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NEW BOOKS. 417 Matter, Energy, Force and Work : a Plain Presentation of Funda- mental Physical Concepts and of the Vortex-atom and Other Theories. By S. W. HOLMAN. New York and London : Macmillan & Co., 1898. Pp. xiv., 257. Price, $2.50. The object of this excellent little book is to " present in a plain and logical manner some fundamental ideas and definitions of physics ; . . . to proceed in an orderly manner to develop the concepts and definitions ". The author has been most successful in his attempt ; and his work may be recommended both to physicists and to metaphysicians. That the scientific man may not rashly venture on philosophical territory has been abundantly proved by certain recent essays in epistemology. It is not less important that the philosopher should have a clear understanding of the concepts and theories with which he is called upon to deal in his endeavour to harmonise the standpoints and hypotheses of the special sciences. The book falls into two parts. Part i. includes chapters on substance and matter, motion, energy, forms of energy, force, kinetic energy, force measurement, work, and potential energy ; part ii., chapters on the func- tion of theory and hypothesis, the kinetic theory of gases, Le Sage's theory of gravitation, the vortex-atom theory, and the nature of energy and matter. Mathematical Essays and Recreations. By H. SCHUBERT. Translated by T. J. M'CoRMACK. Chicago : Open Court Publishing Co., 1898. Pp. 149. Price, $1.00; 5s. A collection of six essays on mathematical subjects. The first, on the notion and definition of number, defines counting as (1) regarding things as the same in kind ; (2) associating other things to them, ordinally, accu- rately and singly ; and (3) expressing the result of such association (number) by a conventional sign. The second, on monism in arithmetic, explains the introduction of zero, negative, fractional, irrational, imaginary and complex numbers by appeal to a psychological law, the ' principle of no exception '. The third, on the nature of mathematical knowledge, discusses the conservatism, developmental progression, and self-suffici- ency of mathematical thought. The fifth, on the fourth dimension, deals at length with the spiritualism of Zoellner and Ulrici. The remaining two are entitled "The Magic Square" and "The Squaring of the Circle". The volume is interesting throughout, and the translation well done. The Elements of Sociology : a Text-book for Colleges and Schools. By F. H. GIDDINGS. New York and London : Macmillan & Co., 1898. Pp. xi., 353. Price, $1.10. Prof. Giddings' Elements is in part a redaction of his larger book, The Principles of Sociology, and in part a further development of the working hypotheses there adopted. The work is clearly written, and furnishes a serviceable educational tool to those teachers who adopt the author's sociological standpoint. Whether this standpoint is at present securely enough established to justify the introduction of the book into the curricula of colleges, and more especially of schools, is a matter for the expert to decide ; the lay reader inclines to doubt. And the doubt is not removed by a perusal of the new matter dealing with the analysis of the social mind (sympathetic like-mindedness and impulsive social action, formal like-mindedness, tradition and conformity, rational like-minded- ness, public opinion and social values), interesting as the analysis is. 27