiments gave results in accordance with the theory , and it found that the charge on a positive ion in a gas was double that of a tive ion , the latter being equal to the on a monovalcnt ion in a liquid electrolyte . The ratio of the obtained was The ions were produced by secondary rays emitted by a surface , and further } riments have shown that ions with double or atomic* may be produced , number of either kind on 1latnre of the secondary rays , is determined the state of the surface from which In all cases the negative ions have atomic euce between the positive and tive ions also been found . It ill be seen from the expelin)ents to be described that the motion of a atiye ion in an electrlc held is iuflneuced to a by the sencG of water val , our in very small quantities , there no eHect with positive ions . 2 . In set of ) eriments t were no particular attention as to state of the sulface } the secondary were ( l1en the cover off the it was facc I. The sulface of sufficient nnmber of ions ellerated in the city t. ion in ] be atomic clllll.ge . enoting its in units then nu1nber of lnolecules in a cubic ( .entimetre of at 1nm . 1908 . ] The Charges on lons in , etc. at low pressure with a small intensity of primary rays . Under these conditions both positive and negative ions have each one atomic careful experiment gave the values No for positive ions and No for ative ions . Several other experiments confirmed this result . Hence positive ions with single or double atomic can produced by the secondary rays . Experiments were made with various surfaces in order to find more exactly the conditions under which positive ions with double the atomic charge are produced . The simplest method obtained was to rub vaseline on the surface from which the secondary rays emanated . A large proportion of the positive ions then have double , as is shown by the following values of No , for positive and for negatiye ions , deduced from experiments in which a very thin layer of vaseline was used . The vaseline*absorbs the secondary rays , and a very small layer on the surface has the effect of reducing the ionisation in the gas to about one-tenth of the intensity obtained with a polished surface . This does not affect the accuracy of the results , as it is possible to obtain any desired intensity of ionisation by the interrupter or the Similar effects were found by Prof. Perrin , ' Comptes ' vol. 124 , p. Prof. J. S. Townsend . [ Nov. 3 , potential of the battery connected to the primary of the coil with which the Ront ray bulb was worked . vould appear from this that positive ions with two atomic are produced by the more penetrating secondary radiation . 3 . In order to explain the effect of slight traces of moisture on the motion of tlJe negative ions , it is necessary to refer more particularly to the theory of the experiments . The shows the ement of the apparatus . The primary enter the apparatus through ar , aluminium window in the brass cover ( not shown in the ) , an passing through an annular in the thick upper plate , fall on plate S. Some of the ions oenerated by the rays pass the under the electric force , and then through the aperture A into the lowe ] field . The stl.eam of ions opens out , and the central portion falls on disc , and the rest on the , the charges and received by eacf measured accurately by a special form of induction balance . Inter . mediate between the ring with the aperture A and the ring were a of flat rings at equal distances apart , connected in series by high resistancef so that when is put to earth and the plate was raised to a potential there is a perfectly uniform field in the space below the rating G. disc and plate were cut from the same sheet of brass so that be no contact potential between then In the iirst form of the apparatus the was placed touching grating just below it ; afterwards placed at a centimetre below grating , as it was considered that the miby of the lower field would better secured by that arrangement . of this however , very slight , as the same results vere obtained with both apparatus when change in distance of the di the lower plate was taken into consideration . When a uniform stream is the aperature , the essure of the ions at any point in the field of uniform ce is iven b the , ( 1 ) an ion and the numl ) of ions per cubic kinetic cquired by an ion the force the is to Z. 1 , and when this is small }ared the ( of nslation of a of the , thon the equation 1908 . The on Tons in , etc. holds for the ions , since the kinetic energy of translation of a given number of ions will then be equal to the energy of translation of an equal number of molecules . In equation ( 2 ) , is the number of molecules per cubic metre in a gas at atmospheric pressure , and at temperature equal to that of the gas in the experiments . Eliminatir ) , equation ( 1 ) becomes N. . . ( 3 ) This equation can be easily solved , and the ratio of the charge received by the disc to the whole charge be found in terms of N. Thus . ( 4 ) The function is a somewhat complicated expression when expanded in a series of Bessel 's functions , so that for of reference it is convenient to represent graphically . The continuous curve 1 , fig. 2 , represents the values of corresponding to force which is expressed in volts per centimetre , No being taken as . The curve corresponds to an apparatus in which the aperture A is . iu diameter and 7 cm . from the and disc I ) . In order to be certain that equation ( 2 ) is satisfied , it is necessary to make experiments and see that is independent of the of the gas in the apparatus , and ( b ) that varies with the force according to equation ( 4 ) , when a definite value is to No . The latter condition can be tested by means of the ctlrve . These two conditions and ( b ) have been found to hold with various forces and pressures in all the experiments that have been made , except in the case of negative ions when the gas is very dry . 4 . In order to obtain this effect , it is necessary to have the inside the cover of the apparatus or in vessels connected to the apparatns by short lengths of wide tubing . After the has been going on for three or four days , a decrease can be observed in the ratio for ative ions with the higher forces and lower pressures of ths ) . As the proceeds the effect becomes noticeable with the smaller forces and larger The three dotted curves , fig. 2 , represent the values of obtained experimentally after the gas had been for several weeks , and no further changes were noticeable . The curves correspond to pressures 11 , and 5 5 mm. of the gas . Prof. J. S. Townsend . [ Nov. 3 , , It is remarkable thab the of ions the aperture opens out considerably when pressure is lowered ( diminishes ) , also for the values of the forces the of the stream is not much ltered 1 changing the force ( nearly constant ) . FIG. 2 . These results have been with ions both when the surface olished and when t thin layer of vaseline on it . ( effect has observed with 1 ) ositive ions , for which the valncs of continue to satisfy itions and ( b ) when the small alIltllllt of water vttl ) ] ) sily admitted to the ) tus it a to an a little water . The tlios pve ions then return htGS this kind always the to } ) amount to further ittld i of ) ) 1908 . ] The on Ions in , etc. . There is no noticeable change in the number of the ions produced by the rays when this small quantity of vapour is admitted , so that it is improbable that the process of ionisation of the molecules of the is in any way . The experiments cannot be satisfactorily explained by supposing the to be variable and less than the atomic when the gas is dry , but it can easily be seen than an increase of the partial pressure of the ions due to the action of the force would produce results of the kind that have been observed , the charge on each negative ion equal to the atomic charge . In all cases there must be a limit to the range of forces over . which equation 2 ) will be satisfied . It has beenl that the negative ions produced by the rays from molecules of a are smaller than the positive ions , and therefore their free paths longer , so that it is to be expected that the limit would be reached with a smaller force for negative ions than for positive ions . The effects observed , however , are probably not due ether to the difference in the free paths of the kinds of ions , but may artly arise from the diffel.ence between their masses . The velocity of translation of the ions increases under the electric force , and when collisions with molecules occur the ions do not in general lose all the energy they acquire but continue to move in all ections with increased after several collisions . The partial pressure of the ions is in excess of that of an equal ilumber of the surrounding molecules ) the force , but the difference would quite inappreciable except when the force is large and the pressure small . The value of the force where this effect begins to be of importance could be found by these experiments , since the partial pressure of a iven number of ions would exceed the value by a which depends on the force , so that equation ( 4 ) would no longer hold . When is increased to the action of the force , an equation , ( 5 ) must be used to determine for substitution in equation ( 1 ) , and the differential equation for determining at any point in the field of uniform force becolnes ( 6 ) where . is greater than unity , increasing with the electric force , and diminishing with increase of pressure of the gas , since an increase in number of collisions with molecnles diminishes the free J. S. Townsend , ' Phil. Mag June , 190 ] , p. VOL. LXXXI.\mdash ; A. 2 I Prof J. S. Townsend . [ Nov. 3 , paths and tends to equalise the energy of translation of the ions and the molecules . The definition of the quantity . is contained in equation ( 5 ) , it represents the ratio of the partial pressure of the ions to that of an equa ] number of molecules of the surrounding gas . The solution of equation ( 6 ) is of the same form as that of equation ( 3 ) since does not vary from point to point in the gas , so that . ( 7 The value as given by this equation for a force is the same the ratio for a smaller force when the gas is htly moist an6 There is one simple relation that should hold between the values of the different forces and pressures which may be tested by the experimental results . It is obvious that must depend only on Z. or , since free path is inversely proportional to the pressure of the gas , so that must be a function of . The values of corresponding to the different forces and pressures can be found from the experiments , and it may be seen that the condition is satisfied . If be the ratio corresponding to the force for the dry gas , the force which would give the same ratio when may be found from the continuous curve , fig. 2 , so that is easily determined . The following table gives the values of for the different forces and pressures Thus the results ined with variations of the force and pressure bhow thal does not alter when and are changed in ] same proportion , so that the above condition satisfied . The effects ) served with tive ions in a dry gas may therefore attributed to partial pressure which they can acquire are of small . Since the motion of tive ions that particles larger dimensions positive ions ) , ' is scnt it llay concluded that the water } ) at ( low ur tellds to dense on the ative ions . of ative ions was first observed 1908 . ] The on Ions in Gases , etc. in the experiments on diffusion of ions gases at atmospheric pressure . * Prof. Zeleny also , in his experiments on the velocity of ions under an electromotive force , observed a corresponding effect . The changes were produced by pressures of water vapour , and were comparatively small . The effects of small traces of water vapour could not have been investigated by the methods employed in those experiments , as large volumes of gas were used . Possibly the motion of ions in gases at high presures is not influenced by small traces of water vapour , but experiments on the velocity of ions under an electromotive force are being made to investigate the matter . It may be seen from experiments that have made on the genesis of ions collisions that water vapour does not condense on the ative ions when they are travelling with high velocities under large forces and small pressures . Thus , values of of the order of 50 and upwards , the negative ions in water vapour , at a of millimetres , are the same as those in dry gases , and are small compared with positive ions . * J. S. Townsend , ' Phil. Trans vol. 193 , 1899 , p. ] . Zeleny , ' Phil. Trans vol. 195 , 1901 , p. 193 . . S. Townsend , ' Phil. 1903 , p. 389 ; 'Phil . Mag 1902 , p. 8 .

rspa_1908_0107

0950-1207

Measurement of rotatory dispersive power in the visible and ultra-violet regions of the spectrum.

472

474

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

T. Martin Lowry, D. Sc.|Prof. Armstrong, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1908.0107

en

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0107

10.1098/rspa.1908.0107

Optics

Atomic Physics

Optics

472 Measurement of Rotatory Dispersive Power in the Visible and Ultra-violet Regions of the Spectrum . By T. Martin Lowry , D.Sc . , Lecturer on Physical Chemistry and Instructor in Crystallography at the Central Technical College . ( Communicated by Prof. Armstrong , F.R.S. Received November 3 , \#151 ; Read November 19 , 1908 . ) The following is a brief preliminary account of improvements effected in the method of determining rotatory dispersive power which have made it possible to observe accurately not only in the bright regions of the visible spectrum , but throughout the scale from the region of the lithium red line into that commanded by the photographic plate . Two methods have generally been used for the purpose , namely , ( 1 ) Broch 's method , in which a spectroscope is arranged in series with the polarimeter and a narrow strip of a continuous spectrum is picked out for \#166 ; observation\#151 ; a method which is much improved by using a constant-deviation spectroscope in place of one of the variable-deviation type , * and { 2 ) Landolt 's method , in which a white light is reduced by means of filters to approximate homogeneity in the red , green , light-blue , or dark-blue parts of the spectrum . Neither method fulfils the fundamental condition that the field of the polarimeter shall be uniformly lighted with monochromatic light\#151 ; many of the measurements that have been made , therefore , possess only a qualitative value . A much better method is due to the late Sir William Perkin , who introduced the use of a spectroscope-eyepiece as a means of purifying the sodium light , and used it on a limited scale for measuring rotatory dispersive power in the red ( lithium ) , yellow ( sodium ) , and green \lt ; ( thallium ) parts of the spectrum . " The method now described resembles Perkin 's method in its essential feature , namely , the use of monochromatic or multiehromatic light ( spectroscopically purified ) in place of a band from a continuous spectrum . It has the advantage that it renders available for polarimetric measurements , in " addition to the flame spectra , the large series of intense line spectra produced by the metallic arcs , which , with the one exception of the enclosed mercury , arc , f do not appear to have been usecl previously for this purpose . Up to the present , measurements have been made with 26 lines ranging from w.l. 6708 to w.l. 4359 ; beyond these limits the visual intensity of the light * F. Twyman , 'Phil . Mag. , ' 1907 , vol. 13 , p. 481 . t Disch , 'Ann . Phys.,5 1903 ( 4 ) , vol. 12 , p. 1155 . Measurement of Rotatory Dispersive , etc. 473 is so small that polarimetric observations become very difficult , but in the intermediate part of the spectrum the list might , without difficulty , be extended considerably . The mercury lines referred to in the table were produced by a Bastian lamp ; the copper and zinc spectra were produced by means of copper or brass electrodes rotating in opposite directions , as recommended by Baly in the case of the iron arc ; the cadmium spectrum was obtained by means of rotating copper or silver electrodes coated with the metal . In order to utilise the arc spectra for polarimetric observations , a parallel beam from the arc is thrown on to the widely-opened slit of a constant-deviation spectroscope . An achromatic lens of 22 " focus is substituted for the observing telescope of the spectroscope , and is used to cast a magnified image of the slit on to the polarising prisms which produce the horizontally-divided triple field of the polarimeter . By turning the constant-deviation prism to a suitable position , the field can be illuminated from top to bottom by a brilliant band of pure monochromatic light , the maximum width of the band being determined by the openness of the spectrum and , in a very important manner , by the efficiency of the dispersive system . By using a C.D. prism of high density in conjunction with the long-focus lens , it is possible to read separately the two lines 5790 and 5769 which constitute the yellow mercury doublet , although these differ in wave-length o by only 21 Angstrom units ; the yellow doublet and green triplet in the copper spectrum can be read with ease and accuracy as broad bands each occupying a width rather greater than one-third of the 8-mm . aperture of the triple field ; the chief lines in the mercury and cadmium spectra can be made to cover practically the whole field without overlapping . In order to eliminate stray light , which would give rise to serious errors in the red and violet readings , a Perkin spectroscopic eye-piece is used . In measuring rotatory dispersive power in the ultra-violet , a parallel beam of light from an arc formed between a carbon and a magnetite electrode is cast directly by a quartz condenser on to the triple field of the polariser , Foucault prisms being substituted for the Nicol prisms to ensure transmission . A quartz-calcite lens of 13 " focus is substituted for the analyser-telescope ; this casts a diminished image of the triple field on the slit of an ultra-violet spectroscope . The spectrum thus produced is photographed in the ordinary way by means of a camera provided with a quartz-calcite lens of 22 " focus ; the division produced by the triple field can be seen clearly , and it is easy to pick out and identify on the negative the line which is of equal intensity in its three sections . By taking photographs with the analyser in different positions 474 Measurement of Rotatory Dispersive , etc. it is possible to determine the rotatory power of a substance throughout the transmitted spectrum . The results obtained with water , carbon bisulphide , and other liquids in a magnetic field will be dealt with in a later communication ; the method is .one which is likely to be of special value as affording a means of determining , the homogeneity of apparently simple liquids . The polarimeter readings shown in the table were usually concordant within a few hundredths of a degree : the absolute values may differ by as much as 1 ' in different specimens of the ester , but the relative values a/ \#171 ; D are probably reliable within one or two units in the last figure . Table of Wave-lengths used in the Measurement of Rotatory Dispersive Power , together with the rotations produced by 100 mm. of Methylic Camphocarboxylate at 20 ' C. w.l. a. \#171 ; / " D. w.l. a. d \#171 ; /\#171 ; D. Li red 6708 48 '32 0-728 Cu green 5154 94'-93 1 -430 Cd red 6438 53 -41 0-805 Cu green 5105 97 -52 1 -469 Zn red 6364 54 -91 0 -827 Cd green 5086 98 -60 1 -486 Na yellow ... 5893 66 -37 1 -ooo Zn blue 4811 116 -15 1 -750 Hg yellow 5790 69 -40 1 -046 Cd blue 4800 116 -93 1 -762 Cu yellow ... 5782 69 '83 1 -052 Zn blue 4722 122 -92 1 -852 Hg yellow ... 5769 70 -09 1 -056 Cu blue 4705 124 -38 1 -874 Cu yellow ... 5700 72 -38 1 -090 Zn blue 4680 126 -36 1 -904 Ag green 5469 80-75 1 -217 Cd blue 4678 126 -55 1 -907 Hg green 5461 80 -94 1 -220 Cu blue 4651 128 -34 1 -933 T1 green 5351 85 -59 1 -290 Cu blue 4587 134 -60 2-028 Cu green 5219 91 -73 1 -382 Cu violet 4378 157 -62 2 -375 Ag green 5209 92 -17 1-389 Hg violet 4359 165 -07 2-487

rspa_1908_0108

0950-1207

Results of magnetic observations at stations on the coasts of the British Isles, 1907.

475

476

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

Commander L. Chetwynd, R. N.|Rear-Admiral A. M. Field, R. N., F. R. S.

abstract

6.0.4

http://dx.doi.org/10.1098/rspa.1908.0108

en

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0108

10.1098/rspa.1908.0108

Meteorology

Tables

Meteorology

475 Results of Magnetic Observations at Stations on the Coasts of the British Isle , 1907 . By Commander L. Chetwynd , R.N. , Superintendent of Compasses . { Communicated by Rear-Admiral A. M. Field , R.N. , F.R.S. Received July 14 , \#151 ; Read December 10 , 1908 . ) ( Abstract . ) With a view to comparing the values of secular change of declination , horizontal force , and inclination , at various stations on the coasts of the British Isles , with the values derived from the continuous records at Kew Observatory , the Hydrographer ( Rear-Admiral A. Mostyn Field , F.R.S. ) directed that observations should be made at certain stations selected from those occupied by Rucker and Thorpe during their magnetic survey for the \#171 ; poch January 1 , 1891 . The observers detailed to make the observations were:\#151 ; Captain M. H. Smyth , R.N. , H.M.S. " Research " ; Captain W. Pudsey-Dawson , R.H. , H.M.S. " Triton " ; and Captain J. W. Comb , R.N. , H.M. surveying vessel \#166 ; " G-ladiator . " The stations selected were fairly distributed around the coasts , so that a mean of the results would represent the mean for the whole .area embraced . , The observations have been reduced to the epoch January 1 , 1907 , by means of comparisons with the records at Kew Observatory . The resulting values of mean annual changes for the British Isles are as follows:\#151 ; ( a ) ' ( b ) 21-year period . 16-year period . ( 1 ) Declination 1886\#151 ; 1907 . - 5'*7 1891\#151 ; 1907 - 5'T ( 2 ) Horizontal force + 19 7 + I87 ( 3 ) Inclination - l'*6 - l'-4 ( 4 ) Vertical force ( excepting the results at Dublin and Tanera Mor ) \#151 ; 14 7 The mean annual changes of declination at Kew comparable with ( 1 ) a and b are respectively 5''2 and 4''9 . Thus the mean for the British Isles during the 16-year period is 0''2 greater than at Kew . The mean horizontal force change appears to have been 3 \lt ; y less than at Kew . The mean inclination change during the 21-year period was O'T less , and during the 16-year period 0'-6 less , than at Kew . 476 Magnetic Observations on Coasts of British , 1907 . The mean vertical force change during the 16-year period has been 87 less than at Kew . Diagrams showing the mean annual changes at Kew from 1889 to 1904 indicate that the declination change , which since 1894 has been decreasing in amount , is now increasing , and that the probable mean value for January 1 , 1907 , Kew , is 4'-8 . For the whole of the British Isles , therefore , the mean value is assumed to be 5 ' . The annual increase of horizontal force continues to diminish and is at the present time very small ; there has been a very marked diminution during the last two years , and the annual increase may shortly become a decrease . The annual change of inclination continues to decrease in amount , and is now 1 ' ( nearly ) . A comparison of the value of the mean annual change of declination at Kew , Greenwich , and Stonyhurst shows that whereas , during the period embracing Biicker and Thorpe 's survey ( 1886\#151 ; 1894 ) , the change at Stonyhurst was considerably greater than at Kew and Greenwich , this being in accord with the results found by Bucker and Thorpe , that the secular change was greater in the north-west than at Kew . Since the year 1894 , however , the values have been in closer agreement , that at Stonyhurst being slightly less than at Kew . Thus it is indicated that the variations of secular change are not , over the area referred to , synchronous . Comparisons of results of declination observations made at sea with those made on shore show considerable differences , and although the sea observations cannot be considered to the same degree of accuracy as the shore observations , the differences are in most cases outside the margin which might be assigned to this cause . The results indicate that the values at sea are , off the east coast generally greater , and on the west coast generally less , than the corresponding values adduced from observations made on shore . It is intended to investigate this subject further .

rspa_1908_0109

0950-1207

Potential gradient in glow discharges from a poInt to a plane.

477

495

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

J. W. Bispham, B. A., B. Sc.|Prof. Sir J. J. Thomson, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1908.0109

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1908_0109

10.1098/rspa.1908.0109

Electricity

Tables

Electricity

477 Potential Gradient in Glow Discharges from a Point to a By J. W. Bispham , B.A. , B.Sc. , Research Exhibitioner and former Scholar of Emmanuel College , Cambridge . ( Communicated by Prof. Sir J. J. Thomson , F.R.S , Received November 11 , \#151 ; Read December 10 , 1908 . ) ( 1 ) Description of Apparatus and General Description of Phenomena . Preliminary . The original object of the experiment described in this paper was the investigation of the distribution of electric force along the axis of glow discharges from a charged point to a neighbouring plane in the case when striae are visible . Such discharges are described by Y. Obermayer.* The appearance of the discharge\#151 ; as Prof. Thomsonf has pointed out\#151 ; suggests that the current is not merely carried by ions of the same sign as the discharging point . Obermayer notes , however , that the type of discharge obtained varies considerably with the capacity shunted across the terminals of the discharge , and also depends on the self-induction in the circuit , indicating that the discharges are of an oscillatory or intermittent character ( see fig. 6 , A , B , D , and E ) . The following experiments lead to the conclusion that the types of striated glow discharge described by Obermayer , in which the glow spreads out from the point to the plate in a more or less conical form , are of an intermittent character . Speaking generally , it was found that in the case of hydrogen , when the pressure was about 1 cm . of mercury , two types of continuous discharge were possible , one for small currents and the other for larger currents . In the first there was only luminosity in the neighbourhood of the point . But for larger currents , both for positive and for negative direction of the current , this point glow form changed over unstably to another form , in which a much lower E.M.F. maintained the larger current , and the form of discharge was then that obtained between small plane electrodes . See fig. 6 ( E and F ) . With a large external resistance in circuit an intermediate unstable condition could be examined in which the discharge was intermittent ( fig. 6 , A , B , D , and E ) . Apparatus . The distribution of electric force along the axis was obtained by first observing the distribution of potential along the axis , and hence deducing the * Y. Obermayer , 'Wien . Sitzungsberichte , ' c.p. 127 , 1891 . t J. J. Thomson , 'Conduction of Electricity through Gases , ' 1st ed. , p. 411 . Mr. J. W. Bispham . Potential Gradient in [ Nov. 11 , electric force graphically . For this purpose it was necessary to produce relative axial motion of the exploring electrode and discharge . In the apparatus finally used , the explorer remained stationary and the discharge was moved past it on geometrical guides . The discharge apparatus was enclosed in a large bell-jar 12 inches high and of 8 inches diameter ( fig. 1 ) . The whole discharge apparatus was supported Fig. 1 . 1908 . ] Glow Discharges from a Point to a Plane . on a large glass cylinder which floated on mercury . The motion of a mercury surface exposed to the atmosphere produced similar motions of the mercury surface at almost barometric height above it . The latter surface floated the discharge , and was itself in contact with the rarefied gas under observation . Two brass plates , 12 cm . in diameter and 1 mm. thick , were fixed at a distance of 7*5 cm . apart by three glass tubes , cemented into three collars on the outer side of each plate . Another brass collar , of internal diameter 4 mm. , pierced the upper plate at its centre and passed through at right angles to its surface , extending about 1 cm . on either side . In this collar slid a brass rod to the end of which the discharge needle was soldered axially . This arrangement furnished an adjustable electrical contact between the point and the upper plate . The discharge point and the lower plate were fixed relatively during the experiments , but the whole system was moved up and down by flotation on mercury . Attached to the lower plate by a central brass collar was a long cylindrical glass bulb which floated on mercury in a coaxial glass cylinder with a clearance of 2 mm. A rubber U-tube connected the outer cylinder with a reservoir of the type usually employed for Toepler pumps . Its vertical motion was controlled by suspending it from a string fixed to the circumference of a pulley . The pulley was screwed tightly back against a wooden surface , so that it was held by friction in any position in which it was left . The pulley was adjusted by hand , and it was found possible to produce very small motions of the discharge . The three glass tubes previously mentioned as holding the parallel plates apart also served as movable guides for the motion . Through these tubes ran three other tubes of stout glass of smaller diameter . The inner tubes ( G ' , G , fig. 1 ) forming the fixed guides passed eccentrically through the movable ones , and a vertical line of contact was formed between each pair which served as a geometrical guide . This arrangement also possessed the advantage that the guides were on the same level as the actual displacement required , and so completely controlled it . When viewed through a cathetometer it was seen that the relative motion of the exploring electrode and discharge point was very accurately parallel to the vertical cross wire . The motion was very slow and steady by reason of the damping due to the viscous and surface resistances of the thin annulus of mercury between the float and its concentric chamber . The cylindrical float was loaded with lead shot at its lower end to make its displacement more definite , to steady the motion , and to locate the Mr. J. W. Bispham . Potential Gradient in [ Nov. n \gt ; inertia of the movable system more nearly at the point of application of the hydrostatic forces . The three tubes which formed the fixed guides G , Gi were securely cemented by a mixture of resin and beeswax into three vertical holes in an ebonite stopper ( X ) , closing the neck of the bell-jar . The guides were also fixed relatively at a lower point by another piece of ebonite ( Y ) . The fixed guides were thus knit rigidly together . The bottom of the bell-jar was closed by a stout zinc plate ( Z ) cemented to the flat glass welt of the jar . In the centre of the zinc plate was a circular hole with an ebonite collar ( M ) to receive the chamber which contained the float . A glass tube ( B ) cemented through the ebonite stopper in the neck of the jar served as an inlet for gases , while a brass rod ( C ) also cemented through the stopper allowed electrical contact to be made with the discharge needle through a spiral of wire soldered to it and to the rod carrying the discharge needle . The brass plate forming the flat electrode , was connected by a loose spiral of copper wire with the stout zinc plate , closing the bottom of the jar . In the experiments the flat electrode was always earthed and the needle charged to a high potential by a Wimshurst machine , or by a large battery of lead cells . The Exploring Electrode . Earlier experiments were made with another form of apparatus in which the exploring electrode was a ring of wire arranged to move with its centre on the axis of discharge . This form was subsequently discarded , because it was necessarily of a size large enough to produce quite marked disturbances in the electric field between the point and plate . The form finally adopted was similar to that used by H. A. Wilson* in his experiments on potential gradient between plane electrodes . A fine platinum wire E , 1/ 1000 inch in diameter , was covered by a-very fine capillary tube of glass to within 1/ 5 mm. of its tip . The apparatus was exhausted by means of a Toepler mercury pump , and the pressures were read by a McLeod gauge which normally gave a magnification of 38 . These are not indicated in diagrams , as they presented no peculiar features . The apparatus was kept dry by two phosphorous pentoxide bulbs , and the hydrogen and air used were respectively passed through sulphuric acid and dry granulated calcium chloride to dry them before they entered the apparatus at all . The hydrogen was prepared from * H. A. Wilson , ' Phil Mag. , ' vol. 49 , p. 505 , 1900 . 1908 . ] Gloiv Discharges from a Point to a Plane . pure sulphuric acid and pure zinc . In the earlier experiments the hydrogen was washed through permanganate solution . But the gas always behaved after sparking as if it were moist , and it vras suspected that oxygen was carried over with the hydrogen . In subsequent experiments the pressure remained constant for days and consistent readings were obtained . Electrical Connections . The circuit was a very simple one and is shown diagrammatically in \#166 ; 2 . A battery B had one terminal earthed through a lead Lx . Its high potential terminal was connected to the discharge point P through an adjustable resistance It . The plate electrode was connected to earth directly or through the telephone T and galvanometer G- . Fig. 2 . If necessary , a condenser C , with one terminal earthed ( Ei ) , was connected to P , so as to shunt the main circuit as shown . The exploring electrode X was connected by a wire W in a shielding tube S to the leaf of the gold-leaf electroscope Q. Mr. J. W. Bispham . Potential Gradient in [ Nov. H The case of Q and the shielding tube S were connected by a lead L8 to an intermediate point on the battery B. The movements of the gold leaf were observed by means of a microscope with 100 divisions in the eye-piece scale . The external high resistance consisted of two parts\#151 ; a megohm coil adjustable by tenths of a megohm and an electrolytic resistance continuously adjustable from zero to several megohms . The electrolytic resistance was mainly used for producing rapid changes of resistance in making observations of effects . In taking potential curves , the coil was used whenever possible , as the liquid resistance increased with time to a maximum . The current obtained from a battery of small storage cells was remarkably constant , and under these conditions it was particularly easy to obtain steady and reliable readings of the potential from point to point in the discharge . Measurement of Potential . The pressures used in these experiments were fairly high , generally of the order of 1 cm . of mercury , and hence the potential fall between point and plate was of the order of 1000 volts , and never less than 300 volts , of course . It was accordingly necessary to devise a method for measuring the potential accurately to a volt over a range of 1000 volts . The method employed was as follows:\#151 ; The exploring point was connected by means of shielded wires to the leaf of a gold-leaf electroscope . A potential difference of 120 volts deflected the gold leaf to such an angle that it was just off the eye-piece scale of the microscope used to view it . There were a hundred divisions to the eye-piece scale , and a gold leaf was cut which was found on calibration to move roughly 1 division per volt , when the potential difference between the case and the leaf was between the values of 40 and 100 volts . The potential of the electroscope case could be brought to any required value by connecting it by another lead Z2 to an intermediate point on the battery supplying the discharge current ( see fig. 2 ) . The battery maintained its potential when supplying the small currents used in the experiments , and it was found by testing from time to time that the cells remained very steady for a week at a time , each 20 cells giving consistently 41 volts as measured by a Weston voltmeter . The shielding tubes around the wire leading from the exploring point to the gold-leaf electroscope were electrically connected by soldered wires with the electroscope case , and the case and tubes carefully insulated . In taking a reading , the shielding tubes and electroscope case were raised to such a potential that the gold-leaf image was always on a calibrated 1908 . ] Glow Discharges from a Point to a Plane . portion of the scale of the microscope eye-piece . In making a detailed exploration of a small portion of the field , as , for instance , the region from a striation to its neighbour , all the readings were on the scale , and the potential of the case needed no adjustment . This allowed an accuracy of 0T of a volt ( eye estimated ) over a range of 60 volts at least . The capacity of the electroscope system was very small indeed , only a few centimetres . On moving the discharge relatively to the exploring electrode , the gold leaf moved rapidly up to within a division or so of its final position , and then crept slowly to its final equilibrium position . This occurred when the motion was either upward or downward and the positions finally assumed were identical for currents larger than 10-6 ampere . The exploring electrode used produced no visible disturbance of the discharge and the results justified the conclusion that the disturbing effects were small , except in cases in which the discharge was intermittent . Glow limited to Neighbourhood of Point { Hydrogen ) . For small currents and fairly large pressures the glow was confined to the immediate neighbourhood of the point . The results of the experiments are expressed as curves in which the ordinates are electric force and the abscissa distance from the point . The diagrams for positive point discharges are named Pi , P2 , etc. , and those for negative point .Ni , FT2 , N3 , etc. , and they will be referred to by these names . Only a few of those taken have been included . A particular diagram , e.g. , P3 , refers to results obtained at a particular pressure and the different curves refer to discharges with different values of the current . All the curves refer to a stable condition , that is , the E.M.F. increases as the current increases . It is seen at once that midway between point and plate , the electric force increases as the current increases . This is shown typically in diagram P3 which gives the curves obtained from a set of readings in hydrogen at a pressure of 5*9 mm. The curves A , B , and C refer to discharges in which the currents flowing were:\#151 ; A ... ... . . 1-3 x 10~6 amp . , P.D. 990 volts . B ... ... . . 7*5 x 10"6 " " 1040 " C ... ... . 26-9 xlO"6 " " 1120 " D refers to a slightly different pressure , the discharge was non-luminous and the current too small to measure . For small currents the fall of potential is almost entirely limited to the regions very near the electrodes . Mr. J. W. Bispham . Potential Gradient in [ Nov. li N2.\#151 ; A Current 3'7 x 10 6 amp . , Volts = 1085 B " 61'6xl0-\#171 ; " " =1120 C " 147-2 x 10-6 " " = 1200 D " 246-4X10-6 " " =1210 N4.\#151 ; A Current 5"9 x 10 6 amp . , Volts = 890 B " 53-2 x 10-\#171 ; " " = 905 C " 67-2 x 10-\#171 ; " " =885 Glow Discharges from a Point to a Plane . PLATE POINT P3.\#151 ; A Current 1*3 x 10 6 amp . , Yolts \#151 ; 990 B " 7*5 x 10~6 " " = 1040 C " 26*9 x 10~6 " " =1120 D " very small " = 880 Experiment showed that this form of discharge\#151 ; point glow was only stable within a narrow range of pressures , and even then only for a limited range of current variation . A greater variation in the value of the current was possible in the case of the higher pressures\#151 ; indeed , at a low enough pressure ( about 3 mm. for positive point and 11*3 mm. for negative point ) this form of discharge was unstable . The current passed in an intermittent manner as indicated by a telephone in circuit . Corresponding to this fact , by examination of the curves ( see figs. Ng , is 4 , p3 ) etc. ) it is seen that for pressures well in excess of those mentioned , there is a marked difference between the electric force curves for large and small currents , whereas for pressures approximating to those mentioned the curves for large and small values of the current are almost coincident ( see fig. N4 ) . VOL. lxxxi.\#151 ; a. 2 K Mr. J. W. Bispham . Potential Gradient [ Nov. 11 , In fig. N4 the condition of instability has already appeared , for on referring to the figures it is seen that the largest current requires the least terminal voltage to maintain it . The transmission of current always became intermittent if the current was sufficiently increased . Further increase of electrical transfer was accompanied by a fall and not a rise of terminal potential difference . The glow gradually took up the conical form shown in fig. 6 , A and D , and the telephone emitted a loud note . Further increase of current finally produced a discharge which was continuous and stable , fche glow being very bright ( fig. 6 , C and E ) . In the case of negative point discharge , for example , for small currents , a glow on the point was obtained . As the current was increased the telephone began to sing for a definite value of the current , and then the discharge spread away from the electrodes until a general faint luminosity was apparent between the point and the plate . This ultimately took the form of a positive column extending from the plate\#151 ; a dark space and a negative glow encircling the -discharge needle . Further increase of the current caused the positive column to recede to a flat disc of luminosity on the plate . Still further increase of current caused the luminosity on the needle to extend all over the cathode . The experiments point to thq condition " point glow " being a form of discharge only possible for certain limits of pressure and current . Within the limits of pressure for which it is stable , increase of current , produces ultimately an intermittent form of discharge . Decrease of pressure ultimately leads to this intermittent discharge again , even for the smallest currents . It was not possible with the available voltage to test higher pressures . Some experiments were made in cases in which the discharge was *non-luminous by reason of the extreme smallness of the current . In these cases the potential curves were of the form shown in D , diagram P3 , which give an actual case observed . The fall of potential was limited to the immediate neighbourhood of the electrodes . Curves such as A and B , fig. H2 , would tend to indicate that the discharge in some cases consists of two parts , a discharge from the point to the surrounding gas and another from the gas to the plate . Small variations in the potential curves are associated with relatively large variations in the electric force curves , so that the point must not be unduly emphasised ; but the form of curve is a very general one for these sets of readings , and the point is therefore worth consideration . Many curves of the same type were obtained . 1908 . ] Glow Discharges from a Point to a Plane . The Intermittent Positive Discharge without ( Fig. 6 , A ) . As has been pointed out , with a high resistance in circuit it was possible to obtain an intermittent discharge for currents intermediate in value between those accompanying " point glow " and the steady discharge form represented in fig. 6 , C. This intermittent form is represented typically in fig. 6 , A. It was noted that the negative glow was a doublet divided into two portions by a dark interval p ( fig. 6 , A ) , although the Faraday and Crookes dark spaces were quite typical . As the pressure was reduced , the whole doublet moved away from the cathode . Potential readings were taken at various pressures and curves plotted . The curves were all of one type , there was an apparent reversal of field between the surface of the negative glow next the cathode and the dark interval ( p ) referred to above . That is to say , the surface of the negative glow corresponded to maximum and the layer to a minimum of potential . The curves obtained are not published , as they are of exactly the same type in this particular as the portion AA ' of the curve of fig. 3 . With all external inductances and capacities removed , the discharge retained the same character , and for large currents a note could be heard without the telephone in circuit . The readings of potential\#151 ; the apparent reversal referred to above\#151 ; probably depended on the capacity of the electroscope system . Probably the potential as each intermittent discharge occurred tended to rise to a certain value , and the actual reading depended on the number of ions present to convey electricity to and from the exploring point . A test established this to be the case . If was found that whereas the readings of the electroscope were independent of its capacity for continuous discharges , whether the current was large or small , for intermittent discharges the potential curves did depend on the capacity of the electroscope system . Headings are given which were made to test this point . Increase of capacity was found to increase the maximum of potential , such as A , fig. 3 , and decrease the minimum of potential ( A ' , fig. 3 ) . Increase of the capacity of the electroscope system thus increased the distortion of the curve . Readings . Four readings were always made alternately with and without augmented capacity of the electroscope , of the maximum and of the minimum potential:\#151 ; Mr. J. W. Bispham . Potential Gradient in [ Nov. 11 , With condenser on electroscope Without condenser Yolts . Maximum . Minimum . 292 '5 ( mean ) 282 -5 " 239 " 5 ( mean ) 248 The results might he explained by supposing an excess of negative ions at the minimum of the curve , and an excess of positive ions at the points corresponding to the maxima . The maxima were found to correspond very closely to the surface of the negative glow nearest the cathode , while the minima were closely in agreement with the dark interval ( p ) which divided the negative glow into a doublet . A similar apparent reversal of field was obtained near the point in the case in which the point was made the cathode . The apparent reversal seems clearly to be due to the positive electrification of the Crookes dark space , and to an excess of negative electrification at a point farther away from the cathode . At some intermediate point in the negative glow the number of ions of opposite sign are equal . A similar series of apparent reversals were obtained in plotting the potential curves from stria to stria in the striated form of discharge . ( See fig. 3 . ) Intermittent Discharge with Striae\#151 ; Hydrogen . When a condenser was shunted across the terminals of the discharge , and the total E.M.F. applied through an external resistance was greater than that necessary to maintain the discharge , the discharge passed in an intermittent manner . The period became very large when the condenser used had a capacity of a microfarad . By adjusting the resistance the period became as long as 1 second , and the discharge passed by a brilliant flash of such intensity as to cause anxiety for the safety of the apparatus . This flash was followed by an interval of darkness for a second , and then another such discharge occurred . By decreasing the shunted capacity and decreasing the series resistance , the period could be steadily reduced until the note was of a pitch so high that it passed out of the range of audibility , as indicated by the telephone in circuit . Under these conditions , stake ( fig. 6 , B ) were generally observed . It was noted that the distance apart of the striae did not perceptibly change ( in this particular type of discharge ) when quite large changes in current were made , whereas , in the steady and continuous forms of discharge ( fig. 6 , C ) the disposition of the striae changed very rapidly as the current was varied . An attempt was made to obtain potential curves under these conditions . 1908 . ] Glow Discharges from a Point to a Plane . Both curves ( figs. 3 and 4 ) refer to hydrogen . The discharge from the negative point was first examined , and the potential curve obtained was of the form shown , fig. 4 . On this diagram , both the potential and the corresponding electric force curves are given . The electric force curve is probably unreliable , to judge from the type of potential curve obtained in the case of the positive discharge ( fig. 3 ) . But it was observed that the fall of potential was steep in the bright parts of the striae , and fiat in the intermediate dark layers . It is probably more easy to interpret the results +V*E POINT + -POINT by reference to the diagram , fig. 3 , in which the results for positive discharge are given . The maximum A of the curve is of the type previously described ( in the case of the curves of intermittent discharges without striae ) and has been shown to depend on the capacity of the electroscope measuring the potential . Both the maximum A , and the minimum A ' , are exaggerated by increasing the capacity of the electroscope , A then probably corresponds to a region of positive electrification and excess of positive ions , while A ' corresponds to a region of negative electrification . Probably each of the maxima B , C , D , etc. , are of the same type and correspond to regions of resultant positive electrification while the corresponding minima refer to regions of negative electrification . Mr. J. W. Bispham . Potential Gradient in [ Nov. 11 , Referring still to the case of positive discharge , fig. 3 , it is seen that on this supposition there is an excess of positive electrification on the anode side of the bright portion of a stria , and an excess of negative electrification on the cathode side of the bright part of the stria . In fig. 3 , the apparent reversal is dotted if no intermediate point on the curve was obtained . In the case of the negative glow , it is seen that there is an excess of positive electrification on the Crookes dark space side of the negative glow , while in the Faraday dark space negative electrification is in excess . If the same line of reasoning TENTIA- GtIRVt RCE CURVE POINT 33cm . ||B6cm . 2|0 be applied in the case of the discharge from the negative point , it is seen that the curve should have a more uniform slope if these positive and negative excesses of electrification did not affect the electroscope . The excesses of positive and negative electrification are very much more marked in the case of the discharge from positive point than in the case of the discharge from negative point . It is possible that equalisation of potential is much more rapid when the discharge is occurring from a negatively charged point , because the negative ions are then in excess on the whole and they have a 1908 . ] Glow Discharges from a Point to a Plane . smaller mass and are more mobile than the positive ions , so that the local discrepancies are less marked . The curves seem to be more reliable as indicating resultant electrification than as potential curves pure and simple . The curve for negative point perhaps approximates to the truth . It refers to a discharge in which the pressure was 3-9 mm. and the current 1*2 x 10-4 ampere . Fig. 3 for the striated discharge from positive point refers to the same pressure 3-9 mm. , the current being 1-6 x 10~4 ampere and the average potential difference across the terminals being 800 volts . Continuous Discharge for Large Currents\#151 ; Air { Fig. 6 , C and F ) . As has been previously pointed out , the smallest currents at certain pressures were accompanied by a discharge in which luminosity was only appreciable near the point . Increase of current produced an intermittent discharge in which the terminal potential decreased as the average current increased . Still further increase of the current produced a discharge in which a large current was maintained by a terminal potential difference much less than was necessary to maintain the small current of the " point glow " type of discharge . It is obvious that in the absence of the large external resistance which was always in series during the experiments , that the first condition would have passed over spontaneously to the second . The resistance in question rendered possible an intermittent and otherwise unstable condition of flow . The distribution of potential was examined for these larger currents , and the curves obtained point to the view that the point and a small area of the plate acted merely as small electrodes and that there was very little real modification of the discharge due to the point . The platinum needle apparently acted as a cylindrical electrode merely . The appearance of the discharge also tended to support this view . When the platinum needle was made the cathode , the negative glow which surrounded it was of the lipped test-tube shape examined by Prof. H. A. Wilson . The positive column extended from the plate towards the point and was separated from the negative glow by a typical Faraday dark space . The luminosity , however , was limited to a narrow axial pencil and apparently the current did not flow from any but a limited area of the anode plate . On increasing the current , the negative glow grew so as to envelop more of the cathode , while the positive column slowly shortened and retreated till it was merely represented by a very bright circular disc of light on the centre of the plate . When the point was negative , striae were never obtained with these larger currents , but when the point was positive , striae were obtained , the discharge still being limited to a narrow pencil ( fig. 6 , C ) . 492 Mr. J. W. Bispham . Potential Gradient in [ Nov. li With the point positive the discharge again presented the typical appearance , an almost cylindrical positive column extending from the point towards the plate . A brilliant and somewhat peculiar negative glow at an unusually large distance from the cathode was separated from the above mentioned positive column by the usual Faraday dark space . Gn increasing the current the positive column became striated , and on still further increasing the current the positive column shrunk back , stria by stria , into the point anode , until only a brilliant light on point and plate remained . Meanwhile , the negative glow had spread itself over the whole plate . Unfortunately , in the case of hydrogen , the narrow pencil of discharge y^as often not axial . Apparently the dimensions of the apparatus introduced an instability for this type of discharge when it occurred in hydrogen . No such instability was observed in the case of air . Sets of readings were taken for the distribution of potential ( both for positively and negatively electrified point ) in discharges for relatively large currents in air . The curves are not given , as they exactly resembled those obtained by Prof. Wilson for ordinary discharges . The curves served to indicate , however , that the exploring electrode was acting in a constant and reliable manner . When the plate was cathode the curves very clearly indicated that th e cathode fall was continuous throughout the dark space . On making the-^1 plate positive the anode fall of about 35 volts was very abrupt . A constant cathode fall of 340 volts was obtained\#151 ; the cathode being lead . The cathode fall was independent of current and pressure for large changes and was scarcely increased when the point was made cathode , indicating that the influence of the " point " was no longer very great . The electric force in the negative glow was very small indeed . The curves gave very satisfactory testimony as to the efficiency of the explorer . Abnormal Thickness of the Dark . Space in Air and Hydrogen . For these readings the plate wTas always made the cathode . The boundary of the negative glow ( both for large continuous currents and also for the oscillatory types of discharge described above ) was definite and constant , and as it was very nearly parallel to the cathode plate , readings of considerable accuracy were possible , until the pressure became so low that the \#166 ; boundary was no longer distinct . The thickness of the dark space was measured by the movement of the discharge necessary to bring first the plate and then the boundary of the negative glow into coincidence with the exploring point . The appearance of the negative ' glow was extraordinary for large steady currents , and J2 Glow Discharges from a Point to a Plane . o \lt ; / ) RECIPRpCAL Fig. 5.\#151 ; Cathode space in air . erves special mention . The negative glow was of the form represented grammatically in fig. 6 , C. It closely resembled one of the striae of the fitive column ( m ) embedded in a blue halo ( n ) in the case of hydrogen , e striae and the central portion of the negative glow were of a bright mon-red colour . The negative glow was surrounded by a blue halo . VOL. lxxxi.\#151 ; A. 2 L 494 Mr. J. W. Bispham . Potential Gradient [ Nov. 11 , Moreover , the cathode dark space was unusually large , and instead of being concave , the negative glow , like the striae , was convex to the cathode , as was also noticed in the case of the intermittent type of discharge . Some results will be detailed for the case of air . The thickness of the dark space was measured to the strongest line of demarcation between the glow and the dark space . In the case of the continuous discharge as shown in fig. 6 , C , the reading to the boundary of the blue halo ( n ) gave a very different value from the reading to the strong line of demarcation which divided the red glow mfrom the blue halo . Sets of readings were taken and curves drawn to compare the values of the dark space with those obtained by Ebert* and Ashtonf . INTERMITTENT CURRENT * CONSTANT CURRENT LARGER CURRENT WITHOUT STRI/ E. . PLATE eZZZZZ ? 22ZZZZZZZZZ ) LARGER CURRENT GLOW COLUMN COLUMN TCOLUMN Fig. 6 . The curves were of similar type , but the values obtained , both in air and hydrogen , were uniformly greater than those of Ebert and Ashton . Thus in fig. 5 the curves BB and DD refer to measurements in air for large steady currents ( BB up to red glow , DD to the vague blue halo ) . Curves CC and AA refer to intermittent discharges respectively with and without condenser shunted in . EE and EE are the values obtained by Ebert and Ashton . As has been mentioned , the negative glow was unusual in appearance , and * Ebert , ' Wied . Ann. , ' vol. 19 , pp. 200 , 372 , 1899 ; and * Verhand . Deutsch . Physik-Ges . , ' vol. 2 , p. 99 , 1900 . t Ashton , 'Roy . Soc. Proc. , ' April , 1907 . 1908 . ] Glow Discharges from a Point to a Plane . 495\gt ; looked\#151 ; in the case of large steady currents\#151 ; like a stria embedded in a blue halo . The unusually large values of the cathode dark space indicated by the curves may be due to the proximity of the point , or to the large size of the cathode as compared with the distance between the electrodes , but these points have not been investigated . The readings were taken because it was observed that the cathode space was unusually large . It was impossible to continue the investigation . Some diagrams of discharges are given in fig. 6 . The above experiments were carried out at the Cavendish Laboratory , , Cambridge , and I am much indebted to the inspiration of that Institution , , and more particularly to Prof. Sir John Thomson for his constant interest and advice .

rspa_1909_0001

0950-1207

Address of the President, Lord Rayleigh, O.M., D.C.L., at the anniversary meeting on November 30, 1908.

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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., D.C.L.

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6.0.4

http://dx.doi.org/10.1098/rspa.1909.0001

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1909_0001

10.1098/rspa.1909.0001

Biography

Formulae

Biography

PROCEEDINGS OF THE EOYAL SOCIETY . Section A.\#151 ; Mathematical and Physical Sciences . Address of the President , Lord , O.M. , D.C.L. , at the Anniversary Meeting on November 30 , 1908 . Since the last Anniversary the Society has sustained the loss of eighteen Fellows and four Foreign Members . The deceased Fellows are:\#151 ; The Right Hon. Lord Kelvin , died December 17 , 1907 . Sir Alfred Baring Garrod , died December 28 , 1907 . Robert Lewis John Ellery , died January 14 , 1908 . Prof. James Bell Pettigrew , died January 31 , 1908 . William Ashwell Shenstone , died February 3 , 1908 . Sir John Denis Macdonald , died February 7 , 1908 . Lieutenant-General Sir Richard Strachey , died February 12 , 1908 . Dr , William Edward Wilson , died March 6 , 1908 . Dr. Henry Clifton Sorby , died March 9 , 1908 . Sir John Eliot , died March 17 , 1908 . The Duke of Devonshire , died March 24,1908 . Dr. James Bell , died March 31 , 1908 . Colonel Andrew Wilson Baird , died April 2 , 1908 . Sir John Evans , died May 31 , 1908 . Lord Blythswood , died July 8 , 1908 . Arthur Lister , died July 20 , 1908 . The Earl of Rosse , died August 29 , 1908 . Prof. William Edward Ayrton , died November 8 , 1908 . VOL. lxxxii.\#151 ; A. B Anniversary Address by Lord Rayleigh . [ Nov. 30 , The deceased Foreign Members are:\#151 ; Pierre Jules C4sar Janssen , died December 23,1907 . Franz von Leydig , died April , 1908 . Henri Becquerel , died August 25,1908 . ^leuthere ISlie Nicolas Mascart , died August 26,1908 . The list of deaths this year is exceptionally heavy , and includes the name of one of the most eminent scientific men of our generation , who occupied the Presidency of this Society from 1890 to 1895\#151 ; I refer , of course , to Lord Kelvin . We are fortunate in having secured for our ' Proceedings ' a review of Kelvin 's life and work , written by one who is especially well qualified for the difficult task . I do not doubt that Professor Larmor is right in placing in the forefront of that work those fundamental advances in Thermodynamics which date from the middle of the last century . It was Kelvin who first grasped the full scope of the principle known as the Second Law , a law which may indeed well be considered to stand first in order of importance , regarded from the point of view of man 's needs and opportunities . It would be futile to attempt here a re-survey of the ground covered by Professor Larmor . My acquaintance with Kelvin was limited , until about 1880 , a time when I -was occupied with measurements relating to the electrical units , and received much appreciated encouragement . From then onwards until his death I enjoyed the privilege of intimacy and , needless to say , profited continually from his conversation , as I had done before from his writings . Our discussions did not always end in agreement , and I remember his admitting that a certain amount of opposition was good for him . Such discussions often invaded the officers ' meetings during the time that we were colleagues , not always to the furtherance of the Society 's business . But I must not linger over these reminiscences , interesting as they are to me . We shall never see his like . By the death of Sir Richard Strachey we have lost a man well known to the senior Fellows , who served repeatedly upon the Council and whose advice was always valued . He was a born administrator ; and by his work in India and afterwards at the Meteorological Office he rendered splendid service . Dr. Sorby 's researches extended over many fields , and in several of them he was a pioneer . I suppose that his greatest achievement was the introduction of the method in which thin slices of rock are examined under the microscope . Among his many interesting observations are those upon the retardation of freezing in capillary tubes . It appears that the walls exercise Anniversary Address by Lord Rayleigh 1908 . ] an influence at distances much greater than those usually regarded as molecular\#151 ; evidence apparently of structure upon an extended scale . Dr. Sorby belonged to a class on whom England has special reason to congratulate herself , men who pursue science unprofessionally . The names of Cavendish , Young , Joule , and Darwin at once suggest themselves . It is to be feared that specialisation and the increasing cost and complication of experimental appliances are having a prejudicial effect in this regard . On the other hand , the amateur is not without advantages which compensate to some extent . Certainly , no one who has the root of the matter in him should be deterred by fears of such difficulties , and the example of Sorby suffices to show how much is open to ingenuity unaided by elaborate appliances . The name of Sir John Evans must not pass without special notice . There are few in recent years to whom the Society has been more indebted . Many of our Fellows hardly realise how important and laborious are the services rendered in the office of Treasurer . Evans ' scientific attainments , his knowledge of the world and of business , and his personal characteristics specially qualified him for office . An appreciation , signed by well-known initials , has recently appeared in our ' Proceedings . ' On the Foreign List also the losses are heavy . We have especially to condole with our colleagues in France upon the havoc caused by death within the last year or two . Janssen , and Mascart , who was much missed at the recent Electrical Conference , had reached a full age . But Becquerel was in the full tide of life , and we had hoped to learn much more from him ; as the discoverer of radio-activity , he had opened up inquiries whose significance seems ever on the increase . Science has lost a leader ; his friends and the world a charming personality . During the time that I was Secretary , and so concerned with the passing of mathematical papers through the Press , I was much struck with the carelessness of authors in the arrangement of their manuscript . It is frequently forgotten that a line of print in the ' Transactions ' and in the new form of the ' Proceedings ' will hold much more than a line of ordinary manuscript , unless , indeed , the handwriting is exceptionally small . Unless the authors ' indications were supplemented , it frequently occurred that several lines of print were occupied by what might equally well , and in my judgment much better , be contained in one line . Even practised writers would do well , when they regard their manuscript as complete so far as regards matter and phrasing , to go over it again entirely from the point of view of the printing . In this way much expense and space would be spared , and the appearance of the printed page improved . Professor Larmor has 4 Anniversary Address by Lord Rayleigh . [ Nov. 30 , drawn up a paper which has received the sanction of the Council and is appended to this Address , and will , it is hoped , be of service at once to authors and to the Society , Apart from questions of printing , the choice of symbols for representing mathematical and physical quantities is of some importance , and is embarrassed by varying usages , especially in different countries . A Committee now sitting is concerned with the selection of symbols for electrical and magnetic quantities , but the question is really much wider . One hesitates to suggest another international conference , and perhaps something could be done by discussion in scientific newspapers . Obviously some give and take would be necessary . When the arguments from convenience are about balanced , appeal might be made to the authority of distinguished men , especially of those who were pioneers in the definition and use of the quantity to be represented . As an example of the difficulties to be faced , I may instance the important case of a symbol for refractive index . In English writings the symbol is usually fi , and on the Continent n. By the early optical writers it would seem that no particular symbol was appropriated . In 1815* Brewster has m. The earliest use of fi that I have come across is by Sir John Herschel , f and the same symbol was used by Coddington ( 1829 ) and by Hamilton ( 1830 ) , both distinguished workers in optics . On the other hand , n was employed by Fraunhofer ( 1815 ) , and his authority must be reckoned very high . As regards convenience , I should suppose that the balance of advantage would incline to / x , since n is wanted so frequently in other senses . Another case in which there may be difficulties in obtaining a much to be desired uniformity is the symbol for electrical resistance . On a former occasion I indulged in comment upon the tendency of some recent mathematics , which were doubtless understood as the mild grumbling of an elderly man who does not like to see himself left too far behind . In the same spirit I am inclined to complain of what seem unnecessary changes in mathematical nomenclature . In my youth , by a natural extension of a long established usage relative to equations , we spoke of the roots of a function , meaning thereby those values of the argument which cause the function to vanish . In many modem writings I read of the zeroes of a function in the same sense . There may be reasons for this change ; but the new expression seems to need precaution in its use ; otherwise we are led to such flowers of speech as " zeroes with real part positive , " which I recently came across.^ * 'Phil . Trans. , ' 1815 . t ' Phil. Trans. , ' 1821 , p. 230 . + *Proc . Math. Soc. , ' vol. 31 , p. 266 . 1908.1 Anniversary Address by Lord Rayleigh . 5 But though I may use a little my privilege of grumbling over details , I hope I shall not be misunderstood as undervaluing the progress made in recent years , which , indeed , seems to me to be very remarkable and satisfactory , regarded from the scientific point of view . On the other hand I cannot help feeling misgivings as to the suitability of the highly specialised mathematics of the present day for a general intellectual training , and I hope that a careful watch may be maintained to check , in good time , any evil tendencies that may become apparent . Among the notable advances of the present year is the liquefaction of helium by Professor Onnes of Leiden . It is but a few years since Sir J. Dewar opened up a new field of temperature by his liquefaction of hydrogen , and now a further extension is made which , if reckoned merely in difference of temperature , may appear inconsiderable , but seen from the proper thermodynamical standpoint is recognised to be far-reaching . The exploration of this new field can hardly fail to afford valuable guidance for our ideas concerning the general properties and constitution of matter . Professor Onnes ' success is the reward of labours well directed and protracted over many years . The discovery and application by Rutherford and Geiger of an electrical method of counting the number of a-particles from radio-active substances constitutes an important step , and one that appears to afford better determinations than hitherto of various fundamental quantities . It would be of interest to learn what interpretation is put upon these results by those who still desire to regard matter as homogeneous . Another very interesting observation published during the year is that of Hale upon the Zeeman effect in sun-spots , tending to show that the spots are fields of intense magnetic force . Anything which promises a clue as to the nature of these mysterious peculiarities of the solar surface is especially welcome . Until we understand better than we do these solar processes , on which our very existence depends , we may do well to cultivate a humbler frame of mind than that indulged in by some of our colleagues . A theoretical question of importance is raised by the observations of Nordmann and Tikhoff showing a small chromatic displacement of the phase of minimum brightness in the case of certain variable stars . The absence of such an effect has been hitherto the principal argument on the experimental side for assuming a velocity of propagation in vacuum independent of frequency or wave-length . The tendency of the observations would be to suggest a dispersion in the same direction as in ordinary matter , but of almost infinitesimal amount , in view of the immense distances over which the propagation takes place . Lebedew has pointed out that 6 Anniversary Address by Lord Rayleigh . [ Nov. 30 , this conclusion may be evaded by assuming an asymmetry involving colour in the process by which the variability is brought about , and he remarks that although the dispersions indicated by Nordmann and Tikhoff are in the same direction , the amounts calculated from the best available values of the parallaxes differ in the ratio of 30 to 1 . In view of this discrepancy and of the extreme minuteness of the dispersion that would be indicated , the probabilities seem at the moment to lie on the side of Lebedew 's explanation ; doubtless further facts will be available in the near future . I cannot abstain from including in the achievements of the year the remarkable successes in mechanical flight attained by the brothers Wright , although the interest is rather social and practical than purely scientific . For many years , in fact ever since I became acquainted with the work of Penaud and Wenham , I have leaned to the opinion that flight was possible as a feat . This question is now settled , and the tendency may perhaps be to jump too quickly to the conclusion that what can be done as a feat will soon be possible for the purposes of daily life . But there is a very large gap to be bridged over ; and the argument urged by Professor Newcomb and based on the principle of dynamical similarity , that the difficulties must increase with the scale of the machines , goes far to preclude the idea that regular ocean service will be conducted by flying machines rather than by ships . But , as the history of science and invention abundantly proves , it is rash to set limits . For special purposes , such as exploration , we may expect to see flying machines in use before many years have passed . The Report of the National Physical Laboratory for the year again indicates remarkable growth . The various new buildings , which have been erected and equipped during recent years at a cost of about \#163 ; 33,000 , are now occupied ; and the result is that both researches and test work can be carried out with much greater ease and efficiency than previously . The Executive Committee in charge of the Laboratory is indebted in the first instance to H.M. Government , and then to the numerous friends whose assistance has made this possible . At the same time , the needs for buildings are not nearly satisfied . There has been during the year a very marked and important growth in the demand by manufacturers and others for assistance in metallurgical enquiries , which require investigations , frequently of a very complex character ; and with the present accommodation for much of the Metallurgical Department this demand is difficult to satisfy . Thanks in great measure to the Goldsmiths ' Company , the chemical side of this department is well provided for ; but new buildings for the other branches of metallurgy are an urgent want . 1908 . ] Anniversary Address by Lord Rayleigh . The Report of the Treasury Committee of Inquiry referred to in the address of last year was communicated by the Treasury to the Royal Society , with the intimation that Their Lordships accept the recommendations of the Committee , and trust that the Royal Society may see their way to do the same . In their reply the President and Council , with the concurrence and advice of the Executive Committee of the Laboratory , expressed their readiness to use their best endeavours to carry the Report into effect . The Report has since been presented to Parliament . The buildings of the Magnetic Observatory at Eskdalemuir are now occupied ; but , unfortunately , difficulty has arisen in making the magnetograph rooms which are underground completely watertight , and the recording apparatus is not yet properly installed . The third and fourth volumes of ' Collected Researches ' of the Laboratory have been published during the year , and testify to the vigorous scientific activities of the staff . The third volume is occupied chiefly with the account of the prolonged series of experiments on electric units carried out at the Laboratory by Prof. Ayrton , Mr. Mather^ Dr. Lowry , and Mr. Smith . These researches proved of great value in the discussions at the International Conference on Electric Units , for which recently the Society provided accommodation and entertainment at the request of the Government . The progress of the ' Royal Society Catalogue of Scientific Papers ' has advanced a definite stage during the year , through the publication by the Cambridge University Press of the Index Volume of Pure Mathematics for the Nineteenth Century . Owing to the magnitude of the material to be indexed in the several sciences , it has been necessary to adopt drastic measures of compression , and the 40,000 entries involved in the present section have thus been condensed into one royal octavo volume of some 700 pages . An essential element in this saving of bulk has been the grouping of titles within each heading so as to avoid reprinting the leading-words , It was , perhaps , inevitable that this device would occasionally be mistaken for an attempt at organic classification within the limits of the main headings , which are substantially those of the yearly ' International Catalogue of Scientific Literature . ' This had , indeed , been foreseen in the preface of the volume . As regards new actual sub-headings which have been introduced occasionally , the Committee remark that " These minor classifications , being often made mechanically on the basis of the explicit mention of the sub-heading , are not to be taken as exhaustive ; cognate entries may be found elsewhere under the same main heading . The unit of classification is thus the complete numbered heading . " The Committee of the Catalogue have indeed been fully conscious Anniversary Address by Lord Rayleigh . [ Nov. 30 , throughout of the difficulties of the task which they supervise ; and it must be gratifying to the Director of the Catalogue and his staff to have the support of high authorities , not confined to this country , in their decision that in so extensive an undertaking practical feasibility must be the aim rather than an elusive theoretical perfection . One advantage , at any rate , will accrue from bringing out a single volume well in advance , in that the Committee will be able to profit in the future work from the experience they have acquired . Through the kindness of Dr. Schuster I had the opportunity of submitting to the Council , before the expiry of my term of office , a generous proposal which he makes for instituting a fund of \#163 ; 1500 , the interest of which is to be applied to pay the travelling expenses of delegates of the Society to the International Association of Academies . Dr. Schuster felt that the absence of such a provision laid a burden upon delegates , and might operate to limit the choice of the Society . I was empowered by the Council to convey their cordial thanks to Dr. Schuster , and I have now the pleasure of making his benefaction known to the Society at large . In taking leave of the honourable office which I have occupied for three years , I desire to thank the Society and especially my colleagues , the officers , for the consideration which they have uniformly shown me . All the omens indicate that the Society will be represented by one well versed in its affairs , and whose scientific distinction and wide experience justify the highest hopes for his tenure of the chair . ' . MEDALLISTS , 1908 . Copley Medal . The Copley Medal is awarded to Dr. Alfred Russel Wallace , E.R.S. It is now sixty years since this distinguished naturalist began his scientific career . During this long period he has been unceasingly active in the prosecution of natural history studies . As far back as 1848 he accompanied the late Henry Walter Bates to the region of the Amazon , and remained four years there , greatly enriching zoology and botany , and laying at the same time the basis of that wide range of biological acquirement by which all his writings have been characterised . From South America he passed to the Malay Archipelago and spent there some eight fruitful years . It was during his stay in that region that he matured those broad views regarding the geographical distribution of plants and animals which on his return to this country he was able to elaborate in his well-known classic volumes on Anniversary Address by Lord Rayleigh . 1908 . ] that subject . It was there , too , amid the problems presented by the infinite variety of tropical life , that he independently conceived the idea of the theory of the origin of species by natural selection which Charles Darwin had already been working out for years before . His claims to the admiration of all men of science were recognised by the Eoyal Society forty years ago , when , in 1868 , a Eoyal Medal was awarded to him . Again , when in 1890 , the Darwin Medal was founded , he was chosen as its first recipient . He is still full of mental activity and continues to enrich our literature with contributions from his wide store of experience and reflection in the domain of Natural History . As a crowning mark of the high estimation in which the Eoyal Society holds his services to science , the Copley Medal is now fittingly bestowed on him . Eumford Medal . The Eumford Medal is awarded to Prof. H. A. Lorentz , For . Mem. E.S. \#171 ; Prof. Hendrik Antoon Lorentz , of Leiden , has been distinguished during the last quarter of a century by his fundamental investigations in the principles of the theory of radiation , especially in its electric aspect . His earliest memoirs were concerned with the molecular equivalents which obtain in the refractive ( and dispersive ) powers of different substances ; in them he arrived at formulae that still remain the accepted mode of theoretical formulation of these phenomena . The main result , that ( / a2 \#151 ; l)/ ( ya2 +2 ) is proportional jointly to the density of distribution of the molecules , and to a function of the molecular free periods and the period of the radiation in question , rests essentially only on the idea of propagation in some type of elastic medium ; and thus it was reached simultaneously , along different special lines , by H. A. Lorentz originally from Helmholtz 's form of Maxwell 's electric theory , and by L. Lorenz , of Copenhagen , from a general idea of propagation after the manner of elastic solids . The other advance in physical science with which Prof. Lorentz 's name is most closely associated is one of greater precision , the molecular development of Maxwell 's theory of electro-dynamics . This subject was never entered upon by Maxwell himself , on the ground , probably , that the general relations of the aether , and in particular their dynamical bearings , offered a definite field which must be fully probed and explored before the uncertainties connected with molecular complexity became ripe for effective detailed treatment . But the theoretical difficulties connected with the simple law of the astronomical aberration of light , and particularly with the entire absence of any effect of the Earth 's uniform motion in space on Anniversary Address by Lord Rayleigh . [ Nov. 30 , terrestrial phenomena involving radiation , had more recently rendered this problem urgent . Following on various purely optical papers on the phenomena of moving bodies , Prof. Lorentz , in 1892 , elaborated a general molecular treatment in the memoir *f La Th4orie Electro-magn4tique de Maxwell , et son Application aux Corps Mouvants , " which appeared in the ' Archives N^erlandaises , ' and contains substantially the main root ideas of the subject . In 1905 it was re-expounded with further development in a tract entitled " Yersuch einer Theorie der Electrischen und Optischen Erscheinungen in Bewegten Korpern , " the main feature being the elimination of the dynamical element in the previous discussion in favour of a formulation by a system of abstract equations , after the way first set out by Maxwell himself as a summary of his final definite results as distinct from the formative ideas underlying them , and afterwards brought into prominence by the expositions of Heaviside and Hertz . By these writings Prof. Lorentz has taken a predominant place in the modern evolution of electric and optical theory . He has since been active in special applications , of which the best known has been his theoretical prediction of the physical features of the alteration of the lines of the spectrum in a magnetic field , which had been discovered and has since been developed by his colleague Zeeman . Boyal Medals . The assent of His Majesty the King , our Patron , has been graciously signified to the following awards of the Medals presented annually by him to the Society . A Royal Medal to Prof. John Milne , F.R.S. , for his work on Seismology . In 1875 , Dr. Milne accepted the position of Professor at Tokyo , which was offered to him by the Imperial Government of Japan . His attention was almost immediately attracted to the study of earthquakes , and he was led to design new forms of construction for buildings and engineering structures with a view to resisting the destructive effects of shocks . His suggestions have been largely adopted , and his.designs have been very successful for the end in view . Incidentally he studied the vibrations of locomotives , and showed how to obtain a more exact balancing of the moving parts , and thus to secure smoother running and a- saving of fuel . Here again his suggestions were accepted , and his work was recognised by the Institution of Civil Engineers . He next devoted himself to the study of artificial shocks produced by the explosion of dynamite in borings . He then studied actual shocks as observed at nine stations connected by telegraph wires . A seismic study of Tokyo , and subsequently of the whole of northern Japan , followed . In this Anniversary Address by Lord Rayleigh . 1908 . ] latter work he relied on reports from 50 stations . The Government then took up the matter , increased his 50 stations to nearly 1000 , and founded a Chair of Seismology for Mr. Milne . It is due to his energy , skill , and knowledge that the Japanese School of Seismology stands as the first in the world . While still in Japan he attempted to obtain international co-operation through the representatives of 13 nationalities . This first effort failed ; but subsequently , on his return to England in 1895 , he succeeded , and reports are now received by him from some 200 stations furnished with trustworthy instruments , and scattered all over the world . On his return to England he at once established his own observatory at Shide , in the Isle of Wight , and the work has been carried on continuously from that time up to now , mainly by his own industry and resources . In Great Britain we owe everything in seismology to the British Association . Their Committee was founded in 1880 , and since that date Milne has been the moving spirit in the long career of its activity . He has been the author of 29 annual reports , and these form in effect a history of the advance of seismology since it has been recognised as a definite branch of science . The knowledge which we have now acquired as to the internal constitution of the earth is more due to Milne than to any other man . The work of Dr. Henry Head , F.B.S. , on which is founded the award of the other Boyal Medal , forms a connected series of researches on the Nervous System ( made partly in conjunction with Campbell , Bivers , Sherren , and Thompson ) , published for the most part in ' Brain ' at various times since 1893 up to the present date , and constituting one of the most original and important contributions to neurological science of recent times . His first paper ( 1893 ) , founded on minute and laborious clinical investigation , established in a more precise manner than had hitherto been done the relations between the somatic and visceral systems of nerves . He confirmed from the clinical side the experimental researches of Sherrington on the distribution of the posterior roots of the spinal nerves . An inquiry into the pathology of Herpes Zoster ( 1900 ) , which he proved abundantly to be due to inflammation of the posterior root ganglia , indicated that the areas of referred pain in visceral disease corresponded specially with the distribution of the fibres of the posterior roots subserving painful cutaneous sensibility . Continuing his investigations on the peripheral nerves , partly by experiments on himself , in conjunction with Kivers , and partly by examination of cases of accidental injuries to nerves , Head was led to formulate ( 1905 ) an Anniversary Address by Lord Rayleigh . [ Nov. 30 , entirely novel conception and differentiation of the functions of the peripheral nerves , and of the paths for the respective forms of sensibility which they convey\#151 ; epicritic , protopathic , and deep sensibility . This is generally regarded by neurologists as a research of quite exceptional originality and ability . Following the course of afferent impulses , Head next showed ( 1906 ) that the sensory paths of the peripheral nerves at their first synaptic junction with the spinal cord ^become re-arranged , and ascend in different relations in certain definite tracts . Davy Medal . The Davy Medal is awarded to Prof. William Augustus Tilden , F.R.S. The researches of Prof. Tilden extend into many domains . His work on the specific heats of the elements in relation to their atomic weights , described to the Society in the Bakerian Lecture for 1900 and in two later papers published also in the ' Philosophical Transactions/ was of high theoretical importance . The employment of liquid oxygen as an ordinary laboratory reagent , rendered possible by the researches of Dewar and others , enabled Prof. Tilden to test the validity of Dulong and Petit 's Law and of Neumann 's Law over a much wider range of temperature than was possible before , and gave a truer estimate of the nature of their validity . In the region of organic chemistry , he has carried out important researches on the terpenes , such as that on the hydrocarbons from Finns on terpin and terpinol , and on limettin . In inorganic chemistry , his investigation on aqua regia and on nitrosyl chloride are especially noteworthy . He has assisted much in clearing up many points with regard to aqua regia about which obscurity remained . His introduction of nitrogen peroxide and especially of nitrosyl chloride as reagents has proved , in his own hands and in those of other workers , to be of very high value . Darwin Medal . The Darwin Medal is awarded to Prof. August Weismann for his contributions to the study of evolution . He was one of the early supporters of the doctrine of evolution by means of natural selection , and wrote in support of the Darwinian theory in 1868 . His great series of publications from that date onward must always remain a monument of patient inquiry . In forming an estimate of his work it does not seem essential that we should 1908 . ] Anniversary Address by Lord . decide on the admissibility of his germ-plasm theory . It is in like manner unimportant that he was , in certain respects , forestalled by Galton , and that his own views have undergone changes . The fact remains that he has done more than any other man to focus scientific attention on the mechanism of inheritance . By denying the possibility of somatic inheritance , he has compelled the world to look at this question with a closeness of criticism that is wanting in all earlier inquiries . In the opinion of what is perhaps the majority of naturalists , he has achieved much more than this\#151 ; he has convinced them that the solution of the problem of evolution must be sought along the lines of his doctrine of germinal continuity . Thus the preformist 's point of view , for which he has done so much , forms the basis on which Mendelians and Mutationists are at work . Weismann 's work was highly estimated by Mr. Darwin . Thus he writes , in 1875 ( 'More Letters , ' i , 356 ) , of Weismann 's paper on Seasonal Dimorphism : " No one has done so much as you on this important subject , i.e. , on the causes of variation . " Again ( ' Life and Letters , ' iii , 198 ) : " I have been profoundly interested by your essay on ' Amblystoma , ' and think you have removed a great stumbling block in the way of evolution . " And , once more , in January , 1877 ( ' Life and Letters , ' iii , 231 ) , Darwin wrote of Weismann 's ' Studien sir Descendenzlehre ' : " They have excited my interest and admiration in the highest degree , and whichever I think of last seems to me the most valuable . " Hughes Medal . The Hughes Medal is awarded to Prof. Eugen Goldstein . Prof. Goldstein was one of the early workers on the modern detailed investigation of the electric discharge in rarefied gases , and by long continued researches has contributed substantially to the systematic analysis of the complex actions presenting themselves in that field . Of these researches may be mentioned his observations of the effect of magnetic force on striations , of the phosphorescence produced by the cathode rays , and of the reflection of cathode rays . By his discovery of the so-called Kanal-Strahlen , or positive rays , he has detected an essential feature of the phenomenon , which , in his own hands and in those of other workers , has already thrown much needed light on the atomic transformations that are involved . A nniversary A [ Nov. 30 , ( APPENDIX . ) Practical Suggestions on Mathematical Notation and Printing . It is a subject of common complaint that mathematical manuscripts are often prepared for press without due regard for the difficulties encountered in setting up the type , or for the appearance of the printed page . The Council of the Royal Society have had under consideration for some time the desirability of taking steps with a view to diminish the expense of printing and proof-corrections , and to avoid waste of space , and undue variety of notation in papers by different authors in the same volume . They have approved of the reprinting , with modifications and additions , of the substance of a Report to the British Association on this subject , in the hope that greater uniformity and facility in mathematical typography may thereby be promoted . The recommendations which follow are now offered , not in any authoritative way , but simply as a consensus of opinion ; to this end it is understood that they were submitted in advance , for consideration and criticism , to the Council of the London Mathematical Society . Abstract of Report of British Association .* With a view to the questions referred to them for consideration , the Committee appointed by the British Association made inquiries into the nature and processes of mathematical printing , and the difficulties attendant thereon ; and it appeared to them that a statement of the results of these inquiries would form the best introduction to the suggestions which they had to make . The process of " composition " of ordinary matter consists in arranging types uniform in height and depth ( or " body " as it is termed ) in simple straight lines . The complications peculiar to mathematical matter are mainly of two kinds . First , figures or letters of a smaller size than those to which they are appended have to be set as indices or suffixes ; and consequently , except when the expressions are of such frequent occurrence as to make it worth while to have them cast upon type of the various bodies with which they are used , it becomes necessary to fit these smaller types in their proper positions by special methods . This process , which is called " justification , " consists in filling up the difference between the bodies of the larger and smaller types with suitable pieces of metal . * Report of the Committee , consisting of W. Spottiswoode , F.R.S. , Prof. Stokes , F.R.S. , Prof. Cayley , F.R.S. , Prof. Clifford , F.R.S. , and J. W. L. G-laisher , F.R.S. , appointed to report on Mathematical Notation and Printing , with the view of leading mathematicians to prefer in optional cases such forms as are more easily put into type , and of promoting uniformity of notation.\#151 ; 'B . A , Report , ' 1875 , pp. 337-339 . Mathematical Notation and Printing . 1908 . ] The second difficulty arises from the use of lines or " rules " which occur between the numerator and denominator of fractions , and ( in one mode of writing ) over expressions contained under radical signs . In whatever part of a line such a rule is used , it is necessary to fill up , or compensate , the thickness of it throughout the entire line . The complications above described may arise in combination or may be repeated more than once in a single expression ; and in proportion as the pieces to be " justified " become smaller and more numerous , so do the difficulties of the workman , the time occupied on the work , and the chances of subsequent dislocation of parts augment . The cost of " composing " mathematical matter may now ( 1908 ) in general be estimated at somewhat more than twice that of ordinary or plain matter , the recent adoption of the point system in the casting of types having greatly simplified mathematical justification . There are many expressions occurring in mathematics which are capable of being written in more than one way ; and of these some present much greater difficulties to the printer than others . This being so , the Committee were of opinion that instead of making any specific recommendations , the most useful course they could take would be to append a table of equivalent forms specifying those which do and those which do not involve justification , and also a list of mathematical signs which may fairly be expected to be found , in the usual sizes , ready to hand among a printer 's matltials . In recommending in this qualified way some forms of notation in preference to others , the Committee wished it to be distinctly understood that they were speaking from the printing , and not from the scientific point of view ; and they were quite aware that , even if some of the easier forms should be adopted in some cases , they may still not be of universal application , and that there may be passages , memoirs , or even whole treatises in which they would be inadmissible . The Committee drew attention to the advantages which may incidentally accrue to mathematical science by even a partial adoption of the modifications suggested . Anything which tends towards uniformity in notation may be said to tend towards a common language in mathematics ; and whatever contributes to cheapening the production of mathematical books must ultimately assist in disseminating a knowledge of the science of which they treat . Mathematical Signs not involving " Justification . " \#151 ; + = \#177 ; \gt ; 4a a ' iii a2 \#171 ; 2 a~ x A nniversary A Equivalent Forms [ Nov. 30 , Involving justification . X a A X Vx Ax-y v/ TI x , x + a njrx " a Not involving justification . xfa or x-~aor : Ax or xi Z/ x or xk A{x - y ) or - yf l or i x ( x + a ) rnrx/ a This British Association List , which has been abbreviated and modified , is now incorporated in the following:\#151 ; ^Recommendations regarding Mathematical Notation and Printing . Always-\#151 ; instead of write a H- b x \ ( a a -*fc d 3+4 \amp ; ~^ \/ X ^ ^ X xn ^c + \d y/ x or xk l or i 1 instead of \/ x\#151 ; y nnx e a write x ( x + a ) 1 S u 0 " Si 1 N ? gnnx/ a In current ordinary text- , . X instead of - a ct -f- b c + d X y+1 / a xly + b^e write xja ( a + b ) ! ( c + d ) x a y b Excessive use of the slanting line , or solidus , is , however , undesirable ; it may often be avoided by placing several short fractions or formulas , with the intervening words if any , on the same line , instead of setting out each one on a line by itself . The last of the examples given above illustrates an improper use , in which symmetry is spoiled while nothing is gained ; either both fractions should be written with the solidus , as or else neither as above . Mathematical Notation and Printing . 1908 . ] The solidus should be of the same thickness as the horizontal line which it replaces ; in some founts of type it is too thick and prominent . Irregularities in the spacing of letters and symbols in the formulas as printed are often the cause of a general unsatisfactory appearance of the page . For centimetres , millimetres , kilometres , grammes , kilogrammes , the abbreviations should be cm . , mm. , km . , gm . , kgm . ( not eras . , etc. ) , and so in similar cases . Present custom is against the use of the signs . * . and . . . . Symbols which are not provided in the usual founts of type are , as a rule , to be avoided . Compounded symbols such as a or a usually involve justification , and are thus liable to become deranged or broken . The two examples here given have , however , become so essential that separate founts should be provided for them . The use of a smaller fount for numerical fractions is now customary ; thus always instead of a/ 3 . The use of negative exponents often avoids a complex fractional form ; as also the use of the fractional exponents , such as \ and In the latter case x ? is usually preferred to x1^2 , notwithstanding that the latter is more legible . Much is often gained in compactness and clearness by setting out two or more short formulae on one line , instead of on consecutive lines ; in that case they should be separated by spaces , indicated by the sign $ on the MS . This would apply with even greater force to expressions such as In the Preface to his ' Mathematical and Physical Papers , ' vol. i , 1880 , the late Sir George Stokes successfully introduced the limited use of the solidus notation , obtaining the assent and support of Lord Kelvin , Prof. Clerk Maxwell , Lord Eayleigh , the Editors of the 'Annalen der Physik , ' and many other mathematicians . He defined its use as restricted to the symbols immediately on* the two sides of it , unless a brace or stop intervenes ; thus sin mrxja is to mean sin ( mrx/ a ) ; but sin nd . / rn , in case it is used , would mean ( sin n0)/ rn . vol. lxxxii.\#151 ; A. c

rspa_1909_0002

0950-1207

The charges on ions produced by radium.

18

22

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

C. E. Haselfoot, M. A.|Prof. J. S. Townsend, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1909.0002

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1909_0002

10.1098/rspa.1909.0002

Electricity

Atomic Physics

Electricity

18 The Charges on Ions produced by Radium . By C. E. Haselfoot , M.A. , Hertford College , Oxford . ( Communicated by Prof. J. S. Townsend , F.R.S. Received November 3 , \#151 ; Read November 12 , 1908 . ) In a paper* on " The Charges on Positive and Negative Ions in Oases , " Prof. Townsend has described a method for the direct determination of the quantity No , where N is the number of molecules in a cubic centimetre of a gas at standard pressure and temperature and e the charge on an ion . His experiments were carried out on ions produced by the action of secondary Rontgen rays , and he showed that for negative ions the method led with great accuracy to the value 1'23 x 1010 for No , the same as that for NO , where E is the charge on a monovalent ion in a liquid electrolyte . For positive ions the value obtained in the first set of experiments was 2*4 x 1010 , but subsequently with less penetrating secondary rays it was found to be as low as 1*26 x 1010 . It would therefore appear that the positive ions have in some cases a single and in others a double atomic charge , whereas the charge on the negative ions is always the same . With a view of testing the theory for ions produced by radium , experiments have been made with an apparatus precisely similar to that used by Prof. Townsend , and the results obtained confirm the reliability of the method . After making due allowance for experimental and other known sources of error the positive ion appears to behave at all pressures and under all forces in accordance with the theory , but in the case of the negative ion some considerable deviations were observed , if the gas is very dry , but these disappear as soon as some water vapour is added . The method consists essentially in the production of ions in a field A , from which those of one sign are passed into a field B through a hole of definite size . Here they diffuse and the charge received by a disc placed immediately below and of the same size as the hole is compared with the total charge received by the disc and a ring which surrounds it . From the observed value of this ratio the quantity No is deduced . Some modifications of the apparatus used for Rontgen rays were necessary , in order to deal with the ions produced by radium . In these experiments the ions are generated in the space A by radium placed in shallow horizontal grooves / , covered with thin aluminium foil , in brass blocks F , standing on the ring E. The space B is bounded by a series of brass rings G , kept at * 'Roy . Soc. Proc. , ' A , vol. 8 ] , 1908 , p. 464 . The Charges on Ions produced hy Radium . definite potentials in order to maintain the constancy of the held . C is a plate whose potential determines the held A. The ions generated in A pass through the grating g and then through the hole h. They diffuse , and the ratio of the charges received by the disc D and the ring R is measured . c Field A Field d G G G G G G G R D R Fig. 1 . In conducting the experiments it is necessary to allow for the ions which are generated in the held B and also for the self-repulsion of the stream coming through the hole . The charge acquired by the disc and ring due to ions produced in the held B is easily found by observing these charges when the held A is reversed . Subtracting them from the charges received when the held A is the same as the held B , we obtain the charges due to ions coming through the aperture . The special difficulty , however , is to avoid the large effects due to the emanation and to the induced radio-activity in the held B. These become larger the longer the apparatus is left undisturbed , and in one experiment , made about two months after the apparatus was set up were found to be more than twice the effect due to the held A. They were due to the emanation escaping through and round the aluminium foil , which was kept thin in order to obtain measurable effects , and the movements of this gas would probably account for the considerable irregularities observed during preliminary experiments . Now it has been shown by Mine . Curie that the activity induced on surfaces is greatest for the lower portions of the vessel containing the emanation , so that it was considered advisable to invert the apparatus ( in the original form of which , shown in the figure , A was the upper field ) , and thus cause the more radio-active surfaces to be in the lower space A. A means was also provided of drawing a current of air through the apparatus from B to A , and it was then found that the number of ions produced in the space B could be made small , thereby diminishing this correction . The other correction is for self-repulsion . It can be shown that this effect varies inversely as the square of the electrical force Z in the field B , and approximately directly as the square of the pressure . It can thus be reduced at will by diminishing the pressure and increasing the force , but a Mr. C. E. Haselfoot . [ Nov. 3 , diminution of pressure , beyond a certain point , decreases too seriously the charge to be measured , whereas an increase of force concentrates such a large proportion of ions on the disc that the effect of the clearance between the disc and the ring may become comparatively large , and , further , any percentage error in the determination of the ratio leads to a far larger percentage error in the value of Nc . This will be clear from an inspection of the graph given in fig. 2 . O 2040 60 80 100 120 140 160 l80 200 Fig. 2 . The method of deducing Ne from the observed value of R has been explained in the paper already referred to . The connection between these quantities is best shown by means of a curve , and the graph in fig. 2 gives R in terms of ( Ne . Z)/ P , where Z is the electric force , and P atmospheric pressure . The curve corresponds to the case in which the aperture is 7 cm . from the disc , and the diameter of the aperture 1*5 cm . When N. is 1*23 x 1010 and Z 1 volt per centimetre ( Ne . Z)/ P is approximately 40 . Observations were made at pressures of 4*5 , 9 , and 14*5 mm. with forces of 1 , 2 , and 4 volts per centimetre both for positive and negative ions . Rejecting those subject to various sources of error , the following results remain:\#151 ; For positive ions , three at 2 volts per centimetre giving Ne = P26 x 1010 , and five at 4 volts per centimetre giving Ne = 1*37 X 1010 ; for negative ions , three at 2 volts per centimetre giving Ne = 1'24 x 1010 . The observations at 1 volt per centimetre are almost all subject to too large a correction for self-repulsion , rising in some cases to 20 per cent. , to make them reliable . Those for 4 volts per centimetre are subject to greater experi1908 . ] The Charges on Ions produced by Radium . 21 mental errors than those at 2 volts per centimetre , and this may possibly account for the large value of No deduced in the case of positive ions from observations at this force . The most accurate results can be obtained at pressures of from 4 to 6 mm. and forces of 1*5 to 2 volts per centimetre . Further experiments are to be made under these conditions with air and other gases , and it is hoped by reducing the ionisation in the field B to obtain more accurate results . As in the case of ions produced by Rontgen rays , it was found that the negative ions produced by radium did not obey the simple laws of diffusion when the air is very dry . This appears from the fact that the ratio R does not vary with the force Z as given by the theory , and that it depends on the pressure . As the drying proceeds , the departure of R from the value given by the curve ( assuming No = 1*23 x 1010 ) is most marked with large values of Z and small pressures . Thus the mean of six observations at the force of 4 volts per centimetre , all giving very low values , is 0'584 ( instead of 0,682)\gt ; With a lower force this departure from theory occurs less frequently , and then as a rule at low pressures . With a force of 1 volt per centimetre , and pressures varying from 8 to 2*5 mm. , the numbers found on one day varied from 0'390 to 0329 ; the theory gives 0429 . For a force of 2 volts per centimetre and a pressure of 2*5 mm. the number obtained was 0311 , that given by the theory being 0572 . These experiments were then repeated after admitting moisture , and the values of the ratio obtained agreed with the theory within the limits of experimental error . A point of some interest is the fact that it was found easier to experiment with negative than with positive ions . This is probably due to the action of the emanation . By placing the field B , in which the diffusion takes place , at the top of the apparatus , the radio-activity caused by the emanation is confined as far as possible to the lower field A , and it is then found in the case of negative ions that the charge due to the ionisation occurring in field B seldom exceeds one-third of that coming from field A. With positive ions , however , it is frequently as large as one-half . In a strong electric field the excited radio-activity is confined entirely to the negative electrode , and Rutherford has found that this is the case down to a pressure of 10 mm. When the disc D and ring R are receiving negative ions the force would tend to keep the emanation in the lower field , but for positive ions , when the disc and the ring round it form the negative electrode , the electric force tends to bring the emanation into the field B. The correction for the ionisation in the field B is therefore large and subject to variations in the experiments with positive ions , and also from the same cause difficulties arise in making an accurate estimate of the effect of self-repulsion . 22 Mr. T. Royds . A Comparison of the Radium [ Nov. 26 , So far the results are in satisfactory agreement with those obtained by Prof. Townsend , with Rontgen rays , and it is hoped to make further experiments and to see if it is possible to obtain positive ions with double the atomic charge by means of radium rays . Possibly the molecules of a gas are ionised in different ways by the a , ,6 , and \lt ; y types of radiation , and it is not quite certain which kind of radiation had the predominating effect in the production of the ions in these experiments , though probably the greater numbers were due to the a-rays . I am greatly indebted to Prof. Townsend for most valuable advice and assistance throughout . A Comparison of the Radium Emanation Spectra obtained by different Observers . By T. Boyds , M.Sc . , 1851 Exhibition Scholar . ( Communicated by Prof. E. Kutherford , F.R.S. Received November 26 , \#151 ; Read December 10 , 1908 . ) In 1904 Sir William Ramsay and Prof. Collie* gave a list of lines produced by the discharge in a vacuum tube containing radium emanation , but the uncertainty of these numbers made a redetermination desirable . A later determination by Mr. Cameron and Prof. Ramsayf was communicated to the Royal Society on June 25 , 1908 , and was published on August 27 , together with corrections , and a final compilation of verified emanation lines added on August 5 . After Prof. Rutherford had completed the measurements of the volume of the radium emanation , he and the writer were able to photograph the spectrum that had been observed in the course of this work , and we published in ' Nature , ' July 9 , 1908 , the wave-lengths of the stronger lines observed by us in the emanation spectrum , and a more complete list , containing 73 lines , with an accuracy of 0'5 A.U. , was given in the c Philosophical Magazine ' of August , 1908 . Measurements which I have recently made to within OT A.U. by means of a concave grating confirm the accuracy of our previous determinations . The complete purification of the radium emanation demands a lengthy and painstaking procedure , and is a matter of considerable difficulty , for the volume of pure emanation available in our experiments would occupy at * ' Hoy . Soc. Proc. , ' vol. 73 , p. 470 , 1904 . t ' Hoy . Soc. Proc. , ' vol. 81 , p. 210 , 1908 .

rspa_1909_0003

0950-1207

A comparison of the radium emanation spectra obtained by different observers.

22

25

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

T. Royds, M. Sc.|Prof. E. Rutherford, F. R. S.

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10.1098/rspa.1909.0003

Atomic Physics

Thermodynamics

Atomic Physics

22 Mr. T. Royds . A Comparison of the Radium [ Nov. 26 , So far the results are in satisfactory agreement with those obtained by Prof. Townsend , with Rontgen rays , and it is hoped to make further experiments and to see if it is possible to obtain positive ions with double the atomic charge by means of radium rays . Possibly the molecules of a gas are ionised in different ways by the a , ,6 , and \lt ; y types of radiation , and it is not quite certain which kind of radiation had the predominating effect in the production of the ions in these experiments , though probably the greater numbers were due to the a-rays . I am greatly indebted to Prof. Townsend for most valuable advice and assistance throughout . A Comparison of the Radium Emanation Spectra obtained by different Observers . By T. Boyds , M.Sc . , 1851 Exhibition Scholar . ( Communicated by Prof. E. Kutherford , F.R.S. Received November 26 , \#151 ; Read December 10 , 1908 . ) In 1904 Sir William Ramsay and Prof. Collie* gave a list of lines produced by the discharge in a vacuum tube containing radium emanation , but the uncertainty of these numbers made a redetermination desirable . A later determination by Mr. Cameron and Prof. Ramsayf was communicated to the Royal Society on June 25 , 1908 , and was published on August 27 , together with corrections , and a final compilation of verified emanation lines added on August 5 . After Prof. Rutherford had completed the measurements of the volume of the radium emanation , he and the writer were able to photograph the spectrum that had been observed in the course of this work , and we published in ' Nature , ' July 9 , 1908 , the wave-lengths of the stronger lines observed by us in the emanation spectrum , and a more complete list , containing 73 lines , with an accuracy of 0'5 A.U. , was given in the c Philosophical Magazine ' of August , 1908 . Measurements which I have recently made to within OT A.U. by means of a concave grating confirm the accuracy of our previous determinations . The complete purification of the radium emanation demands a lengthy and painstaking procedure , and is a matter of considerable difficulty , for the volume of pure emanation available in our experiments would occupy at * ' Hoy . Soc. Proc. , ' vol. 73 , p. 470 , 1904 . t ' Hoy . Soc. Proc. , ' vol. 81 , p. 210 , 1908 . 1908 . ] Emanation Spectra obtained by different Observers . 23 atmospheric pressure not more than one-tenth of a cubic millimetre . The vacuum tube employed must therefore be of small dimensions , and all traces of foreign gases have to be removed from the walls and the electrodes of the tube . In the experiments of Rutherford and Royds , using the method of purification recently developed by Prof. Rutherford , * a complete day 's work was taken up before the vacuum tube was filled with the pure emanation . We have observed the spectrum of the radium emanation at least eight times , and have obtained almost exactly the same spectrum on each occasion . We have drawn attention to variations in the relative intensities due to the presence of foreign gas . In the different experiments of Cameron and Ramsay , however , the spectrum is seen to vary considerably . In their first experiment , the spectrum consisted chiefly of hydrogen , together with nitrogen , and also ( presumably ) mercury , f and of the lines remaining , which alone are given in their list , the strongest are quite absent from our spectrum ; a few of the fainter lines are probably identical with some of the strongest emanation lines . In the second experiment of Cameron and Ramsay , allowing for a possible error of 4 or 5 A.U. in their measurements , the strongest lines in the spectrum are , roughly speaking , those strongest in our spectrum . At the end of their final list of August 5 , Cameron and Ramsay state that our figures show a very close agreement with theirs . A careful examination shows , however , that there are striking differences too marked to be explained as errors in measurement or variations of intensity due to impurities , for many of the strongest lines are absent altogether from our spectrum , and also from their own previous determinations . Investigating these differences several weeks ago , I noticed that after leaving out the well-marked emanation lines , the final spectrum of Cameron and Ramsay was almost identical with the xenon spectrum obtained by the discharge from a Leyden jar with spark gap . ! An examination of the accompanying table shows that the spectrum attributed by them to the radium emanation is mainly a compound of the xenon spectra obtained with and without Leyden jar , the jar spectrum having been brought out , probably , * 'Phil . Mag. , ' May , 1908 . t In none of our photographs have the mercury lines been present , though the green line 5461 has been seen faintly in visual observations . Neither were the hydrogen lines , except seen when preliminary precautions had been taken for the removal of hydrogen from the electrodes . + The author is reminded that Prof. Living had remarked last summer the similarity of this emanation spectrum to that of xenon ; Sir J. Dewar reported the circumstance at the British Association meeting in September . The author is convinced that there is no real coincidence in the emanation spectrum with the spectra of any of the rare atmopheric gases . Mr. T. Boyds . A Comparison of the Radium [ Nov. 26 , by the heaviness of the discharge employed . Practically the only strong xenon line not included in their list is the line 4862'69 ( intensity 8 ) , which was doubtless hidden by Hp 4861*49 . After eliminating the lines due to xenon from their last photograph containing 54 lines , there remain 11 . Of these , eight are seen to be some of the strongest lines of our spectrum . Taking into account the complete list of Ramsay and Cameron 's lines , including those printed in italics , which were seen only in previous photographs , the number of emanation lines amounts to 16 ; there are , of course , numerous coincidences within the accuracy of their measurements , of xenon lines with possible emanation lines . Table . Cameron and Ramsay 's emanation spectrum . Inten- sity . Xenon ( Baly ) . \#166 ; f. Inten- sity without jar . Inten- sity with jar . Rutherford and Royds 's values . Inten- sity . 7050 2 ' 1 ! 6150 2 * 6101 2 6097 *80 \#151 ; 7 6055 2 6051 *36 \#151 ; 7 5980 *5 2 5976 -67 \#151 ; 7 5679 *5 2 ! 5586 2 i 5582 -2 8 5446 1 5439 *19 \#151 ; 8 5419 4 5419 *40 \#151 ; 10 5370 2 5372 -62 \#151 ; 8 5335 3 5339 *56 \#151 ; 9 5289 6 5292 -40 \#151 ; 10 5083 2 5080 *88 \#151 ; 7 Probably 5084 -45 4 4979 2 1 4978 *49 ' 4 Possibly 4979 *02 4 4936 2 Possibly H(C . andR . ) 4920 3 4921 -68 \#151 ; 6 | 4919 -85 \#151 ; 4 4883 2 4883 -68 \#151 ; 6 4873 2 4876-68 \#151 ; 7 4843 -5 10 4844 -50 \#151 ; 10 4816 2 4818 -15 \#151 ; 4 Possibly 4817*33 4 4806 -5 1 4807 -19 6 1 4768 2 4769 *21 \#151 ; 4 4731 *5 2 4734 -30 8 1 4722 4 ' 4721 -70 4695 *5 2 4698 -20 \#151 ; 5 4697 *17 7 \#151 ; 4681 5 4683 -76 \#151 ; 5 Possibly 4680 '92 10 4672 7 4671 42 10 2 4652 -5 3 4652 -15 \#151 ; 6 4645 *5 6 4644 -29 10 4626 '5 10 4624 46 15 2 . Possibly 4625 -58 8 , 4616 2 4615 -72 \#151 ; 5 4610 2 4609 '40 7 4605 10 4603 -21 \#151 ; 10 Possibly 4604 '46 4 4592 1 4592 -22 \#151 ; 6 Doubtful ( C. and R. ) 4585 4 4585 -65 \#151 ; 10 4578 *5 3 ! 4577 -36 \#151 ; 6 Possibly 4577 '77 7 4545 -5 2 1 4545 34 \#151 ; 8 \#166 ; 4541 1 4541 -03 \#151 ; 8 4532 5 2 4532 -67 I \#151 ; 5 1908 . ] Emanation Spectra obtained by different . 25 Cameron and Ramsay 's emanation spectrum . Inten- sity . Xenon ( Baly ) . Inten- sity without jar . Inten- sity with jar . Rutherford and Royds 's values . Inten- sity . 4524 4 4524 *83 6 - Possibly H ( 0 . and R. ) 4524 38 \#151 ; 5 4509 4 4508 -68 9 4505 2 t - 4503 -89 2 Doubtful ( C. and R. ) 4501 3 4501 -13 10 2 4481 4 4481*01 \#151 ; 7 4463 5 8 4462 -38 \#151 ; 20 Possibly 4460 '0 10 4449 4 4448 *28 \#151 ; 10 4441 -5 \lt ; 1 4441 -08 \#151 ; 3 Possibly 4439 -88 2 4436 -5 \lt ; 1 4434-35 \#151 ; 6 Possibly 4435 -25 8 4416 5 4 4415 -00 \#151 ; 7 4391 3 4395 -91 \#151 ; 10 4393 -34 \#151 ; 10 4349 6 i 4349 -81 15 4331 4 4330 -63 \#151 ; 15 4307 2 4308 -3 10 4246 4 4245 -54 \#151 ; 10 . - . 4239 3 4238 -37 \#151 ; 10 4204 5 ' 4203 -39 10 4189 3 4193 *25 8 8 Probably 4188 -2 5 4180 -20 \#151 ; 10 4167 6 4166 -6 20 4114 3 4116 -25 \#151 ; 7 Probably 4114 *71 7 4018 . 4 4017 '90 10 3982 8 3981 83 12 3973 6- 3971 -71 9 3958 . 3 3957 -30 7 3879 . 10 3880 *60 \#151 ; 6 3877 -95 \#151 ; 8 3866 -5 6 3867 -6 4 3856 . 4 It is not possible to explain the presence of so large a quantity of xenon as must have been in the spectrum tube as being due to a leakage of air into the apparatus . Prof. Rutherford and I have made special experiments to test whether xenon was present with our preparations of emanation , but could not detect any trace of this gas . It is probable that there has been , in the experiments of Cameron and Ramsay , an unsuspected contamination with xenon . Cameron and Ramsay attribute a line at 4058'5 to the active deposit of the radium emanation , since its relative intensity increases with the length of time that the discharge has passed . Mercury lines will , of course , behave similarly as the emanation is driven into the walls . It appears probable that they have overlooked a mercury line at 4057'9 , which is present , according to Eder and Yalenta , in the vacuum tube discharge at ordinary temperatures , with an intensity 4 compared with intensity 10 for the mercury line 40468 .

rspa_1909_0004

0950-1207

The extension of cracks in an isotropic material.

26

29

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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10.1098/rspa.1909.0004

Measurement

Fluid Dynamics

Measurement

26 The Extension of Cracks in an Isotropic Material . By A. Mallock , F.R.S. ( Received November 9 , \#151 ; Read December 10 , 1908 . ) The formation and extension of cracks in solids is a matter of considerable practical importance , but , as far as I am aware , the strains in the material at the extremity of a spreading crack have not been considered in detail either by engineers or physicists . It is a matter of common observation that in some materials a crack will spread with great facility whilst in others the reverse is the case . Glass and indiarubber may be mentioned as extreme cases . Between these two , endless gradations of brittleness and toughness can be found . That the facility with which a crack spreads does not depend only on the breaking strain of the material or on the work required to cause rupture is apparent from the fact that ( a ) although the tension modulus of ruptuie for glass is comparable with ( though less than ) the same modulus for cast iron and brass , the facility with which a crack can be started and spread in it is immensely greater ; and ( b ) though the modulus of rupture for indiarubber is comparatively small it requires more work to break a piece of this substance by tension than to break in the same way a piece of glass of equal area : the reason of course being the very small extension which can be given to glass without rupture . Any specified strain in a solid can be represented as a combination of shear and volume extension or compression , and both for volume extension and shear there are limits which if exceeded either cause rupture or leave the material in an altered condition when the stress is removed . The ordinary tests which are applied to structural materials involve in general both volume alteration and shear , but the limits for the two forms of strain are distinct and perhaps independent of one another . In liquids the coefficient of distortion is evanescent and there is no limit as regards the magnitude of the shear , but k the volume coefficient is finite and comparable with that for solids , and there are limiting values for the volume expansion of liquids which if exceeded cause discontinuity . In many liquids , e.g.f water and mercury , it is known that the breaking strain for volume extension is large although there are experimental difficulties The Extension of Cracks an Isotropic Material . in measuring the exact amount . There is , however , no known limit of rupture for the volume compression of either solids or liquids.* * . It would be a matter of interest and importance to determine for solids whether , and how far , the existence of one form of strain influenced the limits of the other : whether , for instance , a body subjected to volume extension would require more or less shear to rupture it than when the volume was normal . This point has not , as far as I know , been made the subject of experiment , but for the purpose of this note I shall assume that if a strain which .exceeds either of the limits is applied to a solid , rupture will be due to that property of the substance for which the limit is least , and that if the distortion limit is the smaller of the two , breakage will occur at right angles to the lines of greatest extension , whereas if the volume limit is the least the direction of the break will be indeterminate . Consider a solid partly divided by a crack in a certain plane and subject to equal and opposite forces symmetrically applied at points on either side of and equidistant from the plane . Since the plane of the crack is a plane of symmetry , the solid on one side of this plane may be supposed to be absent and its place to be taken by the tractions required to keep the strain unaltered . The problem then becomes one regarding the strain produced by a given distribution of stress over a finite area of the plane surface of an otherwise infinite solid . The further development of the crack depends only on the action which takes place in the immediate vicinity of its end for the time being . It would be superfluous therefore to refer to the solutions of the above problem which have been given by Boussinesq and others , for these solutions do not apply to points extremely close to the margin of the area of the applied stress , and for the present purpose it is only with regard to such points that information is required . It may be seen , however , that lines of strain near the margin must be of the type sketched in the accompanying diagram , and that the strain and stress would be infinite at the end of the crack if there were no elastic limits . Hence one may conclude that even the smallest force when applied to a cracked solid will cause some permanent set at the end of the crack if the material can yield in this * This may give an explanation of the difference between malleability and ductility . Under the hammer the strain is a shear combined with volume compression , while in * . drawing " the material undergoes shear combined with volume dilatation . In general , a body which is ductile will also be malleable , but the converse need not hold . 28 The Extension of Cracks in an Isotropic Material . way , * or , if rupture ensues when the elastic limit is exceeded , that the crack will he extended . In most homogeneous solids the area over which the stresses exceed the mean stress at some moderate distance-from the end of the Crack will be of the same order as the square of the width of the crack , an area so small that it is not unlikely that the elastic and other limits , of the material within it may be altered by the same cause which produces surface-tension in liquids . The proportion of shear to volume extension is dependent on the value of Poisson's-ratio for the substance , and increases indefinitely as this ratio approaches one-half , but the limits to which the volume can be altered , or the substance distorted , without rupture do not necessarily involve a at all . If the conditions of strain at the end of the crack are such that material gives way from over-distortion , the fracture will occur in the plane of theexistmg crack , which will therefore spread continuously : while if the over- dilatation is the origin , the breakage may take place in any direction. . If at any place the plane of the new fracture cuts the plane of the crack there will be a rearrangement of stresses , and a relatively considerable length of material will have to be strained before further rupture is possible , and thus the cross fractures will act as a bar to the further extension of the crack . in rr teref0re , that " materials such as glass or other substances to theLwt T\gt ; m , nearly ''nstant Actions that rupture is due wanderinu ^ that Where a crack extends with difficulty in IZZtT ' 6 dUatati0D Umit is the \#153 ; which has been " iv ? eri ; ;Pld " 'n 'f the \#187 ; which fracture takes place nra ILTs inU ! dbr aP~ WWch 'ften 8hows itself on broke When the limits for both ^ time , a very small change in a\gt ; nd k are reached at nearly the same either , such as might occur in a body to act is evidence that WWn ^ forC8 which caused ifc eeas Rotation of the Electric Arc in a Radial Magnetic Field . 29 nearly but not quite homogeneous , would alter altogether the appearance of a fracture . In this note only isotropic materials are considered , but it seems probable that the same principles might be used to explain the cleavage of crystals . The Rotation of the Electric Arc in a Radial Magnetic . By J. Nicol , B.A. , B.Sc. , Wheatstone Laboratory , King 's College , London . ( Communicated by Prof. H. A. Wilson , F.R.S. Received October 1 , \#151 ; Read December 10 , 1908 . ) The following paper contains an account of a series of measurements of the velocity of motion of an electric arc in a magnetic field at right angles to its length . The experiments are similar to those made by Prof. Wilson and Mr. G. H. Martyn* with the electric discharge in a vacuum tube and were suggested by Prof. Wilson . The apparatus consisted of a vertical iron rod ( fig. 1 , A ) magnetised by two solenoids B at its ends , wound in opposite directions , so as to give a pole in the middle of the bar . With this arrangement the field round the middle of the bar is uniform and radial . The distance between the two solenoids was fixed by a quartz tube C , which also served to protect the iron rod from the heat of the arc . The arc passed between two copper tubes D , 2 cm . in diameter , held coaxial with the iron rod by a clamp made of wood and brass . The copper tubes were clamped in holes cut in two pieces of thick ( 5 mm. ) sheet brass E , fixed to the top and bottom of a block of hard wood F. The required arc length was obtained by clamping the electrodes while they were pressed firmly against a gauge of sheet brass held between them . The base of the iron rod and the stand carrying the arc electrodes each rested on three screws in a hole slot and plane fixed to the table by paraffin wax . Thus the whole apparatus could be quickly taken down and set up again in the same position . This was necessary to enable the electrodes to be renewed after each experiment . The arc was in all cases started with the magnetic field already in action , by momentarily bringing a piece of arc-lighting carbon in contact with the two electrodes . * 4 Roy . Soc. Proc. , ' A , vol. 79 , 1907 .

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0950-1207

The rotation of the electric arc in a radial magnetic field.

29

42

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

J. Nicol, B. A., B. Sc.| Prof. H. A. Wilson, F. R. S.

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10.1098/rspa.1909.0005

Electricity

Tables

Electricity

]\gt ; Rotation of the Arc in Radial Magnetic Field . 29 nearly but not quite homogeneous , would alter altogether the appearance of a fracture . In this note only isotropic materials are considered , but it seems probable that the same principles might be used to explain the cleavage of crystals . The Rotation of the Electric Arc in a Radial Magnetic Field . By J. NICOL , B.A. , B.Sc. , Wheatstone Laboratory , King 's College , London . ( Communicated by Prof. H. A. Wilson , F.RS . Received October 1 , \mdash ; Read December 10 , 1908 . ) The following paper contains an account of a series of measurements of the velocity of motion of an arc in a magnetic field at right angles to its length . The experiments are similar to those made by Prof. Wilson and Mr. G. H. Martyn*with the electric discharge in a vacuum tube and were suggeste by Prof. Wilson . The apparatus consisted of a vertical iron rod magnetised by two solenoids at its ends , wound in opposite directions , so as to give a pole in the middle of the bar . With this arrangement the field round the middle of the bar is uniform and radial . The distance between the two solenoids was fixed by a quartz tube , which also served to protect the iron rod from the heat of the arc . The arc passed between two copper tubes , 2 cm . in diameter , held coaxial with the iron rod by a clamp made of wood and brass . The coppel tubes were clamped in holes cut in two pieces of thick ( 5 mm. ) sheet brass , fixed to the top and bottom of a block of hard wood F. The required arc length was obtained by the electrodes while they were pressed firmly against a gauge of sheet brass held between them . The base of the rod and the stand carrying the arc electrodes each rested on three screws in a hole slot and plane fixed to the table by paraffin wax . Thus the whole apparatus could be quickly taken down and set up again in the same position . This was necessary to enable the electrodes to be renewed after each experiment . The arc was in all cases started with the netic field already in action , by momentarily bringing a piece of arc-lighting carbon in contact with the two electrodes . 'Roy . Soc. Proc , vol. 79 , 190 Mr. J. Nicol . The Rotation of the [ Oct. 1 , Experiments were first made with carbon electrodes , but though the discharge could be started and would occasionally make a few revolutions it never lasted for more than one or two seconds . An iron-iron and an ironmercury arc were tried with equally unsatisfactory results . Then a copper 1908 . ] Electric Arc in Radial Magnetic Field . had to be put in the circuit . A few experiments were done with the 100volt supply , but the arc was then much more liable to go out before the necessary reading had been obtained ; it was therefore preferred to use the -volt supply . The current used was measured by means of an Elliott ortable standard ammeter reading up to 15 amperes . the copper arc was much more stable than any of the others which had been tried , the discharge seldom lasted for longer than thirf , seconds , and then only when brightly polished electrodes were used . After every second or third discharge thel.efore , the apparatus was taken down and the electrodes replaced by fresh ones while the old ones were repolished in a lathe with fine emery paper . As the discharge only lasted for so short a period , a stroboscopic method of lneasuring the speed of rotation was out of the question , and in place of it a photographic one involving the use of a rotating mirror was employed . The mirror was fixed not quite normally on one end of the shaft of a electric motor . When the motor was working , a point source viewed in the mirror appeared drawn out into a circle of light , and if the point source was intermittent this circle was broken into as many dots as the number of times the source became active during each revolution of the motor . The intermittent source was obtained by a vertical slit in front of the arc . Thi was illuminated by the arc once every time it revolved round the iron bar . The image of the slit in the rotating mirror was then photographed with an ordinary camera . The shutter was adjusted so that the plate was exposed for a little longer than the time taken by the mirror to make one revolution . By this means a slight overlapping of the dots at the beginning and end of the exposure was insured and it was consequently easy to count to the nearest tenth the number of revolutions made by the arc during one revolution of the lnirror . Imperial Special Rapid plates were used and satisfactory results ; isochromatic ( Imperial N.F. ) plates were tried but did not give nearly so dense an image . Three exposures were taken on each plate , the rising front of the camera being moved between each pair of exposures . To count the number of dots the negatives were copied on tracing paper , as the counting was more easil . done on these tracings than on the original negatives . turn the mirror an . series motor designed for 100 yolts employed . It was used , however , as a separately excited machine , the field magnet circuit being connected to the 100-volt mains through an 8-C.P . lamp , and the armature windings supplied with current from an 8-volt accumulator . The speed was regulated by an adjustable resistance in the armature circuit . The number of revolutions made by the motor was The motor was run at about 250 revolutions a minute , and the camera exposure was about of a second ( a nominal second with a Unicum shutter ) . The relative positions of the arc , motor with mirror , and the camera , are shown in fig. 2 . Theory of the Rotation of the Arc. If and are the velocities of the ions due to unit electric force , the rate at which the arc moves is given by the expression* , or ' if is the number of revolutions the arc makes per second , and and X the magnetic and electric forces , and the radius of the electrode . The following is a proof of this relation . The velocity of drift of an ion along the arc is . This motion of the ion in a magnetic field causes a *Wilson and Martin , . cit. 1908 . ] Electric Arc in a Field . transverse electric force H. to act on the ion which ives it a transverse velocity HXk2 . Hence the transverse displacement of an ion while it passes from one electrode to the other is where is the arc length . Although , unless the velocities of the two ions are the same , the arc will not remain parallel to the axis during rotation , the two ends will eventually move at the same speed and their position will be iven by for anode end , for cathode end . A positive ion starting from the anode and moving to the cathode in a time must then travel a distance transversely . Similarly , the transverse motion of a negative ion is these to the values previously found , we get : thus Eliminating instead of from the above two equations , we . The maximum value of used was , and the velocity of the ions in unit ( C.G.S. electromagnetic ) field is not greater than so that which measures the inclination of the arc to the axis , is always very snlall . This explains the observation made by Wilson and Martin that the in their experiments always remained perpendicular to the jtrodes d its motion . Jleasurement of the Magnet Field H. The current was supplied from an -volt accumulator , and measured by means of an } eter similar to the one used for the measure- meant of the arc current , but reading only to 5 amperes . The ammeters are issued as correct to 1 per cent. , and they were found to agree with one another perfectly . A reversing key was included in the circuit , and the current was frequently reversed when any change was made in the netisation . In oing from a higher to a lower netisation , the iron was first by the method of reversaIs , in order to insure that the field should be a detinite function of the current and } ) endent of the permanent magnetism retained by the bar . The actual values of the field ( or rather of , which is for a radial field ) for rent m currents , were found as follows , the method the sanlC { that used by Wilson and MarCin . Two coils of 50 turns each vere wound in grooves turned on a vood cylinder of the same dianleter as tlJe copper tub used as electrodes the arc . The two coils were first connected in opposition and placed in VOL. LXXXII.\mdash ; A. Mr. J. Nicol . The of the [ Oct. 1 the position usually occupied by the arc . The coils were connected to a low resistance Broca ballistic galvanometer , and the deflections produced by reversing val.ious currents in the netising solenoids of the iron bar observed . The connections of the coils were then so altered that they were in series , and that a rrent would pass round them in the same direction . The coils were removed from the iron bar and placed along axis 01 a long solenoid at its centre , and the deflection produced by reversing the current in the solenoid observed . Let be the number of turns in each coil on the boxwood cylinder , radius of mean area of section of these coils , their separation , number of turns on long solenoid . and its length and radius . the current in amperes reversed in it . and the galvanometer swings produced by reversing the field due to the iron bar and to the long solenoid respectively ; then ubstituting the values used , The values of S were plotted on squared paper against values of the magnetising current in amperes , and were found to lie on a straight line . Substituting the value thus found , we get . As occurs in the expression for the ionic velocities , it is obvious from the above deduction that it is not necessary to know either the diameter of the coils on the boxwood cylinder , or the number of turns in them . The diameter of the coils was , however , made equal to the diameter of the arc electrodes , to avoid any error which would result from the field not being radial . The separation of the coils was four or five times the length of arc usually employed , but this does not introduce an error , as experlment showed that the field varied very little the iron bar , the variation being under 1 per cent. per centimetre . The equality of the number of turns in the two coils was tested by placing them , ether with an iron core , inside the long solenoid while they were connected in opposition . The defleotion obtained on reversing the current in the solerloid was negligible compared with 1908 . ] Electric Arc in Radial Magnetic Field . the time it lasted being necessary to read the ammeter and take a photograph . The speed of rotation was found to increase with current approxinlately linearly , and a rough value of the rate of increase was used to reduce each observation of to the value corresponding to the nearesb whole number of amperes . Means of the readings for each current were then taken and plotted against the current . The values of obtained for the same current in different experiments.showed very considerable variations ( 10 to 20 per cent. in extreme cases ) , but these variations were irregular , and there was no evidence to show that depended on the nitude of as it would do were the speed of rotation not proportional to the of the magnetic field . The final results reduced in the aboye way are collected in the following table corresponding to fig. 3\mdash ; . 22 . 23 . ( 10 ) 8.5 48 . The numbers in brackets indicate the number of experiments used in getting the mean value . *These numbers are obtained from experiments made with electrodes used a second time without cleaning . The actual values of the field used varied from 35 to 140 C.G.S. units . The of rotation observed varied from 30 to 170 revs . per second onding to linear velocities of from 200 to cm . per second . The values of in the above table have been plotted against the current in , and it will be seen that the points lie approximately on the line or substituting the values , and . Substituting the experimental numbers for , and X in the equation we obtain the following values of the product of the two ionic velocities per unit electric intensity for different values of the current . If and 1908 . ] Electric Arc in gnetic F Assuming that the negative ion in these is a corpuscle , its velocity caIl be calculated from the expression\mdash ; Neglecting any effect its may have , the mean free path of a corpuscle in air should , owing to its small size , be four tinles that of an air molecule , a relation which agrees with experim ent.f the } ) creature of the arc to be 2000o C. and the mean free path of an air molecule at , we get . To finld , the mean agitation velocity of the nscle , assume that the equation of holds between the corpuscles and the particles ; this ives t , it we take metres a second as the velocity of a hydrogen molecule at C. Substituting in the expression for , we but , and therefore this with the value found for for a current of amperes , we have a value cm . per second per volt per centimetre . This is about one-thirtieth of the velocity of the ative corpuscle , and since from the above deduction of this velocity it is evident that is propor- tional to , the mass of the positive ions must ) about 900 times that of a corpuscle , or about the same as that of a hydrogen atom . The positive ions then cannot be either copper or air molecules , but may be the same as carriers of positive electricity detected by Prof. J. J. Thomson in the Kanalstlahlen . On this view , vever , it is rather difficult to give a satisfactory explanation of the way in which increases the current . For is only directly proportional to the temperature , and the experiments show that is trebled by a rise in the current from 2 to 9 amperes . This would indicate a rise in temperature from 1000o to 3000o , ) is larger than is probable . If the positive ions were groups of copper or molecules the rise could be explained as due to a rise in temperature accompanied by dissociation of these groups . * Langevin , Theses , Paris , 1902 , p. 47 . Townsend , ' Phil. Mag 1901 , p. 198 . 42 Rotation of the Electric Arc in gnetic Field . In this conn ection it may be mentioned that the negative electrode was always much more oxidised and corroded than the positive , but this may have been due to its being the lower electrode , and thus meeting the upward convection air current and robbing it of its oxygen before it reached the positive electrode . Conclusions.\mdash ; The speed of the electric arc across a transverse magnetic field has been measured and found to be sensibly ( 1 ) independent of the arc length , ( 2 ) proportional to the netic field strength , and ( 3 ) to increase linearly with the current . From the experiments the value , the product of the speeds of the ions carrying the current , has been calculated . From this value , by assuming the negative ion to be a corpuscle and calculating velocity , it has been shown that the carriers of positive electricity have a mass of the same order as that of the hydrogen atom . In conclusion , I wish to thank Prof. H. A. Wilson for esting to me the subject of this research and for much kind advice and encouragement during its progress .

rspa_1909_0006

0950-1207

The isothermal layer of the atmosphere and atmospheric radiation.

43

70

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

E. Gold, M. A.|Dr. W. N. Shaw, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1909.0006

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1909_0006

10.1098/rspa.1909.0006

Thermodynamics

Atomic Physics

Thermodynamics

]\gt ; The of the and Atrnospheric Radiation . By E. GOLD , M.A. , Fellow of St. John 's College , , and Reader in ( Communicated by Dr. W. N. Shaw , F.R.S. Received October 5 , \mdash ; Read December 10 , 1908 . ) I. The of the Isothermal liay and the Experi tncntal of its Existence . The ation of the upper air by means of balloons carrying selfinstruments , which have furnished values for the atmospheric temperature up to between 15 and 20 kilometres , ha revealed the existence of an abnormal change in the vertical temperature gradient . After a fairly uniform fall , with altitude , of about C. per kilometre , a height is reached above which the temperature very little , sometimes increasing , sometimes slowly . The phenomenon was first noticed by M. Teisserenc de Bort*in a communication to the Societe de Physique in June , 1899 . He improved his apparatus and made further investigations , in many cases up the balloons by night to eliminate any possible insolation effects . He foumd the average , at which the change began , to be about 11 kilometres . He discovered also that the height was greater near the centre of high pressure areas than in low pressure areas , the average heights for the two cases being and 10 kilometres respectively . More recently he found that the height increased with approach towards the equator and that near the equator , ballons-soncles , ascending to kilometres , had failed to reach this layer if it existed there . He proposed to call this layer , in which little temperature occurred , the ' Isothermal Layer of the Atmosphere , 't and the name has been generally accepted . The main results have been corroborated by other observers . In September , 1906 , a series of ascents was made at Milan , in which the isothermal layer was reached at heights varying from 8 to 13 kilometres and at tempera'tures between C. and C. The smaller heights and 'Comptes Rendus , ' vol. 134 , April , 1902 ; vol. 138 , January , 1904 ; vol. 145 , July , 1907 . The term " " isothermal layer\ldquo ; is slightly misleading , inasmuch as it appears to produce the conception of a definite stratum of uniform temperature lying between two regions where the temperature decreases at a rate approximately adiabatic . The term " " isothermal region suggested by Prof. H. H. Turner , is free from this objection . Mr. E. Gold . The of the [ Oct. 5 , higher temperatures were found generally over low pressure areas and the greater heights and lower teulperatures accompanied anticyclonic conditions . Over Berlin , 1906 , the height at which the layer was reached varied from 10 to 13 kilometres and the temperatures were between C. and C. , the average being C. These ascents were made at different times of the year , but in all cases during anticyclonic conditions or on the outer of a cyclone advancing from the west . This may account for fact that the layer was not found at smaller heights in any of the ascents . In England , during 1907 , the height of the layer varied between 8 and kilometres and the temperatures between C. and C. , the mean height being about 11 kilometres and the mean temperature The was generally less than the average over low pressure areas , although there were anomalies , notably on November 11 , when the height increased fhtly and the temperature diminished rapidly in passing from Ditcham Park , which was on the ridge between two low pressure areas , to Manchester , which was under the influence of the northerly system whose centre was between Iceland and Norway . The layer has also been reached in Lapland , the Arctic circle ( and simultaneously at Trappes , near Paris ) , at crhts varying from 8 to 12 kilometres ; also by otch , S in America , in latitude N. , where the average height appears to be greater than in Europe . Further , in an ascent near Brussels ) July , 1907 , the layer was found to extend with slightly increasing temperature from 12 to 26 kilometres altitude and near Strassburg in 1905 , the temperature recorded at 26 kilometres was higher than that at 14 kilometres . There can be no question , therefore , of its being merely a local or temporary phenomenon . It is clear that there cannot be convection curreuts to any marked extent in this region , and I propose to show that in an atmosphere which is not transparent but absorbs and emits radiation , the process of radiation would prevent the establishment of the temperature gradient necessary for conyective equilibrium , in the upper layers of the atmosphere ; and that in the lower layers of our atmosphere it can be maintained only by transference of energy from the earth to the atmosphere by direct convection or by the process of evaporation of water at the earth 's surface and subsequent 'Ergebnisse der Arbeiten des Koniglich Preussischen Aeronautischen Observatoriums , ' 1906 . Petavel and Harwood , 'Quart . Journ. Roy . Met . Soc January , 1908 ; Dines , ' Nature , ' February 27 , 1908 . ' Met . Zeit 1907 , pp. 498 , 499 . S . cit. ibid. , 1907 , p. 366 . 1908 . ] Atmosphere and Atmospheric condensation in the atmosphere . The heat necessary for the evaporation of water-vapour at the earth 's surface is supplied mainly by absorption of solar radiation and is not aken from the atmosphere , but the heat given up on condensation is added almost entirely to the heat of the atmosphere , and in this way we get a supply of heat to the atmosphel.e at a rate that may be estimated approximately from the annual rainfall . II . Gcneral of the Possible ibution s in an Atmosphere . Summary of now reached . It is clear that if the atmosphere were transpal'ent to radiation of all wave-lengths a state of convective equiiibrium would exist up to a certain limit , after which the collision frequency would be too small to admit of mass-acvitation and the permanent state of this outer layer would be one of conductive equilibrium . But this state could only persist so as the temperature of the earth was , because there would be a continuous flow of heat outwards by conduction . This would produce an accumulation of heat in the upper layers of the conyective atmosphere , and the adiabatic temperature gradient could be maintained only by up the lower layers ; since if we assume that there is no radiation from the atnlosphere , the difference of temperature could not be renewed by } the upper layers . If , however , the temperature varied over the surface of the earth a persistent limited convection would be } ) , provided that the lowest surface temperatures were below the upper air temperatures , so that conduction of heat took place downwards over these regions and balanced the upward conduction over those places where convective equilibrium The temperature of the earth in that case would be such that the heat radiated into space would balance the incident solar radiation absorbed by it . The minimum possible value would be obtained by taking the earth to be a full radiator for its own temperature . The effect of clouds would be to diminish the mean temperature owing to their greater reflecting power for solar radiation . They would either transmit the earth 's radiation or act themselves as radiators for the wave-lengths absorbed . The reflection of radiation of long wave-length would be small . But if we have an atmosphere which and radiates there will be a theoretical temperature distribution in which there is equilibrium between the and absorl ) tion of each elenrent . We may describe such a state as one of radiation equilibrium . If the vertical telnperature gradient for this state is less corresponding to convective equilibrium , it will be ) possible for the Cter state to persist and the atmosphere will tend to radiation Mr. E. Gold . The Isothermal Layer of the [ Oct. 5 , There may , however , be a limited convective equilibrium arising from causes which supply sufficient energy to balance the excess of the radiation in the convective state . An example will suffice to explain this . Suppose the state of radiation equilibrium were isothermal , and that in this condition the atmospheric radiation just balanced the absorption of solar and terrestrial radiation . Consider , now , the effect of a direct communication of heat to the atmosphere at a definite rate at the earth 's surface . The temperature of the lower layers of the atmosphere would be raised and a state of convective equilibrium would supervene , but only up to a sufficiently great for the increased atmospheric radiation , due to increased temperature , to balance the energy supplied . The assumptions which form the basis of the theory developed in the following sections are these:\mdash ; ( i ) The constituents of the atmosphere radiate for the same for which they absorb , and according to the thermal law . ( ii ) The curvature of the earth 's surface may be neglected in considering radiation in the atmosphere . ( iii ) Owing to the large portion of the spectrum which the constituents of the atmosphere radiate , their radiations may be taken to be proportional to the fourth power of the absolute temperature . This I attempt to justify by the experimental data in Section III . ( iv ) The temperature in the adiabatic state may be represented sufficiently closely by the equation , in which is taken to be 4 instead of theoretical value for dry air . v ) A necessary condition ( . supra ) for convection , which forms the keystone of the present discussion , is that , in the upper part of the convective system , the radiation from any horizontal layer ( or any elementary sphere ) should exceed the absorption by it . ( vi ) Where convection is absent the outward and vard radiations across any horizontal plane are equal , conduction being so slow as to be negligible . ( vii ) The power of the earth 's atmosphere diminishes with height owing to the diminution in the proportional amount of waGer-vapour present , and it may be represented with tolerable approximation by ; where and are constants and is pressure . The principal results obtained are as follows:\mdash ; ( a ) By the use of ( i ) and ( ii ) alone , general expressions are found for the intensity of atmospheric , terrestrial , and solar radiation at any point in the atmosphere ; and for the absorption and emission by any horizontal layer of finite thickness . The conditions for convection to be possible and for thermal equilibrium in the absence of convection are also found . 1908 . ] Atmosph ere Atmospheric ( b ) By the introduction of ( iii ) to ( vi ) it is proved that , for an atmosphere uniform in constitution , the adiabatic state could not extend to a height reater than that for which , where is the surface pressure . It is also proved that , if the atmosphere were isothermal , the absorption of solar radiation in any layer of it , beginning from , would be equal to the sorption of terrestrial and atmospheric radiation , and each would be equal to the radiation in either direction from the layer . By the use of ( vii ) it is proved that for the earth 's actual atmosphere the height to the adiabatic state can extend is limited . Values deduced from the experimental evidence are then substituted for and it is found that if the atmosphere consist of two shells , the inner in the adiabatic , the outer in the isothermal , state : ( i ) the inner cannot extend to a reater than that for which ( 10,500 metres ) ; ( 2 ) the innel must extend to a height greater than that for which ( metres ) . ( d ) It is shown that the radiation from the lower layers of the atmosphere exceeds absorption by them , and that the deficiency of energy is such that it could be supplied by conyection from the earth 's surface , and by condensation of water-vapour . The deficiency for the layer to is practically yible , that convection above will be very slight . ( e ) Minimum possible temperatures for any point in the atmosphere over a place at A. ( absolute ) are A. or 20 A. , as the atmosphere radiates throughout the spectrum or only for a part of it per cent. of the energy of full radiation for its tenlperature . values are deduced from what would be the radiation intensity across the upper strata of the atmosphere , supposing it were maintained in adiabatic throughout . For this radiation must correspond to a temperature which is less than that for any other possible temperature distribution , when the surface temperature is III . Data on Gaseous Radiation Absorption . Before to formulate the conditions of radiation equilibrium and to obtain expressions for the intensity of atmospheric radiation , it will be convenient to describe briefly the results of experiments on the radiation and absorption of the constituents of the atmosphere . The pioneer in this region of research was Tyndall , conducted a series of careful and elaborate experiments with gases contained in tubes closed by rock-salt plates . He used as his sources a Leslie 's cube at 10 C. , and a copper plate heated to about 20 C. , and measured the radiation by a thermopile . He found large 'Contributions to Molecular Physics . ' Mr. E. Gold . The Isothermal of the [ Oct. 5 , absorption by water-vapour and , but practically no absorption by oxygen and nitrogen . He found also that ozone exercised a remarkable absorbing power . Except for the results of his observations on these yases are mainly qualitative in character and designed to show the greater absorbing power of dalnp air . Arrhenius*used a tube 50 cm . long and examined the absorption of at various pressures for radiation from sources at and C. His results fairly well with Tyndall 's , the absorption for a path length of cm . at atmospheric pressure about 10 per cent. for the 10 C. source and 15 per cent. for the C. source . J. measured the absorption by in tubes of different lengths at three different pressures , 380 , 760 , and 1520 mm. Koch 's results proved what had previously been pointed out by that the absorption depends on the density of the gas as well as on the total mass of gas in the path of the radiation . ngstrom found that a tube 1 metre long , containing at a pressure of 4 atmospheres , absorbed per cent. of the radiation from a source at 30 C. , while a tube 4 metres , containing at a pressure of 1 atmosphere , absorbed only per cent. of the radiation from the same source . The effect of this remarkable result can also be seen in Tyndall 's observations ; but it is complicated by his use of a different source in his experiments at constant pressure . The distribution of absorption bands in the spectrum has been the subject of researches by Angstrom , S Paschen and ubens and Aschkinass . Absorption bands were discoyered from to to , and to 16 . The last is the most important for radiation at terrestrial temperatures . The absorption in a path 22 cm . for radiation from a zirconium mantle was per cent. at the maximum and per cent. on the average for the to . For a path of 65 cm . there was total absorption from 14 to , the at atmospheric pressure and temperature . The absorption by 33 . of gas at atmosl ) heric pressure and temperature for the band to was 90 per cent. , and for the band to and the same layer it was 40 per cent. , the source ) hot blackened platinum . has investigated the on the absorption bands of varying the pressure . He found that the bands were . widened by the 'Ann . der Physik , ' vol. 4 , 1901 , Ofversigt af K. Vet . Akad . , p. fversigt , ' 1901 , p. 378 . S 'Ann . der Physik , ' 1894 , vols . ) , 53 . ournal , ' 1898 . 'Ann . der Phyhik , ' vol. 16 , 1905 . 1908 . ] Atmosphere Atmospheric pressure , while an increase in the length of path sufficient to make the mass of in the path of the radiation the same as when the pressure was increased did not produce this widening . He concludes that a variation in the amount of in the atmosphere would not materially affect its absorbing power for solar radiation , since the amount present , equivalent for vertical transmission to a path of 250 cm . at a pressure of 760 mm. , is much more than sufficient to exert full absorption for the width of band corresponding to the density of in the atmosphere . The principal feature of water-vapour absorption is the number of spectral regions in which it occurs . The bands up to in the solar spectrum have been carefully observed by Abney , Langley , others . Paschen observed the bands up to 10 as source a blackened iron plate at 40 C. Bubens and Aschkinass measured the absorption between 10 and 20 , and at 24 , using as source a zirconium mantle . The following table gives the absorption for different wavelengths by a 7 cm . layer of water-vapour at 10 C. and atmospheric pressure , deduced from Paschen 's observations . If the ption by the water-vapour in the atmosphere were given by 100 , where is the of water-vapour in the path of the radiation and is a constant , different for different , deduced from these results , we find that for an atmosphere of average humidity water-vapour equivalent to a layer of liquid water 2 cm . thick , there would be total absorption for wave-lengths 5 to 8 From the observations of Rubens and Aschkinass we deduce the following values for the absorption by cm . of water-vapour at C. and atmospheric pressure . Mr. E. Gold . The Layer of the [ Oct. 5 , Of the remaining constituents of the atmosphere , ozone is the only one which shows considerable absorption . Tyndall* found ozone exercised a remarkable absorption for his low temperature radiation . E. Meyer observed the absorption by ozone of short wave-length radiation . Taking the ozone in the atmosphere to be milligrammes per kilogramme of air , the following table gives approximately the percentage absorption for vertical transmission for different ] engths , according to Meyer 's results:\mdash ; . A. per cent. . A. per cent. found no ozone absorption bands between wave-lengths and . He found bands at Sharp , Uncertain , Weaker , 9 to Verv strong , and no further bands up to 14 The band 9 to 10 corresponds to an absorption band found by Langley in his work on the temperature of the moon ; and as there are no bands there , and the water-vapour absorption is weakest in that part of the spectrum , the existence of this band is incidentally strong evidence of the presence of a considerable quantity of ozone in the atmosphere . The oricD of this is possibly indicated by an observation of Fr. Fischer , S who found that ozone was formed by the action of ultra-violet light as well as by electric discharge . Ladenberg and Lehmann verified Angstrom 's results for ozone absorption at and 9 to 10 , and obtained additional maxima of absorption at , but these were weak compared with the 9 to band . von BahrlT measured the absorption of low temperature radiation by ozone . The percentage of the total radiation absorbed approached an asymptotic value as the ozone in the path was increased . This asymptotic value agreed with the assumption that the absorption took place in two bands , to and to * Tyndall , Contributions , ' p. 102 . Ann. der Physik , ' vol. 12 , 1903 , p. 856 . 'Arkiv for Matematik Ast . och Fysik , ' vol. 1 , 1903\mdash ; 4 , pp. 34 395 . S 'Ann . der Physik , ' 1903 . Ibid. , 1906 , vol. 21 , p. 313 . 'Arkiv for Ast . och Fysik , ' vol. 3 , 1907 , No. 15 . 1908 . ] Atmosphere and Atmospheric measured the absorption by 100 metres of air , relative humidity 60 per cent. , dew point C. , iving water-vapour in the path equivalent to cm . of hquid water . He found 21 per cent. of the radiation from a C. source was absorbed . With air of different rees of dampness he found the following results , where is the equivalent amount of liquid water in the path : A. mm. per cent. 0 . , , 14.6 The observations of the absorbing power of the diff'erent gases are nol . entirely in accordance with one another , and it appears that the absorption by water-vapour , as well as that by , depends on the density as well as on the total absorbing nlass . If we use the results obtained , we find that for , at a pressure less than 760 mm. , the maximum possible absorption for radiation from a C. source in the bands discovered is about 18 per cent. of the complete energy in the spectrum of a perfect emitter , as iven by Planck 's formula , , where being measul'edJ in terms of mm This rees nearly with the value obtained by Ekholm for the absorption by in the atmosphere , by Koch 's results for the absorption of the total radiation . we apply the results of Paschen and Rubens and Aschkinass , we find that the water-vapour in the atmosphere would absorb 95 per cent. of the earth 's radiation for vertical transmission , but if we assume that the apparent absorption between 8 and is spurious , we find that 25 per cent. is transmitted . If we use 's observations and assume that the absorption place throughout the spectrum , we fi1ld 94 per cent. of earth radiation absorbed in vertical transmission . no absorption between 8 to , we per cent. of the total radiation absorbed . To obtain an estimate of the possible absorption of solar radiation , it is necessary to know the distribution of in the solar spectrum . I have for this purpose assumed that the effective temperature of solar radiation varies with the wave-length and is given by the equation , where is measured in terms of . With this value of and Planck 's formula find a value for the solar constant ( the value . to the best recent 'Memoirs Not . Acad vol. 4 , Ninth Memoir , p. 184 . ' Met . Zeit 1902 , p. 496 . Mr. E. Gold . The Layer of the [ Oct. 5 , determinations is and a maximum intensity at wave-length agreeing with Langley 's estimate . The following table gives the values of the intensity of radiation at different wave-lengths calculated on this sssumption : . With these values of we find the following values for the percentage amount of solar radiation absorbed in vertical transmission , the water-vapour in the path being equivalent to 2 cm . of liquid water:\mdash ; Thus the absorption of solar radiation would be about 12 per cent. for zenith sun ; and about 10- per cent. for low sun , when the absorption in the bands would be full . The largest observed percentage absorption of solar radiation by water-vapour , given in the 'Annals , ' etc. , is per cent. , the transmission being atmosphe . res and the surface vapour pressure being mm. The radiation from . gases has formed the subject of researches by Maurer , ' Annals of the Astrophysical Observatory of the Smithsonian Institntion , ' vol. 2 , 1908 . Vol. 2 , 1908 , p. 131 . See ' Met . Zeit 1901 , p. 223 . 1908 . ] A tmosphere Atmospheric Radiation . and Pearson , * Paschen , and Very . From meteoroIogical ervations , Maurer deduced that an air layer 1 cm . thick radiated to another at 1o C. lower temperature gm . . per hour from each cm.2 of surface . This agrees with the value deducible from 's observations on absorption for air of 60 per cent. relative humidity and C. dew-point , on the assumption that absorption and emission follow the same law and that the intensity of radiation varies as the fourth power of the absolute temperature . From the experiments of Hutchins and Pearson on the radiation from a hot air column , the corresponding radiation be Paschen 's results are chiefly of importance as identifying the spectral regions of emission with those of absorption for the same gases . found from his experiments a value gm . . per hour , a yalue intermediate between that of Maurer , and Hutchins and Pearson . The experiments on which Very relies for his results were made by enclosing the air in a tube with a moveable radiating disc and a rock salt face . The tube was heated from below by Bunsen burners and the radiation was observed first with the disc near to the rock salt and secondly with the disc drawn back so that a layer of air intervened in the path of the radiation . It is assumed that the radiation from this air is measured by the difference , corrected for absorption , between the total radiation in the two positions , no radiation from the walls of the tube reaching the bolometer . Now if the gas and the disc have the same temperature and the disc radiates fully ( the disc used was blackened copper ) , it appears certain that the gas will absorb just as much disc radiation as it itself radiates . Any additional radiation , therefore , in the second position , must have been due to a change in the temperature of the solid parts or to an excess in the temperature of the over that of the disc , and of this no account is taken . We shall therefore assume that the absorption results are the more correct and utilize them in the application to the atmosphere . IV . Gmeral Expressions for the Badiation from the Atmosphere , and Conditions of its Let us consider the radiation and absorption in a gas stratified in horizontal layers in which the pressure at any point is due to the weight of the gas above it . Since the radiations are thermal , the emission will follow the same law as the absorption . Thus if an element of gas of mass 'Amer . Journ. of Sci 1904 , p. 277 . Paschen , ' Ann. der Physik , ' 1894 . Very , ' Atmospheric Radiation . ' Mr. E. Gold . The Isothermal of the [ Oct. 5 , occupying an element of volume of unit sectional area and thickness emits radiation of wave-length equal to , where is the intensity .of radiation of wave-length for a full radiator at the temperature of the gas , them the same element will absorb radiation if radiation of wave-length is incident normally on unit area . For the absorption by .a length of the gas we find at once , on putting , the expression , where and a value for the emission . Divide up the gas into horizontal layers across which the pressure change is so that the mass of gas in each layer is proportional to . The intensity of radiation from a layer at pressure emitted in a direction inclined at an angle to the normal will be , per unit area , The intensity of this at a point at pressure and distant from the layer will be This will also be the amount entering a spherical element of radius at the point ; and we get , for the whole amount of radiation from the layer entering such an element per unit time , , say . Thel'efore from the whole mass of gas situated above the layer we get radiation of wave-length entering the element per unit time , Similarly , from the gas below the element we get , For the radiation crossing unit area of a horizontal plane at downwards and upwards we find respectively , 1908 . ] Atmosphere and Radiation . For the radiation from the earth entering the spherical element and crossing unit area of a horizontal plane , upwards , we get . The corresponding values arising from the ayerage direct intensity of solar radiation are where and is latitude and declination . Now the absorption , by a spherical element , of a strealu of radiation is Jbfzd , where is the length of path in the sphere , i.e. , it is volume of sphere . But radiation from the element is The condition of radiation equilibrium is therefore , ( I ) where may vary with , expressing that the radiation absorbed in the spherical element must be equal to that emitted : it is included in the condition , ( II ) expressing that the outward and inward radiations across any horizontal must be equal to each other . If we take of the scattering and reflexion of direct solar radiation , we must subtract from the ayerage vertical component of this and add to its average intensity . If , instead of using the spherical element , we wish to deal only with horizontal layers , we must find the absorption of radiation in such a layer . Leb us then consider the absorption of the radiation from a layer from . to by a layer to . The radiation entering the second layer in a direction inclined at an to the vertical is per unit and the total amount absorbed will be . E. Gold . The lsotherm of the [ Oct. 5 , Putting , we find , or Therefore , where Similarly , for the absorption of radiation from a layer to below the absorbing layer , we find where If we put , we obtain the expressions for the total atmospheric radiation absorbed in any layer . We will use with this special meaning . The earth radiation absorbed in the layer is , and the radiation absorbed is where is ( vide supra ) with substituted for The radiation from the layer is , per unit area , , say . Thus we may replace the first condition by where the integration extends to all . We shall need both forms of the condition infra . The writer has verified analytically that I can be deduced from III and that II follows from III if we introduce the condition that the downward and upward radiations balance at the earth 's surface . 1908 . ] Atmosphere and Atmospheric Radiation . If convection takes place in the it must always involve a flow of heat upwards from the lower layers . Further , any upper layer receives at least as much heat as it loses by convection , and generally more . Consequently , the effect of convection would be to add a positive term to the right-hand side of II and to the left-hand side of III , i.e. , convection is only possible if everywhere in the actual state , and at the same time for the upper layers . pplication to an Atmosphere of UniJorm C. Impossibility of jctive Elibrium tsuch an Atmospher If we have an isothermal atmosphere , we find the following expressions for , etc. , on putting , , , , , . It is . to be noted that and are independent of the temperature distribution in the gas . Substituting in equation III , we find Mr. E. Gold . The Isothermal of the [ Oct. 5 , or if If we put , we see that the solar radiation absorbed in the atmosphere must be equal to the terrestrial radiation absorbed and each must be equal to one-half the radiation from the atmosphere . urther , the solar radiation absorbed in any layer of the atmosphere , starting from , must be equal to one-half the radiation from that layer . Again , if we substitute in equation II , we iind and if is small this becomes or the temperature for the isothermal state must be such that a full radiator at that temperature would radiate with an intensity equal to the average vertical component of the intensity of solar radiation . For a dry atmosphere in convective equilibrium we have , be temperature , nearly , where , and consequeutly . We cannot rate our results for thia value of , but remembering that near the maximum and that , we may put as an approximation , corresponding to a temperature diminution rather slower than that for dry air in the convective state . Let us also take to be constant , i.e. , assume that there is no in the constitution of the atmosphere with change of height . We find , then , for the values of , etc. , , subscripts , here I refers to the temperature at 1908 . ] Atmosphere and Atmospheric Taking I and substituting in equations I and II , we find . ( i ) and . ( ii ) But if , the left-hand side of ( i ) is always positive , and , consequently , for all altitudes at which the pressure is less than half the surface pressure , the absorption exceeds the radiation and the state of conyectiye equilibrium could not persist . Moreover , the -hand side of ( ii ) ] the same value at both limits of the atmosphere , and therefore there could be no absorption of solar adiatiou in an atmosphere of uniform constitution in convective equilibrium . The values of X , in this case are as follows:\mdash ; X . Therefore , putting , we get for the value 'or Now this represents the excess of the absorption over the radiation for any layer , apart from absorption of solar radiation . But by h.ypothesis , and therefore any layer for which absorbs more radiation than it emits . Clearly , if the radiation decreases with height at a rate faster than that assumed , the decrease in the radiation received lawyer will be less than the decrease in that emitted by the layer , so that in the upper half of the atmosphere the absorption would exceed the radiation and the temperature would rise . Moreover , if the temperature of the upper layers rises , the absorption of radiation near will also rise , and therefore the rise in temperature must extend at least as far as if the lower layers are to be in convective equilibrium . Therefore , in an atmosphere of un iform Mr. E. Gold . The Isothermal of the [ Oct. constitution , the rate of temperature diminution corresponding to convective equilibrium cannot be maintained to a greater than that for which the pressure is half the surface pressure . VI . Application to the Earth 's Atphre , taking into account the Diminution of Water-vapour with Height . Limits to which Convective Equilibrium can subsist . We proceed to take into account the fact that in the atmosphere itself there is a rapid diminution in the proportion of water-vapour present as the height increases . There is therefore a decrease in the value of with increasing height . We may represent this approximately by taking equal to , , where and are constants . We get , then , and similar expressions for , while If is constant , with similar expressions for and Q. Writing , we get and similar expressions for , while Substituting in equation I ) , we get , after reduction , Now near , and so that the term involving becomes positive , indicating that , even apart 1908 . ] Atmosphere and At nospheric Radiation . from absorption of solar radiation , there is an excess of absorption over radiation . The upper layers therefore be warmed up , so that with the modified value of also the state cannot exist hout the atmosphere . To find we notice that and Substituting these values , we find If we put , this gives the excess of absorption over radiation in the atmospheric layer from the outer limit to a place at pressure . On simplifying , we find that the sign of the integrand is always positive . Thus , under the condition , any such layer of the atmosphere would absorb more radiation than it emitted , even apart from solar radiation . It is therefore tcertain that if in the lower part of the atmosphere , in the upper part the temperature must be considerably greater than would correspond to such a radiation law . If we put , we get for the excess of absorption over radiation in the layer extending from the earth to a point at pressure .and this must be negative if the state is to hold up to . Also , if it is negative , its value must not be greater than the absorbed solar radiation plus the energy convected from the earth 's surface . The values of and will vary for different wave-lengths , but to obtain an approximate result we may take mean values for these quantities . We therefore put , which gives a diminution in the absorption more rapid than the observed diminution in the proportion of water-vapour present . We will consider also the case , for which the rate of decrease : slower than that of water-vapour . Mr. E. Gold . The lsothermat Layer of the [ Oct. 5 , The intensity of the transmitted radiation for a vertical path bears to the initial intensity the ratio , or fqr the values of taken above , and respectively . Langley*estimates the transmitted radiation to be and to but states that his estimate is probably too high . Lowell takes the absorption of terrestrial radiation to be , and is followed by Poynting . ( i ) Let us assume that per cent. of the radiation is transmitte , freely without absorption , and that -thirds of the remainder is absorbed in vertical transmission . This gives and for the values of taken . ( ii ) Let us take the absorption to extend throughout the spectrum and to be such that at the surface 100 metres of air of humidity absorbs 20 per cent. of the low temperature radiation passing through it , in accordance with 's observations . This gives and 4 for the two values of For the purpose of calculation we use the following table , iving the values of for ? , 2 , 3 and different values of . The values for are given by J. W. L. GlaisherS :\mdash ; 1908 . ] Atmosphere and Atmospheric We observe also that ' where and . have , too , and if and Bu6 if , we have ince L , where is Euler 's constant . * Thus putting for , we find for the value of the integral We denote by , etc. , the values of , etc. , and we calculate values for I constanlt and for . The values are given in order corresponding to the four values of ; the first pair corresponds to , and the second pair to At or or For constant I , ; * Bromwich , 'Infinite Series , ' p. 460 . Mr. E. Gold . The Isothermal oj the [ Oct. 5 , We notice here a somewhat surprising result . Since the value of in aease ( 4 ) \mdash ; is always greater than the value for the corresponding pressure in case ( 2 ) \mdash ; the radiation from any .element of an atmosphere corresponding to case ( 4 ) is greater than the radiation for the corresponding element in case ( 2 ) . Yet the outward the whole atmosphere in case ( 4 ) is considerably less than in .case ( 2 ) . The values of and for the four cases are given by ; Now the values of at when are less than for any other part of the atmosphere for any possible temperature distribution with the same surface temperature . But the radiation from any element must be greater than the amount of . Thus if and we remember that in cases ( 1 ) , ( 3 ) only 75 per cent. of the radiation suffers absorption , we find as lower limits for I ' , where I ' is the radiation intensity of a full radiator at the temperature of the element . If I correspond to a temperature 30 A. , the lower limits for the temperature at any point in the atmosphere are therefore , 15 A. At the earth 's surface , or . and For constant I , ; and For ; and At or or For constant I , For Also if denote the radiation to earth from the layer extending up to and , the radiation to space of the upper half of the atmosphere , we find for I oe 0\amp ; rI , 1908 . ] Atmosphere and A By applying the results of S for , we find for the atmospheric 1adiation absorbed in this upper layer , The terrestrial radiation absorbed in the layer is Hence if , the total absorption , apart from that of solar radiation , is radiation from the layer in case is downwards , upwards , or in all . As we expect , the total radiation is less than the total absorption . If the were isothermal the amount of absorption by it would be the same , but the radiation would be in each direction , where is the intensity of radiation corresponding to the temperature of the layer , i.e. is , since in the lower layer . The radiation would therefore exceed the absorption by These amounts are too large to be supplied by the absorption of solar radiation in the upper half of the atmosphere , and we conclude that we could not have the isothermal state for so large a part of the upper atmosphere . If such a state existed at any time the temperature of the layer would fall , and this would allow the convection currents of the lower atmosphere to penetrate to greater heights and establish the state in the lower part of ] layer . We proceed to consider the case when the diyision is taken to be at . For or or For constant For VOL. LXXXII.\mdash ; A. Mr. E. Gold . The lsothermal Layer of the [ Oct. 5 , If denote the radiation to earth of the layer 4 to and the radiation to space of the layer 4 to , we find ; We find as above for the atmospheric and terrestrial radiation absorbed in the upper lay er , giving for the total absorption , apart from that of solar radiation if The radiation from the layer if the law still held would be which is much less than the absorption . If this layer were isothermal , the radiation from it in each direction would be where corresponds to the temperature of the layer , i.e. , I. The radiation is therefore and does not exceed the absorption apart from that of solar radiation . We conclude that if the outer layer of the atmosphere is isothermal it must extend at least until the layer is reached . It appears also that the greater the power of the atmosphere for terrestrial radiation the greater will be the height at which the isotbermal condition begins , apart from other considerations . The radiation from the layer to is down , up , or in all . The absorption in it is from the outer layer , and from the earth , or if The radiation therefore exceeds the absorption in this layer by 1908 . Atmospnere A and this must be made up by absorption of solar radiation and by convection of from the earth 's surface either in the form of warmed air or water vapour . If we take the mean value to be , and assume that solar radiation and convection are absent , and that in consequence the temperature of the layer falls uniformly , the fall per minute is , or about 1o C. in 24 hours if I correspond to a temperature 30 A. The radiation to earth from the atmosphere if up to , and is constant afterwards , is Frol measurements made at urich by Maurer , was found that the radiation from the atmosphere was calories per minute , the air tennperature C. , and the of the observing station being 440 metres above M.S.L. This gives a down radiation equal to Similar measurements made at Rauris ( 950 metres ) , at a temperature of C. , gave for the atmospheric radiation calories per minute or found values for the effec.tive temperature of the sky from adiation measurements from C. to C. With a cirrus haze he found C. If we take a 1llean value C. , we get for the ratio of sky radiation to that from a black body at temperature C. , the value These values agree best with the values obtained on assumption ( 1 ) regarding the absorbing power of the atmosphere . The radiation from the layer to is The radiation absorbed comes from the earth , from the layer to and from the outer layer to The amounts from these three sources are respectively and Thus if total absorption in the layer to is The balance of energy to be supplied by solar radiation and convection is * Hann , ' Lehrbuch der Meteorologie , ' p. 36 . ' ' Temperature of the Moon Mr. E. Gold . The Isothermal of the [ Oct. 5 , By subtracting these values from those found for the more extensive layer , we get the energy to be supplied by convection and solar radiation to the layer to , i.e. , These amounts could be supplied by absorption of solar radiation alone , so that there will be little vertical convection above . In fact , in case ( 4 ) the layer is absorbing more energy than it radiates . The outward radiation across the outer limit of the atmosphere in the case when the layer above is isothermal is ; or if But this radiation must be equal to the difference between the incident and the reflected solar radiation , including in the reflected , the part of the diffused radiation which is returned to space , say one-half . According to Abbott and Foul , *clouds reflect 65 per cent. of th ' solar radiation . We may take the amount of diffused radiation to be 40 per cent. or to the cloud level l per cent. Thus , if there were no clouds present the incident solar radiation which the above to balance would be 80 per cent. of the total incident solar radiation , and if clouds were present the amount would be 100 per cent. per cent. , so that if the average intensity of solar radiation , the temperature of the upper layer in the cases of boreater absorption must be than that corresponding to the isothermal state from upwards . The presence of clouds will not materially aHect the terrestrial and atmospheric radiation , since they reflect it but little and if they absorb they will also radiate for the same wave-lengths . VII . Application to the Consideratvon of the Daof the Earth 's If we would apply our results to a consideration of the day and night 'Annals of Astrophysical Observatory of the Smithsonian Institution , ' 1908 , p. 144 . , p. 129 . 1908 . ] and Atmospheric Radiation . temperature of the earth 's surface as Pointing *has(ione , we find , if we neglect oonduction , where are the diations at the time of maximum and temperature , is the downward atmospheric radiation , and are the rates at which energy is convected from the surface or is being lost by eyaporation . is probably small and may be positive or ative , but will be considerable . To produce an annual rainfall of 200 cm . , which we may take as value for the equatorial zone , the rate at which energy is lost by evaporation is calories per minute per . If the process goes on only the day , the average rate is per nlinute , and it seems fair to take the rate at the time of maximum temperature to be at least twice the average rate , so that we may put calories per minute . and taking the mean air temperature to be 30 A. , so that , we or and ( i ) or ( ii ) two cases corresponding to the two assumptions as to the absorbing power of the atmosphere . The temperatures would be A. or 34 A. A. or 29 A. At an altitude of 5 kilometres , oolresponding to a pressure equal to half the surface pressure , we have ( i ) or in the two cases . Further , nearly , and in order to obtain an approximate value for let us put it equal to , where is the mean air temperature . The value of will be or that the surface values are correct . The equations for then become . Mag , 1907 . See Angstrom , ' Met . Zeit 1901 , p. 187 . The Isothermat Layer of the Atmosphere , etc. or , ( ii ) where A. , corresponding to a sea-level temperature of A. These give A. ( i ) or 31 A. ( ii ) , and the value of is nearly . The values of are A. ( i ) and 2 1o A. ( ii ) . These results indicate that the effect of solar radiation would be to set up convective streams in the atmosphere for a considerable height above an elevated plateau . Thus in case ( i ) , at the time of the maximum , it would be necessary to ascend kilometres with an adiabatic gradient before reaching a place where the temperature was equal to the mean daily temperature at the surface ; and the effect of radiation in the atmosphere would not be in the direction of the adiabatic fall , since this fall would be in the lower layers of the atmosphere over the plateau , and would , in fact , be istent with radiation equilibrium to a height at least to that at which the pressure was equal to half the pressure at the surface of the plateau .

rspa_1909_0007

0950-1207

Note on the effect of hydrogen on the discharge of negative electricity from hot platinum.

71

72

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

Professor H. A. Wilson, F. R. S.

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6.0.4

http://dx.doi.org/10.1098/rspa.1909.0007

en

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10.1098/rspa.1909.0007

Tables

Electricity

Tables

]\gt ; Note on the Effect of Hydrogen on the of Electricity from Hot Platinum . By Professor H. A. WILSON , F.B.S. , King 's , London . ( Received October 6 , \mdash ; Read November 19 , 1908 . ) In a recent paperlon " " The Effect of Hydrogen on the Discharge of Negative Electricity from Hot Platinum , a calculation of the thickness of the double layer on the surface and of the number of free electrons inside the . Professor O. W. Richardson has pointed out to me that two terms in of the equations , one of which I discarded as being small compared , ith } other , are really of the same order of nitude . The results of the calculation are consequently wrong , and the estimate of the number of free electrons is considerably too high . The difficulty mentioned in the paper , that the required to raise the temperature of the electrons is apparently reater than that required to raise the temperatul.e of the platinmn , consequently disappears . In the equation the terms and 1 are quite igible compared with , so that we get , which gives , without further approximation , . Substituting , and , this gives . Comparing this with , we . 'Phil . Trans vol. 208 , A 432 . . cit. , p. 270 . On the of Electricity Hot Platmum . Now , since , we see that is equal to the gas constant ; hence . Hence If we take two values of , and , and the corresponding values and , we get This equation , with the values found for A and , gives hence . The expression for then gives the values : Q. A. cm . The five values of agree as well as could be expected . ince and is about , we get . Patterson* calculated the number of free electrons per cubic centimetre of platinum from the change in its resistance due to a magnetic field , on J. J. Thomson 's theory , and got It is interesting to apply the formula for to platinum polarised with hydrogen in dilute sulphuric acid . The potential fall in this case is about volt , which corresponds to a value of about . If , then , we suppose to be small , which is the case in at high pressures , we get , which gives , at cm . The thickness of the double layer in this case has been estimated by several observers from the polarisation capacity and found to be about cm . ' Phil. Mag 6 , vol. 3 , p. 643 .

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0950-1207

The yielding of the earth to disturbing forces.

73

88

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

A. E. H. Love, F. R. S.

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10.1098/rspa.1909.0008

Fluid Dynamics

Tables

Fluid Dynamics

]\gt ; The Yietding of the Earth to Forces . By A. E. H. LovE , edleian Professor of Natural in the University of Oxford . ( Received November 28 , 1908 , \mdash ; Read Januar.y14 , 1909 . ) 1 . Any estimate of the rigidity of the Earth must be based partly on some obscryations which a deformation of the Earth 's surface can be inferred , . and partly on some hypothesis as to the internal constitution of the Eartb . The observations may be concerned with tides of period , variations of the vertical variations of latitude , and so on . The hypothesis must relate to the arrangement of the matter as ards density in different , and to the state of the parts in respect of solidity , compressibility , and so on . In the simplest , the one on which Lord Kelvin 's well-known estinlat was based , the Earth is treated as absolutely and of uniform density and rigidity . This hypothesis was adopted to simplify the problem , not because it is a true one . No matter is absolutely incomessible , and . the Earth is not a body of uniform density . It cannot be held to be probable that it is a body of uniform rigidity . But when any part of the hypothesis , e.g. , the assumption of uniform density , is discarded , the estimate of rigidity is affected . Different estimates are obtained when different laws of density are assumed . , whatever hypothesis we adopt as reg the ement of the matter , so as we consider tlJe Earth to be absolutely incompressible and of uniform rigidity , different estimates of this rigidity are obtained by observations of different phenomena . Variations of the vertical may one value , variations of latitude a notably different value . It follows that ' the rigidity of the " " is not a definite physical constant . But there are two determinate constant numbers related to the methods that have been used for , estimates of the rigidity of the Earth . One of these numbers specifies the amount by which the surface of the Earth yields to forces of the type of the erenerating attractions of the Sun and Moon . The other number specifies the amount by which the potential of the Earth is altel.ed through the rearrangement of the matter within it when this matter is displaced by the deforming influence of Sun and Moon . If we adopt the ordinarily-accepted theory of the Figure of the , the so-called theory of ' fluid equilibrium and if we make the very probable assumption that the physical constants of the For Lord Kelvin 's work on the subject , reference may be made to his ' Math. and Phys. Papers , ' vol. 3 , or to omson and Tait 's 'Nat . Phil Part 2 , SS Prof. A. E. H. Love . [ Nov. 28 , matter within the Earth , such as the density or the incompressibility , are nearly uniform over any spherical surface having its centre at the Earth 's centre , we can determine both these numbers without introducing any additional hypothesis as to the law of density or the state of the matter . We shall find , in fact , that observations of variations of latitude lead to a determination of the number related to the inequality of potential , and that , when this number is known , observations of variations of the vertical lead to a determination of the number related to the inequality of added , December 15 , 1908.\mdash ; This statement needs , perhaps , some additional qualification . It is assumed that , in calculating the two numbers from the two kinds of observations , we may adopt an equilibrium theory of the deformations produced the Earth by the corresponding forces . If the constitution of the Earth is really such that an equilibrium theory of the effects produced in it by these forces is inadequate , we should expect a marked discordance of phase between the inequality of figure produced and the force it . Now Hecker 's observations , cited in S6 below , show that , in the case of the semidiurnal term in the variation of the vertical due to the lunar deflexion of gravity , the agreement of phase is close . If , however , an equilibrium theory is adequate , as it appears to be , for the semidiurnal corporeal tide , a similar must be adequate for the corporeal tides of period and for the variations of latitude . ] 2 . We take to represent the mean radius of the Earth and to represent the mean density . In the undisturbed state the Earth will be taken to rotate as if about a principal axis . We shall denote by the density , pressure , and potential in the undisturbed state . In the theory of fluid equilibrium is supposed that , for a first approximation , may be taken to be a function of , the distance of a point from the centre . If , were known , would be known , and then would be determined by the equation and the condition that vanishes at . In the same theory it is supposed that , for a second approximation , the surfaces of equal density , which are also equipotential surfaces and surfaces of equal pressure , may be regarded as oblate ellipsoids of revolution about the polar axis , the ellipticity of the ellipsoids a function of , which is small for all values of in the . Thus a surface of equal density , ooriven , to a first approximation , by the equation , is given , to a second approximation , by the equation 1908 . ] The Yielding of the to Disturbing Forces . where is the colatitude measured from the polar axis . Then the theory leads to the equation* , ( 1 ) where denotes the value of at ? denotes the ular velocity of rotation , and denotes the value of gravity at the surface , so that constant . being denoted by . Further , if , A denote the moments of inertia of the body about its axis of figure and a perpendicular axis passing through its centre , there is no difficulty in obtaining the equation . ( 2 ) In calculating the constant of precession , we may , with sufficient approximation , take A to be given the formula . ( 3 ) The values of are pretty accurately known by obSeryation . This outline of the theory is sufficient for our purpose . We shall not need to take account of those further refinements in which quantities of the order are retailled . 3 . Now consider the rotating body subjected to deforming forces . With a view to calculating the deformation we may yard the ects of rotation and consider the undisturbed body as spherical and of density at a poin distant ! from its centre . Let the forces be derived from a potential which , in the region , is expressible as a sum of spherical solid harmonics of positive integral degrees . Let be a spherical harmonic term of this sum , degree of this term a positive integer . Under the action of the forces derived from the potential the body will be deformed . Let denote the radial component of the displacement , and the cubical dilatation at any point P. The density at in the disturbed state will not be the value of which belongs to the point , but it will be . ( 4 Whatever theory of the constitution of the Earth may be adopted provided that the physical constants , such as density or incompressibility , are *Cf . J. H. Pratt , Figure of the Earth , ' 1865 edition , p. 79 . See the note added at the end of S 1 . Prof. A. E. H. Love . [ Nov. 28 , functions of , the quantities and will be products of the spherical solid harmonic and some functions of . The potential V of the disturbed body at a point will not be but it will be the sum of and the potentials due to : ( i ) a volume distribution of density throughout the region , and ( ii ) a surface distribution of density over the surface . Hence the potential will differ from by terms which are the products of the spherical solid harmonic and functions of . In the most important cases , and we may write where , functions of , and constant has been inserted in the expression for for the sake of convenience . If , in fact , is a periodic term of the tide-generating potential , is the " " true equilibrium \ldquo ; of the corresponding tide , that is to say , it is the height of the harmonic inequality which the forces answering to would produce in an ocean a igid spherical nucleus , of the same size and mass as the Earth , if the depth and density of the ocean were negligible . From the definition of we easily find the formula . ( 6 ) In what follows we shall write for and for , so that the equation of the disturbed surface is and the disturbance of potential at the surface is . The numbers referred to above as the inequality of figure and the inequality of potential are the numbers and 4 . The horizontal pendulum is an instrument for measuring small displacements of the vertical . The deflexion is proportional to the gravitational attraction in a direction at right angles to the axis of the instrument . The attraction in question may be regarded as due to the Earth , the Sun , and the Moon . rfhe axis of the instrument may be taken to , be normal to the disturbed surface . The forces acting on the pendulum are : ( i ) a force derived from the potential ; ( ii ) a force derived from the potential ; ( iii ) the component of undisturbed gravity tangential to the surface . If is the disturbing potential due to the Moon alone , the three forces act in the plane containing the Earth 's centre , the Moon 's centre , and the bob of the pendulum . We calculate the forces in this case , rinning with the force ( iii ) . We have 1908 . ] The eldang othe to Iorces . 7/ where denotes the Moon 's mass , the distance of the Earth 's centre from the Moon 's centre , the distance of a point from the Earth 's centre , the angle between the radius vector drawn from the Earth 's centre to the point and the radius vector drawn from the Earth 's centre to the Moon 's centre . The surface is approximately an ellipsoid of revolution , and its eccentricity is given , correctly to the first order , by the equation The angle between the central radius vector and the normal at any point of the ellipsoid is , to the first order , . Hence the component of gravity tangential to the surface is , to the first order , , or sense of this force is that in which increases . The nitudes of the other forces can be written down ; and the resultant force acting at angles to the axis of the instrument is . ( 7 ) If the Earth were absolutely rigid , the force would be . Hence the ratio of the observed deflexion of the pendulum to that which would occur if the Earth were absolutely rigid is This result*has been obtained by arding W as the Moon 's tidepotential , but it is clear that the same expression would be arrived at if were any term of the tide-generating potential due to the action of both Sun and Moon , for the nbers h and are the same for all potentials expressed by spherical solid harmonics of the second degree . 1 An approximate expression for the of any oceanic tide which follows the equilibrium law may be calculated by ' the depth and density of the ocean . Let be a term of the potential . Then the corresponding inequality of the surface of the ocean , calculated in the way described , is , and the inequality of the nucleus is . Thus the height of the corresponding is ated as *An equivalent result for an incompressible sphere with a special of density is given W. Schweydar , ' sir Geophysik , ' vol. 9 , , p. 41 , but his argument , in one place , so briefly expressed that I lind it difficult to follow . This result is , of course , well known . Prof A. E. H. Love . [ Nov. 28 , , and the ratio of the actual height to the true equilibrium height is . Apart , therefore , from a correction depending on the depth of the ocean , the self-attraction of the waters , and the pressure of the tidal wave upon nucleus , the quantity which is measured by means of observations of the long period tides is the as that which is measured by means of the horizontal pendulum . It is , therefore , not surprising that estimates of the idity of the Earth which are based on observations of the fortnightly tide are nearly the same as those which are based on observations of the variations of the vertical . 6 . Lord estimate was based chiefly on observations of the fortnightly tide in the Indian Ocean , from which observations it was inferred that ( 8 ) very nearly . This result has been confirmed by W. Schweydar , an analysis of much more numerous observations of fortnightly tides , and also by an analysis of several sets of observations made with horizontal pendulums . But the most st1iking confirmation is to be found in the investigations of O. Hecker , conducted by means of horizontal pendulums . His very precise and consistent results show that the equation ( 8 ) is remarkably exact . 7 . An vsis of many series of observations of variations of latitude led S. C. Chandler to the conclusion that such motions are periodic with a period of about 427 days . If the Earth were an absolutely body , the figure of an oblate ellipsoid of revolution , with ellipticity equal to that found by geodetic observations , and having that ratio of moments of inertia about polar and equatorial axes which is deduced from the observed amount of precession , it would execute a free oscillation about the steady motion of rotation in a period of about 306 days , and the variations of latitude would have this period . The thening of the period from 306 days to 427 days is due to the defect of tTidity . The result that a yielding of the Earth would then the period was obtained by S. Newcomb , S and the period was ated theoretically by S. S. Hough The theory has been placed in a very clear light by G. 8 . We take the undisturbed axis of figure as axis of , and choose axes of and in the equatorial plane . Let denote the cosines of the angles which the instantaneous axis of the Earth 's rotation makes with the axes of . cit. " " Beobachtungen an Horizontalpendeln Veroffentlichung . Preuss . geodatischen Institutes , ' No. 22 , Berlin , 1907 . 'Astronomical Journal , ' , 12 , 16 , 19 , 21 , 22 ( 1891\mdash ; 1902 ) . S 'Mon . Not . R. Astr . Soc 1892 . 'Phil . Trans , vol. 187 , 1896 . Zeitschr . . Math. . Phys vol. 52 , 1906 , p. 275 . and . The yielding of the Earth may be computed as the yielding of a sphere to forces derived from a potential , where . ( 9 ) It is , therefore , expressed by a radial displacement and a dilatation where This displacement of the matter is to be superposed upon the inequality due to uniform rotation about the axis of . The moments and products of inertia of the deformed rotating body with respect to the axes of can be calculated . The angular velocity of the frame of moving axes of has components referred to their instantaneous positions . The equations of motion of the body with the calculated moments and products of inertia referred to the moving axes can be formed by the ordinary methods of dynamics , and the period of free nutation can be deduced . This is ' method , generalised by the inclusion of the effect of compressibility . 9 . It is found that , to the first order , the moments of inertia , are unaltered , but that small products of inertia are introduced . The values of these products are iven , correctly to the first order , by the equations ; ( 10 ) where the integrations in the left-hand members are taken through mass of the disturbed body . By means of the result ( 2 ) we obtain the products of inertia in the , ( 11 ) where . ( 12 ) The period of free nutation is given by the equation * The formula ( 11 ) and ( 13 ) , and a formula equivalent to ( 12 ) in the case of incompressibility , were given by Herglotz ( loc. cit The constant is equivalent , in this case , to the constant which he denotes by . The result expressed by ( 12 ) and ( 13 ) agrees with that obtained by Hough if the initial density is uniform and the matter incompressible . Prof. A. E. H. Love . [ Nov. 28 , If the Earth were absolutely rigid the period would be , ( 14 ) so that the period is lengthened by the yielding in the ratio 1 : Now if we introduce the results ( 1 ) and ( 6 ) , we find . ( 15 ) It appears , therefore , that the constant is determined . 10 . The denoted by is known from the constant of precession to be about 306 days ; the period denoted by is known from observations of variations of latitude to be about 427 days . The value of is about , and the value of is about . Hence we find nearly . ( 16 ) Since nearly , and nearly , we find nearly . ( 17 ) These results may be expressed as follows : inequality produced in the potential of the Earth , near its surface , by the action of the Sun and Moon , is about four-fifteenths of the tide-generating potential , and the inequality produced in the surface of the Earth is about three-fifths of the true equilibrium height of the tide . The results hold for each of the partial tides answering to the seyeral periodic terms of the tide-generating potential . 11 . If the matter within the Earth is assumed to be absolutely incom- pressible and of uniform density , we should have . If , further , it is assumed to be of uniform rigidity , the theory of the deformation of an elastic sphere would give the result ( 18 ) But actual relation , obtained from the tides and the variations of the vertical , then gives , or . Since nearly in C.G.S. units , we have nearly . Thus the rigidity calculated by this method is about the rigidity of steel ( Kelvin 's estimate ) . If , instead of using the result , we use the value for , we find from ( 18 ) the value , or about . The approximate agreement of this estimate of rigidity with that which has been deduced from the rate of transmission of the second phase of earthquake waves to great distances should not , I think , be regarded as of much importance . 12 . One way of deducing an estimate of rigidity from observations of he Of orces . variations of latitude combined with the hypotheses of absolute incomand uniform density and rigidity is to give to equation ( 15 ) actual values , so that nearly . This method gives nearly , and then , by equation ( 18 ) , we find nearly . A second way is to give to and their actual values , and to the value , which it would have , according to the theory of fluid equilibrium , if the matter were homogeneous . This method* gives and nearly . A third way is to give to and their actual . values , and to and the values which , according to the theory of fluid equilibrium and the theory of precession , they would have if the matter ere ] . We should then find and . In view of these results the approximate reement of 's result with Kelvin 's estimate does not seem to have much importance . . In order to obtain an estimate of the idity of the Earth from observations of variations of latitude , it seems to be necessary to combine the observations with some which will adnit of the ellipticity and the constant of precession , their actual values . One of the simplest admissible constitutions is that which has been proposed by E. Wiechert . He takes the Earth to consist of a solid nucleus of density enclosed in a solid shell of density , the ratio of the radius of the nucleus to the outer radius of the shell being . If we make the further assumptions that there is no slipping at the interface between nucleus and shell , and that the matter is absolutely incompressible and of uniform rigidity , we can calculate the numbers and in terms of the rigidity . If ; then , the rigidity is adjusted so that the period of free nutation may be 427 days , there results nearly . If , however , the rigidity is . adjusted so that the displacement of a horizontal pendulum by tideenerating forces may be two-thirds of what it would be if the Earth were absolutely , there results nearly . The first of these results was obtained by by transforming the equations of elastic equilibrium for a body of variable density , and solving the transformed equations . The second result was obtained by Schweydar using some * It in effect , the method adopted by Hough ( loc. ) . This statement is not meant to suggest any doubt as to Kelvin 's general conclusion that the Earth , as a whole , is a very rigid body . All the astronomical evidence confirms . this conclusion . Kelvin 's rather precise numerical estimate of rigidity , as or 8 times dynes per square centimetre , appears to be rather well by Hough 's estimate of about 9 times the same . Hough described his estimate as founded upon a " " reasonable hypothesis Two other reasonable hypotheses lead to and 17 , where Hough 's leads to 9 . These numbers confirm the general conclusion , not the numerical estimate . Gottingen Nacbrichten , ' 1897 . VOL. LXXXII.\mdash ; A. Prof A. E. H. Love . [ Nov. 28 , analysis due to Chree . By an extension of the analysis which was applied to such problems by Kelvin , I have found the values and . The discrepancy between the two estimates of idity , deduced respectively from the period of free nutation and the displacement of horizontal pendulums , shows , as we should expect , that the assumption of uniform rigidity is untenable . Schweydar has proposed to assume that there is one uniform rigidity for the nucleus and another for the shell , and finds that the results of the two kinds of observations can be reconciled by taking\mdash ; for the nucleus for the shell The values which I have found are and . The slight between my results and those of Herglotz and Schweydar due to slight differences in the assumed data . The general conclusion , that the rigidity of the nucleus may be much greater than that of ordinary materials at the surface , and the idity of the shell smaller than that of most rocks , is more important than the numerical values . 14 . The results } have just been described may be taken as indicating the effect of heterogeneity on the estimate of rigidity . It appears that increase of density towards the centre compensates to some extent for defect of rigidity , and that increase of rigidity towards the centre can compensate for a considerable defect of idity in the superficial portions . The effect of compressibility is not known , it seems improbable that the yielding of a compressible sphere with an assigned rigidity should be less than that of an incompressible one . The result that the rigidity of Wiechert 's shell may be less than that of most surface rocks led Schweydar to adopt Wiechert 's suggestion that there may exist a plastic sheet between the nucleus and the shell . I think it may be regarded as certain that there is not within a of 1400 km . a continuous layer of molten matter , separating the inner portions of the Earth 's body from the outer portions , and behaving as a fluid in respect of forces of the } of tide-generating forces . In order that the astronomical motions may be performed as we know they are , and that the surface not yield to such forces more than we know it does , the portions of the Earth which are outside such a sheet , if it exists , must be ' Cambridge PhiL Soc. Trans , 1889 . rigidities of many kinds of granite and marble lie between and C.G.S. units . See the memoir by F. D. Adams and E. G. Coker , 'Publications of the Carnegie Institution , ' No. 46 . My attempt to determine this effect in ' Cambridge Phil. Soc. Trans vol. 16 , 1900 , does not now appear to me to be satisfactory . 1908 . ] The Yielding of the to Disturbing Forces . much more we can reasonably conceive them to be . No amount of rigidity of the nucleus would enable us to satisfy the conditions . To illustrate this statement quantitatively it will be to set down some of the analysis of the problem . 15 . We consider a sphere of matter stratified in concentric spherical layers . The matter in any layer is taken to be of uniform density and rigidity , these quantities from layer to layer , and it is taken to be absolutely incompressible . If we discard the assumption of inCOItlpressibility , the problem becomes much more difficult . We suppose the sphere to be deformed by body forces derived from a potential , which is a spherical solid harmonic of the . The initial pressure and potential in ] become and , where is the potential due to the inequalities at the disturbed boundaries of all the layers . Let denote the displacement at any point within a layer . The equations of equilibrium are three equations of the type , ( 19 ) and , since the undisturbed state is one of equilibriuul , we can replace these by equations of the type . ( 20 ) have the condition of incompressibility . 1 ) To solve these equations , we put , ( 22 ) where is an inteo.ero , positive or ative , and are to be derived from by replacing successively by and , and successively by and ; also are spherical solid harmonics of the degree , and is a spherical solid harmonic of the defined by the equation . ( 23 ) The summation refers to all the values of that need be taken . 16 . With a view to the expression of the radial displacement and the components of traction across a spherical surface , it is conyenient to introduce a spherical solid harmonic of the degree defined by the equation . ( 24 ) Prof. A. E. H. Love . [ Nov. 28 , Then we find . ( 25 ) The value of at can be expressed by means of ( 25 ) as a sum of spherical surface harmonics of positive degrees , say . We shall write for the corresponding sum of spherical solid harmonics of positive degrees , so that . If is a boundary of a layer in the undisturbed state , and are the densities just inside and just outside this surface , the contribution of this boundary to the inequality of potential is or , ( 26 ) according as the point at which is estimated is within or without the surface . The value of is the sum of such contributions from all the bounding surfaces . The -component of traction across the surface is the value at of the expression or . ( 27 ) The radial component of the traction is the value at of the expression . ( 28 ) The tangential traction across the surface is a vector quantity which has a definite magnitude and direction at each point of surface , the direction being at right angles to the central radius vector . We may resolve this vector into components parallel to the axes . The component parallel to the axis of is obtained by subtracting the -component of the radial traction from the -component of the resultant traction . We find that the -component of the tangential traction is the value at of the expression . ( 29 ) 1908 . ] The Yielding of the to Forces . 17 . The conditions to be satisfied at a disturbed boundary of a layer are conditions of continuity of displacement and traction . Except in the case of the normal traction , it is sufficient to form the conditions at the undisturbed boundary . Let letters with single accents denote the values of quantities such as and just inside a boundary , and letters with double accents denote the values of the corresponding quantities outside the boundary . The condition of continuity of the -component of disis ( 30 ) where we have picked out all the terms which contain spherical surface harmonics of the same degree . We may now as positive . The spherical solid harmonic of the degree , ' vanishes at the spherical surface , and therefore vanishes for all finite values of . We have two other like expressions which vanish in virtue of the conditions of continuity of the y ? - and -components of displacement . Hence , by the usual method , we deduce the two equations same with doubly accented and letters , ( 31 ) same with doubly accented letters . ( 32 ) The condition of continuity of the -component of traction is same with doubly accented letters . ( 33 ) Prof. A. E. H. Love . [ Nov. 28 , From the three equations ( two independent ) of this type we obtain in the usual way equation - same with doubly accented letters . ( 34 ) In forming the condition of continuity of normal traction at a disturbed boundary , we may calculate all the terms that arise from the additional stress as if the boundary were the sphere The only terms in which we need take account of the displacement of the boundary are those that arise from the initial stress . The initial stress being hydrostatic pressure , the corresponding normal component of traction across any surface at a point is the pressure at that point with its sign changed . The initial pressure at a point on the surface is expressible as the value of at a point on the surface . When is a boundary of a layer , is continuous in crossing the boundary , but is not , for its value is , and is discontinuous . Hence the condition of continuity of normal traction at the surface is - same with doubly accented letters . It is convenient to eliminate and by means of the equation ( 34 ) . We thus obtain the equation same with doubly accented lettel'S . ( 35 ) It is clear from these equations that in general the ] functions of type which occur are , and the only functions of type which occur are and the corresponding 's and . In the central portion of the sphere the only functions which occur are those of 1908 . ] The eldvnq oto orces . the types . All these can be expressed in terms of byolvi ( linear equations . It appears that and are multiples of the surface harmonic I obtained the results stated in S13 above by . the above analysis to the case of a central spherical nucleus and an shell with Wiechert 's values for the densities and radii . 18 . We prcceed to the example of an absolutely rigid nucleus , of density and , separated by a layer of fluid* of density from a solid shell of density , rigidity , and inner and outer radii and , the whole subjected to body force derived from a potential , which is a spherical solid harmonic of the second . Let denote the spherical solid harmonics of the second degree to which the radial displacement becomes equal at tho surfaces respectively . Then at any point in the solid shell we haVe ( 36 ) and . ( 37 ) The displacement at any point in the solid shell is expressed in terms of the functions . Equation ( 25 ) gives ( 38 ) The traction vanishes at and at , and hence we the ( 39 ) The condition of continuity of normal traction at is obtained from equation in the form In regard to the question of the cy of the statical theory to determine the behaviour of the supposed fluid layer , reference may be made to the Note at the end of S :88 The Yietding of the Earth to Disturbing Forces . and the condition that the normal traction at vanishes is obtained in the same way in the form . ( 41 ) 19 . It is sufficient to consider the case in which , or ) density of the fluid layer is the same as that of the solid enclosing shell . Writing for the value of gravity at the surface and for the mean density , so that and putting ( 42 ) we find that the value of is given by the equation . ( 43 ) 20 . Suppose the fluid layer to be thin , and consider the case where the density is distributed to Wiechert 's law . We have then that nearly , and adjusting so that may have its actual value , we find nearly . It appears , therefore , , even if the solid nucleus were osolutely , and the enclosing shell were 1400 km . thick , the presence of a layer of fluid separating the nucleus from the shell would increase very much the yielding of the surface . To prevent the surface from yielding more than it actually does , the rigidity of the shell would have to be nearly five times that of steel . If the enclosing shell were thinner , a still higher rigidity would be needed . For example , if it were 64 km . thick , and of density half the mean density , or about , the requisite rigidity of the enclosing shell , the nucleus being absolutely rigid and the fluid layer thin , would be about dynes per square centimetre , or about sixty-six times the rigidity of steel . These numbers seem to me to be decisive against the hypothesis of the fluid layer . This conclusion does not negative the possible existence of areas of continental dimensions beneath which there may be molten matter . It means that such areas must be isolated ; the molten matter beneath them can form a continuous sheet separating a central body from an enclosing crust . The conclusion does not negative the possible existence of a layer of comparatively small rigidity ; but , if there is such a layer , it must be rigid enough to prevent a finite slipping of the enclosing crust over the central body .

rspa_1909_0009

0950-1207

The relation of the earth's free precessional nutation to its resistance against tidal deformation.

89

96

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

Prof. J. Larmor, Sec. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1909.0009

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1909_0009

10.1098/rspa.1909.0009

Fluid Dynamics

Tables

Fluid Dynamics

]\gt ; The of the Earth 's Free Nutation to its Resistance Tidal By Prof. J. LARLfoIt , Sec. R.S. ( Received December 18 , 1908 , \mdash ; Read January 14 , 1909 . ) The modern investigation of the of the Earth 's axis of rotation : considered as a physical problem relating to the actual non-rigid Earth , be said to have been initiated in Lord Kelvin 's address to the Physical Section of the British Association in 1876 . After referring*to the scrutin of the recorded observations of of latitudes , conducted by Peters and independently by Maxwell in , in search of the ular Eulerian free period of 306 days which would belong to a Earth , negative results , he insisted that the irregular motions brought out in analyses are not merely due to imperfections , but represent true motions of the Pole , due to displacement of terrestrial material . For example , he estimates that shifts of material , of type , are competent to produce displacements of the axis of rotation from 1/ 2 to 1/ 20 of a second of arc . A sudden shift of material on the Earth will not at once affect the axis of rotation , but will start it into motion round the altered axis of inertia , with a period of 306 days if the Earth were which will go on displacing the Pole until it is damped out by the frictional effects of the tidal motions thus inated . A radius of rotation of 1 second of would raise an ocean tide of the same period as the rotation , ) as ntuch as 11 cm . of maximum rise and fall . Thus the motion of the Pole is to be considered as continually renewed by meteorological and other displacements , as it is damped off by tidal and elastic friction ; it therefore , perhaps , not to be expected that it would show much periodicity , though the movements were eminently worthy of close investigation . Their nature was examined more closely by Newcomb at Kelvin 's request ; but not much more had been done arding their cause when Chandler announced that the records of changes of latitude did actually indicate a period of precession\mdash ; of 427 days , however , instead of the Eulerian period of 306 days , which , if any , had previously been taken for ranted . Soon after , in 1890 , observations were organised systematically by the International Geodetic Union on the motion of Prof. Foerster , of Berlin ; already , in 1891 , he was able to inform Lord Kelvin that a comparison Reprint in ' Popular Lectures and Addresses , ' vol. 2 , see pp. Prof. J. Larmor . Earth 's Free Preces.vional [ Dec. 18 , of 'European observations with synchronous ones made at Honolulu gave direct proof of his conclusion of lS76 ( supra ) , " " that irregular movements of the Earth 's axis to the extent of half a second may be produced by the temporary changes of sea level due to meteorological causes.\ldquo ; * In the following year the synchronous observations had already indicated periodicity , apparently in about days , considerably less than Chandler 's estimate , which , however , longer observation has since confirmed substantially . Lord Kelvin remarks in his next annual address as Newcomb , in a letter which I received from him last December , gave what seems to me undoubtedly the true explanation of this apparent discrepance from dynanlical theory , attributing it to elastic yielding of the Earth as a whole . He added a suggestion , especially to myself , that investigation of the periodic variations of latitude may prove to be the best means of determining approximately the of the Earth . As it is , we have now for the first lime what seems to be a quite decisive demonstration of elastic yielding of the Earth as a whole , under the influence of a force , whether of centrifugal force round a axis , as in the present case , or of tide-generating influences of the Sun and lIoon , with reference to which I first raised the question of elastic yielding of the Earth 's material many years ago But " " when we con sider how much water falls on Europe and Asia during a month or two of rainy season , and how many weeks or months must pass before it gets to the sea , and where it has been in the interval and what has become of the air from which it fell , we need not wonder\ldquo ; that the amplitudes of the polar wanderings " " shoul often vary by 5 or 10 metres in the course of a few weeks or months It will be recalled that the main object of the calculations of Lord Kelvin , which assigns to the Earth as a whole an effective rigidity of the same order as that of steel , to combat the view then prevalent which assumed for the Earth a fluid interior . Even a solid shell of very considerable thickness , enclosing a fluid core , was thus ruled out , unless its were preternaturally rigid ; and it is clear that placing a solid core in the middle of the iluid interior cannot affect this conclusion so as an equilibrium theory is applicable , i.e. , so long as the layer of fluid material is not so thin or viscous as to prevent its adjusting itself immediate]y by flow to the alternating tidal stresses impressed from its solid walls . By passing to the other limit , and thus taking it so thin that the outer shell 'Presidential Address R.S. , ' Nov. 30 , 1891 ; 'Popular Lectures vol. 2 , p. 504 . Lord Kelvin 's investigations up to are collected in ' Math. and Phys. Papers vol. 3 , especially pp. ) 'Presidential Address R.S. , ' Nov. 30 , 1892 ; . cit. , p. 525 . 1908 . ] Nutation against practically rides on the solid nucleus , but without effective tangential stressconnection , we obtain a hypothesis to which this objection does not apply . In a brief note in 'Monthly Notices B.A.S. ' this year ( 1892 ) , Newcomb showed , by a general estimate , that the effect of elastic is competent to prolong the free period to about the amount required by observation . A formal mathematical discussion on the bases of calculation of the elastic deformation of a homogeneous sphere was first given by . S. S. , now H.M. Astronomer at the Cape of Good Hope , in a memoir on " " The Potation of an Elastic Spheroid in ' Phil. Trans 1896 . He concluded that the Chandler free period required an effective idity of the whole Earth of the order of that of steel , reeing with Lord Kelvin 's previous estimates from tidal phenomena ; and his result seems to have been substantially confirmed by more recent calculations , iving for the average effective idity estimates derived from various possible hypotheses and simplifying assumptions between extreme values and , while Hough 's estimate was put at . This shows an even striking degree of agreement in calculations necessarily vague on account of the unknown constitution of the Earth 's interior , especially in so far as observations of the equilibrium tides of long periods , and of the deviation of sea level due to tidal attraction which is essentially the same thing , lead to results of the same order as those of free precessional rotation . * It , indeed , suggests , as we shall actually recognise , that this internal terrestrial constitution really is not involved in these various phenomena , except in the common feature of determining the surface effects arising from a given tidal or rotational stress . The key to the matter , from the general point of view , is contained in the remark of that the free precession of the yielding Earth is the same as that of a rigid one of the shape that would result when the bulging arising from the centrifugal force of diurnal rotation is removed . It is not difficult to show , from geometrical considerations regarding momentum , that this result is general , and extends to an Earth of any degree of heterogeneity or plasticity . The argument may be reproduced in analytical form and rather wider scope , from another placeS ( with definition of I rewritten ) , as follows:\mdash ; Let be the ular velocity of the Earth about the instantaneous axis , *Cf . Prof. A. E. H. Love , ' Roy . Soc. Proc supra , p. 73 . To this paper I am indebtecf for information as to results of recent calculations . The identity of these two types runs through the discussions in Thomson and Tait 's ' Natural Philosophy . ' Proc. Camb . Phil. Soc May , 1896 , S E. H. Hills and J. Larmor , " " The Irregular Movement of the Earth 's Axis of Rotation ' Monthly Notices R.A.S. , ' Nov. , 1906 , p. 24 . Prof J. Larmor . Earth 's Free Precessional [ Dec. 18 , its components referred to the principal axes in the configuration that the Earth would have if the motion were steady . The Earth is deformed from this configuration by the inequality of centl.ifugal force due to the deviation the instantaneous axis from the axis , with which it would coincide if the motion were steady . This defrming force is the resultant of the centrifugal force , directed outwards from the instantaneous axis , and the reversed centrifugal force , directed inwards towards the principal axis in question . A linear law of elasticity applies to the small resultant of these two forces . If the same law applied to the two forces separately , the reversed force would the moments of inertia to certain values , which might , under hypotheses , be calculated from the theory of the deformation of an elastic sphere ; and the centrifugal force directed outwards from the instantaneous axis would produce a certain change of density at each internal point , and would raise a certain protuberance on the surface , which might be calculated by the same theory . Let I denote the moment of inertia ( about the instantaneous axis ) of a mass arranged as specified by this change of density and this protuberance . The instantaneous axis is a principal axis of this mass , and therefore the contributions of this mass to the components of moment of momentum are . The complete expressions for the components of moment of momentum are therefore The equations of motion referred to the axes are of the well-known vector type , When A and are equal , the third of them is where is the effective moment of inertia : when is null is thus constant , say , up to the first order . other two equations are which in the case of approximate symmetry involve a free period , and similarly in the general case , thus depending only on when I is small . The esult is that the period of the free precession is not days , as it would be for a rigid Earth , but approximately , where the 1908 . ] Nutation and Resistance against Tidal Deformation . 93 denominator is that difference of principal moments of inertia which would remain after the imposition of a bodily forcive potential , namely , that of the centrifugal force reversed , representing the zonal harmonic cos2 . The first part of , the term , corresponds to slight contraction of volume , which is immaterial as regards the desired quantity . The other part , , will produce an extension , of the same harmonic type as itself , the polar axis , which will in turn alter the potential of the Earth 's attraction at its own surface by , where the value of depends on its effective resistance to deformation . Moreover the Earth 's potential is at distant points , by Laplace 's formula , , which ives in the present special case ; and if , as in the actual circumstances , further harmonics do not occur to sensible amount , this expression holds right up to the Earth 's surface . The free surface , of ellipticity , is , where . The value of is determined by the constancy over the ocean surface of the total potential , as is the potential of the centrifugal force , viz. , of ; whence , equating to zero the coefficient of ( C\mdash ; A ) thus from data of the distribution of gravity , or of the form of the Earth 's surface , the value of , which determines the astronomical precession . Again , if taking off the centrifugal force would change C\mdash ; A to , it would alter by , which must , ing to the above specification of , be equal to . Thus Prof J. Larmor . 's Free Precessional [ Dec. 18 , Hence , if is the periodic time of actual free precession and is what it would be if the Earth were rigid , . This is the formula ( 15 ) in Prof. Love 's paper before referred to ; it is there deduced from a hypothesis of concentric spheroidal stratification of the Earth 's interior , after the manner of Laplace . We have found that , like Clairaut 's formula for gravity , this relation is independent of any hypothesis as to the Earth 's internal structure , except such as is involved in the definition and value of As is 1/ 289 and is found to be 428 days , and is 306 days , this relation makes equal to 4/ 15 . The values of corresponding to various moduli of rigidity and comsibility of the Earth considered as a eneous globe might perhaps be deduced and tabulated for comparison , from Lord Kelvin 's and similar elastic analysis . The height of the long-period equilibrium tides proyides different data ; corresponding to an extraneous tide-producing potential of this type , the absolute rise of the water is , from which has to be subtracted for the rise of the solid Earth due to this tide-producing potential , thus leaving a factor for the relative tide which alone can be the subject of observations . The reductions of tidal data for the Indian Ocean gave Kelvin and G. H. Darwin the for this factor , which is confirmed by more recent discussions : the observations of Hecker with a horizontal pendulum at the bottom of a well , which ] obviously determine the same thing , viz. , the change of level due to tide-producing potential , concur in a remarkable manner . Thus These values of and , as defined in the last paragraph , would not be independent for a homogeneous incompressible globe : they would , in eneral , require for their consistency both elasticity of volume and of form . The phenomena of free precession give the value of , but with reference to compression the polar axis ; those of tidal change of ] evel give the value of , or rather its mean value , with reference to compl.ession along axes in the neighbourhood of the equator . * This statement is the purest and simplest expression of the information to the solid Earth 's resistance to deforming forces that the data of periodic change of latitude Cf . Prof. Love , supra , p. 81 , to whom this proposition is substantially due , having been reached by him through analysis appropriate to a centrically stratified body . The quantities and , in other notation , enter essentially into the tidal discussions by Kelvin and Darwin in Thomson and Tait 's ' Not . Phil. ' 1908 . ] Nutation Deformation . 95 and of equilibrium ( i.e. , long-period ) tides can supply , prior to any hypothesis regarding the internal distribution and the effective elasticity or plasticity of its materials . [ Added February 2.\mdash ; It has been remarked above , after Lord ICelvin , that a sudden shift of material from one part of the Earth 's surface to another would alter the position of the principal axis of inertia round which the free precession of the Earth 's axis of rotation takes place , and thus cause a sharp bend in the path of the Pole . If the shift were merely local , such as an earthquake may be expected to produce , the effect would be inappreciable . The connection of sharp curvature in the path of the Pole with seismic disturbance , if it really exists , would thus be indirect , the earthquake being itself started possibly by the slight or other , of distribution of surface load , wluch are indicated by the disturbance of the free precession . But it is to be noticed that a seismic subsidence , if uncompensated by adjacent elevation , or vice versd , would be competent to produce sensible direct disturbance of the path of the Pole ; for water would have to flow , in part from distant regions , to fill up the defect of level thus produced . The same would be true for earthquake subsidence near coast lines , if it is compensated by rise of the land . In reply to an inquiry on this subject , Prof. Milne writes as follows:\mdash ; " " When a very large earthquake occurs on land , we find vertical and lateral cements of , let us say , 20 feet , along lines which may be one or two hundred miles in length . The majority of big quakes , however , are sub-oceanic in their origin , along lines parallel to mountain ridges , as , for example , at the bottom of the trough which runs parallel to the Andes . The mass movement appears to result in the deepening of the and the rise of coast line . We have measurements where has increased as much as 200 fathoms : see 'Brit . Assoc. Seismic Report , ' 1897 , for a number of these measurements An estimate of the effect of such displacements is easily made . Thus , an uncompensated subsidence of the ocean floor , of volume corresponding to a fall of one foot over a thousand miles square , in middle latitudes , would produce*a direct shift in the Pole of rotation amounting to about one-eighth of a second of arc ; and at the same time the Pole of the principal axis of inertia , round which the 428-day precession of the axis of rotation takes place , would be displaced in the opposite direction through an angle of the same order of magnitude . In connection with the possibility of irregularity in the Earth 's diurnal . cit. , ' Monthly Notices E.A.S. , ' Nov. , 1906 , p. 26 . VOL. LXXXII . Sir N. Lockyer . On Observations of Sun and [ Dec. 8 , rotation due to causes of this kind , similar considerations arise . * A slight subsidence , due to shrinkage around the equator , unless it extended downward a long way toward the Earth 's centre , would have negligible direct effect on the moment of inertia and , therefore , on the length of the day ; but if it were under sea it would involve transference of water from regions nearer the Earth 's axis , in order to make up the deficiency , and if the equatorial regions were all under water , a contraction of cm . in equatorial radius would in this way alter the length of the year by an amount of the order of half a second of time , which would be astronomically of high importance . ] on Observations of Sun and Stars in some British Stone Circles . Fourth Note.\mdash ; The Circles , St. Just , Cornwall . By Sir NORMAN LOCKYER , Sc. D. , IC. C.B. , , Director Solar Physics Observatory . December Read January Borlase , in his " " Antiquities of \ldquo ; ( p. 199 ) , published in 1769 , refers to what he terms " " the curious cluster\ldquo ; of circles at Botallek , the seeming confusion of which led him to write " " I cannot but think that there was some mystical meaning , or , at least , distinct allotments to particular uses Fortunately for science , he accompanies his account with a plan evidently carefully prepared ( fig. 1 ) , which is now the only thing that remains ; every stone has been utilised in building an engine house , or in other ways . Only the site is shown on the ordnance map . As the " " cluster\ldquo ; of circles exceeds in elaboration anything of the kind with which I am acquainted , it was of great interest to see if could be made of it in the light of other researches in Cornwall already refe , rred to in previous communications to the Royal Society . The first point of *Lord Kelvin , . cit. , 'Roy . Soc. Proc , vol. 76 , 1905 , p. 177 ; , vol. 77 , 1906 , p. 465 ; , vol. 80 , 1908 , p. 285 .

rspa_1909_0010

0950-1207

Notes on observations of sun and stars in some British Stone Circles. Fourth note. \#x2014; the botallek circle, St. just, Cornwall.

96

103

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

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

article

6.0.4

http://dx.doi.org/10.1098/rspa.1909.0010

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1909_0010

10.1098/rspa.1909.0010

Astronomy

Atomic Physics

Astronomy

96 Sir N. Lockyer . On Observations of Sun and [ Dec. 8 , rotation due to causes of this kind , similar considerations arise.* A slight subsidence , due to shrinkage around the equator , unless it extended downward a long way toward the Earth 's centre , would have negligible direct effect on the moment of inertia and , therefore , on the length of the day ; but if it were under sea it would involve transference of water from regions nearer the Earth 's axis , in order to make up the deficiency , and if the equatorial regions were all under water , a contraction of 50 cm . in equatorial radius would in this way alter the length of the year by an amount of the order of half a second of time , which would be astronomically of high importance . ] Notes on Observations of Sun and Stars in some British Stone Circles . Fourth Note.\#151 ; The Botallek , , Cornwall . By Sir Norman Lockyer , Sc. D. , K.C.B. , F.R.S. , Director Solar Physics Observatory . ( Received December 8 , 1908 , \#151 ; Read January 14 , 1909 . ) Borlase , in his " Antiquities of Cornwall " ( p. 199 ) , published in 1769 , refers to what he terms " the curious cluster " of circles at Botallek , the seeming confusion of which led him to write " I cannot but think that there was some mystical meaning , or , at least , distinct allotments to particular uses . " Fortunately for science , he accompanies his account with a plan evidently carefully prepared ( fig. 1 ) , which is now the only thing that remains ; every stone has been utilised in building an engine house , or in other ways . Only the site is shown on the ordnance map . As the " cluster " of circles exceeds in elaboration anything of the kind with which I am acquainted , it was of great interest to see if anything could be made of it in the light of other researches in Cornwall already referred to in previous communications to the Royal Society.f The first point of * Lord Kelvin , loc. cit. , S 38 . t 'Roy . Soc. Proc. , ' A , vol. 76 , 1905 , p. 177 ; A , vol. 77 , 1906 , p. 465 ; A , vol. 80 , 1908 , p. 285 . Stars in some British Stone Circles . 1908 . ] inquiry concerned the N. point given on the plan\#151 ; whether it was true or magnetic . A perusal of Borlase 's volume showed that he was fully acquainted with the necessity of referring in such descriptions to the true north , instead of , as he says , " such an inconstant and fluctuating index as the / \#166 ; \#171 ; .-*\gt ; \#163 ; Bcta/ kA CireltJinJ . Jiui M rmt/ t yr-f at rsJjzert truest it 'd fa/ 71 m.r$\lt ; rr/ \lt ; isc . Fig. 1 . declination of the needle , which is not only different in different places , but varies also at different times in one and the same place " ( p. 115 ) . When the point was settled , it became evident , when the circles were completed and lines drawn from centre to centre , that approximately the same azimuths were in question as those before noted . h 2 Sir N. Lockyer . On Observations of Sun and [ Dec. 8 , Borlase does not give the heights of hills for the various azimuths to \#166 ; complete his plan . I therefore asked Mr. Thomas , an active member of the Cornish Society for the Astronomical Study of Ancient Monuments , to observe them for me . Taking Borlase 's orientation as being near the truth , lines were drawn joining up the approximate centres of the various circles and a list of the various azimuths was sent to Mr. Thomas , who was good enough to comply with my request at once . Among the azimuths were two , the first from the approximate centre of the circle F to the approximate centre of E , N. 83 ' E. , and the second , from the approximate centre of F to that of H , S. 66 ' E. In sending his results to me Mr. Thomas remarked that the former line passes over the Carn Bean barrow and the latter passes 2\ ' to the FT . of the Goon Kith barrow ; thus the azimuth of the Goon Bith barrow would be S. 63| ' E. It struck me that this circumstance would enable us to check the accuracy of Borlase 's N. point . It is much easier to make a careful survey of a monument than to indicate its true orientation , so some slight error has to be expected . Borlase in all probability employed a compass in making his surveys and was , therefore , dependent , for accurate orientation , on a knowledge of the value for the local magnetic variation ; for this he would have to depend upon the results of some general survey . Even at the present day it is a matter of great uncertainty to obtain the variation for any one place without making a special determination on the spot , and we should expect a possible error of several degrees in any orientation made in Borlase 's time . The two directions to two still existing monuments pointed out by Mr. Thomas are common to Botallek and other monuments in Cornwall , we seem justified therefore in accepting them as such . On this assumption , Borlase 's orientation was true , and not magnetic , and , also , was not far from the mark . The next step was to make a very careful determination of the centres of the circles and it was found that the line , centre of F to centre of H , coincided with the line S. 63 ' 45 ' E. from the former to the Goon Rith barrow . In other words , the difference between the azimuth we had provisionally determined from the circles and that of Goon Rith barrow was due to an error of centring , and no doubt was . left that the line between the centres of F and H was really directed to the barrow . Similarly the line N. 83 ' E. joining the centres of F and E was directed to the Carn Bean barrow . Both these lines were recognised as familiar , giving , approximately , the November sunrise and the heliacal rising of the Pleiades in May respectively . In the case of the S.E. azimuth there is an alternative Stars in some British Stone Circles . 99 ' 1908 . ] explanation of the sight-line . Both in Cornwall and Wales we have found that azimuth-marks ( barrows , etc. ) , were sometimes erected so that they gave the direction of sunrise a fortnight or three weeks before the critical date . I therefore decided to adopt the Pleiades azimuth , N. 83 ' E. , as the fundamental line by which to fix the N. point , and it followed that Borlase 's 1ST . point was less than 3 ' to the west . Working on this basis , I joined up the centres of the circles , as shown on the plans ( figs. 2 and 3 ) , and carefully measured the resulting azimuths . These I sent to Mr. Thomas , asking him if the slight modifications that I had introduced had sensibly altered his values for the corresponding angular elevations . After a second series of observations , he replied that the elevations were the same for the modified azimuths as they were before . It at once became obvious that the alignments divided themselves naturally into two groups\#151 ; the one erected for the observations of May-year , the other for solstitial , phenomena\#151 ; and with each group there is associated a clock-star which affords a means of determining the approximate date of that group . For this reason I give two separate plans ( figs. 2 and 3 ) showing the separate Fig. 2 . groups of alignments , and two separate tables giving the respective results . I will deal with the May-year circles first ( fig. 2 ) :\#151 ; Sir N. Lockyer . On Observations of Sun and [ Dec. 8 , May-year Alignments at Botallek ( lat. 50 ' 8 ' N. ) . Alignment . Azimuth . Hill ( Mr. Thomas 's ) measures . Decli- nation . Object . Date . Centre of circ . B to cent. O / N. 67 0 E. 0 / 3 0 O f 16 31 N. May sun May 6 ; of circ . H Aug. 7 Cent , of circ . F to cent. S. 63 45 E. 2 44 14 43 S. Nov. sun Nov. 2 ; of circ . H to Goon Rith ( possibly a Feb. 10 barrow Warner ) Cent , of circ . F to cent. N. 83 0 E. 3 35 7 2N . Pleiades 1680 B.c. of circ . E to Carn Bean ( warning barrow May sun ) Cent , of circ . H to cent. N. 3 30 E. 0 0 39 14 N. Arcturus 1730 B.c. of circ . I ( clock-star ) These results agree in a wonderful way with the May-year results previously obtained from the study of other Cornish circles , and to illustrate this I bring together a selection of the results previously published :\#151 ; Similar May-year Alignments in Cornwall ( for comparison ) . Monument . Lat. N. Alignment . Azimuth . Hill . Declina- tion . Object . Date . Merry Maidens Boscawen -Un The Hurlers ... Trippet stones O t 50 4 50 5 50 31 50 33 Circ . to Fougou ... , , stone o / N. 64 0E . S. 66 30 E. N.78 47 E. N. 15 0E . O / 0 30 1 0 0 12 1 30 O f 16 21N . 14 32 S. 7 23 N. 39 1N . May sun Nov. sun Pleiades Arcturus May 5 : Aug. 7 Nov. 2 ; Feb. 10 1610B.C . 1700 B.C. S. circ . to N.E. stone j Cent , of circ . to Rough Tor Examination of fig. 2 shows that the azimuths given in the table are exactly those obtained by joining up the true centres of the circles and adopting the N.\#151 ; S. line derived from Mr. Thomas 's two measures of direction . The results certainly justify the 3 ' change of the orientation . The Solstitial Year . Joining up the centres of H , G , D , and C , as shown in fig. 3 , we obtain the results given in the following table , results which are obviously connected inter se and with the solstitial year :\#151 ; 1908 . ] Stars in some British Sto ? ie Circles . Solstitial Alignments at Botallek ( lat. 50 ' 8 ' N. ) . Alignment . Azimuth . Hill ( Mr. Thomas 's ) measures . Decli- nation . Object . 1 Date . Cent , of circ . H to cent , of cire . C Cent , of circ . D to cent , of circ . C I Cent , of circ . 11 to cent , of small circ . Q- O / N. 53 0 E. S. 49 30 E. N. 16 0 E. 0 / 1 45 1 35 0 0 O f 23 41 N. 23 44 S. 37 28 N. Solstitial sun ( summer ) Solstitial sun ( winter ) Arcturus ( clock-star ) 1420 b.c. 1 Fig. 3 . As before , I give a selection from previous results , showing that the alignments we are now dealing with have become familiar by reason of their occurrence at the Cornish monuments investigated earlier :\#151 ; Similar Solstitial Alignments in Cornwall ( for comparison ) . Monument . Lat. N. | A lignment . Azimuth . Hill . Declina- tion . Object . Date . Boscawen-Un ... The Hurlers ... Tregeseal O / 50 5 50 31 50 9 Circ . to Fine Menhir N. circ . to S.E. stone Longstone to Chun Castle O t N. 53 30 E. i S. 50 50 E. N. 23 30 E. 0 / 2 23 1 18 1 35 O / 23 59 N. 24 17 S. 37 9 N. Solstitial sun ( summer ) Solstitial sun ( winter ) Arcturus 1350b.c . 102 On Observations of Sun and Stars , etc. It will probably be remarked that I attach no dates to these solstitial sight-lines . This is because the data available are not sufficiently certain to justify dating . The solstitial variation takes place so slowly and between such restricted limits that , until the most accurate observations possible have been made at a monument , it is merely conjecture to apply a date ; only at Stonehenge , so far , has this been possible . Under the Botallek conditions , a difference of half a degree in the azimuth would produce a variation of more than 2000 years in the resulting date , and one cannot assume that accuracy in the present case . From the results given above it is evident that in this " curious cluster " of circles at Botallek we have an epitome of the chief sight-lines found in Cornwall . May-year sun , clock-star , warning-star , and solstitial sun are all represented . The occurrence of star circles is fortunate , as it enables us to attempt to arrange the groups in order of date . As shown above , the May-year group , F , H , B , and E , with the clock-star circle I , was probably the first , by something like 300 years , to be erected , and it should be noted that the date for the Pleiades circle E is coincident , within our probable error , with the date of the clock-star alignment H\#151 ; I. Borlase 's plan ( fig. 1 ) affords us evidence on this point , for it shows that the circles F , H , and I are associated by being made up of two concentric rings of stones . The fact that stones were obviously taken from the periphery of E when D was built shows that E , too , was an earlier circle than D ; our results associate E with the May-year and D with the solstitial group . The incompleteness of B suggests partial demolition prior to Borlase 's survey , whilst its relatively smaller size suggests that what remains may have formed the interior ring of a double circle . Conclusions . The cluster of circles at Botallek , St. Just , Cornwall , was erected for astronomical observations , and forms an epitome of the principal alignments to sun and stars previously found in Cornwall and other parts of the British Isles . The results justify the azimuths obtained from Borlases plan and show that his orientation of the plan is not more than 3 ' in error . It appears that in this cluster we have two distinct groups of alignments , one associated with the May-year worship , the other associated with the later solstitial-year ritual . As a clock ; star alignment occurs in each group , we are able to determine that the May-year worship preceded the solstitial-year by something like Passage of Pont gen Rags through Gases and Vapours . 103 300 years , the approximate dates being 1700 b.c. and 1400 b.c. respectively . This sequence is confirmed by the structure of the circles themselves as plotted by Borlase . I have to thank Mr. Thomas for his local observations , and Mr. Rolston , of the Solar Physics Observatory , for assistance in the discussion and computing the various declinations . On the Passage of RontgenRays through Gases and Vapours . By J. A. Crowther , B.A. , Fellow of St. John 's College , Cambridge , Mackinnon Student of the Royal Society . ( Communicated by Prof. Sir J. J. Thomson , F.R.S. Received December 22 , 1908 , \#151 ; Read January 14 , 1909 . ) Introduction . The present work is a continuation of a previous research on the Secondary Rontgen Radiation from Gases and Vapours.* It was there shown that while for gases and vapours containing only elements of small atomic weight the secondary radiation was simply proportional to the density of the gas , those containing elements of higher atomic weight , and notably compounds of arsenic and bromine , gave off quantities of secondary radiation greater out of all proportion than what would be expected from their density . It was also shown that while the secondary radiation from the first class of substances had approximately the same penetrating power as the primary rays producing it , the secondary radiation from the second class was generally of a considerably softer character . A third class of substances , including stannic chloride and methyl iodide , gave off secondary rays , the hardness of which was equal to that of the primary , while their intensity , which , however , varied with the hardness of the primary rays , was intermediate between that of the first and second classes . It was thought that a further investigation of the phenomena attending the passage of Rontgen rays through these different classes of gases and vapours might possibly lead to some interesting results . * 'Phil . Mag. , ' [ 6 ] , vol. 14 , p. 653 , 1907 .

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0950-1207

On the passage of r\#xF6;ntgen rays through gases and vapours.

103

127

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

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

article

6.0.4

http://dx.doi.org/10.1098/rspa.1909.0011

en

rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1909_0011

10.1098/rspa.1909.0011

Atomic Physics

Thermodynamics

Atomic Physics

Passage of Rontgen Rays through Gases and Vapours . 103 300 years , the approximate dates being 1700 b.c. and 1400 b.c. respectively . This sequence is confirmed by the structure of the circles themselves as plotted by Borlase . I have to thank Mr. Thomas for his local observations , and Mr. Rolston , of the Solar Physics Observatory , for assistance in the discussion and computing the various declinations . On the Passage of Rontgen Rays through Gases and Vapours . By J. A. Crowther , B.A. , Fellow of St. John 's College , Cambridge , Mackinnon Student of the Royal Society . ( Communicated by Prof. Sir J. J. Thomson , F.R.S. Received December 22 , 1908 , \#151 ; Read January 14 , 1909 . ) Introduction . The present work is a continuation of a previous research on the Secondary Rontgen Radiation from Gases and Vapours.* It was there shown that while for gases and vapours containing only elements of small atomic weight the secondary radiation was simply proportional to the density of the gas , those containing elements of higher atomic weight , and notably compounds of arsenic and bromine , gave off quantities of secondary radiation greater out of all proportion than what would be expected from their density . It was also shown that while the secondary radiation from the first class of substances had approximately the same penetrating power as the primary rays producing it , the secondary radiation from the second class was generally of a considerably softer character . A third class of substances , including stannic chloride and methyl iodide , gave off secondary rays , the hardness of which was equal to that of the primary , while their intensity , which , however , varied with the hardness of the primary rays , was intermediate between that of the first and second classes . It was thought that a further investigation of the phenomena attending the passage of Rontgen rays through these different classes of gases and vapours might possibly lead to some interesting results . * 'Phil . Mag. , ' [ 6 ] , vol. 14 , p. 653 , 1907 . 104 Mr. J. A. Crowther . On Passage oj [ Dec. 22 , The phenomena which it was proposed to measure were :\#151 ; ( i ) the absorption of the primary rays by the gas ; ( ii ) the ionisation produced in the gas by the passage of the rays ; ( iii ) the secondary radiation given out by the gas . Of the first two quantities , determinations have already been made by various experimenters , for some of the commoner gases and a few vapours . Thus Rutherford , * in the early days of X-ray work , measured both the coefficients of absorption and the relative ionisations of some dozen different substances . In addition to this , determinations of the relative ionisation in different gases and vapours have been made by Perrin , t J. J. Thomson^ Strutt , S McClung , || and Eve . H Many of these measurements , however , were made without any care being taken to prevent the Rontgen rays from falling on the sides of the ionisation chamber and on the electrodes themselves . Under such circumstances , as we shall show later , a large proportion of the ionisation in the gas is due , not to the X-rays themselves , but to soft secondary ^-radiation from the material of the walls and the electrodes . The amount of this secondary ionisation will depend upon the material and construction of the vessels used . Since the soft ^-radiation is practically totally absorbed in the gas , its effect is in every case to add a nearly constant amount to the ionisation produced by the Rontgen rays , and thus to reduce the apparent relative ionisation , in gases which are more ionised than air . The experiments of Prof. Thomson , and of McClung , which were free from this objection , unfortunately did not include the gases whose behaviour it was most desired to study . Moreover , as the experiments of the latter conclusively showed , the relative ionisation of any gas compared with air is not a constant , but depends upon the nature of the X-rays employed . As there is at present no very satisfactory way of standardising Rontgen rays , or of comparing results obtained by different observers , it was felt that the only possible way of obtaining a set of comparable results was to determine the whole of the quantities concerned at the same time and with the same apparatus . Apparatus . The apparatus employed was , in the main , the same as that used in the previous experiments , and described in detail in the previous paper , certain * Rutherford , ' Phil. Mag./ [ Y ] , 43 , p. 241 , 1897 . + * Ann. de Chimie et de Phys./ [ 7 ] , vol. 11 , p. 496 , 1897 . I ' Camb . Phil. Soc. Proc./ vol. 10 , p. 10 , 1900 . S ' Roy . Soc. Proc./ vol. 72 , p. 209 , 1903 . || 'Phil . Mag./ [ 6 ] , vol. 8 , p. 357 , 1904 . 1 'Phil . Mag./ [ 6 ] , vol. 8 , p. 610 , 1904 . 1908.1 Rontgen Rays through Gases and Vapours . 105 alterations and additions being made to allow of the measurement of the ionisation and absorption in the gas , in addition to the secondary radiation . ^ The gases , as before , were contained in two similar brass boxes A , A ' ( fig. 1 ) arranged symmetrically with respect to the focus tube F. The rays enter by the thin aluminium windows c , c ' , and a portion of the secondary rays pass upwards through aluminium windows d , d ' into two cylindrical ionisation chambers B , B . A portion of the primary beam , after traversing the length of the box , passes out through a third aluminium window e , as is shown in the plan of the apparatus given in fig. 2 , and is measured in the ionisation chamber P. The amount of absorption of the rays in the gas can thus be determined . To determine the ionisation produced in the gas by the passage of the rays , electrodes were inserted in the gas chambers A , A ' themselves . In order to avoid intercepting any primary rays , these took the form of parallel plates of aluminium r , s , r ' , s ' placed at opposite sides of the boxes , and outside the path of the primary rays . The electrodes were insulated from the walls of the boxes ( which were earthed ) by quartz tubes , the joints being made 106 Mr. J. A. Crowther . On Passage of [ Dec. 22 , '-\gt ; 5 . " \#166 ; : air-tight with sealing wax , and , except in the case of one or two vapours when near their saturation pressure , no trouble was experienced from insulation leaks . The plates s , s ' were charged to a high potential by a battery of storage cells ; the others , r , r ' which were surrounded by earthed guard rings , were connected to a Wilson electroscope . The whole of the Vo Cells Fig. 2 . apparatus was made in duplicate , one of the boxes being filled with air and kept as a standard . The different ionisation chambers were connected in pairs to three Wilson inclined electroscopes , each chamber in the one set being connected , together with its duplicate in the other , to a separate instrument . By means of highly insulating keys , which could be operated from a distance , it was arranged that either the test chamber , or the corresponding standard , could be connected at will with the electroscope . By measuring the current through first one and then the other , the ratio of the ionisation in the test chamber to that in the standard could be accurately obtained . For a Wilson electroscope , where the zero and the sensitiveness are both liable to fluctuation , this method of comparing two ionisation currents is both more convenient and more accurate than the use of two separate instruments . The appliances for measuring the pressures in the two chambers , and for introducing the various gases and vapours , were the same as those employed in the previous paper , and fully described there . The various connections and keys were shielded from induction effects in the usual way , by earthed metal tubes . 1908.1 Rontgen Rays through Gases and Vapours . 107 Experiments . The actual experiments were performed in various ways , according to the nature of the observations which it was desired to make . At least one set of experiments was made with each substance in which simultaneous readings were made of the relative ionisation , coefficient of absorption and secondary radiation , so as to avoid all possibility of any difference in quality of the rays employed . In other cases , when some particular point was to be investigated , as , for example , the variation of the relative ionisation with pressure , it was found more convenient to make the desired observations by themselves , the quality of the rays being regulated by the length of the spark gap , which was just sufficient to extinguish the bulb . In practice it was found that , using the same coil and the same Bontgen bulb , this control was quite sufficient , and readings could always be repeated by bringing the bulb back to the same equivalent spark gap . It was not found possible , however , to compare the hardness of different bulbs by this method , as two bulbs having the same equivalent spark gap would give out rays of apparently very different character . In order to afford some idea of the meaning of the different values given in this paper for equivalent spark lengths , it may be mentioned that X-rays began to be given out in appreciable quantity when the equivalent spark gap was about 0*6 cm . At this stage the whole bulb was filled with a bluish glow . This glow disappeared when the equivalent spark gap had increased to about 1*2 or 1*3 cm . , and the green phosphorescence of the walls was then alone visible . At an equivalent spark gap of about 2-6 to 2*8 cm . the coil ( a large Budge coil working with a hammer break ) ceased to send any discharge through the bulb . Ionisation and Pressure . The ionisation produced in a gas by the passage of Bontgen rays , in the absence of any secondary radiation , should be proportional to the mass of the gas present , that is , if the temperature is constant , to the pressure of the gas . On the other hand , as was shown in the previous paper in the cases of air and carbon dioxide ( and has since been confirmed for the more powerful radiators ) , the energy of the penetrating secondary radiation is also simply proportional to the pressure of the gas ; and thus the ionisation produced by it in the radiating gas itself should be proportional to the square of the pressure . We should expect that any soft secondary radiation which might be emitted would follow the same law , so long as it was sufficiently penetrating to reach the walls of the gas chamber . If , however , owing to the softness Mr. J. A. Crowther . On Passage of [ Dec. 22 , . of the radiation , the distance of the boundaries , or the pressure of the gas , , the radiation was totally absorbed in the gas before reaching the boundaries , , the ionisation produced by it would depend solely on its intensity , i.e. , it-would be simply proportional to the pressure , and the whole ionisation in the gas would again follow a simple pressure law . Neglecting , for the-moment , the penetrating secondary radiation , we should expect that if any soft secondary radiation were present the ionisation in the gas would , , at high pressures , be simply proportional to the pressure . Then , as the pressure was reduced , and the absorption of the rays in the gas became less and less , a point would be reached when the secondary rays began to reach the electrodes , and the ionisation would then vary more rapidly than the pressure . Experiments were made with various gases to test these conclusions . The electrodes in the gas chambers were placed some distance from the front window in order to avoid the soft secondary radiation from the aluminium . The rays had thus to pass through a certain thickness of gas before reaching the electrodes , and a certain amount of absorption occurred . Knowing , however , from other measurements , the coefficient of absorption of the gas for the rays , it was easy to calculate the amount of this absorption at any given pressure , and to apply the necessary correction . This has been done in all cases , in the results given below . The first observations , made with the electrodes at opposite sides of the-gas chamber , failed to reveal any departure from a simple pressure law . It was thought , however , that this might be due to the secondary rays being so* soft as to be unable to penetrate to the boundaries of the gas , even at the lowest pressures used . The distance between the plates was , therefore , , reduced to 5 mm. , the primary beam being limited by a lead slit 1*2 mm. wide , so that the rays still passed between the plates without striking them . With this arrangement , a penetration of only 2 mm. would have sufficed to allow some of the soft secondary rays to reach the boundaries of the gas . Some of the curves obtained are shown in fig. 3 . For convenience in representation , the ordinates , in the case of methyl iodide , have been considerably reduced . The curves obtained for ethyl bromide and methyl iodide at low pressures are shown on an enlarged scale in fig. 3a . It will be seen that although experiments were made with air down to a pressure of 10 mm. , and with methyl iodide and ethyl bromide with pressures as low as 0'7 mm. and 0*2 mm. respectively , the curves obtained are perfectly straight ( except in so far as the curve for ethyl bromide is influenced at high pressures by the ionisation due to the penetrating secondary Kflntgen / ontza tion 1908 . ] Rontgen Rays through Gases and Vapours . 109 radiation ) , and there is no evidence of any departure from a simple pressure law . The experiments were repeated with ethyl chloride and methyl bromide with similar results . We must assume , therefore , that the soft secondary radiation from a gas is either too absorbable to penetrate 2 mm. of the gas even at these low pressures , or as on the whole seems more probable , that the ionisation produced by it , compared with that due to the direct action of the primary beam , is too small to have any appreciable effect on " FVe.ssv.re ----------------\#166 ; ' Fig. 3.\#151 ; Ionisation\#151 ; Pressure Curves . the shape of the curves . In this case the bulk of the ionisation in a gas must be due to the direct action of the primary rays . It is well known that when Rontgen rays fall upon a solid body they cause it to emit soft secondary rays in very appreciable amounts . Unless the action of the Rontgen rays upon the gaseous molecule differs very materially from its action upon the molecule in the solid state , the above result would appear to show that the soft secondary ionising radiation emitted by solids only represents a very small part of the whole effect of the primary rays ; the 110 Mr. J. A. Crowther . On the Passage of [ Dec. 22 , bulk of the secondary rays , that is to say the portion which in a gas manifests itself as direct ionisation , being too soft to ionise . The penetrating secondary radiation is in most cases too small in amount to make any appreciable alteration in the ionisation pressure curves . Barkla* has shown that the energy of the secondary radiation from a cubic centimetre of air at atmospheric pressure is only about 0-00024 that of the primary beam . Taking this value as approximately correct , we see that even / oo *---- Pressure . Fig. 3a.\#151 ; Ionisation\#151 ; Pressure . Low Pressures . in the case of ethyl bromide , which gives the maximum amount of radiation of any of the gases employed , the energy of the secondary radiation at a pressure of 160 mm. of mercury is only about 3 per cent , of that of the primary beam . Since the secondary is in this case about three times as absorbable as the primary beam , the amount of secondary ionisation should be about *9 per cent , of that produced by the primary rays at the pressure * 'Phil . Mag. , ' [ 6 ] , vol. 7 , page 543 , 1904 . Ill 1908 . ] Rontgen Rays through Gases and Vapours . named . It is evident , therefore , that for air , carbon tetrachloride , or even methyl iodide , it would be quite inappreciable . On turning to fig. 3 , it will be seen that the upward tendency in the ionisation-pressure curve for ethyl bromide is quite marked , and from the magnitude of its departure from a straight line , it is easy to deduce that at a pressure of 160 mm. of mercury , the ionisation due to the secondary rays is about 16 per cent , of that due to the primary . As the secondary rays , being scattered in all directions , traversed the whole of the gas between the electrodes , while the primary beam , in order to avoid any possibility of its striking the electrodes , was only allowed to pass through the central portion of the gas , the agreement is sufficiently satisfactory . Absorption of the Primary Rays . When Kontgen rays pass through a gas they are more or less absorbed by it . In order to measure this absorption it is necessary and sufficient to find the ratio of the ionisation current through P ' to that through P when the gas Fig. 4.\#151 ; Absorption Curves . VOL. LXXXII.\#151 ; A. I Mr. J. A. Crowther . On Passage of [ Dec. 2\#163 ; , chamber A ' is , first , evacuated , and , second , filled with the gas under observation . The first gives a measure of the initial intensity I0 of the beam ; the second the intensity I after passing through the gas . Experiments were made with the different gases at different pressures , and the values thus obtained for logi01/ I0 are plotted against the pressures in fig. 4 . The amount of absorption was found to vary considerably with the hardness of the rays , and a certain amount of difficulty was experienced in keeping the bulb quite constant during a long series of readings . It will be seen , however , that within the limits of experimental error , the curve obtained is in every case a straight line . The law of absorption is , therefore , exponential and may be written I/ I0 = where p is the pressure of the gas , 7r is the normal atmospheric pressure , d the distance traversed by the rays in the gas , and X a constant which we may call the coefficient of absorption of the rays for the gas . The values of X for the different gases employed are given for soft and hard rays , in the third and fifth columns of Table I. With the apparatus employed , it was not found possible to measure the coefficients of absorption of air , hydrogen , or carbon dioxide , as the amount , of absorption of the rays in the length of the box ( 20 cm . ) was too small to be appreciable . It certainly was not more than 2 or 3 per cent. , and this was practically within the limits of experimental error . In view of the very Table I. Soft rays . Hard rays . Secondary radiation . Relative density . Relative ionisation . A. Relative ionisation . A. Air 1 00 1-00 1 00 1*00 Ho o-oi ... - 0*18 s _ 012 0*07 oo2 1-57 . _ 1 -49 1-54 1*53 OH3.coa . OH3 ... C , H^C1 4*95 18 -0 0 02 0-044 3-90 17 -3 4 0-005 ' 0-022 2*72 3*2 2*57 2*24 C.CI4 67*3 0*24 71 0-06 8*6 5*35 Ni(CO)4 89 0*20 97 0-136 8*1 5*90 CoHJBr 72 0-30 118 0-14 217 3*78 OH3Br 71 0*29 \#151 ; 215 3*30 CHoI 146 0-30 125 0-18 41*5 4*96 Hg(CH , )2 425 1-16 \#151 ; 7*93 1908 . ] Rontgen Rays through Gases and Vapours . peculiar behaviour of hydrogen with regard to ionisation by Rontgen rays , which will be described later , it would be very interesting to have a measure of the absorption of hydrogen for rays of varying quality ; and it is hoped to make some experiments on this point in the near future . Relative Ionisation in Different Gases . In calculating the relative ionisations for different gases , air was taken as the standard , and all other gases and vapours were compared with air at the same pressure . Writing A ' and A for the ionisation currents across the two gas chambers , the ratio of the values of A'/ A when A ' is filled first with the gas under observation , and then with air at the same pressure , gives the value of the relative ionisation for the given gas compared with air . As pointed out in a previous part of the paper , the values thus obtained have to be corrected for the absorption of the rays in the gas before reaching the electrodes . When the ionisation due to the penetrating secondary radiation from the gas is appreciable , as in the case of ethyl bromide , this has also been corrected for . It may be mentioned , in passing , that it was found very difficult to " saturate " the current through the more ionisable gases , 120 to 150 volts per centimetre being required to produce even approximate saturation for ethyl bromide or methyl iodide at pressures of 250 mm. In order to attain saturation without applying too high a potential , the electrodes in the vessel A ! were approached to about 2'5 cm . apart ; the primary beam being limited as before by a lead slit to prevent the rays from falling on either electrodeThe values obtained for the relative ionisation , for soft and hard rays , are ' given in the second and fourth columns respectively of Table I. For purposes of comparison , the amount of secondary radiation , relative to air , is given in the sixth column of the same table , while the seventh contains the relative densities of the different substances . It is at once evident that there is no close connection between the ionisation and the secondary radiation . The former , for example , appears to* increase more or less uniformly as we pass to compounds containing elements of higher and higher atomic weight ; the maximum ionisation occurring in . mercury methyl , the ionisation in which is over 400 times that in air . The secondary radiation , on the other hand , reaches a maximum in the neighbourhood of bromine , ethyl bromide giving off the largest amount of secondary rays of the gases included in Table I. For ethyl bromide and methyl iodide , the values obtained depend upon the quality of the rays employed , and we-shall consider them in more detail further on . 114 Mr. J. A. Crowther . On Passage of [ Dec. 22 , \#166 ; I . Prof. Thomson has suggested that the relative ionisation in a gas is an additive property , depending only on the number and nature of the different atoms present . The values given in column 2 of Table I enable us to test this suggestion . Using carbon dioxide , air , ethyl chloride , and methyl bromide , together with the value for hydrogen , we obtain , on this assumption , the following values for the ionisation per atom in the different elements concerned:\#151 ; [ H ] = 0-005 , [ 0 ] = 055 , [ C ] = 0-46 , [ Cl ] = 17*0 , [ Br ] = 70*5 . Using these values , we can now calculate the relative ionisation of methyl acetate , carbon tetrachloride , and ethyl bromide . The results are contained in the following table:\#151 ; Table II . CH , C09CHs Relative ionisation . Calculated . Observed . 2*52 68-4 71 5 4-95 67-3 72*5 CC14 CoHJJr It will be seen that the agreement is good for carbon tetrachloride and ethyl bromide , but not very satisfactory for methyl acetate . It appears , therefore , that the ionisation is not altogether independent of the state of combination of the element and the complexity of the molecule . Assuming , however , that|the law is approximately correct , we obtain from the results in Table I the further values [ Ni ] = 85 , [ I ] = 144 , [ Hg ] = 424 . It will be noticed that , with the exception of nickel ( which for soft rays gives a some what larger value than bromine ) , the relative ionisation increases steadily with the atomic weight . If we repeat the calculations , using the values obtained with the harder rays , we obtain similar results . The discrepancy in the case of methyl acetate is , however , in this ca^e considerably less ; the calculated value of the ionisation being 2*81 , the observed value 3'90 ; and possibly with still harder rays the effect of the complexity of the molecule might disappear altogether . Variation of the Ionisation with the Hardness of the Bays . The variation in the relative ionisation due to change in the quality of the ionising Rontgen rays has been previously investigated by McClung* for hydrogen , oxygen , carbon dioxide , and sulphur dioxide . His results are contained in the following table:\#151 ; * McClung , 'Phil . Mag. , ' [ 6 ] , vol. 8 , p. 357 , 1904 . 1908 . ] Rontgen Rays through Gases and Vapours . Table III . Relative ionisation . Soft rays . Hard rays . Air ib 1*0 h2 Oo 0*10 1*80 0*18 1-17 co9 1 *46 1 -33 so2 no 4*8 Comparing these figures with those given in Table I , it will be seen that in the cases of the two gases common to the two tables the results are in general agreement . The relative ionisation of hydrogen increases with an increase in the hardness of the rays , while that of carbon dioxide diminishes . The value obtained for the relative ionisation of hydrogen for hard rays in the present experiments coincides with that obtained by McClung . The value for soft rays is only about one-tenth of the smallest value he obtained , but it is comparable with the value 0*026 obtained by Perrin * The rays in McClung 's experiment entered his apparatus through a recessed aluminium plate , which must have been considerably thicker than the thin foil ( 0*05 mm. thick ) used for the windows in the present experiments . It is probable , therefore , that the very soft rays which give these very small values for the ionisation of hydrogen were unable to penetrate into his ionisation chamber , being practically all absorbed by the aluminium of the window . Table IV has been drawn up to show in more detail how the relative ionisation of the hydrogen varies with the hardness of the rays , the hardness being represented , as usual , by the length of the spark gap , which is just sufficient to extinguish the bulb . Table IV.\#151 ; Hydrogen . Equivalent spark gap . Relative ionisation . mm. 8 0*010 12 0*013 14 0*021 16 0*068 18 0*107 20 0*135 24 0*152 28 0*180 * Perrin , 'Ann . de Chimie et de Phys.,5 vol. 11 , p. 496 , 1897 . Mr. J. A. Crowther . On Passage of [ Dec. 22 , These figures are represented graphically by the curve drawn in fig. 5 . It will be noticed that the rate of increase is particularly rapid as the equivalent spark gap increases from 14 to 18 mm. Although not so noticeable as in the case of hydrogen , it will be seen from .Table I that the relative ionisation of ethyl bromide also increases as the rays get harder . Ethyl chloride and carbon tetrachloride remain practically Equivalent S^arJc G-ajo Fig. 5.\#151 ; Ionisation\#151 ; Hardness . Hydrogen . constant , while methyl iodide and methyl acetate show a decided decrease as the hardness of the rays increases . During the progress of the above experiments my attention was somewhat forcibly directed to the necessity for avoiding any contact between the Eontgen rays and the electrodes in all measurements of the relative ionisation produced by these rays in different gases . Having had occasion to remove the gas chamber A ' to make some necessary repairs , I found on replacing it that the values now obtained for the relative ionisation were considerably smaller than before . For example , the value for ethyl bromide was reduced from 72 to 29 , and that for methyl iodide from .145 to 54 . This discrepancy was finally found to be due to the fact that , owing to the vessel A ! having been replaced slightly out of adjustment with respect to the focus tube , the Eontgen rays no longer passed centrally down the vessel , but just grazed one of the electrodes . 1908.1 Riintgen Rays through Gases and Vapours . 117 Townsend* and other observers have shown that when Kontgen rays fall on a metal plate they cause it to emit soft secondary radiation , consisting principally of soft ^-radiation , which from its very absorbable nature , produces in the neighbourhood of the plate an amount of ionisation far exceeding that due to the primary rays themselves . The effect of the secondary radiation on the relative ionisation in different gases is not difficult to see . If the pressure of the gas is so high that the secondary rays are totally absorbed before reaching the boundaries of the vessel , then , since the total ionisation produced by these rays is not very different in different gases , the effect will be in every case to add a practically constant amount to the ionisation produced by the primary beam , and thus to reduce the apparent relative ionisation in every gas for which the relative ionisation is greater than unity . On the other hand , since the relative ionisation produced in different gases by ^-radiation is very nearly proportional to the density , if the rays are not totally absorbed by the gas , the result will be in this case to add an amount , proportional to the density , and thus to bring the apparent relative ionisations more nearly into accord with a density law . In either case there would be a large reduction in the values obtained for the relative ionisation of such vapours as methyl iodide , ethyl bromide , or carbon tetrachloride , compared with air . By turning the vessel A. ' with respect to the focus tube , so as to allow a larger proportion of the primary beam to impinge on the aluminium electrode , the values obtained for the relative ionisation of ethyl bromide compared with air was further reduced , first to 10 and finally to 3'62 . This is very nearly equal to the relative density of the gas . Under these circumstances , the pressure-ionisation curve is no longer a straight line , but bends over towards the axis of pressure , as shown in the curve in fig. 6 , which represents the results obtained for air , with the primary beam grazing one of the aluminium electrodes . These results throw considerable doubt upon some results of Evef on the relative ionisation produced by very penetrating Rontgen rays , in which he obtained values for the relative ionisations in various gases and vapours agreeing very nearly with a density law . In these experiments the gases were contained in a cylindrical ionisation chamber of brass with an insulated central wire connected to a gold-leaf electroscope . In this system the central wire forms one electrode , the walls of the cylinder the other . As the rays were passed into the chamber straight through the walls of the vessel , it will be seen that they thus impinged directly on both electrodes . * 'Camb . Phil. Soc. Proc. , ' vol. 10 , p. 217 , 1899 . + Eve , 'Phil . Mag. , ' [ 6 ] , vol. 8 , p. 610 , 1904 . Mr. J. A. Crowther . On Passage of [ Dec. 22 , The conditions were thus favourable for the production of a large amount of secondary ionisation , and its presence is clearly shown by the shape of the curves connecting ionisation and pressure , which are given in Eve 's paper . These are similar to the curve given in fig. 6 , which represents the relation between ionisation and pressure for air when the rays are allowed to fall upon one of the electrodes . Eve further states that " the portion of the curve between 18 and 50 mm. [ pressure ] was found to be a straight Pressure Fio . 6 . line , and the readings for the gases used were taken between these limits . " A little consideration will show that it is just in these earlier portions of the curve where the amount of the secondary ionisation compared with that of the primary has its largest value . It is only when the pressure is high enough to produce a total absorption of the secondary rays that the slope of the ionisation-pressure curve assumes the value proper to the primary Rontgen rays . The curve then has the form I = I#+Io 1908.J Rontgen Rays through Gases and Vapours . 119* where I is the ionisation in the gas , I , the ionisation produced by the total absorption of the secondary rays from the walls of the chamber , and I0 .^\gt ; -represents the ionisation produced by the direct action of the primary rays , which , as has been shown above , is proportional to the pressure From the shape of his curves there can be little doubt that , at the lower pressures used by Eve , the ionisation was very largely due to secondary radiation from the walls of his vessel , and that consequently the values given by him in his table refer not to penetrating Eontgen rays , as he supposes , but to the soft secondary rays excited by them in the material of his chamber , that is , , in the main , to soft y9-rays . There is no evidence that the ionisation produced by penetrating Eontgen rays in different gases follows a density law . Drawing tangents to Eve's-curves for H2S and air , at the highest pressures given , where , as shown above , , we get an approximation to the true slope for the primary rays , we find the value 4 for the relative ionisation of these two gases , as against 0*9 given in Eve 's table . Eve was not unaware of the presence of much secondary radiation in his experiments . He states that " with Eontgen rays there was abundant evidence of secondary and tertiary radiation , " and found that lining the brass cylinder with sheet aluminium 0 85 mm. thick reduced the ionisation current from 100 to 22 . With the chamber thus lined he repeated his original experiments , and obtained values agreeing with his previous ones , , and concludes from this that " there cannot be any wide divergence between the relative conductivities from primary and secondary rays . " The results obtained during the present experiments with the rays-striking on the aluminium electrodes show , however , that even aluminium gives off amply sufficient soft secondary rays to entirely mask the effect of the primary ionisation , and that the similarity between the results obtained with the brass , and with the aluminium plated walls , was due not to any similarity between the primary and the secondary rays , but owing to the ionisation produced by the direct action of the primary rays being so small compared with that due to the secondary as to be practically negligible in both cases . Laby and Kaye* have recently shown that when 7-rays are passed into-a gas through the walls of the containing chamber the ionisation in the gas-is due almost entirely to the ^-radiation from the metal of the walls . The similarity between the results obtained by Eve for penetrating Eontgen rays and for 7-rays would thus appear to be explained by the fact that in * ' Phil. Mag. , ' December , 1908 , p. 879 . 120 Mr. J. A. Crowther . On Passage of [ Dec. 22 , both cases the bulk of the ionisation was due , not to Rontgen rays or 7-rays , but to secondary / 9-rays from the walls of the containing chamber . The results of the present experiments on the variation of relative ionisation with the hardness of the rays certainly do not seem to indicate Any approximation to a " density law , " such as Eve suggests , as the rays become harder . Among the lighter gases , as McClung 's results also showed , the value for hydrogen increases with the hardness of the rays to a value considerably above that given by the relative density , while , on the other hand , the value for carbon dioxide , which for soft rays is nearly normal , falls below that to be expected on a density law as the hardness of the rays increases . Again , among the more ionisable gases and vapours , although the relative ionisation of methyl iodide , compared with air , decreases as the rays become harder , that of ethyl bromide shows , on the other hand , a very perceptible increase , while the values for ethyl chloride and carbon tetrachloride remain practically constant . Secondary Radiation . Variation of Secondary Radiation with the Hardness of the Rays . The . amount of the secondary 'Rontgen radiation from different gases and vapours was investigated in the previous paper , * and the results there described have been verified in the course of the present experiments . Some additional observations have been made , which it may be of interest to record . It was shown that for most gases and vapours the amount of secondary radiation given off when compared with that from air remained sensibly .constant over the range of primary rays employed . For stannic chloride and methyl iodide , however , there was a distinct increase , with increasing liardness of the primary rays . It was thought of some interest to investigate this matter further . Accordingly a comparison was made between the relative amounts of secondary radiation emitted by air , ethyl bromide , and methyl iodide for .different degrees of hardness of the primary rays . The results obtained are given in Table V. The first column of this table gives the hardness of the rays used , as measured by the equivalent spark gap of the focus tube ; the second column gives the amount of secondary radiation from ethyl bromide ^compared with that from air , the ratio for the softest rays being reduced to unity to facilitate comparison ; the third column gives , in the same way , the ratios for methyl iodide and air ; and the fourth the ratio for methyl iodide * \#171 ; Phil. Mag. , ' [ 6 ] , vol. 14 , p. 653 , 1907 . 1908.1 Rontgen Rays throvgh Gases and Vapours . compared with ethyl bromide , calculated in the same way . In the fifth column the relative ionisation of methyl iodide compared with that of ethyl bromide is given for the sake of comparison , the ratio for the soft rays having been reduced to unity , as in the other columns . Table Y. Equivalent spark gap . Secondary radiation . Relative ionisation . CH3I/ C2H6Br . C2H6Br/ Air . CH3I/ Air . CHsI/ C2H6Br . mm. 8 1 00 1 00 1 *00 1 00 14 1 00 1-27 1*27 \#151 ; 18 0 98 1-60 1*63 \#151 ; 22 0*91 2-08 2*28 \#151 ; 26 0*80 2*42 3*03 0-52 All the values given have been corrected for the absorption of the primary rays in the gas , and for the absorption of the secondary rays by the aluminium of the window d. The latter correction was not necessary in the case of methyl iodide and air , which give out rays of approximately the same penetrating power . It was , however , necessary in the case of ethyl bromide , where the secondary radiation is considerably softer than that given out by either air or methyl iodide . A reference to Table Y will show the general nature of the results obtained . It will be seen that the amount of secondary radiation given off by ethyl bromide compared with air is practically independent of the hardness for soft and moderately hard rays , that is for rays with an equivalent spark gap of between 8 and 18 mm. For very hard rays , however , there is a distinct diminution in the values obtained , the ratio for the hardest rays used being 20 per cent , less than that for softer radiation . For methyl iodide , * on the other hand , as was noted before , the amount of secondary radiation , compared with that from air , shows a rapid increase , with an increase in the hardness of the rays , the ratio for hard rays being nearly 2^ times that for the softer radiation . Comparing , now , methyl iodide with ethyl bromide , we see that the relative amount of secondary radiation given out by the former compared with that given out by the latter is trebled as the equivalent spark gap increases from 8 mm. to 26 mm. On the other hand , the ratio of the ionisations in the two gases decreases to about half . Since the radiation from ethyl bromide is greater than that from methyl iodide , while the relative ionisation is less , the effect of this double change is to bring these two vapours more nearly into Mr. J. A. Crowther . On Passage of [ Dec. 22 , agreement with each other as the hardness of the rays increases . They give , however , no evidence of approximating to the lighter gases , such , for example , as air or carbon dioxide . Absorbability of the Secondary Radiation . The absorbability of the secondary radiation from gases containing only elements of low atomic weight is similar to that of the primary producing it . Beatty , * who has made some careful experiments on the secondary radiation from air , concludes that even for air there is evidence of a certain amount of transformation of the very penetrating rays into a slightly softer type of radiation . The effect is , however , very small , and the general statement made above certainly holds to within a few per cent. The rays from methyl iodide and stannous chloride are also of the same type as those from air . From ethyl bromide , on the other hand , we get radiation of a much softer character , the coefficient of absorption for tin foil being nearly three times as great for the secondary as for the primary . It was thought interesting to see if the ratio of the two coefficients had the same value for the absorption of the rays by the gas itself , as for absorption outside the gas , by tin foil . No direct experiments have as yet been made on this point , but some experiments , which were made on the variation of the amount of secondary radiation emitted , with variation in the pressure , allow at any rate a rough calculation to be made of the coefficient of absorption of the secondary rays in the gas itself . The experimental curve connecting the amount of secondary radiation from ethyl bromide with the pressure is given in curve I , fig. 7 . It will be seen that it bends over considerably towards the axis of pressure . Now it has been shown in the previous paper that where there is no appreciable absorption , the amount of secondary radiation emitted is simply proportional to the pressure . The departure of the experimental curve from the linear law at higher pressures is due\#151 ; ( i ) to the absorption of the primary rays in the gas ; ( ii ) to the absorption of the secondary rays in the gas . Now the absorption of the primary rays can be easily measured , as has been described above . We can therefore correct the experimental curve for the absorption of the primary rays . The curve so obtained is marked II , in fig. 7 . This curve still bends over towards the axis of pressures . Since the actual amount of secondary radiation emitted is represented by the straight line III , tangential to curve II at its origin , while the amount * 'Phil . Mag. , ' [ 6 ] , vol. 14 , p. 604 , 1907 . 1908 ] Rontgen Rays through Gases and Vapours . 123 emerging from the gas after partial absorption is represented by curve II , the ratio of the ordinate of the latter to that of the former for any given pressure gives the ratio I/ Io for that pressure . Plotting the logarithm of I/ I0 for different pressures against the pressure , we obtain curve IY . This , as will be seen , is a straight line within the limits of experimental error , and represents the absorption of the secondary rays from the gas by the gas itself . Taking 34 cm . as the mean distance in *Pressure Fig. 7 . the gas traversed by the secondary rays before reaching the window , we obtain the value 0*40 as the coefficient of absorption of the secondary rays from ethyl bromide , in ethyl bromide itself . The coefficient of absorption of the primary rays in the gas for the rays used ( which were hard ) was found to be 0T6 . The ratio of the two coefficients is therefore 2*5 . On measuring the absorption of tin foil , first for the primary beam and then for the 124 Mr. J. A. Crowther . Passage of [ Dec. 22 , secondary , the ratio of the coefficients of absorption for tin foil was found o be 2'7 . A repetition of the experiments , with methyl bromide as the radiating gas , gave very similar results . The calculations are only approximate , but as far as they go they would seem to indicate that a gas or vapour is neither exceptionally transparent , nor exceptionally opaque , to the radiations it emits . Total Ionisation . The total ionisation produced by the complete absorption of Bontgen rays of the ordinary type in different gases has not yet been directly measured . If q is the relative amount of ionisation produced in a given gas , and the coefficient of absorption of the rays for the gas , then it can easily be shown that the relative total ionisation T is given by the equation T = of e~Xxdx* Jo i.e. , T = q/ X. Both q and X are already known . We can , therefore , calculate the value of T for the different gases employed . If q/ X is the same for all gases , the total number of ions produced in different gases by rays of given intensity will be the same . The values obtained for the ratio q/ X for the different gases are given both for soft and hard rays in Table VI . As it was not possible to measure the Table VL Total ionisation ( calculated ) . Total ionisation : ( experimental ) . Soft rays . Hard rays . a-rays.# Air __ _ 1 00 CH3C02CH3 1 -oo 1 00 \#151 ; C2H5C1 1-64 1 -o 1 '32 C.C14 1*12 1 -5 1 -32 Ni.(CO)4 1 -76 0*91 " C2H5Br 0*96 1 -08 -\#166 ; CH3Br 0-98 \#151 ; 1 *32 ch3i 1-92 0*88 1 -33 Hg(CH3)2 1*46 * Kleeman , 'Roy . Soc. Proc. , ' A , yoI . 79 , p. 222 , 1907 . coefficient of absorption for air , the value of q/ X for methyl acetate has been taken as the standard and reduced to unity . For the sake of comparison , * J. J. Thomson , ' Conduction through Gases , ' p. 303 , 1906 . 1908 . ] Rontgen Rays through Gases and Vapours . 125 some experimental values obtained by Kleeman for the relative ionisation produced in different gases by the total absorption of a-rays are given in the last column of the table . It will be seen that the ratio q/ X for different gases is not a constant , the variations being considerably greater than can be accounted for by experimental error . The relative ionisation q is easy to measure with accuracy , and in the case of such gases as methyl iodide , mercury methyl , ethyl bromide , and carbon tetrachloride , where the absorption is high , the coefficient of absorption X can also be measured with a fair degree of accuracy . The values of X for hard rays are less reliable than those for soft , as not only is the absorption of its rays in the gas much less , but also it is more difficult to keep the rays constant during a series of observations . Even with hard rays the values for methyl iodide and ethyl bromide are probably not more than a few per cent. out . It will also be noticed that the relative values of q/ X for the different gases vary with the hardness of the rays , especially in the case of methyl iodide and nickel carbonyl , the properties of which seem very sensitive to fluctuations in the quality of the rays . Thus for soft rays methyl iodide gives a value almost exactly twice as large as ethyl bromide , while for hard rays its value is only about four-fifths that of the latter gas . The values obtained for the hard rays are more nearly constant than those for the softer radiations . Carbon tetrachloride appears out of place , but the absorption of the hard rays in this vapour is small , and too much importance should not be attached to this result . It may be mentioned that the measurements of q and X for any given gas were made simultaneously , in order to ensure their being strictly comparable . As both q and X vary with the hardness of the rays , this precaution is of considerable importance . Energy spent per Ion . If the whole of the energy absorbed by a gas were spent in ionising the gas , then the work done in making one ion in the gas would be inversely proportional to the total number of ions made\#151 ; that is to say , it would be inversely proportional to the total ionisation . Some of the energy absorbed , * however , is given out again as secondary radiation . In the case of ethyl bromide , for example , as much as one-third of the energy absorbed may be given out as secondary rays . Since the relative ionisation has been corrected for any ionisation due to the secondary rays , we must regard this energy as adding nothing to the total ionisation in the gas . The amount of secondary radiation from the different gases and vapours is known ; it is therefore quite easy to make correction for the energy lost in 126 Mr. J. A. Crowther . On Passage of [ Dec. 22 , this way . The values , thus corrected , for the energy spent per ion in the -different vapours are given in Table VII , methyl acetate being again taken as the standard in the absence of any reliable data for air . Table VII . Energy spent per ion . Soft rays . Hard rays . ch3co2ch3 1 -oo 100 C.vH5C1 0-61 1 -o CC14 0*89 0*7 Ni(CO)4 0*57 1 1 C2H5Br 0-86 0-7 CH , I 0*52 1*0 Hg(CH3)2 0 69 \#151 ; If there is no further loss of energy in addition to secondary radiation , these figures give the relative amount of energy required to produce an ion in the different vapours . It will be seen that the results obtained , though all of the same order , are somewhat different for different gases . Ethyl chloride , carbon tetrachloride , and ethyl bromide , give figures distinctly smaller than those for methyl acetate . The values for nickel carbonyl and methyl iodide vary Tapidly with the hardness of the rays . Unless some of the energy absorbed is dissipated in other ways than ionisation and secondary radiation , it would seem that in these gases soft rays produce an ion with the expenditure of -only about half the energy required in the case of hard rays . Summary and Conclusion . In the present work a series of experiments has been made , under comparable conditions , on the behaviour of different gases and vapours with respect to the passage of Kontgen rays through them . The results obtained may be briefly summarised as follows :\#151 ; ( i ) The amount of ionisation produced by the direct action of the primary Rontgen rays on a gas is simply proportional to the pressure of the gas . Ho evidence was obtained of the emission of any appreciable amount of soft secondary radiation by the gas . the ionisation , being apparently due to the direct action of the primary rays . ( ii ) The relative ionisation in the different gases compared with air as the standard varies considerably with the hardness of the rays . Hydrogen and ethyl bromide show an increase as the hardness of the rays increases . 1908 . ] Rontgen Rays through Gases and Vapours . Other gases remain constant or give a diminution . There is no indication of any approximation to a " density law " as the hardness of the rays is-increased . ( iii ) The relative ionisation in a gas follows approximately an additive-law . It does depend somewhat , however , on the state of combination , especially for soft rays . ( iv ) The absorption varies with the pressure according to an exponential law . ( v ) The amount of secondary radiation emitted by different gases relative to air is , generally , approximately independent of the hardness of the primary rays . For very hard rays ethyl bromide shows a slight decrease . On the other hand , the values for methyl iodide increase fairly rapidly as the hardness of the rays is increased . ( vi ) The coefficient of absorption of the secondary rays emitted by a gas , in the gas itself , is not abnormal . ( vii ) The total ionisation in different gases is not a constant , and the relative values obtained differ with the hardness of the rays . ( viii ) The amount of energy required to produce an ion in different gases is different , and also varies with the hardness of the rays . No relationship has been found between the relative ionisation and the secondary radiation , or between either , and any other known property of the gases and vapours , and the explanation of the relatively large amounts of secondary radiation emitted by ethyl bromide and its class compared with air , and of the large relative ionisations in methyl iodide , ethyl bromide , etc. , still remains to be sought . It appears that on the whole less energy is required to produce an ion in the more ionisable gases , but the values obtained do not differ very largely ; and are totally inadequate to explain the very large amounts of ionisation in these gases and vapours . Both the ionisation and the secondary Bontgen radiation follow , at any rate approximately , an additive law . It appears , therefore , that these properties are properties of the atoms themselves , and that an explanation must be sought in their atomic structure . In conclusion , I wish to express my warmest thanks to Sir J. J. Thomson , , for his helpful advice and stimulating interest during the course of the present experiments . VOL. lxxxii.\#151 ; A. K

rspa_1909_0012

0950-1207

On the velocity of the cathode rays ejected by substances exposed to the \#x3B3;-rays of radium.

128

145

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

R. D. Kleeman, B. A., B. Sc.| Prof. Sir J. J. Thomson, F. R .S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1909.0012

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rspa

http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1909_0012

10.1098/rspa.1909.0012

Atomic Physics

Electricity

Atomic Physics

128 On the Velocity of the Cathode Rays ejected by Substances exposed to the y-Rays of Radium . By K. D. Kleeman , B.A. , B.Sc. , 1851 Exhibition Scholar of the University of Adelaide , and Research Student of Emmanuel College ; Emmanuel College , Cambridge . ( Communicated by Prof. Sir J. J. Thomson , F.R.S. Received December 22 , 1908 , \#151 ; Read January 14 , 1909 . ) Si- The cathode radiation from a substance exposed to the 7-rays of radium consists , as is well known , partly of rays of a very penetrating character . Thus Eve found that the secondary rays from a lead plate , which in his experiments were deflected by a strong magnet into an ionisation chamber , possessed approximately the same penetrating power as the / 3-rays of uranium . He tested the penetrating power of these deflected rays by placing successively different thicknesses of aluminium foil over the opening of the chamber and measuring the changes produced in the leak . This paper gives an account of some experiments of a more elaborate .character by the writer on the subject . Two different methods were used in these experiments . One of the methods consisted in measuring the scattering of the cathode particles produced by different thicknesses of metal foil placed in the path of the rays . In the other method the cathode rays were deflected into an ionisation chamber by means of a strong electromagnet , and the ionisation in the chamber measured for magnetic fields of different strengths . It will be then seen that each method has its particular advantages in bringing out thejdifferent properties of the secondary radiation . The form of apparatus used in the first method is shown in fig. 1 . A is an aluminium ionisation chamber 12'5 cm . long , 10 cm . high , and 7 cm . deep , supported by a wooden frame arrangement from which it was insulated . The metal plate B resting on the adjustable table C formed the lower side of the chamber . The plate could be removed and replaced by another after lowering the table a convenient distance from the chamber . Thirty milligrammes of radium bromide ( enclosed in a glass tube ) were placed in the cavity of the lead cylinder D , and a piece of sheet lead 3 mm. thick placed over the opening of the cavity to cut off the / 3-rays . E is another ionisation chamber whose electrode was connected with that of the chamber A. One of the chambers was\#163 ; connected to a positive potential of 200 volts and the On the Velocity of the Cathode Rays , etc. 129 other chamber to a negative potential of 200 volts . The ionisation in both chambers was produced by the 7-rays from the radium , the amount of ionisation in the chamber E being regulated by screens of different thicknesses placed between the radium and the chamber . The object of the chamber E was to partially compensate by means of its leak that part of the leak in the chamber A which is not due to the cathode rays from the plate B. The penetrating power of the secondary cathode rays emitted by the plate B was investigated by measuring the ionisation in the chamber for different thicknesses 61 aluminium or paper foil placed upon the plate . If the radiation from the foil is small in comparison with the radiation from -V ^ Fig. 1 . another sheet of foil of the same mass per cm.2 , but of the material of the plate B , the secondary radiation from a combination of the plate B and a sheet of foil is the radiation from the plate modified by the scattering of the foil . The coefficient of absorption of the foil is in that case easily obtained . Thus , let M denote the leak in the chamber A produced by the secondary cathode radiation from the plate B , and 1ST the remaining leak in the chamber minus the leak in the chamber E. The leak obtained when there is no foil on the plate is then ( M + N ) . When a sheet of foil is placed on the plate the leak obtained is ( \lt ; \#163 ; M + N ) , where \lt ; f\gt ; denotes the fraction of the secondary radiation from the plate which penetrates the foil . If an additional sheet of foil of the same thickness is placed on the plate , the leak obtained is ( \lt ; \#163 ; 2M -t-N ) . The difference between the first and third 130 Mr. Kleeman . Velocity of Cathode Rays ejected [ Dec. 22 , leak divided by the difference between the first and second then gives the value of ( l\#151 ; \lt ; \#163 ; 2)/ ( l\#151 ; \lt ; \#163 ; ) , that is of ( \lt ; /\gt ; + l ) . And if x denotes the thickness and X the coefficient of absorption of the foil , we have e~xK = \lt ; f\gt ; , from which X can be obtained . The value of \lt ; f\gt ; , we have seen , gives the fraction of the amount of radiation from the plate which penetrates a given thickness of foil . But this applies only to the whole radiation from the plate if it is homogeneous , If the radiation is heterogeneous , the value of \lt ; f\gt ; applies only to that part of the radiation which is easily absorbed iii comparison with the remaining part . This follows from the particular way in which ( f\gt ; ft obtained . Thus , let the radiation from the plate be divided into two parts , A and B , and let the values of \lt ; f\gt ; for the two parts be \lt ; f\gt ; i and \lt ; f)2 respectively , The difference between the leak with a sheet of foil on the radiating plate and the leak without the foil is then A(l \#151 ; \lt ; \#163 ; i ) + B ( 1\#151 ; \lt ; \#163 ; s ) . Now , we may suppose the radiation divided into two parts , such that ( l\#151 ; \lt ; f\gt ; a ) is so small that B(1\#151 ; \lt ; \#163 ; 2 ) is negligible in comparison with A(l \#151 ; \lt ; \#163 ; i ) . The difference between the leak with two sheets of foil and the leak without foil is then and the ratio of this difference to the other difference equal to ( 1 + \lt ; \#163 ; i ) . Therefore if the rays are heterogeneous , the value of \lt ; f\gt ; found by the above method and the coefficient of absorption deduced therefrom applies to the set of rays A. This method thus brings the existence of the soft rays in a set of rays into evidence , and furnishes also a measure of their penetrating power . The value obtained for \lt ; \#163 ; , it will be observed , is influenced by the secondary radiation from the foil itself , if this is not of negligible magnitude . For the radiation from the foil , when added to the part of the radiation from the plate which penetrates the foil , has the effect of making the fraction of the radiation which penetrates the foil appear larger than it really is . A smaller value for X than the true value will consequently be obtained . But by using a proper combination of plate and foil , the effect of the radiation from the foil becomes negligible . Thus , if the radiating plate is of aluminium , or of a metal of higher atomic weight than aluminium , and paper foil used to absorb the secondary rays , the effect of the radiation from the paper on the value of \lt ; f\gt ; is small . This was proved in the following manner:\#151 ; The radiations from a sheet of paper and a sheet of aluminium foil were compared with one another , each sheet radiating under the same conditions as the radiating plate . The details of this experiment will be described further on . The sheets of foil were two of those used to absorb the cathode rays in these experiments ; the paper foil weighed GAxlO-3 and the aluminium foil 9'27 x 10-4 gramme per cm.2 It was found that each of these two sheets of foil produced practically the same amount of secondary 1908.1 by Substances exposed to the y-Rays of Radium . 131 radiation . The radiations from aluminium and paper for equal masses per cm.3 are therefore in the ratio of 1 to 0*13 . Consider the effeet of placing a sheet of aluminium foil on an aluminium radiating plate . It is evident that the decrease of secondary radiation from the plate due to the scattering of the foil is exactly counterbalanced by the radiation from the foil . But if a sheet of paper foil of the same mass per cm.2 as the aluminium foil be placed on the plate , the radiation from the paper , according to the foregoing , would be only about 0*13 of that from the aluminium foil . But the amount of scattering produced would be the same in each case . This follows from the experiments on the scattering of cathode rays . Thus it has been shown that the amounts of scattering of aluminium and paper for equal masses per cm.2 are equal to one another over a wide range of Velocities of the cathode rays produced in a vacuum tube , and in the case of the / 3-rays of uranium . We may suppose , therefore , as a first approximation , that a sheet of paper foil placed on a plate of aluminium produces only scattering of the radiation from the plate . But this must also be true if a radiator of higher atomic weight than aluminium is used . For in that case , since the radiation from equal masses increases with the atomic weight of the material , the difference between the amounts of radiation of the paper foil and an equivalent piece of foil of the same material as the radiating plate is even greater than in the foregoing case . Further , since the ratio of the atomic weight of lead to that of aluminium is greater than the ratio of the atomic weight of aluminium to the average atomic weight of paper , this will obviously be also true in the case of aluminium foil and a lead plate . The relative amounts of radiation from a sheet of paper and a sheet of aluminium foil were found in the following manner . The table C was removed , and a wire gauze fixed to the chamber so as to form its lower side . The leak in the chamber was then measured . A sheet of paper foil fixed to a metal frame was then placed underneath the gauze so as to be in contact with it , and the leak again measured . In the same manner a leak was obtained with a sheet of aluminium foil fixed to the frame . The first leak was then subtracted from the second and third , the result giving the amounts of radiation from the paper and aluminium foil respectively . Table I gives the values of \lt ; f\gt ; for paper foil obtained with a number of different metals in the manner described . Each of the measurements required for calculating \lt ; f\gt ; is the mean of at least eight readings . The readings were taken in the same manner as described in a previous paper.* * 'Phil . Mag. , 'November , 1907 , p. 619 . 132 Mr. Kleeman . Velocity of Cathode Rays ejected [ Dec. 22 , The apparent leak was usually decreased by about 50 per cent , when a sheet of foil was placed on the plate.* Table I. Radiator and its thickness . \lt ; p for paper weighing 6 *4 x 10~d gramme per cm.2 . mm. Pb 2 0*63 Pb 0-25 0-50 Sn 3 0-54 Zn 3 0*54 Cu 2 5 0*55 Fe 2-5 0*52 Ni 2 *6 0-53 S 4 0-52 A1 3 5 0-63 It will be seen that the value of cf\gt ; is approximately the same for the different metals , the mean value being about 0'53 . Thus part of the secondary cathode radiation from each of these plates is reduced to about one-half by a sheet of paper ( weighing 6*4 xlO-3 gramme per cm.2 ) placed close to the radiating plate . If all the radiation from a plate possessed the same penetrating power as the ^-rays from uranium , the value of would be 0*99 , and a single sheet of paper foil would in that case stop about 1 per cent , of the radiation . It appears , therefore , that the secondary cathode radiation from a plate on the side where the 7-rays enter consists partly of very absorbable rays . The penetrating power and heterogeneity of this absorbable radiation is best brought out by considering the values of \lt ; j\gt ; and X found for aluminium foil . Aluminium foil is more homogeneous than paper , and it is therefore better to use aluminium foil when possible . Table II gives the values obtained for ( fj and X when a radiator of lead was used . The coefficient of absorption of aluminium for the cathode rays in a vacuum tube , and for the yS-rays of uranium oxide , are placed in the table for comparison . The first column in the table gives the nature of the source of cathode radiation . The second column contains values of \lt ; f\gt ; . The , first value of ( f\gt ; given corresponds to the soft secondary rays from a lead plate exposed to 7-rays , and the second to those rays which penetrated a layer of aluminium leaf weighing 2'72 x 10"3 gramme per cm.2 placed upon the plate . The third column gives the values of X for the different cathode rays . It will be seen that the coefficient of absorption of aluminium for the soft * The paper was blackened with graphite in order to make it a good conductor of electricity . 1908 . ] by Substances exposed to the y-Rays of Radium . 133 cathode rays from the lead plate is very much greater than that found for the / 8-rays of uranium , but smaller than that found by Lenard for the cathode rays in a vacuum tube . A comparison of these coefficients of absorption with some coefficients of absorption and corresponding velocities- Table II . Nature of the source of cathode radiation . \lt ; f\gt ; for aluminium leaf weighing 9*27 x 10"4 gramme per cm.2 Calculated thickness of leaf , 3*4 x 10"6 cm . Equivalent in mass to a thickness 0*72 cm . of air . K Secondary cathode rays from a plate exposed to the 7-rays of radium . 0*52 1898 The secondary cathode rays from the lead plate passed through aluminium leaf weighing 2*72 x 10~3 gramme per cm.2 Equivalent in mass to a thickness of 2 cm . of air . 0-804 640 Cathode rays in a vacuum tube . Telocity about 6 x 109 cm./ sec. ( Lenard ) . \#151 ; 7150 \#163 ; -rays from uranium ( Rutherford ) . \#151 ; 14 given by Lenard , * suggests that the velocity of these soft secondary rays , on the supposition that they are homogeneous , is about twice that of the cathode rays in a vacuum tube and one-third that of the / 8-rays of uranium . But the rays are not homogeneous , as will be shown presently , and the velocities therefore range above and below this value . Next let us consider the values of ( f\gt ; , which , it will be remembered , denote ? the fractions of the soft cathode radiations penetrating a piece of foil of a given thickness . Thus aluminium foil 3*4 x 10-4 cm . thick reduces the ' soft radiation from a lead plate to 0*5 of its original value . The sheet of foil is equivalent in mass to a layer of air 0'72 cm . thick . Therefore , if we assume that the absorption of the rays by air and aluminium is the same for equal masses per cm.2 , half of this soft radiation is absorbed in the 0*72 cm , of air adjacent to the plate . When the cathode rays were first sifted through an aluminium layer weighing 2'72 x 10-3 gramme per cm . , the value obtained for \lt ; f\gt ; was Q*82r which is a larger value than that obtained without previous sifting . The radiation which penetrated the aluminium layer did not , therefore , contain as large an amount of soft radiation as the whole radiation from the plate. . * See 'Conduction of Electricity through Gases , ' by Prof. JT . J. Thomson , second edition , p. 381 . 134 Mr. Kleeman . Velocity of Cathode Rays ejected [ Dec* 22 , Some of the soft rays were , therefore , completely absorbed by the aluminium layer . And since the layer is equivalent in mass to about 2 cm . of air , some of the cathode rays from the plate were completely absorbed in the 2 cm . of , air adjacent to the plate . The radiation which penetrated the aluminium layer contained much less :Soft radiation than the whole radiation from the plate . Thus about 0'5 of ; the whole radiation from the plate was absorbed by a sheet of aluminium foil 3*4 xlO-4 cm . thick , while only ( 1\#151 ; 0 82 ) or 018 of the radiation which penetrated the aluminium layer was absorbed by the same sheet of foil . The foregoing considerations show that the soft rays from a plate are heterogeneous . They also show that the coefficients of absorption found apply principally to those cathode rays which have a range of 1 or 2 cm . only . The properties of these soft rays were brought into prominence not ( Only by the particular method of investigation adopted , but also by using very thin sheets of absorbing material . For if a heterogeneous beam of .cathode rays is gradually cut down by successive pieceB of thin foil , the decrease will be more rapid at the beginning on account of the absorbable radiation being more rapidly absorbed than the more penetrating . The .coefficient of absorption obtained with thin foil will therefore be larger than jthat obtained with foil which is much thicker , and thin foil therefore brings out the properties of the soft radiation to a greater extent than thick foil . . Table I shows that the value of \lt ; \#163 ; for a given thickness of paper foil is independent of the nature of the radiating plate . Thus the nature or penetrating power of the soft radiation in . question is independent of the nature of the radiating material . It does not follow , however , that this result must also be true for the penetrating radiation emitted by the plate . It is probable that the penetrating cathode radiation set free in a plate is successively transformed into other radiations of less and less penetrating power , the radiation ultimately produced from all materials being rays , which , in their turn , do not produce any secondary radiation . The soft secondary radiation from a plate produced in that way would be practically independent of the nature of the radiating plate . It seems , therefore , that ishe soft radiation is largely produced by the penetrating / 9-rays ejected by the y-rays . Other experiments seem to point to the same conclusion . Thus it was found that the nature of the cathode rays is practically independent of previous sifting of the y-rays through a thick screen of metal . This result is shown by Table III . The soft radiation is , therefore , not produced by very absorbable rays in the beam of y-rays , for previous sifting of the beam would diminish the very absorbable rays in a greater 1908 . ] by Substances exposed to the of Radium . 135 proportion than the more penetrating rays , and the penetrating power of the secondary cathode radiation would thereby be increased . Table III . Lead screen 1 '3 cm . thick \lt ; f\gt ; = 0 -50 Zinc screen 2 *0 cm . thick ... ... ... ... ... . \lt ; f\gt ; = 0 *50 Lead screen 0 '3 cm . thick ... ... ... ... \lt ; f\gt ; = Q *53 Very little of the soft cathode radiation seems to be produced by the soft 7-rays generated in the plate , for the penetrating power of the radiation is practically independent of the thickness of the radiating plate . Thus the values of \lt ; f\gt ; in Table I for two lead radiators , one of which was 025 and the other 2 mm. " thick , were 050 and 0'53 respectively . Some of the radiation must , however , be produced by the secondary 7-rays , since secondary 7-rays are produced in a substance exposed to 7-rays , which are so soft as to be almost entirely absorbed by the substance.* It may be mentioned in passing that there is some indirect evidence that such soft 7-rays are likely to be produced . Thus Barklaf found that the secondary X-radiation from carbon becomes softer in comparison with the primary X-rays as the hardness of the primary rays is increased . The soft cathode radiation possesses considerable ionising power , since the leaks were not appreciably altered by reversing the sign of all the potentials . If the leaks consisted largely of cathode particles which originated in the plate , the magnitude of the leaks would have been considerably decreased when the potential of the chamber was changed from positive to negative . The foregoing method may also be used to investigate the penetrating power of the soft radiation on the side of the plate where the 7-rays emerge . But in this case the radiations from two sheets of foil of equal mass but of different materials do not differ so much from one another as in the foregoing case . This is due to the fact that the radiation from the side of a plate where the 7-rays emerge does not decrease so rapidly with decrease of atomic weight of the plate as the radiation from the other side . This effect was explained by Prof. Brag and Dr. Madsen by supposing that the secondary cathode rays are initially projected in the direction of propagation of the 7-rays.t The value of \lt ; f\gt ; obtained by this method will therefore be larger than the true value ; but still the results with this restriction will be seen to be of importance . * Kleeman , ' Phil. Mag. , ' May , 1908 , p. 638 . t Barkla , ' Phil. Mag. , ' February , 1908 , p. 288 . X * Phil. Mag. , ' May , 1908 , p. 663 . 136 Mr. Kleeman . Velocity of Cathode Rays ejected [ Dec. 22 , The experiments in this case were carried out in the following manner . The adjustable table was moved to one side of the chamber , and the radiating plate held in position by two arms attached to the table . The radium was placed underneath the plate at a distance of about 9 cm . from its centre . Readings with foil were then taken in the same way as before . The values found for ( f\gt ; for aluminium and paper foil when a lead radiator was used were 0*45 and 046 respectively . These values are smaller than those found under previous conditions , viz. , 0*52 and 0*53 respectively . The difference is greater with paper than with aluminium foil , this being probably due to the radiation from the paper foil affecting the value of to a less extent than the radiation from the aluminium foil . The radiation from the foil , we have seen , affects the values of \lt ; f\gt ; for the side where the y-rays emerge to a greater extent than the values for the other side . And since the effect of the radiation is to make \lt ; j\gt ; greater than its true value , the difference between the values for the two sides of the plate must be even greater than those given by the above values . It appears , therefore , that the soft radiation on the side of the plate where the y-rays emerge is considerably softer than that on the other side . This is an interesting result ; but the true explanation is not at all clear . One way of explaining it is as follows . The soft radiation , we have seen , is to a large extent produced by the cathode rays projected by the 7-rays . Since the cathode rays produced by the 7-rays are projected in the direction of propagation of the rays , it is not improbable , on the aether-pulse theory , that a 7-ray deflects in the direction of its propagation the soft cathode radiation over which it may happen to pass . This may take place principally in the following way . A 7-pulse is probably followed by a number of pulses of much less intensity produced by the same electron as the principal pulse , and also by secondary pulses produced in the matter which it traverses . These pulses will pass over the cathode ray produced by the 7-pulse , since they are all ( for a time at least ) moving in the same direction . The soft radiation produced by the cathode ray might , therefore , be to some extent deflected in the direction of propagation of the pulses . It is not improbable , however , that this is not the true explanation of the effect . Further investigations on secondary radiation and scattering of cathode rays will probably make this clear . Some experiments were also made on the soft radiation produced by the ft- and 7-rays together on the emergent side of a plate . The radiating plate was a sheet of lead 0*25 mm. thick , stretched over a frame . The radium was placed underneath the plate in the same position as in the experiments just 1908 . ] by Substances exposed to the y-Rays of Radium . 13F described . It was not covered by a screen , and some of the / 3-rays which penetrated the glass tube therefore penetrated in part the lead sheet . The soft cathode radiation produced was therefore due to the action of the ft- and . y-rays . The values of \lt ; f\gt ; for aluminium and paper foil obtained with this arrangement were 0*57 and 0*29 respectively . These values are larger than those obtained with a lead plate 2 mm. thick , and with the / 3-rays cut off by a. screen , viz. , 045 and 016 respectively . It appears , therefore , that the soft radiation produced by the / 3- and 7-rays together is of a more penetrating character than that produced by the 7-rays alone . This is probably due , , considering the way \lt ; \#163 ; was obtained , to the / 3-radiation produced by the 7-rays being more heterogeneous than the / 3-rays of radium after having passed through the walls of a glass tube and a sheet of lead . And the less penetrating radiation was therefore smaller in comparison with the remaining radiation when both the \#163 ; - and 7-rays were used , than when the 7-rays alone were used . It would appear afterwards , from the magnetic deflection experiments* that the / 3-rays ejected by the 7-rays are heterogeneous\#151 ; that is , have different velocities . Table IV gives some values of \lt ; j\gt ; obtained for different distances of the-radium from the radiating plate . The values refer to the side of the plate-where the 7-rays entered . It will be seen that there is practically nodifference in the values obtained . The nature of the soft radiation is , therefore , as we would expect , independent of the distance of the radium from the radiating plate . Table IV . Distance of radium from lead radiator . \lt ; f ) . cm . 11 -o 0-50 12 -5 0*53 17-0 0*54 Sn . The experiments in which the velocity of the cathode rays was investigated by deflecting them by a magnetic field will now be described . The form of apparatus used in these experiments is shown in fig. 2 . A is an ionisation chamber ; it consisted of an oblong lead box 8 cm . long , 5'5 cm . high , and 6 cm . deep . The side db of the chamber consisted of tightly stretched tissue-paper . B and C are lead blocks which served to screen the chamber 138 Mr. Kleeman . Velocity of Cathode Rays ejected [ Dec. 22 , from the direct action of the 7-rays from the radium contained in the lead \#166 ; cylinder D , they were 0 cm . and 5*5 cm . thick respectively . But since it is impossible to obtain perfect screening from 7-rays , there was a constant small leak in the chamber due to the rays which penetrated the lead blocks . F is an aperture of square section , 3 x 3 cm.2 , in the lead block B , its cross-section was made Smaller when required by tightly packing its sides with suitable lead strips . A metal plate a few millimetres thick was placed at c , on top of the aperture , or at d , at the bottom of the aperture . This plate was the source of the secondary cathode radiation under investigation . The rays were deflected by means of a magnetic field , whose direction was at Fig. 2 . right angles to the plane of the paper , towards the tissue-paper window of the ionisation chamber A. The increase of leak in the chamber caused by the ^-particles which penetrated into the chamber was measured for magnetic fields of different strengths . The position of the pole-pieces of the magnet ( which were of square section ) with respect to the other parts of the apparatus is indicated in the figure by a dotted square . The beam of cathode rays entering the chamber could be limited to any required size by placing at e a suitable lead stop of the form ' G. First some experiments were made in order to see if previous screening of the 7-rays affects the velocity of the secondary rays . In ' one set of 1908 . ] by Substances exposed to the y-Rays of . experiments the radiating plate was placed at c , no stop of any kind being placed at e. Readings were taken with successively increased magnetic fields . The reading obtained with no magnetic field was subtracted from each of these readings , and the resulting values plotted against the current through the magnet . . Fig. 3 shows some curves obtained in this way . They are the result of combining a large number of observations taken at different times . The sharp bends in the curves indicate the stage when the rays of Magnetising current ' Fig. 3 . the outer edge of the principal stream of rays are deflected just sufficiently to enter the chamber . The curves have been so plotted that they are slightly separated from one another at the bends . The curves A and B were obtained with a lead radiator . The 7-rays were sifted through lead screens of different thicknesses in the two cases , the curve A being obtained with a screen 1*5 cm . thick , and the curve B with 140 Mr. Kleeman . Velocity of Cathode Rays ejected [ Dec. 22 , a screen 3 mm. thick . The difference in the form of the curves indicates that the proportion of electrons moving with a velocity less than that -corresponding to the bends in the curves , is decreased when the thickness of the lead screen is increased . A thick screen thus absorbs a greater proportion of the 7-rays which produce these slow electrons than a thin one . It appears , therefore , that the velocity of the secondary cathode radiation produced in a lead plate decreases with the absorbability of the 7-rays producing it . The curves C and D were obtained with an aluminium radiator , using the .same lead screens as before . The curve C corresponds to the thick screen , and the curve D to the thin screen being used . It will be seen that now there is scarcely any difference between the curves obtained . The previous passage of the 7-rays through a thick lead screen thus affects the more absorbable radiation from an aluminium plate to a less extent than that from a lead plate . If part of the soft radiation from a plate is produced by the 7-rays that are selectively absorbed by the plate we would expect such a result . The substitution of a thick screen for a thin one would then affect the radiation from a plate of the same material as the screen to a greater extent than the -radiation from a plate of some other material , for the 7-rays would be robbed in the first case to a greater extent of the rays most easily absorbed by the plate than in any other case . The rays that are most easily absorbed by a substance , it should be observed , are also the rays that are selectively \#166 ; absorbed by the substance , if selective absorption exists . Two sets of readings were also taken in succession with a zinc screen 2 cm . thick and the thick screen of lead used previously , the radiator being of lead . Curves of the same form as A and B were obtained , the curve obtained with the lead screen being more convex towards the current axis than the curve obtained with the zinc screen . The lead screen thus robbed the beam of 7-rays of a greater proportion of the rays which produce soft \#166 ; cathode radiation from a lead plate than the zinc screen . This is in accordance with what we would expect according to the explanation given of the effect . \#171 ; It should be observed that the soft rays dealt with in these experiments are of a much more penetrating character than those discussed in the previous section . The average range of the latter rays is so small that -scarcely any of them could have entered the ionisation chamber in the experiments just described . A large number of experiments were made under different conditions to make sure that the -effects just described were not due to a disturbing 1908 . ] by Substances exposed to the of Radium . 141 influence of the radiation from other parts of the apparatus than that from the plate at c. Thus , readings were taken with the aperture F of different dimensions , and the pole-pieces at different distances apart ; readings were also taken with the radiating plate placed at But in all cases a difference of the same nature as described was obtained between the curves for an aluminium and lead radiator when a thick and thin screen of lead were used . The difference in the curvature of the curves was , however , for two sets of experiments carried out under the same conditions , not always -exactly of the same magnitude . This was probably due to hysteresis effects of the electro-magnet . The most consistent results were obtained when the radiating plate was placed at d. The reason for this appears to be that less of the very soft radiation , which would be greatly affected by the hysteresis of the magnet for small magnetic fields , entered the chamber in .this case . The conclusion , then , is that the velocity of the cathode radiation from .a plate due to 7-rays decreases with the absorbability of the rays producing it* But the set of rays most easily absorbed by a substance need not necessarily be the same for all substances . Some experiments by Innesf on the velocity of the secondary cathode rays produced by X-rays may be mentioned in this connection . This observer found that the velocity of the cathode radiation from a metal plate decreased with the softness of the X-rays producing it . He also found that , keeping the penetrating power of his X-rays constant , the velocity of the .cathode rays was influenced by the nature of the radiating metal . The effect in the latter case is easily explained by selective absorption of the metals used . The set of rays best absorbed by a substance , not necessarily the same set for each substance , varied probably in degree of absorbability from substance to substance , and cathode rays of corresponding slowness were produced . The bends in the curves in fig. 3 indicate , as already pointed out , that there is a principal stream of cathode rays from the radiating plate . If the rays were ejected from a plate in all directions we would scarcely obtain any indication of bends of any sharpness . The sharpness of the bends w'as found to depend somewhat , as we would expect , on the dimension of the aperture F , and the distance of the ionisation chamber from the aperture . This result confirms the deduction which Prof. Brag and Dr. Madsen{ * Prof. Brag and Dr. Madsen , according to a paper that has just appeared in the *Phil . Mag. ' of December , 1908 , p. 918 , have obtained the same result , but by a different jnethod . + ' Boy . Soc. Proc. , ' A , vol. 79 ( 1907 ) , p. 442 . f Loc . cit. 142 Mr. Kleeman . Velocity of Cathode Rays ejected [ Dec. 22 , made from some of their experiments on secondary radiation , namely , that the secondary cathode rays produced by the 7-rays are ejected in the direction of propagation of the rays . An attempt was also made to determine absolutely the velocity of the fast-moving rays from a plate . But it had to be given up on account of the great heterogeneousness of the rays . The maximum velocity of a pencil of rays was found to depend on the size of the aperture F , and on the size of the aperture of the stop G- placed at e , as we should expect if the rays are heterogeneous . And to obtain the relation between the velocity and amount of radiation , as has been done for the / 3-rays of radium , the apparatus was altogether unsuitable . The rays were therefore compared as a whole with the / 3-rays from radium . The size of the aperture F in these experiments was l'l cm.2 and the lead plate used as radiator was placed at c. A stop of the form G was placed at e , the size of its aperture being 1*3 cm.2 A set of readings was first taken with the lead radiator for magnetic fields of different strengths in the same way as before . A set of readings was next taken with the screen over the radium and the lead radiator removed . A stream of / 3-rays from the radium now passed through the aperture F , and was deflected by the magnetic field towards the ionisation chamber . It should be observed that , if the secondary rays from the lead plate radiator were ejected in the direction of propagation of the 7-rays , the beams in the two cases were similar in respect to the direction of motion of the electrons . The readings obtained in the two cases are plotted against the current through magnet in fig. 4 . The curve E refers to the cathode rays from the lead plate , and the curve F to the / 3-rays from the radium . It may be mentioned in passing that a comparison of the magnetic field with current through magnet by means of an exploring coil and current indicator showed them to be approximately proportional to one another over the whole range of magnetic fields used in these experiments . The curves have been so plotted that they are only slightly separated from one another : actually the maximum leak for the / 3-rays was much greater than that for the secondary cathode rays . It will be seen that in both cases the maximum leak is obtained for approximately the same current through the magnet . The velocity of the secondary cathode rays from a lead plate exposed to the 7-rays is therefore , as a whole , the same as that of the / 3-rays of radium . It will be interesting , without committing ourselves to any particular theory of the 7-rays , to see what this result means in the light of the two theories of the 7-rays at present put forward . According to the theory of Prof. Bragg and Dr. Madsen , the 7-ray consists 1908 . ] by Substances exposed to of Radium . of a negative electron associated with a particle possessing an equal charge but of opposite sign , the combination forming a neutral pair of particles . In traversing matter , the pair is liable to get broken up , with the result that the negative particle proceeds onwards ; the 7-ray now appears as secondary cathode radiation . A 7-ray is supposed to arise by an electron picking up a positive particle which it encounters in traversing matter . Now , if the positive particle has an appreciable mass , the velocity of the pair of particles must be less than that of the negative electron before the pair was formed . Consequently , when the pair is stripped of its positive particle , the velocity of the cathode ray proceeding onwards should be Magnetising current -Fig . 4 . smaller than its velocity before association with the positive particle . If , for example , the mass of the positive particle is equal to that of the negative , the velocity of the secondary cathode radiation should be about 1/ ^/ 2 , or about 0*7 of that of the / 3-rays of radium . In that ease the maximum for the curve for the secondary cathode rays in fig. 4 would be almost half-way between the zero and the maximum for the / 3-rays of radium . But since the curves show that the velocities are practically the same , it follows that the positive particle ( if the neutral pairs are formed in the way described ) must be small in comparison with that of the negative . If the mass of the positive particle is entirely electrical , it follows from the VOL. LXXXII.\#151 ; A. L 144 Mr. Kleeman . Velocity of Cathode Rays ejected [ Dec. 22 , 2 e2 well-known equation m = ^ , which connects the electrical mass with the charge and radius of particle , that the radius of the positive particle must be large in comparison with that of an electron . This condition would be approximately fulfilled by a positive particle the diameter of which is equal to that of a molecule , but whose mass is entirely electrical . On the sether-pulse theory of the 7-rays in its usual accepted form , the pulse is supposed to spread out in the form of a spherical shell with the generating electron as centre . If the energy of an electron ejected by a 7-pulse is derived entirely from that of the pulse , its energy can only be a small fraction of that of the pulse , and therefore of that of the electron which generated the pulse . But this is contrary to experience . To overcome this difficulty , Prof. J. J. Thomson proposed a modified aether-pulse theory* According to this theory , the pulse is supposed to proceed in one direction only from the radiating electron , and that the area of the wave front of the pulse remains constant as the distance of the pulse from the electron increases . The electron ejected by a pulse is therefore able to absorb the whole energy of the pulse ; and if the whole energy of the radiating electron is transformed into pulse energy , the velocity of the secondary electron may be equal , or at least very nearly equal , to that of the electron which produced the pulse . Prof. Thomson also suggested that the wave front of a ray of light may be similarly restricted . It will be interesting in this connection to obtain an estimate of the thickness of a 7-ray pulse . If a ray of light and a 7-pulse are identical in structure the interesting experiments of Ladenburgf on the velocity of the cathode rays ejected by ultra-violet light furnish data from which an estimate of the thickness of a 7-pulse may be made . This experimenter found that the product of the velocity of a beam of secondary cathode rays into the wave-length of the ultra-violet light producing it is constant . An approximate value of this constant for our purpose is obtained by taking the velocity 2x 107 cm./ sec. for the cathode rays ( a value found by Lenard ) to correspond to the wave-length 288/ */ * of ultra-violet light . Therefore , if X denotes the thickness of a 7-pulse , and we take the velocity of the \#163 ; -rays as 2*5 x 1010 cm./ sec. , we have X2*5 x 1010 = 218 / */ *x 2 x 107 , or X == 174 / */ *x 10"3 . From the last equation/ *it will be seen that the thickness of a 7-pulse is about one-thousandth of the wave-length of ultraviolet light . And since the wave-length of ultra-violet light is about one * ' Camb . Phil. Soc. Proc. , ' vol. 14 , part 4 , p. 417 . t ' Yerh . der Deut . Phys. Gesellschaft , ' 1907 , p. 507 . 1908 . ] by Substances exposed to the y-Rays of Radium . 145 thousand times the diameter of a molecule , the thickness of a 7-pulse is about equal to the diameter of a molecule . Summary . Part of the cathode radiation from a plate exposed to the 7-rays of radium consists of very soft rays which are absorbed in 1 or 2 cm . of air . The softness of the radiation is practically independent of the thickness of the radiator , and previous sifting of the 7-rays through a thick screen . The radiation appears to be considerably softer on the side of the radiating plate where the 7-rays emerge than on the side where they enter . Measurements of the softness of the radiation for radiators of different materials on the side where the 7-rays entered showed that it is practically independent of the nature of the material of the radiator . The soft radiation produced by the / 3- and 7-rays of radium together is of a more penetrating character than that produced by the 7-rays alone . The penetrating cathode rays produced directly by the 7-rays have been shown to possess different velocities . It was found that the penetrating power of the cathode radiation from a plate decreases with the increase of absorbability of the 7-radiation which produces it . The velocity of these secondary rays as a whole is , as a first approximation , equal to that of the ^8-rays of radium . It gives me great pleasure to thank Prof. Thomson for his interest and advice during this research . Electrolytes and Colloids.\#151 ; The Physical State of Gluten . By Prof. T. B. Wood and W. B. Hardy , E.R.S. ( Received October 24 , \#151 ; Read December 10 , 1908 . ) [ This paper is printed in Series B ( No. 545 ) , vol. 81 , pp. 38\#151 ; 43 . ]

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Electrolytes and colloids. \#x2014;The physical state of gluten.

145

145

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

Prof. T. B. Wood |W. B. Hardy, F. R. S.

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10.1098/rspa.1909.0013

Atomic Physics

Electricity

Atomic Physics

1908 . ] by Substances exposed to the of Radium . 145 thousand times the diameter of a molecule , the thickness of a 7-pulse is about equal to the diameter of a molecule . Summary . Part of the cathode radiation from a plate exposed to the 7-rays of radium consists of very soft rays which are absorbed in 1 or 2 cm . of air . The softness of the radiation is practically independent of the thickness of the radiator , and previous sifting of the 7-rays through a thick screen . The radiation appears to be considerably softer on the side of the radiating plate where the 7-rays emerge than on the side where they enter . Measurements of the softness of the radiation for radiators of different materials on the side where the 7-rays entered showed that it is practically independent of the nature of the material of the radiator . The soft radiation produced by the j3- and 7-rays of radium together is of a more penetrating character than that produced by the 7-rays alone . The penetrating cathode rays produced directly by the 7-rays have been shown to possess different velocities . It was found that the penetrating-power of the cathode radiation from a plate decreases with the increase of absorbability of the 7-radiation which produces it . The velocity of these secondary rays as a whole is , as a first approximation , equal to that of the / 3-rays of radium . It gives me great pleasure to thank Prof. Thomson for his interest and advice during this research . Electrolytes and Colloids.\#151 ; The Physical State of Gluten . By Prof. T. B. Wood and W. B. Hardy , F.R.S. ( Received October 24 , \#151 ; Read December 10 , 1908 . ) [ This paper is printed in Series B ( No. 545 ) , vol. 81 , pp. 38\#151 ; 43 . ]

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Determination of the surface-tension of water by the method of jet-vibration.

146

146

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

Prof. N. Bohr (Copenhagen)| Sir W. Ramsay, K. C .B., F. R. S.

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10.1098/rspa.1909.0014

Fluid Dynamics

Biography

Fluid Dynamics

146 Determination of the Surface-tension Water the Method Jet-vibration . By Prof. N. Bohr ( Copenhagen ) . ( Communicated by Sir W. Ramsay , K.C.B. , F.R.S. Received Jan. 12 , \#151 ; Read Jan. 21,1909 . ) ( Abstract . ) In the present determination of the surface-tension of water the method of jet-vibration proposed by Lord Rayleigh is used ; this method has the fundamental advantage that a perfectly fresh new-formed surface can be examined . In the theoretical part of this investigation it is shown how Lord Rayleigh 's theory of infinitely small vibrations of a jet of a non-viscid liquid can be supplemented by corrections for the influence of the finite amplitudes as well as for the viscosity . In the experimental part it is shown how it seems to be possible , in a simple manner , to secure that the jet-piece used for the measurements satisfies the assumptions on which the theoretical development rests . As the final result of the experiments , the author finds the surface-tension of water at 12 ' to be 73*23 dine / cm . The Origin of Osmotic Effects . II.\#151 ; Differential Septa . By Henry E. Armstrong , F.R.S. ( Received January 23 , \#151 ; Read January 28 , 1909 . ) [ This paper is printed in Series B ( No. 546 ) , vol. 81 . ]

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The specific heats of air and carbon dioxide at atmospheric pressure, by the continuous electrical method, at 20\#xB0; C. and at 100\#xB0; C.

147

149

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

W. F. G. Swann, A. R. C. S., B. Sc.|Prof. H. L. Callendar, F. R. S.

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http://dx.doi.org/10.1098/rspa.1909.0015

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10.1098/rspa.1909.0015

Thermodynamics

Electricity

Thermodynamics

147 The Specific Heats of Air and Carbon Dioxide at Atmospheric Pressure , by the Continuous Electrical Method , at 20 ' C. and at 100 ' C. By W. F. G. Swann , A.R.C.S. , B.Sc. ( Communicated by Prof. H. L. Callendar , F.R.S. Received October 8 , \#151 ; Read December 10 , 1908 . ) ( Abstract . ) A steady stream of gas was passed through a jacketed tube ( the calorimeter proper ) , in which it was heated by a current of electricity passing through a platinum coil of 1 ohm resistance , the rise in temperature being measured by two 12-ohm platinum thermometers used differentially . If C is the electric current , E the potential difference between the ends of the heating coil , B0 the rise in temperature of the gas , Q the rate of flow of the gas in grammes per second , J the mechanical equivalent of heat , and S the specific heat of the gas at constant pressure , the elementary theory of the -experiment gives CE = JSQ where h B0 is a term representing the heat loss by radiation , etc. A similar experiment with a rate of flow about half the above value , and with the electric current adjusted so that the rise in temperature was about the same as before , gave a second equation ; so that h could be eliminated and -S determined . Before passing into the calorimeter the gas passed through a brass tube packed with copper gauze , the tube , together with the calorimeter jacket , being surrounded by another jacket through which steam or water could be passed , so that the gas entered the calorimeter proper at a constant temperature . The largest currents of gas through the apparatus were of the order of 0'5 litre per second . The rate of flow was kept constant by an automatic pressure regulator . It was measured by passing the gas through 16 fine metal tubes arranged in parallel , and observing the pressure difference between their ends , the mean pressure , and the temperature . The expression giving the rate of flow in terms of these quantities was found by a series of experiments in which the gas was pumped into a reservoir of about 50 litres capacity , and then allowed to discharge through the apparatus . By means of a special device , the times taken for certain quantities of gas to pass VOL. LXXXII.\#151 ; A. M 148 The Specific Heats of Air and Carbon , etc. through the apparatus were recorded automatically while the gas was actually flowing , so that initial fluctuations were avoided . The value of the electric current was obtained by measuring the potential difference set up at between the ends of a standard resistance coil , in terms of cadmium cells . The heating effects of the leads of the heating coil were determined by experiments made under the exact conditions of the main experiments . The rise in temperature in the main experiments was about 5 ' C. , and it was measured to 0'001'C . Thus the specific heats were measured practically at single temperatures instead of over large ranges . In the paper the results of experiments made to test the validity of assuming the heat loss for a given rise in temperature to be independent of the rate of flow of the gas are recorded . The matter is also examined from a theoretical standpoint , and corrections are calculated and applied where the assumptions made in the elementary theory are such as to lead to errors of more than about one part in 10,000 . The corrections are small , only amounting to one or two parts in 1000 . The full details of the various other precautions and corrections are given in the paper , and the mean of a large number of observations gave the following results:\#151 ; Air . Carbon dioxide . 0"24173 cal . per gramme degree at 20 ' C. 0-20202 cal . per gramme degree at 20 ' CL 0-24301 " " 100 ' C. 0-22121 " " 1003 CL The several determinations agree in each case to about 1*5 parts per 1000 , and the mean results are probably correct to one part in 1000 . It is possible to make a comparison of the results with the values deduced on theoretical considerations from Joly 's measurements of the specific heats at constant volume . This comparison is made in the paper , and it is shown that the results agree nearer than to one part in 1000 in the case of air , while in the case of carbon dioxide the results agree to 1 per cent. , which is as near as can be expected , in view of the fact that , in order to compare the results , extrapolations and interpolations have ^to be made over rather wide ranges of pressure and temperature , which is hardly justifiable in the case of carbon dioxide . The values of the specific heats obtained by the author are greater by about 2 per cent , than the corresponding values found by Eegnault , and later investigators who have employed methods similar in principle to that of Regnault . An explanation of this fact is suggested in the paper . It is shown that in Regnault 's experiments , in virtue of the fact that the corrections for the heat conducted through the pipe connecting the heating bath The Depression of the Filament of Maximum , etc. 149 to the calorimeter were determined from experiments in which no gas was flowing through the pipe , the results obtained by him must be too low by a quantity which is uncertain to the extent of 5 per cent , of the value of the specific heat . In virtue of the form of connecting pipe used , the error probably amounts to something of the order of half this amount , which would bring the results into close agreement with the author 's . The work was carried out in Prof. Callendar 's laboratory at the Imperial College of Science , and the method adopted was , in its main features , the* same as that employed by Prof. Callendar for the determination ofj the specific heat of steam . On the Depression of the Filament Maximum Velocity a Stream flowing through an Open Channel . By A. H. Gibson , M.Sc . ( Viet . ) . ( Communicated by Prof. J. E. Petavel , F.R.S. Received December 18 , 1908 , \#151 ; Read January 14 , 1909 . ) When water flows with sinuous motion through a circular pipe the resistance introduced by the solid boundaries reduces the velocity of axial flow as the sides are approached , this velocity being greatest at the centre and least at the sides , as indicated by the transverse velocity curve of fig. 1 . When flow takes place through a closed rectangular pipe , the same effect is Fig. 1 . Fig. 2 . M 2

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On the depression of the filament of maximum velocity in a stream flowing through an open channel.

149

159

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

A. H. Gibson, M. Sc. (Vict.)|Prof. J. E. Petavel, F. R. S.

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10.1098/rspa.1909.0016

Fluid Dynamics

Geography

Fluid Dynamics

The Depression of the Filament of Maximum , etc. 149 to the calorimeter were determined from experiments in which no gas was flowing through the pipe , the results obtained by him must be too low by a quantity which is uncertain to the extent of 5 per cent , of the value of the specific heat . In virtue of the form of connecting pipe used , the error probably amounts to something of the order of half this amount , which would bring the results into close agreement with the author 's . The work was carried out in Prof. Callendar 's laboratory at the Imperial College of Science , and the method adopted was , in its main features , the* same as that employed by Prof. Callendar for the determination ofj the specific heat of steam . On the Depression of the Filament Maximum Velocity a Stream flowing through an Open Channel . By A. H. Gibson , M.Sc . ( Viet . ) . ( Communicated by Prof. J. E. Petavel , F.R.S. Received December 18 , 1908 , \#151 ; Read January 14 , 1909 . ) When water flows with sinuous motion through a circular pipe the resistance introduced by the solid boundaries reduces the velocity of axial flow as the sides are approached , this velocity being greatest at the centre and least at the sides , as indicated by the transverse velocity curve of fig. 1 . When flow takes place through a closed rectangular pipe , the same effect is Fig. 1 . Fig. 2 . M 2 150 Mr. Gibson . Depression of the Filament of [ Dec. 18 , noticed , the transverse velocity curves and the curves joining points of equal velocity , or the contours of equal velocity in a cross-section , being much as shown in fig. 2 . Here , again , the maximum velocity is found at the centre of the pipe . From analogy with this latter case it might be expected that when flow takes place through an open rectangular flume such as would be obtained by taking the portion of the rectangular pipe of fig. 2 below the level AA ' , or indeed through an open channel of any ordinary section , the filament of maximum velocity would be found in the water surface and in the centre of the stream . In the majority of cases the latter assumption is fairly well justified by the results of experiment , although in some instances two points of maximum velocity have been noticed , one on each side of and at some distance from the centre . Further reference to this point will be made at a later stage of the paper . Except , however , in the case of a broad , rapid , and shallow stream , it is found that this filament occurs at some depth below the surface . Its depth varies somewhat with the direction of the wind and with the physical " characteristics of the stream , and , on a calm day , usually ranges from about one-tenth to four-tenths of the depth of the stream . This phenomenon of the depression of the filament of maximum velocity has been much discussed , and three theories have been propounded for its explanation . In the first of these the surface film is supposed to act in much the same way as a solid boundary in producing retardation of the surface layers . This theory is , however , discounted by the fact that , even with a downstream wind of considerably greater velocity than the stream , the filament remains below the surface . In a second theory it is suggested that " eddies of water , stilled by contact with the bed , are thrown off and wander through all parts of the stream , but finally accumulate and spread out at the surface , forming a layer of slowly moving water . " As regards this there would appear to be no special reason why eddies formed near the bottom of a stream should tend to wander upwards and finally stay on the surface . And if this did happen , since according to the theory any given eddy would need to pass through all intermediate sections of the stream before reaching the surface , it would be impressed with the mean axial velocity of each section in succession , and would finally reach the surface with a velocity greater than that of any intermediate section . The third theory suggests that , as the water is less constrained at the Maximum Velocity in a , etc. 1908 . ] surface than at any other point , irregular movements of all kinds are set up here and energy is therefore utilised in giving motions , not of translation , to the water.* This suggestion is directly opposed to the fact brought out by Osborne Reynolds in his researches on the causes of instability of flow in water , viz. , that unconstrained boundaries tend to stability , not to instability , of flow.f The unsatisfactory nature of these theories led the author to an investigation of the question , and as a result of this the following explanation of the phenomenon is offered . In any channel , however smooth its wetted perimeter may be , the velocity of forward flow is greatest near the centre and least near the sides and bottom , and if it were possible to obtain a state of affairs in which motion might take place in stream lines parallel to the axis of the stream , we should have , with steady flow along a straight reach of the channel , the velocity greatest in the surface and at the centre of the stream , and the water surface level from side to side . In practice this is modified by the eddy formation which always takes^ place at the sides of the stream , and the phenomena in question would appear to be due almost entirely to the modification thus introduced . A consideration of the process of eddy formation as it usually occurs at the sides of a stream shows that this involves the temporary existence of a region of less than normal pressure on the downstream side of the projection causing the eddy , and , as a result of this , where eddy formation is proceeding continuously in a uniform stream with a bed which is horizontal from side to side , it is to be expected that the depth of water will in consequence be slightly less at the sides than at the centre . The cross-sectional elevation of the surface thus becomes concave to the bed of the stream . This curvature of the surface profile lias been noticed by several observers , and was commented upon by Messrs. Humphreys and Abbot in their report on the gauging of the Mississippi.^ The superelevation of the surface near the centre creates a tendency to a general outward How from centre to sides of the channel , this , for permanence of regime , being accompanied by an inward flow consisting of water projected in the form of eddies from the sides . Now supposing an eddy , extending from the surface to the bottom , to break away from the side of a stream . Its forward velocity is somewhat less than that of the current in which it finds itself , the difference being greater the * Flamant , ' Hydraulique . ' t ' Roy . lust . Proc. , ' 1884 ; also ' Scientific Papers , ' vol. 2 , p. 153 . X Humphreys and Abbot , ' Report on the Mississippi River . ' 152 Mr. Gibson . Depression of the Filament of [ Dec. 18 , nearer the surface . From a consideration of its direction of rotation and of the external forces acting on its mass in virtue of its rotation in a stream moving more rapidly than its mass centre , it appears that these tend to drive it towards the centre of the stream.* This effect becomes greater as the relative velocity of the mass of water forming the eddy and of the passing current becomes greater , and will therefore increase from the bottom to the surface . It follows that the drift of the " eddy current " will be greatest near the surface and least near the bottom , and , as a nett result , that a system of transverse currents will be set up consisting of an inward surface drift from each side towards the centre ; an outward drift over the lower portions of the stream ; and , accompanying these , a downward current near the centre and an upward current near each side . Since the inward surface drifts consist of water which has travelled up the sides and has come from the region of minimum velocity , they will evidently have the effect of reducing the surface velocity and of depressing the filament of maximum velocity . The sketches in figs. 3 and 4 show respectively the directions of the transverse currents , and of the resultant motion of the stream , the full lines Fig. 3 . aa ' , aa , in fig. 4 representing the direction of the surface currents , and the dotted lines b'b ' , bb , those of the bottom currents . With a view of confirming these deductions , experiments were carried out on a small experimental channel in the hydraulic laboratories of the Manchester University ; on a straight reach of the Mersey , a few hundred yards below the county bridge at Northenden ; and oft two straight reaches of the Derbyshire and Peak Forest Canal near Marple . In the case of the model channel , which has wooden sides and bottom , the * Observation shows that whenever two eddies are moving down stream with different velocities of drift , and at approximately the same distance from the side , the slower tends to move centre-wards relative to the faster . Also that an eddy having greater velocity of drift than that of the current in which it finds itself always tends to move towards that side of the stream at which its direction of rotation would presume it to have been formed . Maximum Velocity in a Stream , etc. 1908 . ] current formation was examined by means of aniline dye introduced to various parts of the stream , and also by means of threads fixed to pins in the bottom and sides . While the latter method did not prove very satisfactory owing to the weight of the threads when wetted , it did show a very definite surface drift from side towards centre , floating threads attached to the sides making an angle of about 5 ' with these . The examination of the filaments of coloured water , however , showed the whole process very clearly and definitely proved the existence of the transverse currents . The Mersey on the reach examined is practically straight , and has an almost uniform width of approximately 36 feet and a mean depth of about 6 feet . The flow throughout the reach appeared to be as nearly as possible uniform , with a mean surface velocity of about 3 feet per second . In this case the side-to-centre surface drift was very apparent . Of 10 float rods , 6 inches in length , thrown into the stream at about 2 feet from either bank , eight arrived within 2 feet of the centre of the stream before having traversed more than 100 yards of the reach . The observed behaviour of portions of water-logged leaves suspended in the stream offered substantial evidence of an upward current near the sides and of a downward current within a few feet of the centre on each side , but the dirty state of the water prevented the behaviour of such bodies being noted for a depth of more than about 6 inches . The two reaches of the Peak Canal are each about 7 feet 6 inches wide and 5 feet deep , and were explored by means of weighted wax pellets . These gave distinct evidence of an upward current at the sides ; a current commencing about 1 inch below the surface towards the centre ; and a downward current commencing about 2*5 feet from the sides . Owing to the muddy character of the water it was impossible to follow the pellets to any considerable depth , and to note the depth of the return current , although their behaviour showed this to be present . In addition to this direct experimental verification of the theory , much indirect evidence of its validity is available in that it explains several interesting phenomena which have been noted and are of importance in stream gauging , and for which the reason has not hitherto been clear . Thus it is well known that the depth of the filament of maximum velocity\#151 ; ( a ) Depends on the physical condition of the channel , and increases as the roughness of the sides increases . ( b ) Depends on the depth of the stream , and especially on the ratio of depth to width , its depth increasing as the latter ratio increases . In a wide shallow stream the filament is found in the surface . 154 Mr. Gibson . Depression of the Filament of [ Dec. 18 , ( c ) Is greater for any given vertical in a rectangular channel as that vertical approaches the side , and is at about mid depth near the side of such a channel . ( d ) Depends on the velocity of flow , increasing as the latter diminishes . Now it is evident that since an increase in the roughness of the sides will tend to increase the surface depression at the sides , this , by increasing the head available for producing a transverse current , will increase the magnitude and the effect of this current and will tend to depress the filament of maximum velocity . As the depth of the stream increases relatively to its width , the influence of the sides will increase , so that the effect will be the same as an increase in their roughness . On the other hand , the roughness of the bottom tends to retard the transverse current without having any compensating effect , so that an increase in the roughness of the bottom as opposed to that of the sides of the channel tends to raise the filament of maximum velocity . An increase in the width relatively to the depth of the stream will have the same effect , and with a very shallow wide stream the influence of the sides will be quite negligible . Also since the effect of the current will diminish as its distance from the sides increases , this explains the greater relative depression of the filament near the sides . In a given channel with a given depth of water , an increase in the mean velocity of flow might reasonably be expected , as is found to be the case , to diminish the relative importance of the transverse current and hence to elevate the filament of maximum velocity . These points are well brought out in the published records of the gaugings of a very large number of rivers and channels by members of the U.S. Geological Survey.* From these the results of a number of gaugings of the experimental canal of the Cornell University have been chosen in illustration . These may be divided into two groups , denoted by A and B The experiments in series A were carried out with high velocities of flow and small depths of water , the mean velocity ranging from 2'06 to 3T6 feet per second , and the depth from 046 to l-88 feet . In series B the depths were greater and the velocities less , the depth ranging from 6'0 to 05 feet and the velocity from 023 to 2 feet per second . The canal is of rectangular section , with concrete sides and bottom having a slope of 1 in 500 , and has a width of 16 feet . Velocity measurements were made in eight verticals in a cross-section by means of carefully * U.S. Geological Survey , ' Water Supply and Irrigation Paper , ' No. 95 , p. 111 . Maximum Velocity in a . 1908 . ] calibrated current meters . The meter station in series A was 234 feet from the head of the canal and in series B was 280 feet from the same point . The curves in figs. 5 and 6 show the variations of velocity in a vertical plane in typical of these experiments , each plotted point giving the mean of all eight observations at that depth in the cross-section . Here the curves of fig. 5 refer to series A and those of fig. 6 to series B. Ft. PeR . Sec. ---Velocity . Fig. 5 . The effect of a large ratio of width to depth in raising the filament of maximum velocity is evident from a comparison of the curves of fig. 5 and of fig. 6 , while the effect of an increased velocity of flow in raising the filament is evident from a comparison of the several curves of fig 6 . The 6 IB 2o 2.2 . Velocity . Ft. Pelr . Sec. . Fig. 6 . Mr. Gibson . Depression of the Filament of [ Dec. 18 , relationship between the velocity of flow and depth of filament , as obtained from the whole of the experiments of series B , is as follows :\#151 ; Mean velocity of flow , feet per second ... . 0*45 080 1'4 1-9 Depth of filament of maximum velocity ... 044^ 0'42/ t 0 ' ? Ah 029 where h is the depth of the stream . The great difference between the several curves of fig. 5 is probably accounted for by the fact that while in some cases discharge at the lower end of the canal was restricted by the partial closure of the outlet gates , in other cases it was free . In experiments ( e ) and ( / ) a definite backwater was caused by the throttling of the outflow , and in these two cases it is definitely known that the flow at the meter section was being retarded . In the other cases discharge is said to have been free , and judging by the low velocities of flow it is certain that the flow was still being accelerated at the meter section , except possibly in experiment ( 0 ) . Before considering these curves further it may be well to see whether an acceleration or retardation of the flow , such as might occur in the one case in a contracted reach of a stream , or , in the other case , above a weir or dam , is likely to have any effect on the position of the filament of maximum velocity . This is evident if it be considered that since any acceleration in the mean flow will be most strongly marked in the central portion of the stream , the surface level at any section which undergoes acceleration will fall to a greater extent at the centre than at the sides . The converse holds if the flow is being retarded . Thus any acceleration of the stream will tend to diminish , and any retardation to increase , the formation of the transverse currents already described . This effect is very marked in the results of experiments ( e ) and ( / ) of series A , where , as compared with experiment with about the same depth of water , the depth of the filament of maximum velocity is depressed 0T5A . To test whether , after all , the transverse currents , when found , are not mainly due to a retardation of the current/ further experiments were carried out on the model channel at the Manchester University with both accelerated and retarded flow . These showed conclusively that in this channel at all events the influence of the sides was the predominating factor producing the currents , these being substantially as already described , with either type of flow . Indeed , unless this is so , practically all deep-river gaugings , showing as they do a depression of the filament of maximum velocity , must have been inadvertently carried out under a retarded flow . The improbability of this having been the case does not need any emphasis . Maximum Velocity in a , etc. 1908 . ] A further verification of this conclusion is afforded by the gauging of the farad flume of the Truckee Eiver General Electric Company * This flume has timber sides and bottom , and was gauged at two cross-sections 200 feet apart . The width was 10-09 feet throughout . The depth at the upper section was 5*98 feet , and at the lower section was 5-96 feet , while the filament of maximum velocity , this being the mean of the maxima in six verticals , had a depth of 0*50A at the upper and 042 at the lower section , in spite of the slightly accelerated flow . It would appear probable that in the comparatively few instances in which the filament of maximum velocity has been found to be in the surface of a river of any considerable depth this is due to the gauging station having been fixed at a section undergoing a strongly accelerated flow . The increasing depth of the filament as the sides of the channel are approached is well shown in fig. 7 , which is an example of a gauging by Darcy of a rectangular channel 0*25 metre deep and 0'8 metre wide . There is still another fact which strengthens the theory , and which will be made clearer by an examination of figs. 8 and 9 . These show velocity curves obtained in horizontal sections of the Cornell Canal , the curves in fig. 8 being examples of those obtained in the accelerated flow experiments of series A , and those of fig. 9 being samples of those obtained in series B.| From these it will be noted that while in series A ( fig. 8 ) the point of maximum velocity in a horizontal plane is approximately in the centre of the stream , the departure from this point being probably due to a greater roughness of one side of the channel , t in each of the curves of series B there are two points in each section , one on each side of the centre , at which the velocity is greater than at the centre . This point was brought out in each experiment of the series . * U.S. Geological Survey , 'Water Supply and Irrigation Paper , ' No. 95 , p. 111 . t ' Water Supply and Irrigation Paper , ' No. 95 , pp. 73 and 74 . + This fact is mentioned in the report . Mr. Gibson . Depression of the Filament of [ Dec. 18 , H QRi ; sor\gt ; fTB t. 1-5 f\ Width of Cflkhu - Ptt Fig. 8 . But this is precisely the effect which a vigorous system of cross currents , such as is shown in fig. 3 , would tend to produce , the central downward current of slowly moving water causing the depression of the centre of the curves of fig. 9 . On the other hand , in series A the depth of stream was small and the action of the sides negligible , so that this phenomenon would not be expected . Korizoktrl Veuocit^ Curves . \ N .SORfncE. . RT- SIX.-TG . NTH\amp ; BS . PTH . Fig. 9 . So far the channel has been assumed to be straight . If it is curved , the state of affairs is further complicated by a current which , as shown by James Thomson , * sweeps up the inner bank , and then , as a surface current , extends from the inner to the outer bank of the bend , thus spreading a layer of slowly moving water over the surface of the stream . * 'Roy . Soc. Proe . , ' 1877 , p. 356 . Maximum Velocity in a , etc. 1908 . ] This will have the effect of depressing the filament of maximum velocity by an amount which will be greatest at the inner bank , and will probably only be slightly felt at the outer bank . In fact , it is probable that , owing to the sweeping of high-velocity water from the centre to the outer side of the stream , the filament of maximum velocity at all points between the centre and outer bank will be in the surface . This conclusion is confirmed by the published results of gaugings of the Oswego River , at Battle Island , New York , * these gaugings being taken in close proximity to a bend . In the majority of rivers this action will sensibly modify the action of the sides and the distribution of the transverse currents . Conclusions . As a result of the investigation , the following points would appear to be well established:\#151 ; ( 1 ) The depression of the filament of maximum velocity in a straight reach of a river or canal is due to the action of the sides of the channel in producing transverse currents inwards along the surface and outwards along the bed of the stream , thus distributing a layer of slowly moving water over the central portions of the stream . ( 2 ) This effect is increased by a retardation and diminished by an acceleration of the flow , but , in the majority of cases in a stream of any considerable depth , is never so greatly diminished by an acceleration as not to be felt . ( 3 ) In a curved channel this effect is modified by the formation of a transverse current , due to the centrifugal action of the water and extending over the surface from the inner to the outer bank , this current tending , on the whole , to depress the filament of maximum velocity at all points between the inner bank and the centre of the stream , and to elevate it at points between the centre and the outer bank . * ' Water Supply and Irrigation Paper , ' No. 95 , p. 129 .

rspa_1909_0017

0950-1207

The photo-electric fatigue of zinc. \#x2014;II.

160

164

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

H. Stanley Allen, M. A ., B. Sc.| Prof. H. A. Wilson, F. R. S.

article

6.0.4

http://dx.doi.org/10.1098/rspa.1909.0017

en

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1909_0017

10.1098/rspa.1909.0017

Electricity

Atomic Physics

Electricity

160 The Photo-electric Fatigue of Zinc.\#151 ; II . By H. Stanley Allen , M.A. , B.Sc. , Senior Lecturer in Physics at King 's College , London . ( Communicated by Prof. H. A. Wilson , F.R.S. Received November 25 , 1908 , \#151 ; Read January 21 , 1909 . ) 1 . Object and Method of the Experiments . In a former paper* an account was given of the way in which the photoelectric activity of zinc diminishes when the metal is exposed to light from a Nernst lamp . It was shown that the photo-electric activity at a time t from the commencement of an experiment could be expressed by the formula I = Kic-A\gt ; J + K2\#171 ; -A2i . In a typical experiment with a polished zinc plate the first exponential term fell to half value in 4*9 minutes , the second in 94 minutes , the constants of change being \\ \#151 ; 0*141 and \2 = 0*00737 ; Ki and K2 were of the same order of magnitude . In an experiment with amalgated zinc the first term fell to half value in 4*2 minutes , corresponding to \i = 0*164 , while the second , term fell to half value in 167 minutes , corresponding to X2 = 0*00414 ; the value of Ki was about six times K2 . The experiments described in the present paper were carried out to determine whether the results were similar when using a source of light giving far more ultra-violet radiation than the Nernst lamp . A mercury-vapour lamp of fused quartz by W. C. Heraeus , supplied with current by a battery of 50 accumulators , was employed.f Photometric measurements with lamps of this kind have been made by R. Kuch and T. Retschinsky in the laboratory of the makers . ] : These experimenters examined the relation between the radiation from the lamp and the energy supplied both for visible and for ultra-violet radiation . The economy curve was found to be of the same general character in the two cases . The spectrum has been photographed and measured as far as wave- * ' Roy . Soc. Proc. , ' A , vol. 78 , p. 483 , 1907 . t I am indebted to the Council of King 's College for a Treasury grant for the purchase of the lamp , and to the Government Grant Committee of the Royal Society for supplying the accumulators . f ' Annalen der Physik ' ( 4 ) , vol. 20 , pp. 563\#151 ; 583 , 1906 . The Photo-electric Fatigue of Zinc . length 3340 A.U. by J. Stark , * using a three-prism spectroscope constructed of Jena ultra-violet glass . [ December 23.\#151 ; Dr. T. M. Lowry has kindly photographed the spectrum of my lamp , using lenses and prism of quartz . With a short exposure a well-marked line spectrum was obtained , extending to about 2400 A.U. ] The emission in considerable quantity of waves of still shorter wavelength is shown by the production of large amounts of ozone , rendering it necessary to place the lamp outside the room in which work is being carried on . Lenard5)- has shown that the ozonising action is due to very short waves , having a wave-length less than 2000 A.U. Regener^ : has shown that there is also a deozonising action for certain waves , whose wavelength falls between 3000 A.U. ( absorption by glass ) and 1850 A.U. ( absorption by quartz ) . As regards the radiation from the Nernst lamp , I am informed by Mr. W. A. Scoble , who has photographed the spectrum , that in no case was any effect produced beyond wave-length 2100 A.U. , and the results were comparatively faint from at least 2500 A.U. By far the greatest photographic effect was obtained in the visible violet and blue . The method of experimenting was similar to that described in the previous paper , but the testing cell , consisting of the zinc plate and a positively charged sheet of wire gauze , was in the open air instead of being-enclosed in a brass case . An electrometer of the Dolezalek type , giving about 500 divisions per volt , was used to measure the leak across the gap between the gauze and the zinc plate . As the leak in some of these experiments was much larger than in those made with the Nernst lamp as a source of light , a parallel plate air condenser of adjustable capacity was constructed and connected with the electrometer so as to secure a convenient rate of deflexion of the needle . The capacity of the electrometer and its connections was about 100 electrostatic units ; by means of the condenser the capacity of the system could be increased up to about 1000 units . The mercury lamp was started 20 minutes before the commencement of a series of observations , so that it might have time to assume a steady state . Readings of the current and voltage for the lamp were taken at intervals during the experiments , but the variations observed were inconsiderable . ( See , however , S 4 . ) Observations of the rate of leak were commenced one minute after the preparation of the plate and were continued at intervals of two minutes . * ' Annalen der Physik ' ( 4 ) , vol. 16 , pp. 490\#151 ; 515 , 1905 . t 'Annalen der Physik ' ( 4 ) , vol. 1 , p. 486 , 1900 . X 'Annalen der Physik ' ( 4 ) , vol. 20 , pp. 1033\#151 ; 1046 , 1906 . Mr. H. S. Allen . [ Nov. 25 , 2 . Results of Experiments with Polished Zinc . The experiments with polished zinc showed that the fatigue took place in exactly the same manner when the plate was illuminated by the mercury vapour lamp as when a Nernst lamp was used as a source of light . A typical experiment is represented by the lower curve in fig. 1 , which is plotted on semi-logarithmic paper . The curve can be represented by the sum of two exponential terms , the first term* falling to half value in eight 10 20 50 40 50 60 70 80 90 100 Time in Minutes . Fig. 1.\#151 ; Photo-electric Fatigue of Polished and Amalgamated Zinc . x Experiment made February 12 , 1908 , with polished zinc at 120 cm . from mercury vapour lamp . . Experiment made April 15 , 1908 , with amalgamated zinc at 63 cm . from mercury vapour lamp . minutes , the second in 100 minutes , the . constants of change being = 0*0867 and \2 = 0*00693 . Expressing the photo-electric current in scale divisions per second , Ki = 30 , K2 = 40 . In this experiment one * It should be noted that the constant of change for the first term , which is found by a difference method , cannot be determined with the accuracy possible in the case of the second term . Ihe Photo-electric Fatigue of Zinc . 16a 1908 . ] division per second corresponded to 0'20 x 10~12 ampere , so that if the . current is in amperes , Ki = 6 x 10"12 ampere , K2 = 8 x 10"12 ampere . The current is about twice as large as that in the experiment of August 7 , 1905 , described in the former paper . The greater activity of the mercury vapour lamp as compared with the Nernst lamp is nearly compensated for by the increased distance ( 120 cm . ) from the source of light . In another experiment the zinc plate was only 63 cm . from the mercury lamp . In this case the fatigue was slightly more rapid , the first exponential term falling to half value in 6*8 minutes , the second in 76 minutes . In scale divisions per second Ki = 26 and K2 = 47 , but as a capacity of about 400 electrostatic units was employed with the electrometer , the current was much greater than in the former experiment , Ki = 26 x 10"12 ampere , K2 = 47 x 10"12 ampere . 3 . Results of Experiments Amalgamated Zinc . A typical fatigue curve for amalgamated zinc is shown in the diagram . It is seen at once that this is similar in character to the curve for the polished metal . In the present case we find that the first term falls to half value in 3'2 minutes , the second in 96 minutes , giving \\ \#151 ; 0'217 and X2 = 0'00722 . The value of Ki is 47 x 10"12 ampere , and of K2 is 57 x 10"12 ampere . Comparing these results with those obtained previously , when a Nernst lamp was employed instead of the mercury lamp , we notice that the second term changes a good deal more rapidly in this case , and that Ki and K2 are now of the same order of magnitude . The slower rate of fatigue with the Nernst lamp may , perhaps , be attributed to the action of the waves of greater wave-length , described in the former paper . This suggestion receives support from experiments made with the plate illuminated by the two sources of light at the same time . In these the fatigue took place more slowly than with the mercury lamp alone . 4 . Minor Variations in the Observations . A close examination of the original curves here reproduced suggests the presence of small undulations superposed on the smooth exponential curves . These variations have a period of about 10 minutes . Similar periodic changes in the rate of decay were observed in curves obtained when using a Nernst lamp as the source of light ( see figs. 3 and 4 of the former paper ) . It does not appear probable that the fatigue really proceeds through a series of small maximum and minimum values , though such periodic changes are not unknown . Eor example , Ostwald has shown that the change involved in the VOL. LXXXII.\#151 ; A. N The Photo-electric Fatigue of Zinc . solution of certain varieties of chromium in dilute hydrochloric and sulphuric acids is oscillatory in character.* The explanation of the small variations observed in my experiments is probably to be found in the character of the source of light . In both theNernst lamp and the mercury vapour lamp we may suppose that continual adjustment is taking place as regards the resistance and the potential difference between the terminals , causing a more or less regular fluctuation in the intensity of the emitted light . 5 . Conclusion . The photo-electric activity of a zinc plate decays in such a way that it can be represented as the sum of two exponential ternls . The constants of change are but little altered by considerable variations in the character and intensity of the illumination employed , though the value of the photo-electric current is changed considerably . The rate at which the surface is altered is not greatly affected by using a mercury vapour lamp in place of a ISTernst lamp . Experiments with other metals are still in progress . In conclusion , I wish to express my thanks to Prof. H. A. Wilson for advice during the course of the work . * Mellor , ' Chemical Statics and Dynamics , ' pp. 348\#151 ; 352 . /

rspa_1909_0018

0950-1207

The mobilities of the Ions produced by R\#xF6;ntgen rays gases and vapours.

165

166

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

E. M. Wellisch, M. A. (Sydney),|Prof. Sir J. J. Thomson, F. R. S.

abstract

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http://dx.doi.org/10.1098/rspa.1909.0018

en

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1909_0018

10.1098/rspa.1909.0018

Thermodynamics

Atomic Physics

Thermodynamics

165 The Mobilities of the Ions produced by Rontgen Rays Gases and Vapours . Bv E. M. Wellisch , M.A. ( Sydney ) , Emmanuel College , Cambridge ; Barker Graduate Scholar of the University of Sydney . ( Communicated by Prof. Sir J. J. Thomson , F.R.S. Received December 19 , 1908 , \#151 ; Read January 21 , 1909 . ) ( Abstract . ) The velocities of the positive and negative ions produced by Rontgen rays in 4 gases and 15 vapours have been measured at normal temperatures over a wide range of pressures and under different electric intensities . Langevin 's direct null method was employed throughout . For a constant pressure the velocity of the ion was found to vary as the electric intensity . It was found that , in general , the mobility ( k ) of the ion varied inversely as the pressure ( p ) . In the case of nitrous oxide and carbon dioxide there was a slight tendency for the product to increase both for the positive and negative ions as the pressure was reduced below about 7 cm . of mercury . In the case of ethyl chloride there was a marked tendency for the product pk to decrease as the vapour approached the saturated state ; there is reason to believe that this tendency for pk to decrease would appear in the case of all the vapours in the neighbourhood of the saturated state . In the case of vapours there was , in general , little difference in the values of the positive and negative mobilities . The mobility of the positive ion was found greater than that of the negative for aldehyde , ethyl alcohol , aceton , sulphur dioxide , ethyl chloride , pentane , ethyl acetate , methyl bromide , and ethyl iodide . There appeared to be no direct relation between mobilities and molecular weights ; the smaller mobilities invariably belonged to gases possessing high critical temperatures ( the vapours ) ; the larger mobilities to gases with low critical temperatures . From the kinetic theory of gases an expression has been deduced for the mobility of an ion moving through a gaseous medium under the influence of an electric field . This expression takes into account the effect of the charge carried by the ion on its mean free path and involves only known physical -constants of the gas . As a result of the theoretical considerations , it appears that the N 2 Prof. H. J. Strutt . The Leakage of [ Dec. 30 , experimental values of the mobilities in the different gases at various pressures , as well as certain observed deviations from the law connecting the mobility and gaseous pressure , can be explained approximately on the supposition that the ion consists of a single molecule of the gas with which is associated a charge equal to that carried by the monovalent ion in electrolysis . The Leakage of Helium from Radio-active Minerals . By the Hon. R. J. Strutt , F.R.S. , Professor of Physics , Imperial College of Science , South Kensington . ( Received December 30 , 1908 , \#151 ; Read January 21 , 1909 . ) In a paper published in ' Roy . Soc. Proc. , ' A , vol. 81 ( 1908 ) , p. 272 , I showed that phosphatised bones and similar materials were notably radioactive , and that helium could be detected in them . The quantity of helium found was not , however , uniformly greater in the geologically older materials than in younger ones of equal activity . This was hypothetically attributed to escape of helium in certain cases . I desired if possible to obtain direct experimental confirmation of this conjecture . It would clearly be impossible to detect leakage of helium from materials such as the mineralised bones , even in a lifetime . For any chance of success it was necessary to have recourse to the ores of uranium and thorium , in which the quantity of helium is something like 100,000 times greater . The method of experimenting was to place a considerable quantity of the ore ( usually a kilo or more ) in a bottle provided with an exit tube and stopcock and connected to a mercury pump . The bottle was exhausted and the stopcock closed . After the lapse of a definite interval of time , usually a day or more , a small quantity of oxygen was admitted to the bottle and then collected through the pump , carrying with it any helium which had come off ' from the mineral . The oxygen was absorbed with melted phosphorus , leaving a small residue of helium , ' together with impurities . Any hydrogen present in the original gas , which may have been liberated by radio-active decomposition of traces of moisture , was burnt along with the phosphorus , and thus got rid of . The residue was transferred to an apparatus consisting of a McLeod gauge in connection with a reservoir containing charcoal . On cooling the charcoal with liquid air , helium was isolated , and the quantity could be measured . As a test of purity , the spectrum could be examined in the capillary measuring tube of the gauge , using external tinfoil electrodes .

rspa_1909_0019

0950-1207

The leakage of helium from radio-active minerals.

166

169

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

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

article

6.0.4

http://dx.doi.org/10.1098/rspa.1909.0019

en

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http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1909_0019

10.1098/rspa.1909.0019

Thermodynamics

Atomic Physics

Thermodynamics

166 Prof. H. J. Strutt . The Leakage of [ Dec. 30 , experimental values of the mobilities in the different gases at various pressures , as well as certain observed deviations from the law connecting the mobility and gaseous pressure , can be explained approximately on the supposition that the ion consists of a single molecule of the gas with which is associated a charge equal to that carried by the monovalent ion in electrolysis . The Leakage of Helium from Radio-active Minerals . By the Hon. R. J. Strutt , F.R.S. , Professor of Physics , Imperial College of Science , South Kensington . ( Received December 30 , 1908 , \#151 ; Read January 21 , 1909 . ) In a paper published in ' Roy . Soc. Proc. , ' A , vol. 81 ( 1908 ) , p. 272 , I showed that phosphatised bones and similar materials were notably radioactive , and that helium could be detected in them . The quantity of helium found was not , however , uniformly greater in the geologically older materials than in younger ones of equal activity . This was hypothetically attributed to escape of helium in certain cases . I desired if possible to obtain direct experimental confirmation of this conjecture . It would clearly be impossible to detect leakage of helium from materials such as the mineralised bones , even in a lifetime . For any chance of success it was necessary to have recourse to the ores of uranium and thorium , in which the quantity of helium is something like 100,000 times greater . The method of experimenting was to place a considerable quantity of the ore ( usually a kilo or more ) in a bottle provided with an exit tube and stopcock and connected to a mercury pump . The bottle was exhausted and the stopcock closed . After the lapse of a definite interval of time , usually a day or more , a small quantity of oxygen was admitted to the bottle and then collected through the pump , carrying with it any helium which had come off ' from the mineral . The oxygen was absorbed with melted phosphorus , leaving a small residue of helium , ' together with impurities . Any hydrogen present in the original gas , which may have been liberated by radio-active decomposition of traces of moisture , was burnt along with the phosphorus , and thus got rid of . The residue was transferred to an apparatus consisting of a McLeod gauge in connection with a reservoir containing charcoal . On cooling the charcoal with liquid air , helium was isolated , and the quantity could be measured . As a test of purity , the spectrum could be examined in the capillary measuring tube of the gauge , using external tinfoil electrodes . 1908 . ] Helium from Radio-active Minerals . 167 I was astonished at the quantity of helium observed in the first experiments . It exceeded anticipation by hundreds , or even thousands , of times . I shall not describe the experiments in the order in which they were made , but rather in that which seems to connect them best . It was found that after a radio-active mineral had been powdered , helium was evolved from it , rapidly at first , then at a diminishing rate . The following observations illustrate this . A quantity ( 337 grammes ) of monazite from the Transvaal was powdered and passed through a wire-gauze sieve of 120 threads to the inch . This took about one hour . Immediately afterwards it was put in a bottle and the air pumped out . The rate of evolution of helium in cubic millimetres per day per kilo of material was as follows:\#151 ; Time ( days ) . Rate . 0*031 261 0-59 76-6 1-6 17-1 2-6 12*3 4-6 9'57 10-6 4-38 33-0 1-14 The first experiment was made as quickly as possible , helium being collected for one hour . Times are measured from the moment when the powdering was half completed to half-way through the period of accumulation . Naturally the first rapid variations can only be roughly investigated in this way . Leakage of helium from this sample is still continuing , and it is intended to watch its future course . It will be observed that the whole quantity which has escaped while the mineral has been under observation is but an insignificant fraction ( probably less than a 500th* ) of the whole quantity present . Mossf has observed that quantities up to 1 per cent , of the helium contained in a mineral can be liberated by grinding in a vacuum . The present observations show that this is but the first rapid stage of a long-continued leakage of helium from the newly created surfaces . The view that heat generated in grinding is the important factor appears untenable ; for in that case escape of helium should cease on cooling . It is uncertain how long this evolution of helium continues ; in all * This sample of monazite was very poor in helium , containing only -Jq c.c. per gramme . + ' Roy . Dub . Soc. Trans. , ' vol. 8 , p. 153 . 168 The Leakage of Helium from Radio-active Minerals . probability , however , the period is prolonged : and since the majority of radio-active materials can only be obtained in the form of pieces which have been broken off from their natural home a moderate number of years back , any observations made upon them are inconclusive as to the rate at which helium escapes when they are undisturbed in their original surroundings . It was found , in fact , that pieces from the same stock of monazite , about the size of a lump of sugar , which had not been fractured since they came into my possession two years ago , evolved helium at the rate of 0-002 c.mm . per kilo of material per diem . This rate , though quite insignificant in comparison with that exhibited by the powdered material , is much in excess of the probable rate of generation of helium by radio-active change . It follows that the present stores of helium could never have been accumulated had the present rate of evolution prevailed throughout the life-history of the mineral . With a view to testing a mineral more nearly in its natural condition , experiments were made on thorianite , which occurs in gravels , in detached cubic crystals , washed out of their original matrix . This , too , showed a considerable leakage of helium ( 0-069 c.mm . per kilo per diem ) . Tests were made at intervals over a considerable period . The rate was found quite uniform , the volume of helium pumped out being proportional to the time of accumulation . A second collection , made immediately after the first , yielded scarcely anything . It is difficult to account for this large evolution of helium from a mineral so nearly in its natural condition . It was thought possible that an explanation might -be found by supposing that the temperature of the laboratory ( 65 ' F. ) was somewhat higher than that of the natural surroundings of the mineral . The latter must , however , be above the freezing point ; and it was decided to test experimentally the rate of evolution at that temperature . The bottle containing the mineral was kept in ice for some days ; under these conditions the helium leakage was reduced to about a quarter of its value at the higher temperature ( 0*018 c.mm . per kilo per day ) . This is still greatly in excess of the rate of accumulation . It seemed possible , though unlikely , that the mineral , when kept in a vacuum , lost helium which it would have retained at atmospheric pressure . To test this explanation , the bottle containing the mineral was left filled with oxygen up to atmospheric pressure . At the . close of several days the oxygen was pumped out , and absorbed with phosphorus . The ordinary quantity of helium was obtained , the rate of escape being undiminished . It was noticed that the surfaces of some of these crystals were somewhat weathered . With the idea that this might determine the escape of helium , another sample of thorianite much fresher in appearance wras tested . The On Electricity of Rain and its Origin in Thunderstorms . 169 i rate of evolution in this case was only 0-0127 , about one-fifth of that observed with the previous sample . The majority of minerals allow water to percolate through them . The effective superficial area must therefore much exceed the external surface . It is probable that loss of helium occurs from the weathering of these interior surfaces as well as from the external faces of the crystals . Abrasion of the external surfaces by comparatively recent rolling in water-courses may have produced some effect . Under laboratory conditions the rate of escape of helium from minerals always far exceeds the rate of production by radio-active change . Therefore the conditions under which the life of the minerals has been mainly passed , , deep down in the earth , where atmospheric agencies have no place , must be supposed more favourable to retention of helium , for otherwise the present accumulation could never have been formed The observations here recorded leave little room for surprise that fossilised bones and other materials do not always contain as much helium as would be expected from their radioactivity and geological age . On the Electricity of Rain and its Origin in Thunderstorms . By George C. Simpson , D.Sc . ( Communicated by Dr. Gilbert T. Walker , F.R.S. Received January 6 , \#151 ; Read February 4 , 1909 . ) ( Abstract . ) During 1907-08 an investigation was undertaken at the Meteorological Office of the Government of India , Simla , into the electrical phenomena which accompany rain and thunderstorms . Two lines of research were adopted :\#151 ; ( a ) A systematic record was obtained by means of self-registering instruments of the electricity brought down by the rain throughout one rainy season . ( b ) Laboratory experiments were made with the object of determining the source of the electricity of thunderstorms . The chief results of the first part of the work may be briefly summarised as follows :\#151 ;

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On the electricity of rain and its origin in thunderstorms.

169

172

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

George C. Simpson, D. Sc.| Dr. Gilbert T. Walker, F. R. S.

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Electricity

Thermodynamics

Electricity

On Electricity of Rain and its Origin in Thunderstorms . 169 i rate of evolution in this case was only 0-0127 , about one-fifth of that observed with the previous sample . The majority of minerals allow water to percolate through them . The effective superficial area must therefore much exceed the external surface . It is probable that loss of helium occurs from the weathering of these interior surfaces as well as from the external faces of the crystals . Abrasion of the external surfaces by comparatively recent rolling in water-courses may have produced some effect . Under laboratory conditions the rate of escape of helium from minerals always far exceeds the rate of production by radio-active change . Therefore the conditions under which the life of the minerals has been mainly passed , , deep down in the earth , where atmospheric agencies have no place , must be supposed more favourable to retention of helium , for otherwise the present accumulation could never have been formed The observations here recorded leave little room for surprise that fossilised bones and other materials do not always contain as much helium as would be expected from their radioactivity and geological age . On the Electricity of Rain and its Origin in Thunderstorms . By George C. Simpson , D.Sc . ( Communicated by Dr. Gilbert T. Walker , F.R.S. Received January 6 , \#151 ; Read February 4 , 1909 . ) ( Abstract . ) During 1907-08 an investigation was undertaken at the Meteorological Office of the Government of India , Simla , into the electrical phenomena which accompany rain and thunderstorms . Two lines of research were adopted :\#151 ; ( a ) A systematic record was obtained by means of self-registering instruments of the electricity brought down by the rain throughout one rainy season . ( b ) Laboratory experiments were made with the object of determining the source of the electricity of thunderstorms . The chief results of the first part of the work may be briefly summarised as follows :\#151 ; Dr. G. C. Simpson . On Electricity of [ Jan. 6 , ( 1 ) The aggregate amount of rain which fell during the periods of rainfall investigated was 763 cm . ( 2 ) The total quantity of positive electricity which fell on each square centimetre of surface was 223 electrostatic units , and of negative electricity 7'6 units ; thus 75 per cent , of the electricity brought down by the rain was positive . ( 3 ) During 71 per cent , of the time that charged rain fell the charge was positive . ( 4 ) Considering that falling rain carrying a positive charge is equivalent to a positive current , and rain with a negative charge to a negative current , then positive currents greater than 300 x 10~15 ampere per square centimetre were measured in six storms and negative currents greater than 300 x 10~15 ampere per square centimetre were measured in two storms . ( 5 ) In seven storms rain was recorded carrying greater positive charges than 6 electrostatic units per cubic centimetre of water , and in two storms a greater negative charge than this amount occurred . ( 6 ) The heavier the rainfall the more the positively charged rain preponderated over the negatively charged rain ; and all rainfall which occurred at a greater rate than a millimetre in two minutes was positively charged . ( 7 ) Light rain was more highly charged than heavy rain . ( 8 ) The proportion of negative electricity brought down by the rain was slightly greater in the second than in the first half of the storms . ( 9 ) The potential gradient was more often negative than positive during rain . ( 10 ) Ho relationship between the sign- of the potential gradient and the sign of the electricity of the rain could be detected . The laboratory experiments showed that when a large drop of water is broken up into small drops in the air the water becomes positively and the air negatively charged . In the first series of experiments drops of water , each having a volume of 034 c.c. , fell on to a vertical jet of air which broke them up into small drops . It was found that under these circumstances the water of each drop , after having been broken up on the jet , carried a charge of 53 x 10-3 electrostatic unit of positive electricity . Further , it was found that the presence of an original charge on the drops did not alter the effect . Drops originally charged positively had their charges increased and drops charged negatively had their charges decreased . In the second series of experiments water was introduced through two small tubes into a vertical current of air which carried the water upwards . Part of the water which escaped from the air current was caught in an Rain and its Origin in Thunderstorms . 1909 . ] insulated vessel and was found to be positively charged , the charge being 15 x 10"3 electrostatic unit per cubic centimetre of water . In the third series of experiments drops of water were broken up in a similar manner to that employed in the first series , but within a compartment from which the air could be drawn through an Ebert apparatus . The result showed that the breaking of the drops caused an ionisation of the air . The breaking of each drop released 3'3 x 10-3 electrostatic unit of free negative ions and IT x 10~3 electrostatic unit of free positive ions ; the excess of negative ions corresponds to the positive charge retained by the water . In 1904 Prof. Lenard* showed that drops of water having a greater diameter than 5*5 mm. are unstable when falling through air and rapidly break up into smaller drops . He also showed that all drops having a smaller diameter than 5'5 mm. have a final velocity when falling through still air of less than 8 metres a second . Thus no water can fall through an ascending current of air having a velocity of 8 metres a second ; for all drops less than 5*5 mm. in diameter are carried upwards , and all drops having a larger diameter quickly break up into smaller drops . These facts , together with the results of the observations and experiments described above , have led to the formation of the following theory for the origin of the electricity of thunderstorms . It is exceedingly probable that in all thunderstorms ascending currents greater than 8 metres a second occur . Such currents are the source of large amounts of water which cannot fall through the ascending air . Hence , at the top of the current , where the vertical velocity is reduced on account of the lateral motion of the air , there will be an accumulation of water . This water will be in the form of drops which are continually going through the process of growing from small drops into drops large enough to be broken . Every time a drop breaks a separation of electricity takes place , the water receives a positive charge , and the air a corresponding amount of negative ions . The air carries away the negative ions , but leaves the positively charged water behind . A given mass of water may be broken up many times before it falls , and in consequence may obtain a high positive charge . When this water finally reaches the ground it is recognised as positively charged rain . The ions which travel along with the air are rapidly absorbed by the cloud particles , and in time the cloud itself may become highly charged with negative electricity . Now within a highly electrified cloud there must be * Lenard , ' Met . Zeit . , ' vol. 21 , p. 249 , 1904 . Mr. G. G. Stony . Tension of [ Jan. 16 , rapid combination of the water drops , and from it considerable rain will fall ; this rain will be negatively charged , and under suitable conditions both the charges on the rain and the rate of rainfall could be large . A rough quantitative analysis shows that the order of magnitude of the electrical separation which accompanies the breaking of a drop is sufficient to account for the electrical effects observed in the most violent thunderstorms . All the results of the observations of the electricity of rain described above are capable of explanation by the theory , which also agrees well with the actual meteorological phenomena observed during thunderstorms . Hie Tension of Metallic Films deposited by Electrolysis . By G. Gerald Stony . ( Communicated by the Hon. C. A. Parsons , C.B. , V.-P.R.S . Received January 16 , \#151 ; Read February 4 , 1909 . ) It is well known that metallic films deposited electrolytically are in many cases liable to peel off if deposited to any considerable thickness . This is the case with nickel which , when deposited over a certain thickness , will curl up into beautiful close rolls , especially if it does not adhere very tightly to the body on which it is deposited . For example , if a piece of glass is silvered by any of the usual silvering solutions , and then nickel is deposited on the silver , it is found that the nickel and silver peel off the glass in close tight rolls almost at once . In ' Practical Electro-Chemistry/ by Bertram Blount , reference is made on pp. 114 and 272 to the tendency of nickel to peel off , and it is stated that it " will peel\#151 ; spontaneously and without assignable cause " ( p. 272 ) , but that a thick coating can be obtained by keeping the solution at between 50 ' and 90 ' C. The late Earl of Rosse* tried , about 1865 , to make flat mirrors by coating glass with silver chemically , and then electroplating with copper ; but he found that , owing to the " contraction " of the copper film , it became detached from the glass . I have had the ' same experience in protecting silver 61ms in searchlight reflectors by a film of electro-deposited copper , it being found that if the film of copper is more than O01 mm. thick peeling is apt to take place . Dr. Gore , F.R.S. , in papers in the ' Phil. Trans./ in 1858 and 1862 , found * ' Nature/ Aug. 20 , 1908 , p. 366 .

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The tension of metallic films deposited by electrolysis.

172

175

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

G. Gerald Stoney.|The Hon. C. A. Parsons, C. B., V. -P. R. S.

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Measurement

Electricity

Measurement

]\gt ; . G. G. Stony . The Tension of [ Jan. 16 , rapid combination of the water drops , and from it considerable rain will fall ; this rain will be negatively , and under suitable conditions both the charges on the rain and the rate of rainfall could be large . A rough quantitative analysis shows that the order of magnitude of the electrical separation which accompanies the breaking of a drop is sufficient to account for the electrical effects observed in the most violent thunderstorms . All the results of the observations of the electricity of rain described above are capable of explanation by the theory , which also rees well with the actual meteorological phenomena observed thunderstorms . The Tension of Films deposited by Electrolysis . By G. ERAL1 ) STONEY . ( Commumicated by the Hon. C. A. Parsons , C.B. , V.-P.R.S . Received January 16 , \mdash ; Read February 4 , 1909 . ) It is well known that metallic films deposited electrolytically are in many cases liable to peel off if deposited to any considerable tbickness . This is the case with nickel which , when deposited oyer a certain thickness , will curl up into beautiful rolls , especially if it does not adhere very htly to the body on which it is deposited . example , if a piece of glass is silvered by any of the usual ions , and then nickel is deposited on the silver , it is found that the nickel and silver peel off the lass in close tight rolls almost at once . In 'Practical emistry , ' by Bertram Blount , reference is made on pp. 114 and 272 to the tendency of nickel to peel off , and it is stated that it " " will peel\mdash ; spontaneously and without assignable cause\ldquo ; ( p. 272 ) , but that a thick coating can be obtained by keeping the solution at between and C. The late Earl of Rosse*tried , about 1865 , . make flat mirrors by coating glass with silver chemically , and then electroplating with copper ; but he found that , owing to the " " contraction\ldquo ; of the copper film , it became detached from the lass . have the same experience in protecting silvel fil1ns in reflectors by a film of electro-deposited copper , it being found that if the film of copper is more than mm. thick peeling is apt to take place . Dr. Gore , , in papers in the 'Phil . Trans in 1858 and 1862 , found ' Nature , ' Aug. 20 , 1908 , p. 366 . 1909 . ] Metatlic deposited by Electrolysis . that antimony , when deposited , was in a very unstable state , and that it was liable to break to pieces by vibration or the local application of heat , this breaking to pieces being accompanied by the evolution of heat , and crackling sounds and cracks wers found due to alterations in the cohesive state of the metal ; while " " in common with electro-deposits generally the inner cmd outer surfaces of these deposits are in unequal states of cohesive tension\ldquo ; ; and he concludes by saying , " " it would be interesting to enquire to what force of mode of phy sical action is the evolution of heat in antimony due In his book , The Art of Electro-Metallurgy , ' he says , " " In common with electro-deposits generally the inner and outer surfaces are in unequal states of cohesive tension , frequently in so great a degree as to rend the deposit extensively and raise it from the cathode in the fornl of a sheet with its side towards the anode Dr. E. J. Mills , in a paper in the ' Proceedings of the Royal Society , ' 1877 , vol. 26 , on " " Electrostriction shows that when thermometer bulbs were coated electrolytically with metals , the mercury rose in the stem , proving that the metal was deposited in a state of strain , also that in the case of and iron , when more than a certain thickness was deposited , the coat split . He found that a pressure of tons per square inch could be obtained with nickel , with iron , with silver , and with copper . It seemed , therefore , that metals are deposited under , and if so that they should strain the material on which they were deposited so as to bend it ; and that by the amount of this the tension under which they were deposited could be determined ; and it was found that when nickel was deposited on one side of a thin sheet of metal very considerable took place . Thin steel rules , 102 mm. , 12 mm. wide , and mm. thick , were varnished on one side and coated with nickel from the usual bath of ammonio-sulphate of nickel , and it was found easy to get these bent to the extent of 3 to 4 mm. The thickness of the film was determined by weighing before and after coating , and was checked in the case of some of the thicker films by micrometer measurements , the density of nickel being taken at , as given by Miller . Owing to the evolution of hydrogen which always takes place , the amount deposited is considerably less than that due to the current used , generally only 50 to 60 per cent. of the theoretical quantity , and therefore . that method could not be used to determine the quantity of nickel deposited . The amount of bending , combined with the thickness of the deposit , enabled the tension under which it is deposited to be calculated . let a thin steel rule of thickness have deposited on it a layer of nickel of Mr. G. G. Stony . The Tension of [ Jan. 16 , small thickness , and let it be curved by the film of nickel to a radius neglectin the thickness of the rule , which is small in comparison with and taking moments for the steel , we have , being the depth from the surface of the rule to the neutral axis , , so that and if is the tension per unit area of section on the film of nickel , resolving horizontally , The curvature measured by the deflections of the rule in a length Thus . Putting in this value for , we have ( 1 ) This equation is only true when the film of nickel is very thin ; but since the properties of nickel closely resemble steel it is easy to allow for the thickness of the nickel film on the assumption that the modulus of elasticity of nickel is the same as steel ; and since this is approximately true for forged nickel , is therefore probably true for deposited nickel , this assumption is allowable without serious error where the thickness of nickel deposited is moderate . Thus , for any thickness of nickel deposited , we have for a further thickness deposited an increase of bending , and equation ( 1 ) becomes , the tension being the same for the successive layers as they are laid on the curved surface , and , integrating differential equation , : ( 2 ) * Forged nickel I have found to have the same modulus of elasticity as steel , that is , 2 , kilogrammes per sq . cm . Prof. Ewing , in 'Strength of Materials , ' gives 2,100,000 kilogrammes per sq . cm . as a mean value for carbon steel , which I have found correct for these rules , and this is independent of the quantity of carbon in the steel and whether it is tempered or not , i.e. , is the same approximately for mild steel and tool steel . Nickel steels with from 3 to 5 per cent. of nickel have about the same modulus of elasticity as carbon steels . Forged nickel as above has a tensile strength of 25 tons per square inch and a yield point of 16 tons per square inch , with an elongation of 10 per cent. in 2 inches , or very similar to wrought iron . 1909 . ] Metallic Films by Electrotysis . The results given in the table are obtained from depositing nickel on a rule 102 mm. by 12 mm. wide . depositednickel . Thickne.snickel *Deposit rough owing to large current . Solution C. The first six were deposited at a temperature of to C. , and with currents varying from to ampere . No. 7 was with a current of ampere at C. , and was very rough and , but until the deposit began to get rough the current density did not affect the tension . It is thus seen that a good deposit has a tension of between 18 and 19 tons per square inch . The last was deposited with ampere at to C. , and the tension obtained was much lower , and this reduction in the tension of the deposit probably accounts for what Mr. Blount found , as mentioned before , that thick deposits of nickel were easier to obtain at higher temperatures . I have not found the strength of the nickel-plating solution to affect the tension under which the nickel is deposited . It was also found on heating these rules to a red heat so as to anneal them that they htened out to a considerable extent , the remaining deflection being only about one-third or one-half of the original .

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0950-1207

A further note on the conversion of diamond into coke high vacuum by cathode rays.

176

176

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

Alan A. Campbell Swinton.|The Hon. C. A. Parsons, C. B., V. -P. R. S.

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Atomic Physics

Thermodynamics

Atomic Physics

176 A Further Note on the Conversion of Diamond into Coke High Vacuum hy Cathode Rays . By Alan A. Campbell Swinton . ( Communicated by the Hon. C. A. Parsons , C.B. , V.-P.R.S . Received January 28 , \#151 ; Read February 4 , 1909 . ) In a previous paper on this subject by the Hon. Charles A. Parsons and the writer , * experiments were described designed to ascertain whether any gas was emitted by diamond during its conversion into coke . Two spectrum tubes were connected to the cathode ray furnace , in which the diamond was heated to destruction . One of these was sealed off just before and the other just after the conversion , but when the spectra of these two tubes were photographed alongside one another the differences that existed did not appear sufficiently marked to determine with exactitude any variation in the nature of the gases present . The present note has reference to further and more detailed investigation made on the suggestion of Mr. Parsons by the writer , with special regard to the possibility of diamonds containing neon , krypton , or other rare gas which would be emitted on the diamond being converted into coke . As before , spectrum tubes connected with the cathode ray furnace were sealed off so as to contain samples of the residual gas before and after the conversion . The spectra of these were compared both photographically and also by direct visual examination in the'spectroscope , with the result that though differences were observed in regard to the relative brightness of various individual lines in the two spectra , careful observation showed that in no single instance was there any line in one spectrum that could not be obtained in the other by suitably adjusting the strength of the electric discharge through the spectrum tube . From this it would appear that the conversion of diamond into coke , if it sets free any gas at all , at any rate does not liberate any other than one or more of the comparatively common gases .that are generally found as residuals in cathode ray tubes exhausted from air in the ordinary way . Though this is a negative result , it has been thought well to put it on record . * ' Roy . Soc. Proc. , ' A , vol. 80 , pp. 184-5 .

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The statistical form of the curve of oscillation for the radiation emitted by a black body.

177

181

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

Prof. Harold A. Wilson, F. R. S.

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Tables

Fluid Dynamics

Tables

]\gt ; Form of the Curve of for the emitted by Black Body . By Prof. A. WILSON , F.R.S. , , London . ( Received January 4 , \mdash ; Read February 25 , 1909 . ) The view adopted in the paper is that the radiation from a black body is an ular disturbance subject to statistical laws . This view is , I , that now fenerally held.* It is shown that these laws can be deduced from the observed distribution of energy in the spectrum and that they enable the general racter of the disturbance to be described . At any point in an actual of the radiation we have a number of simple ] lonic vibrations of arbitrary phases and various amplitudes . The radiation may be arded as the suln of all siulple ations in the spectrum . The component vibrations may be arded ils continually , but the distl.ibution of energy the , }when averaged ovel a short interval remains Suppose that compound a lumber n of simple harmonic vibrations all along the same line and of the same amplitude , but phases distributed at random . It is easy to calculate by the method by Lord the chance that the displacement at any instant selected at random will lie between } nits , say and It is ( where the amplitude of each of the COIll ) onents . If compound a of such sets of rations and in th set denote the amplitude , the number by , and the by the expression for the chance of a iven displacement is Let the in a vibration be , and let . Then in the spectrum of plane polarised radiation let denote the energy between and , so that corresponds with and Hence *Cf . Larmor , 'Phil . Mag vol. 10 , p. 574 , 1905 ; Rayleigh , 'Phil . bIag vol. 11 , p. 123 , 1906 . Theory of Sound , ' vol. 1 , p. 39 . Prof H. A. Wilson . The Statistical [ Jan. 4 , is the chance that the displacement at any instant in the radiation lies between and If denotes one of the component vibraticns , then the amplitude of . Hence the chance that lies between and is whele . The correexpressions for unpolarised radiation can easily be obtained in the usual way , but they have no special advantage . It is more convenient for some purposes to consider as a function of distance along the path of the radiation , which will be denoted by . Then , so that for is equal to Consider the average number of times per centimetre that the curve , representing the radiation , cuts the line constant . Evidently is iven by the equation* for is the length per centimetre in pl occupied by the curve . Hence . Hers may be called the mean wave-length of the radiation . Let denote the average number of maxima in per square ' centimetre at a distance from the axis , and denote the number of minima . The number of times per ntimetre that vanishes is independent of , hence Also . Hence and The number of zeros per centimetre in can be shown , in the same way as for , to be ; hence or is assuming that there is no correlation between and , which can easily be verified . 1909 . ] Forra ojthe urue , etc. Thus the distribution of maxima and minima can be determined from the . In the same way the distribution of maxima and minima and Che number of zeros per centimetre for any of the derivatives of can ) found if desired . In order to calculate the relative values of the 's it will be convenient to take the distribution of energy in the spectrum to be represented by Planck 's formula where denotes the absolute temperaCure and A and are constants whose approximate values are known . This ives , putting The value of is unknown , so we can only calculate relative values of the . The table gives the values ] and The larger values of are iyen almost exactly by the formula . The mean wave-length is equal to , hence . The wave-length , at which the energy in the spectrum is a maximum , is iven by the well-known equation . Hence The total number of maxima and minima in is very ] double the number of zero values , and the number of points of inflexion is a little less than double the number of maxima and minima . Substituting the values found for , and in the expression for we get The Statistical of the ) of Oscillation , etc. following table ives some values of The corresponding values of can be by cbanging ? into The distribution of the zero values of or its derivatives along can easily be obtained . If is the mean number of zeros per centimetre , then the number of spaces between two zeros reater than is , where is the whole number of spaces considered . shows a curve drawn so as to have approximately the statistical properties determined above . The spaces between the zeros maxima and minima and f , he amplitudes at the maxima and minima were selected at random from collections having the proper distributions . It is important to consider under circumstances such a curve will resemble the actual curve showing the displacements in a stream of radiation . Suppose the black body consists of a small hole in one side and an image of this hole is focussed on the slit of a spectrometer . The disturbance at any point on the slit is the sum of the disturbances coming from an enormous number of . electrons on the walls of the inside of the box . Suppose each electron emits a series of more or less separate impulses ; then if the number of electrons concerned is big enough , the displacement at a point on the slit will be at any instant the sum of a large number of displacements each due to one electron . In this case the displacenlent will practically never be zero , because no impulses have arrived , but only when the sum of the displacements in the impulses is zero . This is the case to which the theory given above is intended to apply . In this case , if a large number of short lengths of the displacement curve were selected at random , then most a great many of them would resemble the curve shown in fig. 1 . In this sense this curve may be said to represent the character of the disturbance in the radiation . If the distribution of the energy in the spectrum of the radiation emitted Photographic gement of Small Sotid Objects . by a single electron could be examined it might be found , when ayeraged over a enough period , to be the same as that actually found , but we have no evidence as to this . If the electron were freely moying about it would probably go all the possible states of the electrons , and so would probably the usual distribution of energy on the average over a enough period . The theory given above is not intended to apply to this case . The curve shown does equally well for any temperature proyided the scale of is taken to be proportional to the temperature and the scale of ? / inversely proportional to the temperature . The theory given above applies of course equally well to the radiation emitted by any body or to radiation any kind of energy distribution in its spectrum . Best Conditions for Photographic gement of Solid Objects . A. MALLOCK , F.li . S. ( Received January 26 , \mdash ; Read Febrnary 18 , 1909 . ) Having recently had to photograph some small solids on an enlarged scale , I was led to enquire into the conditions as to the angular aperture and focal length of the lens which would give the best definition in the picture obtained . If the actual distance apart of the closest points in the object which must be separated in the picture is Jreater than several yths of the employed , the problem may be solved by geometrical optics . Let principal focal length of the lens . distance between some part of the object and the lens . the focal length conjugate to diameter of lens . resolving , e.g. , the distance between the closest points which it can separate . nitude of the smallest detail the objects which to appear separated in the picture .

rspa_1909_0024

0950-1207

Best conditions for photographic enlargement of small solid objects.

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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.