﻿•9"2 Dr. A. D. Fokker : A Summary of 



potential. We expect that our differential equation will be 



Gnv = kT, 



GV, 



where Q av denotes a tensor derived by differential operations 

 from our potentials, containing differential coefficients up to 

 those of the second degree. It has in special cases and with 

 certain simplifying neglections to become the same as Acp. 



Now, when we put T TV = Gc av //c in the right-hand side of 

 the first equation of the previous section, we ought, as the 

 second equation indicates, to be able to show that the right- 

 hand side is identical with a sum o£ differential coefficients. 



Indeed, Einstein has succeeded in doing this. He finds 

 that the identity exists if we put 



yd/ /— ~dvnv\ 



... (4) 



Here g denotes the determinant of the g and § w a quantity 

 which equals for a =£ v and 1 for a = v. 



dt 



identity are the differential coefficients of the tensor 



(5) 



so that the stresses, momenta, and energy of the gravitation 

 field are to be taken as given by this formula. 



A very important result is seen when we compare this 

 formula with the preceding. It then appears that 



It appears that the differential coefficients 



<T. + W)=|^(V-, 7 ^|^), (6) 



i. e. the tensor of stresses, kc. of the gravitation field enters 

 exactly in the same way into the differential equations 

 determining the potentials as the material tensor does. The 

 gravitational stresses, momenta, and energy exert the same 

 power in creating the field as the material ones do. This is 

 quite satisfactory. There is no reason why the energy kc. 

 of the field would behave otherwise than energy of matter. 



