August 12, 1898.1 



SCIENCE. 



191 



those principles apply. The old notion that 

 mechanics is merely a branch of applied mathe- 

 matics is giving way to the more philosophical 

 •view that the core of the science consists in its 

 physical principles and that mathematical anal- 

 ysis plays the secondary though wonderfully 

 important role of the most effective instrument 

 for investigating mechanical phenomena. 



Students who are acquainted with Routh's 

 Rigid Dynamics will easily anticipate the char- 

 acter of his Analytical Statics ; and students 

 not familiar with either should hasten to pur- 

 sue both works, for in many respects they are 

 the best treatises extant. Their excellence con- 

 sists in clear exposition of principles, in de- 

 tailed application of those principles to typical 

 examples, and in elaborate collections of in- 

 structive problems. 



Volume I. of the work on statics consists of 

 eleven chapters having the following titles : 

 The Parallelogram of Forces; Forces Acting at a 

 Point ; Parallel Forces ; Forces in Two Dimen- 

 sions ; On Friction ; The Principle of Work ; 

 Forces in Three Dimensions ; Graphical Statics ; 

 Centre of Gravity ; On Strings ; and The Ma- 

 chines. Amongst these the chapter on the 

 principle of work is of most practical impor- 

 tance. That on strings, subject to any forces 

 and including the elastic catenary, is also re- 

 plete with useful as well as instructive informa- 

 tion. 



Volume II. consists of three parts, devoted to 

 attractions, including the theory of the poten- 

 tial function ; to the bending of rods ; and to 

 astatics, respectively. While each of these is a 

 capital contribution, the first is by far the most 

 interesting and important. Though not exhaus- 

 tive, it is probably the most readable and in- 

 structive exposition of the theory of attractions 

 and potential function in the English language. 

 The part devoted to the conditions of equi- 

 librium of bent rods is somewhat novel in a 

 treatise on statics. It would seem rather to 

 belong in a work on the theory of elasticity. 

 Without going into the complex details of the 

 latter, however, the author has considered 

 many of the most important properties of bent 

 and twisted rods, including the case presented 

 by helical springs. The last part presents, in 

 about forty pages, an excellent summary of the 



principal theorems which have been discovered 

 in the interesting though not specially useful 

 subject of astatics since its foundation by 

 Moebius in his Lehrbuch der Statik in 1837. 



For more than one hundred and fifty years 

 the French have held first rank in the produc- 

 tion of treatises on mechanics, and their repu- 

 tation is well sustained in the admirable work 

 of Appell. In his two rather bulky octavo 

 volumes he has given a very comprehensive 

 view of the whole science of rational me- 

 chanics. The mode of treatment is distinctly 

 French. One is continually reminded of the 

 clearness and elegance of the great masters, 

 Lagrange, Laplace, Poisson and Poinsot. The 

 salient feature of the work is perfection of 

 mathematical method, the point of view of the 

 author being apparantly that of the mathema- 

 tician rather than that of the mechanician. 



Volume I. consists of three parts. The first 

 of these is devoted to the theory of vectors, 

 kinematics and the elementary theory of ki- 

 netics. The second is devoted to statics and 

 gives a very complete treatment of the sub- 

 ject in all its essential aspects, much space being 

 allotted to the method of virtual displacements. 

 The third part treats of the dynamics of a point 

 and includes a luminous exposition of the 

 principles of d'Alembert, Lagrange and Hamil- 

 ton. 



Volume II. consists of two parts. The first 

 of these treats of the higher methods of Hamil- 

 ton and Jacobi in application to the dynamics 

 of a point, and the second is devoted to the 

 dynamics of systems in general. The author's 

 exposition of the principles of d'Alembert; of 

 the energy method of Lagrange ; of the princi- 

 ple of least action ; and of all the elaborate 

 mathematical machinery of Poisson, Hamilton 

 and Jacobi, seems to be more complete and 

 satisfactory than that afforded by any other 

 single work. Every important principle or 

 process is illustrated by application to one or 

 more typical examples, and many unsolved 

 problems are appended to the main chapters of 

 the work. The text bears evidence of careful 

 proof reading, since the number of misprints is 

 very small for a work of so many pages. 



The defects of this treatise, though unimpor- 

 tant to all but the novice, are characteristic of 



