Caustic coordinates in Platzeck-Gaviola test of conic mirrors.
The centers of curvature of all zones of a spherical mirror coincide at the center of that sphere. In the case of all other conies of revolution, however, the radii of curvature of dif­ ferent zones have different magnitudes; hence their centers of curvature do not coincide but lie along the caustic curve, as shown by Wadsworth. Based on this property Platzeck and Gaviola devised a test to measure the shape of a para­ boloid being figured. What they do is to measure the posi­ tions of the centers of curvature of different regions in the optical surface, then the results are compared with the theo­ retical values. The theoretical positions of these centers of curvature for a paraboloid are computed with two simple formulas given by Schroader, but to our knowledge the ex­ pressions for any conic of revolution have not been given. To derive the expressions for the caustic coordinates (η,ξ) of the centers of curvature of the conic surface (see Fig. 1), we
Wavefronts, caustic, ronchigram, and null ronchigrating of a plane wave refracted by an axicon lens.
The aim of this work is threefold: first we obtain analytical expressions for the wavefront train and the caustic associated with the refraction of a plane wavefront by an axicon lens, second we describe the structure of the ronchigram when the ronchiruling is placed at the flat surface of the axicon and the screen is placed at different relative positions to the caustic region, and third we describe in detail the structure of the null ronchigrating for this system; that is, we obtain the grating such that when it is placed at the flat surface of the axicon its associated pattern, at a given plane perpendicular to the optical axis, is a set of parallel fringes. We find that the caustic has only one branch, which is a segment of a line along the optical axis; the ronchigram exhibits self-intersecting fringes when the screen is placed at the caustic region, and the null ronchigrating exhibits closed loop rulings if we want to obtain its associated pattern at the caustic region.
The Tsetse Problem on the Eastern Cattle Route in the Gold Coast
1. Primary fly-belts round Makongo consisted of three different vegetational communities: a Cynometra-Vitex association along the main length of the Makongo river, on a clay soil; a Ficus congensis association along the river close to the town, on a sandy soil; and Isoberlinia doka woodland on moist sandy soil north-west and south of Makongo. 2. Secondary fly-belts of less dense vegetation occur in the orchard bush savannah round Makongo, and these are not colonised until the commencement of the rainy season. 3. Glossina tachinoides and G. palpalis both occurred in the riverside communities, and G. palpalis alone in the Isoberlinia woodland. 4. Along the river G. palpalis outnumbered G. tachinoides by 3:1 in the dry season. At the commencement of the rains G. tachinoides increased more quickly than G. palpalis , bringing their numbers very nearly equal, but at the end of the rains there was a decrease in G. tachinoides which restored the original proportion. 5. G. morsitans had been found at Makongo formerly but was not met with at the time of this investigation, its absence being due to the disappearance of the larger antelope from the neighbourhood. 6. Smaller game animals, small mammals and reptiles afforded an adequate food supply for tsetse in the fly-belts, and also passing herds of cattle, as well as natives from the village and travellers. 7. The distribution of G. palpalis within the fly-belts was markedly influenced by the proximity of a cattle road along which herds of cattle passed almost daily, and by village water-holes. 8. During the dry season the primary foci were always found to be the places of greatest relative humidity, and the fly does not tend to move out of these until the general atmospheric humidity has reached a certain fairly high degree. 9. In clearing the fly-belts the removal of all primary foci within a quarter of a mile of the town and of thick bush within 100 yards of water-holes was undertaken. The work lasted from the beginning of February to the end of March 1931. 10. The effect of clearing the Isoberlinia doka woodland was to banish G. palpalis completely, and it never returned to these clearings. 11. On clearing the riverside Ficus congensis fly-belt, G. tachinoides was practically eliminated for the first three months, but reappeared in the clearings in June when there was a general increase and up-stream migration of this fly. G. palpalis remained in this clearing in fluctuating numbers up to June, when observations were suspended. 12. 565 marked tsetse were liberated in the fly-belts immediately previous to clearing. Of G. palpalis 12·7% were recaptured in the clearings and 11% outside the clearings. Of G. tachinoides 5·5% were recaptured in the clearings and 6·8% outside.