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may be mentioned the following: singular points of algebraic curves, differential equations and invariants, elliptic functions, theory of numbers, and theory of series. For a brief sketch of the life of Halphen, with some remarks on the character of his work, the reader may consult the Notice by Picard (vol. I, pp. vii-xvi). In the Notice by Poincaré (vol. I, pp. xvii-xliii) we have an excellent systematic analysis of his mathematical contributions. Besides this there is the Notice by Halphen himself (vol. I, pp. 1-47) in which his own contributions were analyzed on the occasion of his candidacy before the Paris Academy of Sciences in 1885, about four years before his death. These excellent brief accounts of his work relieve the reviewer of the duty of making an analysis of the separate memoirs. The entire works (with the exception, apparently, of the Traite des Fonctions Elliptiques) are to be included in four volumes, of which the third is announced as in press and the fourth in preparation.

the mathematical gazette

A History of the Conceptions of Limits and Fluxions in Great Britain from Newton to Woodhouse. By F. Cajori. Pp. 293+viii (contents), + 6 (index). 7s. 6d. 1920. (Open Court.)