August 10, 13S3.] 



SCIENCE. 



175 



WEEKLY SUMMARY OF THE PROGRESS OF SCIENCE. 



ASTRONOMY. 



Astropbysical observations of Jupiter. — 

 Kicco publishes a fine series of eiglileeii drawings of 

 the planet, made, with one exception, in 18S1, 1SS°2, 

 and 18*5, by means of tlie ten-incli telescope of the 

 observatory of Palermo. lie gives, also, a large 

 number of micrometrical measures, and" detailed 

 descriptions of the appearance of llie planet and 

 its 8nrface-ra.irkings, on forty-seven different dates. 

 The effect of the 'red spot' upon the contour of the 

 adjacent belts is well brought out. — (Mem. soc. 

 spellr. Ual., May, 188:!.) o. A. Y. |172 



Photometric observations of eclipses of Jupi- 

 ter's satellites. — Cornu and Obrecht give the re- 

 sults of some experiments upon artificial eclipses 

 made to imitate the eclipses of .Jupiter's satellites, 

 using the method already referred to in these col- 

 umns. Tliey find that the prob:ible error in deter- 

 mining the time when the light of the satellite is 

 reduced to one-half its normal amount is about a hun- 

 dredth of the total time of obscuration. They pro- 

 pose, also, the use of a polariscopic arrangement in 

 place of the 'cat's-eye,' and, in this connection, 

 append the following note: "We have recently 

 learned tliat the astronomers of Harvard college em- 

 ploy an analogous arrangement — of which, however, 

 the description is not known to us — for the purpose 

 of determining the moment of disappearance [pour 

 arriter d defintr Vepoque. de l\'clat uul). If the 

 apparatus is analogous, the method of observation is, 

 as one sees, entirely different." They have evidently 

 been misinformed; for the very essence of Prof. 

 Pickering's plan consists in the determination, not 

 of the moment of disappearance, but of half-bright- 

 ness. — {Comples renda-t, June 2.5, 1SS3.) c. A. Y. 



1 173 

 MATHEMATICS. 



Surfaces of constant curvature. — M. Wein- 

 garten here deals with certain properties of the linear 

 elements on surfaces with a constant measure of 

 curvature. Certain considerations connected with 

 the modern theory of functions, particularly that 

 portion of the theory which deals with linear differ- 

 ential equations of the second order, have led him 

 to conjecture that the determination of the geodetic 

 lines upon a surface of constant curvature, by means 

 of certain given line.ir elements, stands in a close 

 relation to the theory of the linear differential equa- 

 tions of the second order. JI. Weing.irten makes the 

 remark (which, thouj^h not new, is important here) 

 that the extension of those properties of curved sur- 

 faces, studied and enunciated by Gauss, which de- 

 pend upon a given form of the linear element, is much 

 simplified by the introduciion of certain functions of 

 the position of a point upon the surface. The val- 

 ues of these functions are given in terms of the co- 

 eflicients of the linear element in such a way, that, 

 by the introduction of new (two| variables, we arrive 

 again at the original linear clement. The functions 

 possjssiug this (invariantive) property are called 



flexion-invariants (hlcijunfixintarianteti). As an ex- 

 ample of flexion-invariants, we have the 'measure 

 of curvature' of a surface. From the differential 

 coefficients of a fiexion-invariani, and the Gaussiau 

 coefticients, E. F, G, of a linear eli'ment of a surface, 

 an indefinite number of new invariants can be formed, 

 two only of which are independent. The author 

 gives a brief account of IJeltrami's work on these 

 functions, and then considers particularly the sur- 

 faces of constant curvature. The paper is an ex- 

 ceedingly interesting one to the student of this 

 jiarlictilar branch of geometry, and is a valuable ad- 

 dition to the previous memoirs, by M. Weiugarlcn, 

 on this and cognate subjects. — (Juurn. reiiie anp. 

 mai/i., 1883.) t. c. [174 



PHYSICS. 

 Density of the earth — Major R. v. Sterneck 

 of the government Military-geographical institute of 

 Vienna, last year, tried Airy's methoil of the deter- 

 mination of the earth's mean density in the St. Adal- 

 bert shaft of the silver-mines at Piibram, liohemia, 

 at depths of 51<! and 972.5 metres. His average re- 

 sult was 5 ti.i, which agrees closely with the values 

 determined by other methods. On comparing his 

 measures with Airj's, a curious agreement appears 

 in the number of seconds gained by a clock at differ- 

 ent depths, and a continual decrease in the deduced 

 mean density as the depth increases. Airy fimnd 

 ( \ii'>i), at a depth of 3S3 metres, that his clock gained 

 2».2.i a day, and the density was 6..')7; v. Sterneck's 

 figures are 51(5, 2».4, and 0.28, and 972, 2«.3, .^.01, 

 respectively: whence he concludes, "that, in Uie in- 

 terior of the earth, the resultant of gravity, centrif- 

 ugal force, and the attraction of the superincumbent 

 mass, is constant." — {MiUli. k.-k. iuitU.-'jco(ji: inxt. 

 Ifien, I8S2, ii. 77.) w. M. D. 1175 



Electricity. 

 Geographical variation of horizontal in- 

 tensity. — F. Kolilrausch proposes to use a form 

 of his local-variometer (described in Ann. pliyg. 

 cliem., xviii. 54.i) in which the scale is at a distance 

 A from the axis of suspension, and attached to the 

 instrument, and obtains between the horizontal in- 

 tensities at two different places the relation — 

 ir — II _ Un ^ , 



n ~ i~A 



<p being the angle through which the frame of the 

 instrument is turned, n and n' the deflections in 

 scale-divisions, and /i a coellicient of the tempera- 

 ture, t. — {Ann. pUyn. cheiii.,\\\. l:!0.) J. T. [176 

 Thermochemical properties of electromotive 

 force. — Kdlund investigates the Ihi'rmal 'changes at 

 the electrodes of a voltameler by placing the junc- 

 tions of a ihermiipile in front of the electroiles, and 

 enclosing both in a porous membrane. He finds, that, 

 when the electrodes are copper and the liquid copper 

 sulphate, tlie eleciromotive force lietwcen the metal 

 and (he liquid uses less heat for formation of current 

 than is sol free iu the formation of copper suljiUalc. 



(«'- n)+ fi{t - <-); 



