4^6 Leigh Page, 



and are inclined to each other by an angle 



m 



Therefore the deflection of a material particle traveling with 

 the velocity of light is the same as that of a light ray, as indeed 

 the equivalence hypothesis requires. 



Consider a vibrating atom momentarily at rest near the surface 

 of the sun, but free to move in the gravitational field. Let dt 

 be its period of vibration. Then 



ds" = — c"" ii — 2 \ di". 



Now, if dt' is the period of this atom as measured in the system 

 with geodesic time curves in which it is permanently at rest, 



ds'^ — — c" dl''' = — c'' 1/ — 2 J di'. 



If an atom of the same kind be in vibration at a greater distance 

 from the sun (say at the surface of the earth), 



ds^ = - r dr = - r 



Therefore <//, // / \ 



dt \r rj ' 



or, if V denotes frequency, 



1/ / r r \ 



(76) 



^ 



Therefore an atom at the sun's surface should vibrate more 

 slowly than one at the surface of the earth, resulting in a shift 

 of the solar lines toward the red. This shift, which amounts to 

 less than one hundredth of an Angstrom unit in the visible spec- 

 trum, has been sought by St. John, but not found. 



It should be noted that the two predictions which have been 

 verified by observation are consequences of Einstein's law of 

 gravitation, whereas the shift of the Fraunhofer lines is deduced 

 not so much from this law as from the theory on which it is 

 based. While the assumptions from which the theory is built 

 up are open to criticism — particularly the equivalence hypothesis 

 — there can be little doubt that Einstein's law represents a closer 

 approximation to the facts than Newton's does. 



The author wishes to express his thanks to Professor L. P. 

 Eisenhart, of Princeton University, for his kindness in examining 

 the differential geometry involved in this paper. 



