686 



SCIENCE 



[N. S. Vol. XXXIV. No. 881 



As is common in a first edition, there are 

 numerous typographical errors, but usually 

 they are of such nature as not to cause seri- 

 ous ambiguity to the reader. 



The book is published by the McGraw-Hill 

 Book Company, of New York. 



A. P. Wills 



Geometrie der Erdfte. By H. E. Timerding. 



Leipzig, Teubner (Teubners Sammlung). 



8vo. Pp. si + 381. 



This book is an outgrowth of the author's 

 article " Geometrische Grundlegung der Me- 

 chanik eines starren Korpers," in the Enzy- 

 klopadie der Mathematischen Wissenschaften 

 (Band IV., 1, pp. 125-189), which consisted 

 principally in an account of the Ball theory of 

 screws. The volume under review goes far 

 beyond that article in its scope, both in deal- 

 ing with the mechanics of deformable bodies, 

 and in giving presentations of the vector 

 theory and of line geometry. On the other 

 hand it is limited by the desire to present the 

 geometry of forces as an independent subject 

 and to avoid a general treatment of mechan- 

 ics as such, especially since Webster's treatise 

 appeared as a member of the same series of 

 texts. 



The geometry of motion, or kinematics, is 

 better known as a distinct subject than is the 

 geometry of forces. In general the two sub- 

 jects have similar motives and enjoy similar 

 advantages: both seek to present a purely ab- 

 stract geometrical analysis of mechanical con- 

 cepts, and each is suggestive and instructive 

 to the student of geometry as well as to the 

 student of mechanics. 



The author seeks to unify and complete the 

 labors of his predecessors — Varignon, Poin- 

 sot, Chasles, Moebius, W. Thompson, Ball, 

 Study, and others — to form a symmetrical 

 whole and to create a finished theory of forces 

 " disassociated from all physiological, physi- 

 cal, and metaphysical concepts," which shall 

 apply to the kinetics and statics of rigid bod- 

 ies, and to the statics of deformable bodies. 



The first five chapters are devoted to the 

 theory of vectors, following chiefly Grassman 



and Hamilton. The notation employed dif- 

 fers from that of each of these writers, and 

 also from that of Gibbs, thus adding another 

 to the many existing notations.^ The ideas 

 developed in these chapters are used to define 

 the concepts moment of a vector, rotor, dy- 

 name; but otherwise little use is made of the 

 vector theory. The author defends this as 

 against prospective criticism, on the ground 

 that the results can be reached by methods of 

 analytic geometry, and that the extensive use 

 of the vector theory would render the work 

 less accessible to beginners. Under the cir- 

 cumstances a complete presentation of the 

 vector theory might have been dispensed with 

 altogether. 



The following chapters treat of instantane- 

 ous rotation and of forces and dynames. The 

 latter term was introduced by Pliicker^ and 

 has been employed extensively by Study' and 

 others, to denote the geometrical concept which 

 corresponds to either a twist or a wrench in 

 Ball's theory. 



Chapter VIII. is an elementary presenta- 

 tion of line geometry, which the author, fol- 

 lowing many others' makes his fundamental 

 link between geometry and mechanics. He 

 also sets a bound to geometrical developments 

 as a whole by restricting himself to this topic 

 and its applications. 



After a chapter on equilibrium, the theory 

 of screws is presented in detail in six chap- 

 ters, which form the kernel of the entire 

 book, and indeed constituted the motive for 

 the original project. The chapter on the 

 cylindroid is particularly worthy of notice. 



Two chapters on deformable bodies extend 

 the theory beyond the realm of rigid bodies — 

 an extension on which the author lays great 

 weight in the preface. 



The remainder of the book deals with the 

 mechanical concepts in distinction to the 



' See Wilson, Bulletin of Amer. Math. Soc, Vol. 

 16 (1910), p. 415. 



'Philosophical Transactions, 156, 1866; 

 "Works," I., p. 548. 



'"Geometrie der Dynamen," Leipzig, 1903. 



* See, e. g., Klein, Mathematische Annalen, 

 Vol. 4. 



