Mat 18, 1883.] 



SCIENCE. 



427 



manner, a discontinuous group for all points (u, v) 

 of the region D, defined by 



xC- + u'"- + v"^ + b"- < 1, 

 wliere 



u = «' + iu", V = v' + ixi". 



The author shows that every substitution of the 

 group transforms each point of the limit of D into 

 another point of the same limit. He also shows that 

 there exist functions, F, of u and v, only defined in 

 the region D, and which leave invariable all of the 

 substitutions of the group. The only groups con- 

 sidered are those possessing this property; viz., we 

 can always find in the region D a region E, having 

 no point common with the limit of D, and such that, 

 in the interior of E, there is one, and only oue, point 

 which corresponds to any point (u, v) by means of 

 the substitutions of the group. — [Comptes rendus, 

 Jan. 29.) T. c. [862 



Differential equations. — M. Steen treats cer- 

 tain differential equations of the second order, an 

 account of which has already appeared in another 

 place. The differential equations are of the form 

 y" — {a cot ;c — b tang x) y' + cy — 0, 

 v" + (a cot X — b tang x) v' + cv = 0; 



X being the independent variable, and the accents 

 denoting differential co-efiicients. These equations 

 are treated for special values of the constants a, 6, c, 

 and the integrals exhibited in the form of series of 

 trigonometric functions, and also in the form of 

 definite integrals of certain trigonometric functions. 



— {Vidensk. aelsk. skr., (6), naturv. math, afd., i. 6.) 

 T. c. [863 



PHYSICS. 



Mechanics. 

 Radius of gyration of a rifled projectile. — 



Lieut. C. A. Stone deduces a formula for the deter- 

 mination of this value. Applied to the 700-lb. Butler 

 shell, he obtains K = 4.1224"; while the bureau of 

 ordnance, U.S.A., found by experiment for this 

 shell, K = 4.10053.08". Lieut. Stone discusses, also, 

 the ratio of the forces necessary to give translation 

 and rotation to a rifled projectile, and the ratio of 

 the ranges of a projectile measured on the horizontal 

 and on an inclined plane in a non-resisting medium. 



— (Proc. U. S. nav. inst., viii. no. 4.) c. B. M. [864 



Acoustics, 



Hydrogen-Twhistles. — Mr. Prancis Galton has 

 continued his researches upon the production of 

 notes of excessively high pitch, and their audibility 

 to different animals, wishing to test the powers of 

 insects in this respect. The idea has occurred to him 

 of blowing his high-pitched whistle with hydrogen- 

 gas, and so increasing its shrillness. Preliminary 

 experiments with coal-gas have given good results ; 

 and Mr. Galton thinks that he can produce a sound 

 due to 624,000 vibrations per second. — {Nature, 

 March 22. ) c. B. c. [865 



Intensity of sound. — Vierordt has studied the 

 subject of the estimation of the intensity of sound 

 by the process of dropping a body upon a sonorous 

 plate. The intensity of the sound produced is pro- 

 portional to h" , where e is a co-efi3cient to be deter- 

 mined experimentally. A formula given by Oberbeck 

 is, ,„„ P 



if h is the height fallen through by the heavier weight 

 P, and H the greater height fallen through by a 



lighter weight p, when the intensity of the sound 

 produced by striking the plate is the same. A large 

 number of measurements are recorded, from which 

 the author concludes that there is a general measure 

 of the strength of sound. With spheres of the same 

 material, and plates of definite material and weight, 

 the value of e varies but slightly with increasing 

 weight of the sphere, or with variation in the height 

 of fnW. — iAnn. phys. chem., No. 3, 1883.) c. li. c. 



[866 

 Optics, 

 (P/totoffraphy.) 

 Astronomical photography. — At the Meudon 

 (France) observatory they are studying movements 

 of photospheric matter with the aid of series of 

 images obtained with the ' photographic revolver.' 

 They are also working at photographic photometry, 

 the principle being, that the intensities of two light- 

 sources are in the inverse ratio of the time they take 

 for the same photographic work; e.g., producing the 

 same tint on two quite similar plates. The method 

 will be applied to data of the comet of 1881, the full 

 moon, etc. — [Nature, March 1.5. ) w. H. P. [867 

 Astronomical photography. — At the March 

 meeting of the Eoyal astronomical society. Dr. Gould 

 gave an account of his work at Cordova. He consid- 

 ered that he had been successful in photographing 

 stars down to the tenth and a half or twelfth magni- 

 tude. Mr. Common showed a photograph he had 

 taken of the great nebula in Orion, the appearance 

 of which, in many parts, gave rise to an interesting 

 discussion ; the majority of those taking part inclin- 

 ing to the belief that the photograph represented cer- 

 tain unknown dark objects In space. — {Brit, journ. 

 phot., March 23.) 



[No such appearance has been noted here in the 

 excellent photographs of this object taken by the late 

 Dr. Henry Draper.] — w. H. p. [868 



Positive prints from a positive. — MM. Cros 

 and Vergeraud have sent to the French photographic 

 society a communication on the above subject. A 

 suitable paper is covered with a solution of ammo- 

 nium bichromate, 2 grams; glucose, 15 grams; water, 

 100 grams. This is dried, and exposed to the light 

 under a positive. When the uncovered portions of 

 the paper, whicti were at first of a decided yellow, 

 have become gray, the exposure is discontinued, and 

 a rapid immersion made in a silver bath, composed 

 as follows: silver nitrate, 1 gram; acetic acid, 10 

 grams; water, 100 grams. The image appears im- 

 mediately of a blood-red color, formed by the bichro- 

 mate of silver. In all parts where the light has acted, 

 the bichromate has been reduced by the glucose; and, 

 where the variable opacities of the image have pro- 

 tected in different degrees the sensitive film, the bi- 

 chromate of silver remains insoluble in the water of 

 the subsequent washing. If dried by fire, the image 

 remains red; if dried in the open air and in the light, 

 especially in the sun, it becomes dark brown. To 

 obtain a black image, it suffices to expose the dry 

 prints to sulphurous-acid gas. A bath of sulphite of 

 copper and potash in solution gives a more intense 

 black. — {Philad. phot., April.) w. h. p. [869 



Electricity, 

 Electro-optical properties of quartz. — W. C. 



Eontgen confirms and extends results obtained in a 

 former paper {Ann. phys. chem., no. 3). The speci- 

 mens used were a thick circular plate, cut perpendic- 

 ular to the principal axis of the crystal, and a sphere. 

 The apparatus for investigating the quartz-sphere 

 was an old microscope. The quartz was laid on the 



