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THIS is an excellent translation of M. Couturat's well-known Algebre de la Logique. The conciseness and modernity of M. Couturat's book is very apparent when we compare it with the first two volumes of Schroder's bulky, prolix, and somewhat antiquated work. The book under review is, as is remarked in the preface, an exposition of the beautiful and simple calculus of symbolic logic, regarded as a branch of universal algebra. Leibnitz distinguished the two most important aspects of a symbolic language designed for purposes of reasoning, under the names calculus ratiocinator and characteristica universalis the latter indicates broadly the route taken by Frege, Peano, Russell, and Whitehead; the former the route taken by Boole, Jevons, Venn, Schroder, and others, and is that described in the present work. Between these two routes, the logic of relations lies, and this is not dealt with here; but we are given a complete presentation of the important modern work of Whitehead (1898, 1901). Johnson (1901), Poretzsky (1899-1904), and Huntington (1904) on the logic of classes and propositions. Miss Robinson has added several valuable notes to her translation. The volume is neat and handy, and is an important addition to our English mathematical literature. -Nature, Volume 93

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