Woolard — Generalized Relativity and Gravitation. 435 



know, e. g., that light travels slower in glass than it does 

 in air; when a ray of light enters glass, the wave-fronts 

 are rotated, and the ray is bent, or refracted, as we say. 

 As a matter of fact, if we apply our general equations to 

 the computation of the sun's gravitation field and the 

 phenomena therein, taking into account also the effect of 

 the sun's axial rotation, we reach some startling results. 

 If there is a space without any gravitation, then the 

 velocity of light is constant : 



da 



dt 



(16) 



where a- is the differential of arc in ordinary three-dimen- 

 sional space. In this case 



,/,-' = Jdx 1 - da 1 



fd(r\ 



df - d<x Q (17) 



m 



= 



111 a gravitation field also, ds being invariant 



ds = (18) 



In the general equations for the sun's gravitation-field, 

 we get an expression for ds; equating this to zero, and 

 solving for the velocity of light, we find that the equation 

 of a ray of light in the field shows that the ray actually 

 is curved. 1 '' 



A ray of light going from plus infinity to minus 

 infinity and just grazing the sun should be bent from its 

 course l"-75; hence a star observed very near the sun's 

 limb during the time of a total eclipse should be dis- 

 placed from its true position on the celestial sphere by 

 this amount. "Comprehensive arrangements have been 

 made for submitting Einstein's theory to the acid test in 

 connection with the total solar eclipse of June 8, 1918." 

 The observational difficulties are very great, and the fail- 

 ure to find such a displacement may mean that it is not 

 there, or that it has escaped detection. This eclipse is 

 not a very favorable one, either, as there are few stars 

 near the eclipsed sun. 



15. We also find from our equations that at the sur- 

 face of the sun 



18 For approximate concrete demonstrations of this and the following 

 phenomenon, see the introduction to Fokker's paper, cited above. 



