504 



NATURE 



[March 22, 1900 



Dorman B. Eaton, Columbia University receives 100,000 dollars 

 to found a professorship of municipal science and administration, 

 and Harvard University 100,000 dollars to endow a chair in the 

 science of government. Mr. Louis H. Severance, of New York 

 City, has given 60,000 dollars to Oberlin College for a chemical 

 laboratory. The provision made for the college by Mrs. C. E. 

 Haskell amounts to 77,000 dollars. St. Lawrence University 

 has recently received a gift of 24,000 dollars from a friend of 

 that institution. A half million dollars will be distributed by 

 Dr. D. K. Pearsons, of Chicago, among fourteen colleges 

 •throughout the United States. Most of his donations will be made 

 on condition that the colleges raise a certain amount, generally 

 50,000 dollars, or an amount equal to the gift, within a given 

 time. Dr. Pearsons has already given 2,500,000 dollars to the 

 ■cause of education. 



SCIENTIFIC SERIALS. 



Transactions of the American Mathematical Society, January. 

 — At the February meeting of the Society last year, the Presi- 

 dent announced that the Council had reported that it was 

 " desirable and feasible, and in all respects for the best interests 

 of mathematical science in this country, that the Society should 

 ■undertake the periodical publication of Transactions, beginning 

 with January i, 1900." The well-printed and altogether admir- 

 able first part is now before us, and we heartily wish good speed 

 to the venture, "' the success of which is already well assured." 

 The size of the page is approximately 11x8 inches, and so is 

 intermediate between the Bulletin and American Jotirnal of 

 Mathematics pages. — Conies and cubics connected with a plane 

 cubic by certain co-variant relations, by H. S. White, is a paper 

 which was read, with a slightly different title, at the August 

 (1899) meeting. By employing the irrationality that occurs in 

 .Hesse's canonical form of the cubic, the writer is able to identify 

 Hubert's two systems of irrational co-variant conies, and to 

 exhibit certain other relations, and thence to give explicitly co- 

 variant equations of definition for the two cubics which have the 

 same Hessian, and for those which have the same Cayleyan, as a 

 given fundamental cubic. The results are attained by the aid of 

 a canonical form of the cubic containing Hesse's irrationality. 

 The conies discussed are Hilbert's co-variant conies {cf. letter 

 addressed to M. Hermite, Liouville, vol. iv. 1888). The in- 

 variantive proofs of some of the foregoing results are given in 

 the next paper, Formentheoretische entwickelung der in Herrn 

 White's Abhandlung liber curven dritter ordnung enthaltenen 

 -Satze, by Paul Gordan. — Sur la definition generale des fonctions 

 analytique, d'apres Cauchy, by E. Goutsat, has its object thus 

 indicated. — J'ai reconnu depuis longtemps que la demonstration 

 -du theoreme de Cauchy, que j'ai donne en 1883, ne suffisait 

 pas la continuile de la derivee. Pour repondre au desir qui 

 m'a ete exprime par M. le Professeur W. F. Osgood, je vais 

 indiquer ici rapidement comment on peut faire cette extension. 

 — On a class of particular solutions of the problem of four 

 •bodies, by F. R. Moulton, treats the case of three bodies finite, 

 moving in circles according to one or the other of the solutions 

 ■of Lagrange, while the fourth is infinitesimal. — Definition of the 

 Abelian, the two hypo-Abelian, and related linear groups as 

 ■quotient , groups of the groups of isomorphisms of certain ele- 

 mentary groups, by Dr. L. E. Dickson, aims at giving a natural 

 definition of these groups based upon Jordan's " important, but 

 ■artificial, conception of exposants cT^chajige." It is written in 

 the author's usual thorough style. — H. Maschke gives a half- 

 page note on the unilateral surface of Mcebius. — On regular 

 singular points of linear differential equations of the second 

 order whose coefficients are not necessarily analytic, by M. 

 Bocher. The writer remarks that since the time of Cauchy it 

 has been considered of interest to establish the existence of solu- 

 tions of differential equations whose coefficients are functions of 

 a real variable x, and to do this without requiring these co- 

 -efficients to be analytic functions of x, but merely continuous 

 functions. It is a natural extension of this point of view to wish 

 to investigate the nature of singular points of such equations, i.e. 

 of points where the coefficients become discontinuous. It is M. 

 Bocher's object to carry through such an investigation in a special 

 ■case, viz. that of 



dx"^ + ^ dx 



qy 



•where the independent variable (,x) is real, and/, q are functions 

 of X, which are not required] to be analytic. — The elliptic 



(T-functions considered as a special case of the hyperelliptic 

 «r-functions, by O. Bolza. This paper has a two-fold object. 

 In the first place it gives a sketch of the theory of the " elliptic " 

 in the light of the theory of the *' hyperelliptic " functions ; and 

 secondly, it serves as an introduction for a future paper in which 

 an analogous presentation is given of the hyperelliptic <r-func- 

 tions. — Dr. G. A. Miller writes on the groups which are the 

 direct products of two sub-groups, and E. H. Moore discusses 

 certain crinkly curves (reff. are made to papers by Peano, Math. 

 Ann. vol. xxxvi. ; Cesaro, Bulletin des Sciences Math., vol. 

 xxi. 1897; Hilbert, Math. Ann. vol. xxxviii.). There are 

 several diagrams. — Dr. L. E. Dickson gives a new definition of 

 the general Abelian linear group. — If the high character of the 

 present number is maintained, it is safe to prophesy that the 

 Transactions are come to stay. 



Bollettino delta Societa Sismologica Italiana, vol. v. 1899- 

 1900, No. 6. — On seismic registrations of long period, by E, 

 Oddone (see p. 477). — The earthquake of Ventotine on March 

 27, 1899, and the tromometric records obtained at the CoUegio 

 Bianchi, in Naples, and at Reggio di Calabria, by P. G. 

 Costanzo. — Earthquake of Balikesri, in the north-west part of 

 Asia Minor, on September 14, 1896, by G. Agamennone. — 

 Notices of earthquakes recorded in Italy (July 30-October ll, 

 1898), by A. Cancani, the most important being the earthquakes 

 of Janina on July 31, Calabria-Sicily on August 6 and 12, and 

 Umbria- Marches on August 25 and September 11, and distant 

 earthquakes on September I, 13 and 22. 



SOCIETIES AND ACADEMIES. 

 London. 

 Royal Society, February 22. — " The lonisation of Dilute 

 Solutions at the Freezing-point." By W. C. D. Whetham, 

 M.A., Fellow of Trinity College, Cambridge. 



This paper contains a description of the electrical part of a 

 joint research, by Mr. E. H. Griffiths and the author, on the 

 freezing-points and electrical conductivities of very dilute solu- 

 tions of the following substances : — Sulphuric acid, potassium 

 chloride, barium chloride, copper sulphate, potassium per- 

 manganate, potassium ferricyanide and potassium bichromate. 

 In order to eliminate the effect of dissolved glass, the water 

 used as solvent was distilled in a platinum still and collected in 

 platinum vessels ; a known weight was then placed in a platinum 

 cell, and weighed quantities of stock solution added, in suc- 

 cessively increasing amounts. The concentration of the solutions 

 thus prepared was calculated in terms of the number, m, of 

 gram-equivalents of solute dissolved in one thousand granis of 

 solution. In order to control the temperature, the platinum 

 cell was surrounded by a coil of tubing through which evaporated 

 ether vapour could be passed. The whole was surrounded by 

 a brass case fixed in the middle of a large tank filled with broken 

 ice. The walls of the platinum vessel formed one electrode, 

 and a platinum cage suspended within it the other. Inside this 

 cage revolved a platinum tube which contained a thermometer, 

 and also served as the shaft of a screw. This screw kept the 

 contents of the cell at a uniform temperature, and mixed the 

 stock solutions with the liquid previously within the cell. The 

 electrical resistances were measured by the method of alternating 

 currents, the connections of the Wheatstone's bridge with a dry 

 cell and with a D' Arson val galvanometer being reversed simul- 

 taneously by means of a revolving commutator driven by a hand 

 wheel and cord. This arrangement is more convenient and more 

 sensitive than the usual telephone apparatus. The conductivity 

 thus found was corrected for the conductivity of the solvent, and 

 the result, /', divided by ;«, gave the equivalent conductivity of 

 the solution. Curves were drawn between v';;/ and kjm, and the 

 maximum value of these taken to indicate complete ionisation. 

 The ionisation, a, of the solutions was then calculated by 

 dividing the maximum Icjm into its actual value, and new curves 

 were drawn between V;« and o. The general form of these 

 curves resembles that of the corresponding ones obtained by 

 Kohlrausch and other observers at 18°, but the slant of the lines 

 is different both from Kohlrausch's observations, and also from 

 new observations made with the present apparatus at 18°. The 

 abnormal type of curve found at 18° for acids and alkalies 

 is shown to appear at 0° in the case of sulphuric acid, the 

 ionisation reaching a maximum as the dilution is increased, and 

 then suddenly becoming much less. Reasons are .given for 



NO. 1586, VOL. 61] 



