Bulletin of the New York Mathematical Society, vol. iii. No. 2 (November, 1893, New York).—“Lachlan's Modern Pure Geometry”(pp. 33–36) contains a review, by Prof. F. Morley, of Dr. Lachlan's treatise. It mainly points out what the writer considers to be defects in the author's programme, but closes with the hope, since Dr. Lachlan shows so much power in handling his subject, that he will “throw examination schedules to the four winds of heaven,” and deal argely “with some part of the present outlook as stated in Klein's ‘Verglet-chende Betrachtungen.’” Prof. Cleveland Abbe gives (pp. 36–38) an analysis of papers on vortices in a compressible and rotating fluid, by Mr. Charles Chree, and trusts that the strictly meteorological work of his new position (at Kew) will tempt him to apply modern mathematical analysis to the winds, the clouds, and the storms of the actual atmosphere. Dr. T. Craig's high estimate of the Traité d'Analyse, by M. Émile Picard, will be seen from the space (pp. 39–66) he devotes to an account of this first volume. The extraordinary developments in the theory of functions, in differential equations, and in certain purely algebraical theories, and the important applications of the results of these developments to geometrical, physical, and astronomical problems, have made such a treatise almost indispensable. Notes and new publications occupy pages 65–72.