Nov. 17, 1887] 



NATURE 



71 



SCIENTIFIC SERIALS. 



American Journal of Matheviatics, vol. x. No. i (Baltimore: 

 Johns Hopkins University, 1887). — The number opens with the 

 concluding lecture (the 33rd) of Prof. Sylvester's course on the 

 theory of reciprocants, in which is investigated the differential 

 equation of a cubic curve having a given absolute invariant 

 S'VT^- A supplemental "lecture" is supplied by the reporter 

 (Mr. Hammond) from the lecturer's surplus material : this "con- 

 stitutes probably the most difficult problem in elimination which 

 has been effected up to the present time." All admirers of 

 Prof. Sylvester's brilliant genius will be glad to have the fine 

 presentment of his features which accompanies this number. 

 — Algebraic surfaces of which every plane section is uni- 

 cursal in the light of ^-dimensional geometry is devoted to a 

 proof and to illustrations, by Mr. E. H. Moore, Jun., of a 

 theorem due to Picard, viz. " Les seules surfaces algebriques 

 donttoutes les sections planes sont unicursales sont les surfaces 

 reglees unicursales et la surface du quatrieme degre de Steiner." 

 — Mr. Morgan Jenkins, in a paper on Prof. Cayley's extension of 

 Arbogast's method of derivations, presents in a simplified form 

 results given by the elder mathematician in a memoir printed in 

 the Phil. Trans, (read December i860). — Properties of a com- 

 plete table of symmetric functions, by Capt. P. A, Macmahon, 

 R.A., establishes some remarkable features of a tabulation set 

 forth by Mr. Durfee in vol, v. of iha Journal. — Oskar Bolza, in 

 his article on binary sextics with linear transformations into 

 themselves, considers those binary sextics which remain un- 

 changed (or are only changed by a constant factor) for certain 

 linear transformations of the variables. —Prof. Cayley follows 

 with the sequel to his memoir on the transformation of elliptic 

 functions (vol. ix.), and Prof. Woolsey Johnson closes the 

 number with the symbolic treatment of exact linear differential 

 equations. 



Bulletin de la Societe des Naturalistes de Moscou, 1887, iii. — 

 Comparative osteology of the penguins and its bearing upon the 

 classification of birds, by Dr. M. Menzbier (in German ; with a 

 plate).— The Hessian fly, by Prof. K. Lindeman (in German). — 

 Chemical composition of the Lipetsk mineral springs, by A. 

 Kislakovsky. A series of chemical analyses has been under- 

 taken in order to ascertain how far the composition of the 

 springs is liable to undergo changes at different times of the 

 year. The admixture of water flowing from sweet springs 

 makes the amount of FeCO., to vary from o-oi6 to 0-032, and 

 from o-oo8 to 0-025 '" different springs. — On the increase in 

 the number of thunderbolts and its causes, by J. Weinberg (in 

 German). — Enumeration of the vascular plants of Caucasus, by 

 M. Smirnoff (in French). This fourth paper of the introduc- 

 tion which the author has written to precede his enumeration of 

 plants discusses the following important subjects : evaporation, 

 limits of perennial snow in Caucasia and neighbouring highlands, 

 the present and ancient glaciers of Caucasus, and the geology of 

 the country since the later Tertiary. The twelve botanical 

 regions into which the author divides Caucasia are given with 

 short characteristics of their physical features. On the whole the 

 paper is a most valuable contribution to the knowledge of 

 Caucasus. — List of plants growing in the province of Tamboff, 

 by D. Litvinoff (continued). — C/zcr/yw^/^^j- turca, Steven, an 

 enemy of the vine-tree, by E. Ballion. It has been found at 

 Novorosiysk, on the east coast of the Black Sea, and must have 

 immigrated from Asia Minor and Syria. 



SOCIETIES AND ACADEMIES. 

 London. 

 Mathematical Society, November 10.— Sir J. Cockle, 

 F.R.S., President, in the chair.— Prof. Sylvester, F.R.S., being 

 incapacitated by an accident to his leg from attending in person to 

 receive the De Morgan Medal, awarded him by the Council in June 

 last, deputed Mr. J. Hammond to represent him. The President, 

 after a few remarks eulogistic of Prof Sylvester's numerous dis- 

 coveries, presented the medal to Mr. Hammond, who made a 

 felicitous reply. — The Treasurer (A. B. Kempe, F.R.S. ), after 

 having read his Report, announced to the meeting that the 

 Society's application to the Privy Council for the grant of a 

 charter had failed. — The following were elected to act as the 

 Council for the ensuing session :— President : Sir J. Cockle, 

 F.R.S. Vice-Presidents: Dr. J. W. L. Glaisher, F.R.S., 

 Prof Hart, and Lord Rayleigh, Sec.R.S. Treasurer: Mr. A. 

 B. Kempe, F.R.S. Hon. Sees. : Messrs. M. Jenkins and R, 



Tucker. Other Members : Messrs. A. Buchheim, E. B. Elliott, 

 A. G. Greenhill, J. Hammond, J. Larmor, C. Leudesdorf, 

 Captain P. A. Macmahon, R.A., S. Roberts, F.R.S., and 

 J. J. Walker, F.R.S. — The following communications were 

 made :— On pure ternary reciprocants and functions allied to 

 them, by E. B. Elliott.— On the general linear differential equa- 

 tion of the second order, by the President.— On the stability of 

 a liquid ellipsoid which is rotating about a principal axis under 

 the mfluence of its own attraction, by A. B. Basset.— On modu- 

 lar equations and geometry of the quartic, by R. Russell.— The 

 differential equations satisfied by concomitants of quantics, by 

 A. R. Forsyth, F.R.S.— On the stability or instability of cer- 

 tain fluid motions (ii.), by Lord Rayleigh, Sec.R.S.— Notes 

 on a system of three conies touching at one point, by Dr. 

 Wolstenholme. 



Geologists' Association, November 4. —Mr. F. W. Rudler, 

 President, in the chair.— The President delivered the opening 

 address of the session, entitled "Fifty Years' Progress in British 

 Geology." He drew a picture of the state of geology in 1837, 

 and contrasted it with that in 1887. The principal questions 

 discussed were the old controversy between the Catastrophists 

 and Uniformitarians, the development of Palaeozoic geology, the 

 origin of the Drift, and the antiquity of man. In recent years 

 the warmest discussions have referred to the Archxan rocks and 

 to the Glacial Drift. Attention was directed to the debt which 

 geology owes to engineering, especially to the development of 

 our railway system and to artesian borings. The sub-Wealden 

 exploration was explained, and a Jubilee boring suggested. 

 Deep-sea exploration was touched upon. Turning to petrology, 

 its low condition in 1837 was pointed out, and its recent develop- 

 ment traced to the introduction of microscopic methods of 

 research. The history of palaeontology was briefly sketched, 

 special attention being called to the work of the Palaeontographical 

 Society. Improvements in the Geological Department of the 

 British Museum were noticed, and reference was made to the 

 history of the Geological Survey and the Museum of Practical 

 Geology. In conclusion, it was pointed nut that by a happy 

 accident the meeting of the International Geological Congress 

 in London next year will coincide with the centenary of the 

 foundation of British geology — the original publication of 

 Hutton's " Theory of the Earth " in 1788. 



Chemical Society, November 3.— Mr. William Crookes, 

 F.R.S., President, in the chair. — The following papers were 

 read : — Note on the atomic weight of gold, by Prof. T. E. 

 Thorpe, F.R.S., and Mr. A. P. Laurie. — The ni teraction of 

 zinc and sulphuric acid, by Mr. M. M. Pattison Muir and 

 Mr. R. H. Adie. — Note on safety-taps, by Mr. W. A. Shen- 

 stone. — Note on Guthrie's compound of amylene with nitrogen 

 peroxide, by Dr. A. K. Miller. — The dehydration of metallic 

 hydroxides by heat, with special reference to the polymerization 

 of the oxides and to the periodic law, by Prof Carnelley and 

 Dr. James Walker, University College, Dundee. — The bromina- 

 tion of naphthalene /9-sulphonic acid, by Mr. G. Stallard. — The 

 constitution of the three isomeric pyrocresols, by Dr. W. Bott. 

 — Preliminary note on certain products from teak, by Mr. R. 

 Romanis. 



PARIS. 



Academy of Sciences, November 7. — M. Janssen in the 

 chair. — On a paradox analogous to the St. Petersburg problem, 

 by M. J. Bertrand. The paper deals with the doctrine of 

 probabilities, and shows that, if a gambler plays under conditions 

 involving all but inevitable niin, equity requires the remotely 

 contingent prize to be infinite. — On the state of the potassa in 

 plants, in the soil and vegetable humus, and on its quantitative 

 analysis, by MM. Berthelot and Andre. These studies have 

 been undertaken to determine how far the potassa present in 

 plants and arable land is in the condition of salts soluble in 

 water, or of insoluble salts capable or not of resi-ting the action 

 of attenuated acids. The researches are in continuation of those 

 already described connected with the analysis of the soluble and 

 insoluble carbon present in the soil, and of the nitrous com- 

 pounds in their various forms of nitrates, free ammonia, &c. — 

 Inquiry into the two fundamental principles of the accepted 

 doctrines regarding cerebral dualism in voluntary motions, by M. 

 Brown-Sequard. In continuation of his recent communication 

 on this subject, the author here advances facts and arguments, 

 some of which go directly to show that each half of the 

 encephalon may independently serve for the production of 

 voluntary movements in both sides of the body, while others 



