Scientific Serials

Abstract

Bulletin of the American Mathematical Society, November.—The only paper in the present number is a note on geometry of four dimensions, by Prof. Lovett, which was read before this society on April 28 of this year. The writer indicates nine well-defined “trends” which the speculations relative to the geometry of n-dimensional space have followed, and directs his work to following up two out of these, viz., the interpretation of this geometry in the light of the theory of groups as exhibited by Lie, Klein and Poincaré and the extension of the methods of ordinary differential geometry to general spaces, i.e. as worked out by Christoftel, Beltrami, Cesàro, Darboux and others. This he does by constructing four dimensional space by the method of Lie's theory of continuous groups, and studying curves of triple curvature by the intrinsic analysis developed by Cesàro in his Lezioni di geometria intrinseca.—An account of the proceedings at the recent International Congress held at Paris is furnished by Miss C. A. Scott, in which she abstracts the addresses by Prof. Cantor, sur l'historiographie des mathématiques, and Prof. Volterra, trois analystes italiens, Betti, Brioschi, Casorati. Several of the papers communicated are lightly but clearly handled, and M. Poincaré's presidential address, du rôle de l'institution et de la logique en mathématiques, is concisely analysed. She plainly speaks her mind on many points of detail.—Dr. G. A. Miller gives an account of the 49th Annual Meeting of the American Association for the Advancement of Science so far as it relates to the work of the society. The meeting was held at Columbia University, June 23–30, and from the point of view of scientific work it is said to have been one of the most successful that has been held by the association. About twenty papers were read in section A., some of which are given in brief abstract.—In the “notes” additional particulars (to those given in the October number) are given of the mathematical courses to be followed in the coming winter at British and Continental colleges.—Personal details as to deaths and new appointments, with the usual “new publications,” close the number.