A.— MATHEMATICAL AND PHYSICAL SCIENCES. 19 



particle moving in a statical field in general relativity, we find that the 

 motion is determined by Lagrangian differential equations 



1 -0 (r-1,2,3) 



dt \8x r ) 8x r 



just as in the classical dynamics : but L is not now a simple difference of 

 terms of the ' kinetic energy ' and ' potential energy ' types. It shows 

 the sound instinct of the creators of the old dynamics that they almost 

 always studied the equations without making the assumption that L 

 consists of terms of kinetic and potential type : and thus their discoveries 

 remain perfectly valid in the dynamics of general relativity. 



The fundamental researches of Einstein and Hilbert, with the discovery 

 of the field equations of gravitation, were published in 1915. At that 

 time German scientific journals did not reach this country regularly, and 

 British physicists and mathematicians were mostly occupied in one way 

 or another with duties arising out of the Great War ; so that comparatively 

 little notice was taken of the new theory on this side of the North Sea 

 during the first year or two of its existence, and indeed it was not until 

 the end of the War that most of us had any opportunity of studying it. 

 In Germany, however, it was quickly realised that general relativity was one 

 of the most profound and far-reaching contributions that had ever been 

 made to science. Its successful prediction of new phenomena of a most 

 unexpected kind was an event of the first importance, but still more 

 significant was its complete subversion of the foundations of physics and 

 reconstruction of the whole subject on a new basis. From time immemorial 

 the physicist and the pure mathematician had worked on a certain agree- 

 ment as to the shares which they were respectively to take in the study of 

 nature. The mathematician was to come first and analyse the properties 

 of space and time, building up the primary science of geometry ; then, 

 when the stage had thus been prepared, the physicist was to come along 

 with the dramatis persona? — material bodies, magnets, electric charges, 

 light, and so forth— and the play was to begin. But in Einstein's revolu- 

 tionary conception, the characters created the stage as they walked about 

 on it : geometry was no longer antecedent to physics, but indissolubly 

 fused with it into a single discipline. The properties of space, in general 

 relativity, depend on the material bodies that are present ; Euclidean 

 geometry is deposed from its old position of priority, and from acceptance 

 as a valid representation of space ; indeed its whole spirit is declared to 

 be alien to that of modern physics, for it attempts to set up relations 

 between points which are at a finite distance apart, and thus is essentially 

 an action-at-a-distance theory ; and in the new world no direct relations 

 exist at all except between elements that are contiguous to each other. 



The scheme of general relativity, as put forward by Einstein in 1915, 

 met with some criticism as regards the unsatisfactory position occupied 

 in it by electrical phenomena. While gravitation was completely fused 

 with metric, so that the notion of a mechanical force on ponderable bodies 

 due to gravitational attraction was completely abolished, the notion of a 

 mechanical force acting on electrified or magnetised bodies placed in an 

 electric or magnetic field still persisted as in the old physics. This seemed 



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