194 



SCIENCE. 



[N. S. Vol. VIII. No. 189. 



wasting time in a school in giving information 

 that one cannot help picking up in one's ordin- 

 ary practical work after leaving school." 



" In teaching beginners it is well to start on 

 the assumption that students already possess 

 the notions of the differential and integral cal- 

 culus, and it is the teacher's duty to put before 

 them the symbols used in the calculus at once. 

 It is surely much better to do this than to evade 

 the calculus in the fifty usual methods which 

 we sometimes see adopted." 



The book contains thirty chapters, followed 

 by an appendix of useful tables, including 4- 

 place logarithms and anti-logarithms, and a 

 full index. Every chapter is replete with use- 

 ful information, and most topics are treated in 

 ways that are refreshing by reason of the nov- 

 elty of method and the incisive language of the 

 author. We may not in all cases accept his 

 views or approve his style, but there is not a 

 dull page in the text, and his views and style 

 are everywhere entertaining and instructive. 

 There is much new matter In the book, and the 

 numerous illustrations (371 of them) are in 

 general excellent, many of them exhibiting 

 apparatus designed by the author and now pub- 

 lished apparently for the first time. To teach- 

 ers, to engineers and to readers of mechanics, 

 as well as to students, this book cannot be too 

 highly commended. 



During the hundred years ending with the 

 first half of the present century the most im- 

 portant contributions to mechanical science 

 were made by writers who were alike eminent 

 as mathematicians and and mechanicians. Such 

 were the great masters Lagrange, Laplace, 

 Poisson, Cauchy, Gauss, Dirichlet, Lam6, etc. 

 Since that time, however, the mathematicians 

 and mechanicians have parted company to a 

 great extent and their diverging paths have 

 presented little in common. Whether this fact 

 is to be regretted or not must be left for the his- 

 torians of our times to decide. In the mean- 

 time each according to his bias will rejoice that 

 pure mathematics is not, or that pure mechanics 

 is, deeply concerned with things material. 

 Those subject to the latter bias will rejoice that 

 the prestige of the Gottingen school of mathe- 

 maticians is maintained by the presence of 

 Professor Klein in the field of mechanics. 



The volume before us is an elaboration, 

 through the aid of Dr. Sommerfeld, of Professor 

 Klein's lectures at the University of Gottingen. 

 It does not pretend to be a systematic treatise, 

 but, very appropriately, assuming a general 

 knowledge of mechanics on the part of the 

 reader, proceeds to discuss, in considerable de- 

 tail, the typical problem of the top in its ki- 

 nematical, kinetic and mathematical aspects. 



The book is divided into three chapters. The 

 first of these is occupied with the kinematical 

 principles of the problem, and the systems of 

 coordinates required to specify the motion of 

 a top are elaborately considered. The most 

 important novelty of the work in this part con- 

 sists in the very natural introduction of com- 

 plex numbers and quaternions, about one-fifth 

 of the chapter being devoted to the latter. 



The second chapter considers the principles 

 of kinetics and develops the formulas applicable 

 to the notion of a free mass and to the rotation 

 of a rigid body, special emphasis being given 

 to the theory of impulses. The last chapter is 

 devoted to Euler's equations of rotation and to 

 their integration ; and a promise is indicated 

 that the following volumes may treat, among 

 other applications, the important problem of 

 variations of terrestrial latitudes. Both of these 

 chapters present much that is novel with re- 

 spect to matter and mode of presentation, lead- 

 ing us to await With interest the appearance of 

 subsequent volumes. 



In one respect the authors are, we think, 

 open to a criticism which will apply also to 

 many other Continental writers on mechanics. 

 Since the appearance of Thomson and Tait's 

 Natural Philosophy and Maxwell's Matter and 

 Motion, progress in the ideas as distinguished 

 from the methods of mechanics is attributable 

 largely, if not chiefly, to the decapitation of the 

 numerous ' forces ' of the science other than 

 the one which is the product of mass and ac. 

 celeration. It seems like a step backwards, 

 therefore, to encounter in this capital work 

 some new species of force in addition to many 

 of the species which have long been fossil in the 

 best English terminology. Clearness of phys- 

 ical principles would seem to exclude all such 

 terms as Drehkraft, Schiebekraft, Stofskraft, 

 etc. , along with lebendige Kraft. We shall hope 



