﻿Einstein and Grossmann' s Theory of Gravitation. 93 



As already said, the given differential equation fits in 

 with the formula 



^ "d{Tff„+tffv ) _ft ( rj 



*~ *x, ' ' { } 



showing that the laws of conservation are fulfilled. 



Approximative simplifications. 



14. The differential equations for gravitation appear to be 

 very complicated. However, there is a way of simplifying 

 the equations and getting successive approximations. It 

 has already been said that in the case of constant potentials, 

 let us now say in absence of a gravitation field, the funda- 

 mental tensor of the g^ v becomes 



1 















-1 











-1 















c\ 



;ens 



lor of the y^ v 





1 















-1 











-1 















1 



The first thing we can do is to assume that in the actual 

 case of our solar system the values of g^ and y^v will differ 

 only slightly from those given above by very small quantities 

 a and y , and that, therefore, as a first approximation, 

 we can omit in the differential equations those terms con- 

 taining products of two g* or y* or their derivatives. 



When, besides, we abstract from the actual existing 



motions, assuming that the velocities are so small as to 



v v^ . . 



make - and -g negligible, then the equation of Poisson 

 c c 



for g*^ is the only one retained, and we get Newton's theory, 



where </J 4 plays the role of the usual gravitation potential. 



Considering the significance of g u = c 2 + ^* 4 in the form for 



the line-element ds, the conclusions may be drawn about the 



dependency of the velocity of light and of the rate of action 



o£ processes on the gravitation potentials which we mentioned 



before (§5). 



