Gravitation and Light 343 



We have absorbed gravitation into space and time by distorting 

 the latter from its essential Newtonian uniformity: but there can 

 be no illusion about the matter either way, for the theoretical 

 measuring bar of the differential spacial theory is not our only 

 instrument; in the practical world rays of light provide the essential 

 isotropic measures, and the spectroscope is always available to 

 reveal to us what spacial adjustments have been made, in relation 

 to the underlying frame with regard to which the propagation of 

 light is isotropic and has its standard absolute velocity. Light, 

 instead of conforming to local relativity, imposes its own absolute 

 space-time*. 



The argument may be directed tow^ards yet another type of 

 conclusion, as follows. When change is made from Newtonian 

 space and pure time to the uniform space-time fourfold, the 

 equation of a straight path is altered from h^ds = to SJ(Zct = 0. 

 The free orbits in any field of force of potential energy function 

 — F can readily be altered so as to preserve continuity with this 

 change, as above, that is, so that where F becomes negligible they 

 tend to straight lines: they are then given by 



h\{d<j^ + 2Vdt^Y = ^. 



The interpretation is at hand, to regard them as the analogues of 

 straightest paths in a modified space-time, referred to a set of 

 coordinates represented now by colourless symbols x^, x^, Xz, x^ 

 and given in terms of them by 



8a2 = Sa;i2 + Sx^^ + Sx^^ - c^ (1 - 2c-2F) Sx^^ 



As Sct^ does not here involve x^^ explicitly, the differential equations 

 of propagation of free radiation, as expressed in this space-time 

 in terms of these coordinates, have solutions involving the quasi- 

 time, x^ only in the form e'^^*: therefore the radiation from any 

 source, however far it has travelled, retains the same period in 

 regard to x^ as it had at the start. Around a radiating molecule the 

 extension can be taken as practically uniform: therefore the 

 interval of absolute time is equal to (1 — c'W) hx^. It follows thus 

 from the periodicity as regards x^ that the periodic time of a ray 

 alters as it travels so as to be proportional to 1 — c~^V . If the ray 

 belongs to a definite molecular period at the Sun, it has changed 

 when it reaches the Earth so as to agree no longer with that period 

 as reproduced by a local vibrator. 



All this is true only to the first order, but it applies to any law of 

 potential, and is irrespective of any special energy-tensor theory. 

 The point to be brought out is that if influence of gravitation on 



* Prof. Eddington in a recent article, Quarterly Review, Jan. 1920, seems not to 

 disagree with this conclusion: at any rate he contemplates the possibility of an 

 aether. 



