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Elements of the Differential and Inte-gral Calculus. By William Anthony Granville, Ph.D. With the editorial co-operation of Percy F. Smith, Ph.D. New York: Ginn&Co., 1911. 8vo.; 463 pp.; illustrated. Price, $2.50. This is the revised edition of a work already well and favorably known. The fundamental characteristics of the original work have been retained ; but the past few years have niarked an advance in the methods of presenting to students the elements of the calculus, and these progressive methods, after triumphantly surviving the proving-ground of the classroom, have been incorporated into the revised drill book. The authors strive to make each step intuitionally as well as analytically evident to the student, and to this end graphics have been liberally employed. There are biographical sketches of the celebrities connected with the history of the calculus, and many examples and problems designed to test the qualty of the knowledge at command, and to lead on to a well-grounded understanding. Whether preparing classes for elementary work in applied science, or qualifying them for the more advanced problems of pure mathematics, the teacher has here a wealth of well-arranged material from which to select his lessons and develop his theorems. The Teaching of Geometry. By David Eugene Smith. New York: Ginn&Co., 1911. 12mo.; 339 pp.; illustrated. Price, $1.25. Geometry has been the object of many attacks which question the expediency of its inclusion in the mathematical curriculum. It has been condemned as removed from the real problems of human activity, taking up time that might better be devoted to some more practical branch of mathematics. The author, who is a professor of Teachers College, Columbia University, admits the obsolete character of certain portions of the old geometry, and is too fair-minded to attempt a justification of the study as being utilitarian in any narrow sense; yet his chapter, “Why Geometry Is Studied,” puts forward some timely and pertinent considerations. siding on the one hand with those who would radically alter the body of matter now presented to students, or on the other hand with those who are blindly content with the system as it now stands, Prof. Smith believes in a gradual progression toward a more nearly ideal presentment, and nis papers are frankly addressed to those progressive yet well-poised teachers who are striving to invest the subject with vitality and appeal. His purposes are commendable, his ideas well-conceived, and his plans admirably developed in the attractive volume before us. Evolution. By Patrick Geddes and J. Arthur Thomson. New York: Henry Holt&Co., 1911. 12mo.; 256 pp. Price, 75 cents net. Taking the evolution theories as the canvas for their picture, the authors unfold before us, with the effect of panoramic distances, long perspectives, and shifting skies, what they have striven to make “a rational vision of world-development.” They show Us that in spite of the variaions of age, sex, origi, groupings, and occupation, every generation has much more in common than its individuals realize. They develop the theme of unity in diversity, of order in the midst of change, until there grows within us a clear conception of the nature of this continuous progression—of this organic and inorganic. individual and social mode to which we give the name Evolution. The biological research by Darwin made the world almost blind for a time to the pregnant potentials of the social perspective in its application to evolution. The authors avail themselves freely of tbis source of enlightenment, and cite as a proof of its appeal and usefulness the new eugenic movement. They urge the generalization, in unison, of nature studies and social studies, so that concrete and abstract interpretation may meet and into a clear-focused projection of the universal development. Spices. Their Histories. By' Robert O. Fielding. Seattle, Washington : The Trade Register, Inc., 16mo.; 61 pp. ; illustrated. Price, 50 cents. “Spices” is a reprint in booklet form of several articles originally published in the Trade Register. Its information is particularly directed toward retail and is alpha- betically arranged under the various spice-names, each section consisting of a description of the variety, its manner of growth, and its chief uses, with an occasional caution as to the of the market. LEGAL NOTICES over 65 years' experience Trade Marks Designs Copyrights Ac. 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