OcTOBKU 26, 188.".] 



SCIENCE. 



WEEKLY SUMMARY OF THE PROGRESS OF SCIENCE. 



ASTRONOMY. 



The divisions in Saturn's rings. — Professor 

 Kirkwood, in 1nG8. aicimnteil for tlie great division in 

 Saturn's rings by the coninien.Mirabililyof tlie pcilod 

 of a body revolving at tlial distance from Saturn 

 with the periods of the six inner satellites. Dr. 

 William Meyer of Geneva has investigated every 

 possible combination of the commensurabilities of 

 the revolution periods of the satellites, and finds six- 

 other places where a perturbing influence is exer- 

 cised. The divisions most strongly marked seem to 

 be at places where the commensurabilities are the 

 closest, and all the satellites take part. A faint divis- 

 ion should be found in the inner bright ring, accord- 

 ing to Dr. Meyer. Prof, llolden has noted a distinct 

 point at which the .shading-off begins, in the position 

 indicated by Meyer's theory, — a fact which seemed 

 to have escaped Meyer's notice. — (Observ., Sept., 

 trans, from Astr. nachr., 2,.')27, with additions.) 

 M. MCX. [306 



Saturn. — Dr. William Meyer of Geneva gives a 

 new (lotennination of the orbits of six of Saturn's 

 satellites, — Enceladus, Tethys, Dione, Rhea, Titan, 

 and lapetus. From each of these he has determined 

 the mass of Saturn, the reciprocal value of the com- 

 l)ined result being M = 3,482.9 ± .5.5. The original 

 observations are to appear in the Memoires de la 

 xiiciele di- physique de Geneve during the present year. 

 — (.4sfr. ii«c//r., 2,.5-2S.) M. mcN. [307 



MATHEMATICS. 

 Functions of a complex variable. — In the 

 present |)api'r, entitled 'Applications of Fourier's 

 theorem to the theory of the functions of a complex 

 variable.' M. Ilarnaek first shows in what manner the 

 Fourier series are l'> be employed in the discovery of 

 a rigid basis for the Cauchy-Kiemann theorem con- 

 cerning till- development of fimctions of a complex 

 variable. A generalization is also given of the funda- 

 mental hypothesis involved in the C.-R. theorem, 

 as follows: if lo is a function of .t -|- ii/, which over 

 a simply connected plane region is everywhere con- 

 tinuous, atid which ' in general' satisfies the differen- 

 tial equation, — 



'/ 1" dw 

 dx^'dy = ^' 

 then the function to is with its derivatives everywhere 

 finite and continuous, and will possess no singular 

 points. The term 'in general' (im allgemeinen) 

 means that the points which do not satisfy the above 

 differential equation, together with the points for 



. - , . . , , . . din , dw . , 



which the partial derivatives --and , -are inde- 



^ dx dy 



terminate between finite or infinite limits, or are dis- 

 continuous, shall make up simply a discrete system 

 of curves. In the second part of the paper, the author 

 has gone very briefly into the subject of the repre- 

 sentation of an analytical function, without singu- 

 larities, ill the interior of a circle by aid of Dirichlet's 

 principle. — (.V-if/i. rmn., xxi.) t. c. [308 



ENGINEERING. 



Heavy engines and American railroad-tracks. 

 — Mr. O. Chanute states that heavy 'consolidation' 

 engines do not injure the track more than the lighter 

 engines formerly did. Trains have been lengthened 

 from 22 c.irs in 1S74 to 38 in 1S;33; and the weights 

 hauled, from 100 to 228 tons. By strengthening 

 draw-heads, links, and jiins, accidents from breaking 

 apart of trains have been diminished, and the cost 

 of haulage has been reduced from one cent to a 

 half-cent per ton per mile. — (.l/ccAnnirs. July 28.) 

 i:. n. T. [309 



The British institution of mechanical engi- 

 neers. — This society held its summer meeting in 

 Belgium. It was received by the Association of 

 engineers of Lie'ge university, and visited the prin- 

 cipal engineering establishments of the country. 

 Prosidenl Westmacott, in his opening address, called 

 attention to the progress recently made in the rapid 

 production of good articles of manufacture, and to 

 the fact that speed and excellence of work arc not 

 incompatible where machinery is used. The mate- 

 rials must be of the best quality, however, the 

 machines well proportioned, and all working parts 

 well balanced and well fitted. He referred to Thor- 

 neycroft's experience with torpedo-boats, and called 

 attention to the fact, that, at higli speeds, the dif- 

 ficidties of lubrication and the jar observed at lower 

 speeds disappear. In the speed of railway-trains, 

 no advance has been lately made, and the maxi- 

 mum speeds remain at the figures of earlier years. 

 Some economy has been obtained by the use of the 

 crude "products of the distillation of petroleum in 

 the fireboxes of locomotives, this economy sometimes 

 amounting to fifty per cent. Cotton-machinery has 

 been speeded up, until the spindles which formerly 

 made 5,000 revolutions are now making from 8..500 

 to 10,000, on fine American cotton. The increase in 

 speed of woollen-machinery has not been great. In 

 gunnery, the weight of gun and projectile li.ave 

 increased, in twenty-five years, from 5 tons and 00 

 pounds to 100 tons and 2,000 pounds. The shot has 

 an initial energj- of nearly .j0,000 foot-tons. High 

 speed is the direction of change in all departments 

 of enginoeiing. — (.Va(u^e.) n. ii. T. [310 



Hardening soft limestones with fluosilicatea. 

 — The application of alkaline silicates to the exterior 

 of buildings, in order to prevent the deterioration of 

 the stone, has not been attended with satisfactory 

 results. H. L. Kessler proposes to use a solution of 

 fluosilicati's of bases whose oxides and carbonates 

 are insoluble in a free state. When soft limestone 

 is saturated with a concentrated solution of a fluosili- 

 cate of magnesium, aluminum, zinc, or lead, a very 

 considerable degree of induration is soon reached, 

 and the resulting products, except the liberated car- 

 bonic anhydride, are less soluble than the stone itself. 

 No varnish is formed, and therefore no d.inger arises 

 from expansion of frost beneath it. The process has 



