Gravitation and Light 327 



Thus in the preliminary stage it occurred to Einstein that the 

 period of a train of light waves would be no longer uniform 

 throughout its course. Let us consider a mass of hydrogen gas 

 at P, say in the Sun, sending light- waves to an observer Q, both 

 being situated in a region in which there is a field of gravitation 

 of intensity represented by </, directed from Q to P. In terms of 

 the postulate of the relativity of that force this statement would 

 mean that the spacial frame to which the underlying events are 

 referred is rushing as a whole from P toward Q with acceleration g. 

 Let V be the velocity of the frame at the instant when a specified 

 light- wave passes any intermediate point Q' : by the time this 

 wave has reached Q the velocity of the frame as a whole has risen 

 to V -\- g.Q'Qjc approximately, where g is mean intensity along 

 the range from Q' to Q. Thus to the accelerated observers the 

 waves emitted become longer with distance traversed, in the ratio 

 ^ + 9 -Q Q/c^, owing to this velocity of recession from the source : 

 that is, the apparent wave-length undergoes change so that 

 during the progress from Q' to Q it is altered in the ratio 1 — SF/c^, 

 where 87 is the rise of potential (or fall of gravitational potential 

 energy) along that path. 



The period of the light will thus appear to be increased to 

 different observers on the line PQ, all of them travelHng along 

 with the same acceleration g, in different degrees according to their 

 positions. This is what will happen if the observers and their space 

 and optical instruments form a world of their own rushing past, 

 or through, an underlying actual world, with this acceleration g, 

 instead of the actual world rushing past them with the opposite 

 acceleration produced by a force of gravitation. For these alter- 

 natives are not now the same: the finite velocity of propagation c 

 is constant with respect to the actual underlying world, not the 

 observers' moving space. If the radiating hydrogen belongs to the 

 actual underlying world, and the spectroscopes of the observers 

 belong to their own spacial scheme that is imposed on that world, 

 this description is complete: the period of each wave as apparent 

 to observers along its path will increase as the wave travels away 

 to places of lower gravitational potential. The spectral lines of 

 solar hydrogen as observed on the earth ought to be displaced 

 towards the red, by the amount corresponding to the total fall 

 of potential between Sun and Earth. But the postulate of two 

 worlds seems to be here necessarily involved. Which of them would 

 a mass of radiating hydrogen situated half-way to the Sun belong 

 to?* The larger Doppler-Fizeau effect due to the motion of the 

 source itself relative to the observers' frame has not here been 



* All the bodies in the space, being subject to the same gravitation, would 

 move along with it: the waves of light alone would seem to be regarded as inde- 

 pendent: yet they have energy and so inertia. 



