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NEW BOOKS. 267 the spots on the sun, and their connexion with the vortices of Descartes, and the formation of planets, may be referred to. Whether it is alto- gether a work of imagination remains for the scientist to say ; at times,, as, for example, when dealing with what he terms Astrobiologie M. Lagresille passes out of the domain of criticism, whether he rises above it by virtue of the access he claims to regions of experience not open to normal humanity, or falls below it by condescending to mere extrava- gance. I am afraid that neither the philosopher nor the scientist will care much for this book, but the theosophist may find it edifying. DAVID MORRISON. L'fivolutionisme en Morale : tude sur la Philosophie de Herbert Spenoer.. By JEAN HALLEUX. Paris : Felix Alcan, 1901. Pp. 228. This is a critical account of the Evolutionary Philosophy with the Data of Ethics for text. Ostensibly divided into two, it falls easily into three distinct sections. The opening section is a fairly accurate resume of the first eight chapters of Mr. Spencer's work. The second section aims at proving that man's evolution from the ape, or even from a type re- sembling the modern savage, is an open question. In the only part of the work that is strictly ethical the relevant and irrelevant are curiously mingled. Man longs for an ideal, which, the author insists in contrast to Mr. Spencer, must be personal ; the altruism of the Data of Ethics can have no claim on man as he really is, and still less on man as Mr. Spencer conceives him, for the chain of argument by which that altruism is reached will not stand scrutiny. Further, this ideal is not realisable: on earth ; Mr. Spencer's philosophy can give no comfort to the " disin- herited of this life," nor any sound warrant for deferring the gratification of the moment, pleasure- value being purely subjective. The arguments, however, on which most stress is laid are of a different type, namely, that a belief in the supernatural is universal, that duty has always spelt struggle, and that religion and morality have never yet been divorced in the world's history. The civilising effects, for instance, of the various religions, and especially of Christianity, are dwelt upon at great length. The author, in fact, often fails to trace the real starting-point of Mr. Spencer's arguments, and he never seems quite to realise where it is- that he and Mr. Spencer part company. The book, too, as a whole, is excessively wide in scope. Still the criticism is commendably temperate and contains much that is suggestive, in a style that flows, sometimes- sparkling, and always clear. F. G. NUTT. Die Grundsatze und das Wesen des Unendlichen in der Mathematik und Philosophie. Von Dr. KURT GEISSLER. Leipzig : Teubner, 1902. Pp. viii., 417. The present work is not destitute of ability, but unfortunately the author has failed to grasp the importance for his subject of Cantor's work on the infinite, and of the modern elimination of the infinitesimal by the method of limits. Consequently it may be doubted whether his book does more to advance the subject than would be done for Astronomy by a book based upon the Ptolemaic theory. The first 297 pages deal with various special mathematical problems, taken almost wholly from Geometry and Dynamics, not, as might be wished, from Arithmetic. These problems are designed to illustrate the