yune 20, 1889 



NATURE 



191 



in air to //, the part in the denser medium reaches C, where 

 AC = // . ah, and a curvature, F, represented by IjC, is im- 

 pressed on the wave, which thus converges to a point Q. Since 



Kc^ f , 7 AT. 1 l^C AB-AC . BC , / „,, 



AC = h . ab — h . AB, and - — — , . . —,,—l- /^and 



AB AB AB 



the relation between the impressed curvature and that of the 



surface becomes F = R(i - h). By successive application of the 



above method, all the ordinary lens problems may be treated. 



and the resulting expressions are simplified by being expressed 

 in curvatures. The ordinary mirror formula, / — R, becomes 

 Y = 2R, and that for the lenticular mirror, F' — 2R + F. The 

 method readily lends itself to the determination of the changes 

 in the shape of wave-fronts entering or emerging from surfaces 

 of irregular outline. The diopteric spherometer has its outer feet 

 situated on a circle of 4471 millimetres radius, and is provided 

 with a screw of i millimetre pitch. The instrument so con- 

 structed reads off directly in " diopteries," i.e. curvatures ex- 

 pressed on a scale in which that of a sphere of i metre radius is 

 taken as unity. — On the use of the biquartz, by Mr. A. W. 

 Ward. This is a mathematical investigation into the causes of 

 the varying degrees of accuracy obtained by different observers 

 who have used the biquartz in rotation measurements. Assum- 

 ing that ellipticaliy polarized light passes through the biquartz, 

 the equation which must be satisfied to give equality of tint on 

 the two halves is shown to be : cos 27 . sin 20 . sin 2 a> - = o, 

 where tan 7 = ratio of axes of ellipse, <p = rotation produced 

 by quartz for wave-length \, = angle between plane of vibra- 

 tions of analyzer and that of xz, the axis of z being parallel to 

 the direction of transmission, and w — angle between one axis 

 of the ellipse and that of .r. The equation is satisfied by either 

 cos 27 = o, or sin 2(p = o, or sin 2&) - 6 = o. The first solu- 

 tion relates to circularly polarized light, and need not be con- 

 sidered ; the second can only hold for one particular wave-length 

 depending on the thickness of the quartz ; and, in interpreting the 

 third solution, it is shown that a satisfactory result is only obtained 

 when the light is plane-polarized. The deductions are in ac- 

 cordance with experiment, for the biquartz has been used with 

 considerable accuracy when experimenting on isotropic media ; 

 but with doubly refracting substances, where the light is liable 

 to become ellipticaliy polarized, the results are very discordant. 

 Errata. — Page 143, lines 27 and 29, for "volumes" read 

 "densities." 



Mathematical Society, June 13.— Mr. J. J. Walker, F.R.S., 

 President, in the chair. — The President opened the proceedings 

 of this the last meeting of^the session with commenting on the 

 losses the mathematical world had recently sustained by the 

 deaths of Prof. Genocchi, of Turin, Prof. Du Bois-Reymond, 

 Berlin, and M. Halphen, of Paris. — The following communica- 

 tions were made : — The square of Euler's series, by Dr. Glaisher, 

 F.R. S. ; a theorem in the calculus of linear partial differential 

 operations, by Major Macmahon, R.A. ; on crystalline reflection 

 and refraction, by A. B. Basset, F.R.S. ; on some rings of circles 

 connected with a triangle and the circles (Schoute's system) that 

 cut them at equal angles, by W. W. Taylor ; the figures of the 

 Pippian and Quippian of a class of cubic curves, by the 

 President (Sir J. Cockle, F.R.S., in the chair) ; and a genera- 

 lization of Buffon's problem, by Prof. Sylvester, F.R.S., (com- 

 municated by J. Hammond). — The following papers, on the 

 small wave-motions of a heterogeneous fluid under gravity, by 

 Prof. W. Burn>ide, and on the uniform deformation in two 

 dimensions of a cylindrical shell of finite thickness, with applica- 

 tions to the general theory of deformation of thin shells, by 

 Lord Rayleigh, Sec. R. S. , were taken as read. 



Zoological Society, June 4.— Mr. Osbert Salvin, F.R.S., 

 Vice-President, in the chair. — The Secretary read a report on 



the additions that had been made to the Society's Menagerie dur- 

 ing the month of May 1889.— Mr. II. E* Dresser exhibited and 

 made remarks on some eggs of the Adriatic Black-headed Gull' 

 {Lanes melaiiocephalns) and of the Slender-billed Gull {Lams 

 i^elustcs), which had lately been obtained at their nesting-places 

 in the marshes of Andalusia by Colonel Hanbury Barclay and' 

 himself. — Dr. G. J. Romanes, F.R. S., read a paper on the in- 

 telligjence of the Chimpanzee, as shown in the course of experi- 

 ments made with the female Chimpanzee called " Sally," which 

 has been living several years in the Society's Menagerie. — A 

 communication was read from Signor Fr. Sav. Monticelli. con- 

 taining notes on some Entozoa in the collection of the British 

 Museum. — Mr. Sclaler read a list of the birds collected by Mr. 

 George A. Ramage (the collector employed by the joint Com- 

 mittee of the Royal Society and the British Association for the 

 exploration of the Lesser Antilles) in Dominica, West Indies^ 

 and made remarks upon some of the species. 



Entomological Society, June 5. — The Right Hon. Lord 

 Walsingham, F. K.S., President, in the chair. — Mr. S. Stevens 

 exhibited a specimen of Acrolepia asseclella, Zeller, included in 

 a lot of Tineidic, purchased by him at the sale of the late Mr. 

 A. F. Sheppard's collection. He also exhibited, for comparison, 

 a specimen of /^. beiiilctclia.— Mr. J. J. Walker, R. N., exhibited 

 a collection of Lepidoptera made in 1887 and 1888 in the im- 

 mediate vicinity of the Straits of Gibraltar. The collection 

 included sixty-eight species of butterflies, of which thirty-six 

 were obtained on the Rock of Gibraltar itself, and the remainder 

 on the European side of the Straits ; and about 160 species of 

 moths.— Dr. P. B. Mason exhibited a number of specimens of 

 a South European species of ant — Creinatogaster scittsllarisy 

 Oliv. He said that the specimens were all taken in the fernery 

 of Mr. Baxter, of Burton-on-Trent, and had probably been 

 imported with cork. — Mr. O. E. Janson exhibited a pair of 

 Neplunides slanleyi, a species of Cetoniidce, recently received 

 from Central Africa, and described by him in the February 

 number of the Entoinokgisl ; also some varieties of N. poly- 

 cliroiis, Thoms., from the Zanzibar district. — Dr. N. Manders- 

 exhibited a number of Lepidoptera collected by himself in the 

 Shan States, Burmah ; also a collection of Lepidoptera made by 

 Captain Raikes in Karenni. — Mr. McLachlan exhibited over 40a 

 specimens of Neuroptera, being a portion of the collection 

 formed in Japan by Mr. II. J. S. Pryer. They represented nearly 

 all groups (excepting Odonata, now in the hands of Baron De 

 Selys). Some of the Ascalaphidie, Pai/orpida-, and IVichoplera, 

 were of great beauty. — Dr. Sharp exhibited the peculiar cocoons^ 

 of an Indian moth, Lxhodia newara, Moore ; these were the 

 cocoons possessing a drain at the bottom in order to allow 

 water to escape, already described in the Proceedings of the 

 Zoological Society for 1888. p. 120, where, however, their great 

 resemblance to the pods of a plant had not been alluded to. — 

 Mr. Enock exhibited, and made remarks on, specimens of 

 Cecidomyia destructor, bred from American wheat. — Mr. W. 

 Warren exhibited a bred specimen of L-ictinia posticana, Zett., 

 from Newmarket ; also specimens of Eiipithecia jasioneata and 

 Gelechia confinis, bred by Mr. Gardner. — Mr. C. 6. Waterhouse 

 exhibited and explained a number of diagrams illustrative of the 

 external characters of the eyes of insects.— Mr. A. G. Butler 

 communicated a paper entitled "Descriptions of some new 

 Lepidoptera-Heterocera in the collection of the Hon. Walter 

 de Rothschild." He also contributed a second paper entitled 

 " Synonymic Notes on Moths of the earlier genera of Noctuites." 

 —Dr. Sharp read a paper entitled "An Account of Prof. 

 Plateau's Experiments on the Vision of Insects. " Lord Walsing- 

 ham, Mr. Jacoby, Mr. White, and Mr. Waterhouse took part in 

 the discussion which ensued. 



Paris. 



Academy of Sciences, June 11. — M. Des Cloizeaux, Presi- 

 dent, in the chair. — On the exceptional deviations of some 

 tropical cyclones, by M. H. Faye. As far as 35° of latitude 

 tropical cyclones present a remarkable regularity, with the 

 exception that the geometrical figure described by their 

 trajectory is deflected towards the north between 20° and 30° 

 according to the seasons, as has been clearly determined by le 

 Pere Vinez, of the Havana Observatory. But although the laws 

 laid down by this meteorologist appeared to be absolute, they 

 were certainly deviated from by the tornado of September 3-4, 

 1888, in the West Indies, as well as by that of June 1885, in the 

 Gulf of Aden. The disturbing cause in the first instance was 

 attributed by Viiiez to a second cyclone exercising a strong 



