328 Sir Joseph Larmor 



mentioned: that is included satisfactorily in tlie earlier uniform 

 relativity formulation. 



This relation of light to gravitation is thus one of the questions 

 raised by the postulate of the relativity of that universal force. 

 Einstein answered in 1911* in one way, that the spectrum of solar 

 hydrogen, when compared with terrestrial hvdrogen which is con- 

 nected with the observer, should be displaced slightly towards the 

 red: but it is a question whether the consistent development of 

 that train of ideas would not rather require that it be not displaced 

 at all. 



In connexion with his later formal theory of gravitation the 

 same effect is described as due to varying local scales of time, 

 which seem to be carried without change, by the pulsations of the 

 rays, from the place of their origin to all the other parts of the 

 universe: whereas in the above the apparent period f changes as 

 the ray advances. The observers along the ray are supposed to 

 be in communication with one another. In so far as their space 

 moves forward as a whole it is not stretched or shrunk: in that 

 case it can be only their scales of apparent duration of time that 

 are lengthened localh'^ by a factor, the inverse of 1 — V jc^. This 

 involves that the scale of apparent velocity in the unchanged space 

 will be altered in the direct ratio: and rays of light in a field of 

 varying potential, if they were paths of stationary time, might be 

 thought to be deflected. But fundamentally the path of the ray 

 is determined by the number of wave-lengths in its course being 

 made stationary, as compared with neighbouring courses: and this 

 is, in the present case, not the same as minimum time of transit, 

 for apparent time has lost its uniform scale while space has not. 



Thus the path of a ray would be determined by the condition 

 that SSs/A summed along it shall be stationary: but if there is 

 correspondence between the two systems of reference which 

 changes all lengths around each point in the same ratio then hsjX 

 will be everywhere the same in both systems. The circumstances 

 of the path would thus not be altered by this change of view 

 regarding gravitation, and there ought to be no special deviation 

 of the rays involved in it. 



But if g is not uniform along the path r of the ray, is a 

 shrinkage of the accelerated apparent space involved? The answer 



* His exposition which has here been paraphrased is in Ann. der Physik, 35, 

 1911, §3, p. 904. 



The argument of this and the next two paragraphs is based on the implication 

 that in a theory of transmission by contact, radiation like other things, the so- 

 called clocks included, must conform to local measure: the alternative, described 

 at the end of the paper,- that racUation is extraneous in so far as it imposes an 

 absolute scale of space-time of its own on the whole cosmos, was here taken to be 

 excluded in advance from this type of theory. 



•j- Measured on a fundamental scale. 



