Physics. — "On Einstein'*^ Theory of gravitation.''' \^ . By Prof. H. 



A. LORENTZ. 



(Communicated in the meeting of October 28, 1916). 



§ 53. The expressions for the stress-energj-components of the 

 gravitation field found in the preceding paper call for some further 

 remarks. If by rf/,^ we denote a quantity having the value 1 for 

 e =^ h and being for e =\= h, those expressions can be written in 

 the form (comp. equations (52) and (78)) 



1 ( ÖQ dQ 



tA^ = — — *hr- Q + ^ (^^) :^ gab, h -V 2 {abf) gab. fh — 



2x f Ogab,e ^9ab,fe 



-^{obf) — (~^]ga^jA (88) 



They contain the first and second derivatives of the quantities ^«6. 

 Einstein on the contrary has given values for the stress-energy- 

 components which contain the first derivatives only and which 

 therefore are in many respects much more fit for application. 



It will now be shown how we can also find formulae without 

 second derivatives, if we start from (88). 



§ 54. For this purpose we shall consider the complex u defined by 



1 I d / do M 



u,e= \ö,eQ-:E{ahf) — [—^-gaij]\. . . (89) 



2x I 0.17, \OgabJe J \ 



and we shall seek its divergency. 

 We have 



{div \\)h ■=:E {€)-- = --}- ^ {ahje) —-- gab, f 



dXe 2-K [QXh OXeOXh\pgab,fe ^ , 



or 



1 ^R 

 {d{vü)h = --^ (90) 



R^Q-:Eiahfe)-—[—^—gabj] .... (91) 



OXe \Ogab,fe J 



Now Q = ^^ — (/ G can be divided into two parts, the first of 

 which Q, contains diff"erential coefficients of the quantities ^«t of the 

 first Older only, while the second Q, is a homogeneous linear function 



if we put 



