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Professor Clifford's treatise on dynamics-or, as he prefers to call his subject, dynamic- Elements of Dynamic -is a most attractive little volume. I was about to add that the reader would do well to prepare himself by studying the elements of quaternions before taking up this volume; but on the whole I think the present work better fitted to prepare the way for the study of quaternions. For the method of quaternions is here used in such a way that any one who is tolerably well versed in the older mathematical methods need encounter no difficulty, while he cannot fail to appreciate the simplicity introduced by the new notation. The present volume relates only to kinematics; dynamics, properly so called, being left to form a second volume. The clearness of the explanations and the neatness of the demonstrations cannot be too highly commended. Exception may, perhaps, be taken to the nomenclature: not on the ground of its novelty, for there is room for much useful innovation in the verbiage as in the symbols of mathematics, but because some of the new expressions seem unsuitable. Whether general usage will ever allow such Germanisms as dynamic, optic, physic, &c., to replace the familiar dynamics, optics, physics, &c., I do not know; but I should think it more likely that even these cacophonous innovations would be permitted than such odd new words as squirts, sinks, twists, whirls, and so forth, in scientific treatises. Consider, for instance, the incongruity between the old and new words in the following sentence, which, by the way, is the closing statement in Professor Clifford's book: Every continuous motion of an infinite body can be built up of squirts and vortices. I have noticed few errors in the work, and even misprints are few and far between, for a treatise of this kind. There is one rather singular mistake with regard to roulettes. Professor Clifford says that there are three distinct kinds of trochoidal curves, hypotrochoids, epitrochoids, and peritrochoids, -the last being curves traced by a point in the plane of a circle which rolls round a smaller circle with which it is in internal contact. But it can readily be shown, by precisely such reasoning as Professor Clifford has employed to establish the identity of epicycloids and pericycloids, that every epitrochoid is also a peritrochoid. An epitrochoid, having for radii of rolling, tracing, and fixed circles, R, eE, and F, respectively, is identical with a peritrochoid having for corresponding radii e(F+R), (F+R), and eF. - The Contemporary Review, Vol. 33 [1878]

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