1078 



we find that Ö* is a homogeneous quadratic function of the quantities 

 g-/', so that we have 



^0^ = 26* (9) 



The stress-energy-connponents of the gravitation field f," intro- 

 duced by Einstein are connected with ^* by the formula ^) 



.t,=^{^^ö,-2^j,.^y .... ,10) 



where rf./ = 1, 6^' =zO for =|= r. For the diagonal summation we 

 find because of (9) 



X ^ tv" = 6* . . . (11) 



V 



For the diagonal summation of the material stress-energy tensor we 

 have again "j 



7c2l;^=\/^G. . (12) 



V 



By summation we find taking (3) into account 



di>lr 

 H:S'(^/ + t-/) = ^T- (13) 



V T OXx 



An equation of quite the same form is obtained from the fol- 

 lowing formula of Einstein') 



.(.V +.4=-^: ,-(,—.'") (14) 



We thus find that the four-fold vector 51 and the four-fold vector, 



the components of which are — iJ- <7"' have the same divergency ; 



the notations "four-fold vector" and "divergency" have here the 

 meaning ascribed to them in the special theory of relativity. From 

 a private correspondence with Einstein I learned that he has proved 

 that these two vectors are really identical, at least when t^e system 

 of coordinates is thus chosen that V^ — g = 1 . 



Now all general formulae necessary for the following have been 

 cited. We still remark that not yet anything has been said about 

 the units in which the quantities are expressed. In order to obtain 

 the stress- and energy-density in the desired units it may therefore 

 be necessary to introduce in the expressions (2) and (10) a constant 



1) Einstein, Harailtonsches Prinzip, equation (20). 



^} See e.g. J. Dkoste. Het zwaartekrachtsveld van een of meer lichamen volgens 

 de theorie van Einstein. (Diss. Leiden 1916) p. 8 and 12. 

 ') Einstein, Hamillonsches Prinzip, equation (18). 



