334 Sir Joseph Larmor 



a moving body acquires energy and therefore inertia without hmit 

 as its speed approaches c, whereas the energy of a Hght quantum 

 is not supposed so to increase. 



This is all on the older notions: the velocity c is far too great 

 for the new approximate gravitation analysis to be applicable. 

 But the idea of wavefronts and phases must also be introduced 

 somehow. If we imagine a row of these corpuscles of energy coming 

 on abreast, the more distant ones would fall behind in swinging 

 round the Sun and their common front would become oblique to 

 their direction of motion, the exactly transverse directions being 

 now the loci of equal Action not of equal time. If we superposed 

 the Huygenian principle of propagation normal to the front, the 

 orbital deflection would thereby be just cancelled by the swinging 

 back of the front which would retain its direction : and there would 

 be no deflection of direction of propagation. But such ideas are 

 plainly incoherent. 



The earlier development of Einstein sketched above* was 

 driven on other grounds to conclude that light must gain energy 

 in a field of gravitation, but the gain was named potential energy. 

 In the finally developed theory there seems to be no longer energy 

 of motion or other types : energy becomes a single analytic scalar 

 in what is left of the field of interplay of momentum, energy and 

 stress. 



These earlier considerations have doubtless crystallized into 

 the formal theory of which also the result has been illustrated 

 above, in a way which transforms the variational equation of free 

 orbits in ordinary space and time into the variational equation of 

 straightest lines in a non-uniform space-time fourfold given differen- 

 tially. The coordinates are carried over unchanged in values, into 

 this fourfold, but their differentials no longer express in it direct 

 measurements of length and time; these are now imported in the 

 Riemann manner as regards any element of arc or interval of 

 time by the value of the absolute element 8a. As compared with 

 the underlying absolute time determined by Scr, the element of 

 apparent time St of a gravitational world, which is taken over into 

 its expression is variable, proportional to c'"^, with locality. 



The quantities x, y, z, t which are the measures of space and 

 time as apparent in the world of gravitation are now mere co- 

 ordinate quantities in the new differentially given world in which 

 there are elements of absolute length and time both measured by 

 Sct. The final expression for Scr^ with radial symmetry 



,f Sr2+ ... + ... - (^y^^S^^ 

 shows that the element of apparent time in the gravitational world 



* Ann. der Physik, 35, 1911, §2, p. 902. 



