RECENT ADVANCES IN SCIENCE 525 



There is no inherent difficulty in this point of view. Al- 

 though in mechanics we ordinarily deal with forces as if they 

 were something like concrete entities, we are nevertheless 

 conscious of the vagueness of the conception of force. The 

 elementary student may sometimes acquire the notion that a 

 force is a sort of poker used for poking about masses, but in 

 reality all we can say about forces is that they explain the 

 motions — in other words, we invoke the aid of abstract entities 

 called forces. Why, then, should we object to invoking any 

 other aid that enables us to explain the motions with as much 

 ease and with even greater accuracy ? 



The real difficulty lies in the implication that is contained 

 in the principle of equivalence, namely, that Euclidean space 

 is a human myth, and that the nature and properties of space 

 vary from place to place, whilst in any place they vary from 

 time to time. The relativist has a perfect right to urge that 

 physical space, as distinct from the purely abstract philosophical 

 space, must have its properties determined by experimental 

 evidence, and not by pure prejudice. The applied mathe- 

 matician may, nevertheless, deserve some consideration if he 

 attempts to reconstruct the Einstein theory in such a way that, 

 while accepting the fundamental idea of relativity, he need not 

 discard the space that has stood him in such good stead for 

 so many centuries. 



Attempts in this direction are the natural consequence of 

 the reawakening of thought about the foundations of mechanics. 

 At the time of writing no definite results have yet emerged, 

 but interesting developments are to be looked for in the near 

 future. 



The applied mathematician will be interested in the following 

 papers, among others, which deal with the dynamical aspect 

 of generalised relativity : 



Jeffreys, H., Crucial Test of Einstein's Gravitation Theory, M.N., R.A.S., 

 1 919. 80, 138-54, where it is shown that the motion of the perihehon 

 of Mercury cannot be explained by the presence of matter near the sun. 



Crommelin, a. C. D., Comets with Small Perihelion Distance, and the Re- 

 sisting Medium, ibid., 1920, 80, 475-7. where the author considers the 

 evidence from cometary motions as to the existence of such an atmosphere 

 round the sun as would explain the motion of the perihelion of Mercury ; 

 the result is negative. 



Sampson, R. A., On the Validity of the Principles of Relativity and Equiva- 

 lence, ibid., 1919, 80, 154-7. touching on the problem of rotation. 



Page, L., The Einstein Deflection for High Speed Material Particles, Phys. 

 Rev., XV, 4, 1920, 335. The author discusses the motion of a particle 

 towards a centre of force on the Einstein theory, and deduces peculiar 

 results, showing that, under certain conditions, the particle's velocity 

 diminishes as it approaches the centre. A similar statement is given in 

 Nature, 104, 1920, 692-3. A comment by A. S. Eddington is to be 

 found ibid., 105, 1920, 37. 



