346 SCIENCE PROGRESS 



The Theory of the Relativity of Motion. By R. C. Tolman, Ph.D. 

 [Pp. ix + 225.] (Berkeley : University of California Press, 1918.) 



There are two well-known works in English on the Theory of Relativity (in its 

 earlier or "restricted" form)— one by Dr. Cunningham and one by Dr. Silberstein. 

 Both these works present the theory as it grew historically, and deal with the 

 work of Larmor and Lorentz on the modification of Maxwell's equations of 

 the electromagnetic field for moving axes of reference, before passing on to the 

 interpretation of the Lorentz transformation first given by Einstein. 



The volume before us abandons the historical method of presentation, except 

 or a very brief outline of the historical development of ideas as to the nature of 

 the space and time of science, which is given in the first chapter. In Chapter II 

 the author considers the two main postulates of the Relativity Theory and the ex- 

 perimental evidence on which they rest. In the third chapter there is given an 

 elementary deduction of a number of the most important consequences of these 

 postulates. The mathematics employed in this chapter is of the simplest type ; 

 yet the reader is enabled thereby to grasp the new and important ideas as to 

 measurements of time and space in the moving system, the non-additivity of 

 velocities, the variation of mass with velocity, and the practical coalescence of 

 mass and energy as different names for the same fundamental entity — in fact, all 

 the startling and apparently paradoxical results of the new non-Newtonian 

 mechanics. 



Thereafter Dr. Tolman takes up a more analytical treatment of the subject, 

 developing fully the dynamics of particles and rigid bodies, the dynamics of 

 elastic bodies, of a thermodynamic system and of an electromagnetic system, 

 making free use of the principle of Least Action, which is found not to conflict 

 with the requirements of Relativity Theory. The book concludes with an ex- 

 position of four-dimensional analysis as applied in Relativity problems, making 

 use, however, of a real time co-ordinate in place of the more usual imaginary 

 co-ordinate. 



In plunging straightway into problems of dynamics, Dr. Tolman has reversed 

 the order of presentation adopted in the earlier treatises referred to above, and in 

 the German work of Laue. In them electromagnetic theory receives first 

 attention after the development of Einstein's kinematics, and the dynamics of a 

 particle is expounded later on an electromagnetic basis. Also these authors make 

 extensive use of quaternionic or four-dimensional vectorial analysis throughout — 

 weapons which Dr. Tolman avoids introducing until his last chapter. As to the 

 relative values of the two modes ot presentation opinions will differ. Many 

 teachers believe that it is of great advantage to a student to approach a new body 

 of knowledge by the historical path, and learn how tentative and redundant 

 hypotheses were raised only to be dropped and replaced by others of a more 

 convenient character as increasing experimental knowledge or better analysis 

 required. But it is at least arguable that such a procedure involves a certain 

 initial confusion of thought on the part of the student, which is, of course, 

 gradually cleared away, as he arrives at the finally-evolved body of consistent 

 theory, and that a presentation in the first place of the theory in its final form (to 

 be followed by a historical account of its growth) would prove to be a sounder 

 method. On that ground, Dr. Tolman's book is heartily to be recommended. 

 For most students of Mathematical Physics, Dynamics is a fundamental subject 

 on whose principles the interpretation of all physical phenomena must rest, and 

 the writer believes that Dr. Tolman's method is to be preferred — viz., a clear 

 exposition of the manner in which Dynamical principles must be modified in order 



