204 



SCIENCE. 



[N. S. Vol. XXII. No. 555. 



to have sucL. a grasp of mathematics that 

 he is able to work out the problems which 

 arise in connection with his experiments. 

 As Professor Webster points out in his 

 preface, there has been far too much neg- 

 lect with us of the mathematical side, and 

 while this neglect continues we can scarcely 

 hope to produce men of the type of Maxwell, 

 Kelvin, Rayleigh, Helmholtz and others. 



In considering, then, the training of the 

 physicist no less than that of the practical 

 engineer, it is necessary to keep two points 

 steadily in view. The first is a full under- 

 standing of the primary laws which lie at the 

 basis of all physical investigations, and the 

 second is the ability to apply those laws to 

 specific cases. Siraple as are the laws and the 

 methods of applying them, only those who 

 have attempted to teach the subject know how 

 difficult it is for even the best students to 

 acquire a thorough working knowledge of 

 them and how rare it is for the average stu- 

 dent to solve the simplest problems when the 

 latter are anything more than mere applica- 

 tions of results previously obtained. The 

 ability to do this is usually obtained only by 

 long practise, and the time at present devoted 

 to acquiring the facility necessary for success 

 is quite inadequate. To take a simple ex- 

 ample. Most of the volumes on the calculus 

 which are written solely for students of engi- 

 neering and physics contain nothing more 

 than the parts which are necessary to under- 

 stand the mathematics used in solving physical 

 problems. No thorough grasp of the subject 

 is obtained in this way; the student obtains 

 knowledge sufficient perhaps to understand 

 what is presented to him in a finished form, 

 but there is no margin left for independent 

 work on problems which lie a little off the 

 main track. 



Professor Webster has fully recognized this 

 fact. It is true that he presupposes only an 

 elementary knowledge of the calculus and of 

 the earlier parts of algebra and analytic geom- 

 etry, but a student who wishes to make a seri- 

 ous study of the book will require to know 

 these earlier parts thoroughly. Throughout 

 the volume there is no attempt to slur or 

 evade any difficulties because they are mathe- 



matical; practically every result obtained is 

 fully worked out and in many parts the author 

 takes his reader far beyond what is merely 

 necessary. Moreover, he never allows himself 

 to be drawn away from the main lines of his 

 subject by side issues which have little or no 

 bearing on the investigation in progress, and 

 he has avoided the use of special mathematical 

 artifices which are of value only in special 

 problems, so that the methods used are those 

 which can be applied to practically all the 

 problems of dynamics. 



Part I. consists of the development of the 

 general principles of dynamics. In the first 

 chapter the elements of kinematics and the 

 laws of motion are briefly set forth. Then 

 follows a chapter on special motions of a 

 particle, which include parabolic, harmonic 

 and constrained motions, pendulums and cen- 

 tral forces. Professor Webster has avoided 

 the doubtful practise of most of the English 

 text-books which give a disproportionate 

 amount of space to the last, but the eight 

 pages on the spherical pendulum, although 

 the problem is well worked out, might perhaps 

 have been abbreviated by the omission of some 

 of the figures and details. The next two 

 chapters contain an unusually full develop- 

 ment of the principles of work and energy 

 and the methods of Lagrange and Hamilton. 

 Here we find worked out, first, by the use of 

 rectangular coordinates, and afterwards with 

 generalized coordinates, D'Alembert's prin- 

 ciple, canonical equations, least action, vary- 

 ing action, varying constraint, activity, etc. 

 These chapters are important in view of the 

 increasing prominence now given to methods 

 which are of value in every department of 

 mathematical physics, as Professor Webster 

 shows by his use of them in the later parts of 

 his book. This first part concludes with ap- 

 plications to oscillations in general and to 

 cyclic motions. In dealing with the latter, 

 special cases of the general methods of ab- 

 stract dynamics are treated: ignoration of 

 coordinates, effect of linear terms in the 

 kinetic potential, gyroscopic terms, and so on. 

 A few examples are worked out to illustrate 

 the manner in which the various methods are 

 to be used. 



