General Relativity and Einstein's Theory. 415 



center of the sun. It is interesting to note that the deflection 

 {y2) is double that which a material body shot through the sun's 

 field with a velocity close to that of light, should suffer according 

 to Xewton's law. 



It is of interest in this connection to investigate the motion of 

 a material particle which enters a radial gravitational field with 

 a velocity comparable to that of light. In this case the term on 

 the right hand side of (64) which involves the inve'rse cube of r 

 is negligible compared to the remaining terms, and equations 

 (64) and (65) give for the energy integral 



where /3 is the ratio of the velocity v of the moving particle at 

 infinity to that of light. This equation shows that if ^ = i / Vj 

 the velocity of the particle will be unchanged in magnitude by 

 the gravitational field, and that when (3 exceeds this value, the 

 field ^changes from an attractive field to a repulsive one. 



The orbit of a particle moving with the velocity of light is 

 easily determined. For this case (73) reduces to 



l(i) + '1^-K^-7) 



Eliminating 6 by means of (6"/), 



which has the same form as {(^). Therefore the equation of 

 the orbit is 



- = --"? + -cos (^ + 8) (75) 



r p p 



if terms in «r are neglected. If the particle comes closest to 

 the center of attraction when ^ -j- 8 is zero and r has the value R, 



or, in rectangular coordinates 



The asymptotes to this curve are obtained by making x very 

 large compared to y. They are 



('-^^)- 



±2^v + (/-2;,)j' = ^ 



