## Abstract

LONDON.

Mathematical Society, January 10.—Major Macmahon, R. A., F.R.S., President, in the chair. The Chairman gave a short obituary sketch of Mr. A. Cowper Ranyard, in the course of which he pointed out that that gentleman had only been a protem, secretary with the late Mr. G. C. De Morgan.—The secretaries elected at the first meeting of the Society, January 16, 1865, were Messrs. H. Cozens Hardy and H. M. Bompas. Mr. Hardy resigned at the second meeting (February 20), and Mr. W. Jardine was elected in his room.—The following communications were made:—Note on the expansion of functions, by Mr. Edward T. Dixon.