General Relativity and Einstein's Theory. 413 



This is the equation of an elHpse with eccentricity 



' a/Ji 



whose periheHon moves forward through the angle 



, ///'^ 12 -K tn 



p^ a{i-e^) 



(70) 



each revolution. The distance a is equal to the major axis of the 

 elliptical orbit. 



The following table gives the discrepancies in cSw between 

 observation and theory, both for the Newtonian theory and 

 Einstein's theory, together with the probable error of the obser- 

 vations. The units are seconds of arc per century. 



It is seen that Einstein's theory not only removes the large 

 discordance in the motion of Mercury's perihelion, but does not 

 introduce any new discrepancies in the case of the other planets. 

 This is, of course, due to the relatively greater eccentricity of 

 J^Iercury's orbit. 



As the ratio of velocity of light C at any point in a gravitational 

 field to its constant value c in a region free from gravitational 

 effects, is equal to the ratio of k to h [compare (9) and (11)], 

 the expression {(^2) for the line element shows that 



C^c 



= .(.-.^). (7.) 



Consider a ray of light passing through the sun's gravitational 

 field, (Fig. i) so as to come when nearest within a distance 

 R of the center of the sun. 



