Gravitation and Light 333 



changed, being only referred as regards the same points to the 

 other generalised coordinates. But the apparent extent ^pdq does 

 alter when the coordinates are changed, and it would be a limita- 

 tion to keep it constant. See Appendix infra. 



The feature that remains unfathomed as yet is the fact that 

 the velocity of transfer of energy of radiation in undisturbed regions 

 of space is equal to the merely dimensional constant that renders 

 time comparable with space on the fourfold frame of reference : it 

 at any rate suggests a dynamical origin for that mixture of the 

 effective relations of time with those of space *. 



The locus in the fourfold in which a never changes and so ha 

 vanishes has some claim to be called the 'absolute,' in a sense 

 parallel to the ' absolute ' of Cayleyan geometry which for Euclidean 

 space is represented by the equation x^ + y^ + z^ = 0. Everywhere 

 on this locus S.s = c'ht ; thus velocity of displacement is everywhere 

 c', and the rays in it are the paths of shortest time with this 

 velocity. It separates the disparate regions in which ha measures 

 real distance when time is unvaried and in which iSct measures real 

 time when position is unvaried. 



4. It would appear (as infra, p. 335) that if we are prepared to 

 replace a field of potential energy of gravitation or any other type of 

 universal force by a field of varying time-scale without change of the 

 uniform scale of space, on the lines sketched above, this formal 

 change ought not sensibly to affect radiation either as regards its 

 path or its period. To each element of extent there would be a cor- 

 responding element, and all events and measures in one pass over to 

 the other according to rule. 



But we now pass from kinematic discussion of frames of refer- 

 ence to physical considerations. If we are to assert, in agreement 

 with the doctrine of relativity plus Least Action, that inertia is a 

 property of organised energy and proportional to it, therefore not 

 solely of matter, and if we are to admit with Einstein, in the same 

 and other connexions, that light is made up of small discrete 

 bundles or quanta of energy, it would appear to follow that each 

 bundle is subject to gravitation. Therefore if a bundle comes on 

 from infinite distance with velocity c, when it has reached a 

 place of potential V near the Sun its velocity c must be given by 



ic'2 - F - ic2, 



in other words, is increased in the ratio 1 + V jc^. It will swing 

 round the Sun in a concave hyperbolic orbit, and as the result, 

 the direction of its motion will suffer deflection away from the Sun 

 by half the amount that has been astronomically observed. 



This reasoning would not be estopped by the principle that c is 

 the upper limit of possible material velocities: for that is because 



* See final paragraphs. 



