500 On the Orbit of a Planet. 



That this equation may reduce to 



d 2 u m _n 



aW 2 + U ~~h 2 ' 



the ordinary differential equation for elliptic motion, we 

 must have 



7=1 — 2mu, 



, n 1 — 2mu 

 and p = s — , 



and, therefore, a = 1 — 2mu; 



and we have 



*•= (l - ~)dt*- (l -^)rfr«- (l - ^)r* <W, 



which makes the velocity of light constant and equal to 

 unity. 



But the gravitation potentials thus introduced do not 

 satisfy Einstein's contracted-tensor equations. They must 

 be rejected, if these equations are valid. 



If now we wish to explain the unexplained part of the 

 advance of the perihelion of Mercury, the simplest form 

 of the differential equation of planetary motion for that 

 purpose is 



dhi , m O 2 A 



dd l h 2 



and, again, we have y == 1 - 



Hence, 



e = -\ 



— 2mu d , 



or 



j 



and, since uy = /3 2 u*, 





1 





a ~l- 



-2mu ' 



Thus, in this case, 







ds 2 =(l- 



- )dt 2 - 



dr 2 



-r 2 d6 2 . 



