9 DECEMBER 1865, Page 22

The Mathematical Writings of D. P. Grego% MA., late Fellow

of Trinity College, Cambridge. Edited by W. Walton, M.A., with a Biogra- phical Memoir. By R. L. Ellis, M k. (Bell and Daldy.)—Mathemati- cal students will be grateful to Messrs. Walton and Ellis for presenting them with this interesting volume, which is at once a becoming memo- rial to a great Trinity light and an important contribution to speculative mathematics. It consists of a brief memoir, which is chiefly devoted to pointing out Mr. Gregory's place in scientific investigation, and of papers contributed to the Cambridge Mathematical Journal, together with an essay on the "Foundations of Algebra," presented by the author to the Royal Society of Edinburgh. Mr. Gregory directed his attention to the more abstract branches of mathematical thought ; the connection between the symbolism of algebra, and the calculus, and the elucidation of problems belonging to the theories of heat, light, and magnetism. In the latter class of researches the idea of discontinuity is prominent, and the solution of the diffioulties attendant on disconti,nuity is connected with the theory of definite integrals. Thus the majority of the papers in the volume before us relate to abstruse theorems in the differential cal- culus, and the calculus of finite differences, ankthe solution of differen- tial equations, and may suggest to some minds what Fourrier's great work on heat suggested to the author himself, glimpses of a mathema- tical paradise.