REVIEWS 161 



have failed to reveal to us any motion of the earth relative to an assumed fixed 

 ether, a failure incomprehensible, as far as Newtonian dynamics is concerned, 

 except by the adoption of some such hypothesis as the Lorentz-Fitzgerald con- 

 traction of bodies produced by their motion through this ether, a hypothesis which, 

 as has been shown by Lorentz, must be carried down to the electron itself, if 

 consistent results are to be obtained. 



The first four chapters of this book deal with these experiments, and the views 

 advanced, prior to Einstein's work, to account for their failure. The fifth and sixth 

 chapters treat of Einstein's ideas concerning the relativity of space and time 

 measurements to the frame of reference, and the modifications introduced by such 

 ideas into kinematical theory, so as to correlate phenomena as far as possible 

 without any special theories of matter. There follows an account of the applica- 

 tion of four-dimensional calculus which has been made by Minkowski to the 

 Relativity Principle. In it space and time are considered as " complementary 

 aspects of an underlying unity," and just as in the older dynamics and the electrical 

 theory based on it, there was a certain amount of arbitrariness in the choice of 

 axes, in view of the fact that the various relations existed between three-dimensional 

 vectors, so in the Minkowski four-dimensional " World," which embodies ordinary 

 space dimensions and a time-dimension, agreement with Einstein's Principle is 

 ensured by a similar arbitrariness in the choice of the four axes, so as to preserve 

 a vectorial form for all relations. The author does not deal with Minkowski's 

 four-dimensional hyperbolic geometry, but with his geometric method which makes 

 the various transformations formally analogous to the customary change of axes in 

 space by a rotation. Minkowski's method cannot, to be sure, be used directly to 

 devise theories of the constitution of matter, or invent analytical changes to be 

 made in our equations of motion ; but it serves as a criterion for all attempts in 

 those directions. Such attempts, if they are to be consistent with the relativity of 

 phenomena, must be capable of formulation as relations between the four-vectors 

 and six-vectors of Minkowski's "World." The remainder of the book deals with 

 the recent changes which have been made in pure dynamical theory, in elastic 

 solid theory, in the electrodynamics of moving bodies, and in thermodynamics. A 

 chapter is devoted to the first objection mentioned above, concerning the existence 

 of an objective ether, and is an extension of a paper by the author in volume 83 of 

 the Proc. Roy. Soc. It would appear that while the existence of a. fixed ether is 

 impossible on the relativity view, yet it is not inconsistent with that view to assume 

 the existence of an ether which is moving relatively to any observer with the 

 speed of light, the direction of motion at any point depending upon the values of 

 the electric and magnetic vectors at that point. One striking result of this 

 analysis is the conclusion that in the neighbourhood of a stationary point charge, 

 the flow of the ether is radially outwards from the point, inasmuch as it recalls the 

 " Ether-Squirt " theory of matter propounded some years ago by Prof. Karl 

 Pearson. 



The mathematical treatment given in this volume is adequate and complete 

 without undue elaboration, vectorial methods being employed throughout. In fact 

 there is a very judicious division of space between the mathematical development 

 and a philosophic discussion of the results and concepts obtained from and 

 embodied in the analysis. It seems a pity that some kind of symbolism cannot be 

 devised which, while preserving for the reader an easy method of perceiving that 

 he is dealing now with scalars, now with three-dimensional vectors, and now with 

 four- and six-vectors, would at the same time remove from the printed page all the 

 weird and wonderful types that have recently invaded Vectorial Analysis. 

 II 



