If for (f^Q and d,Q the expressions (48) and (44) are taken, the 

 equation 



öQ-ö,Q = (f^Q (50) 



is an identity for every choice of the variations. 



It will likewise be so in the special case considered and we shall 

 also come to an identity if in (50) the terms with the derivatives 

 of ^ are omitted while those with | itself are preserved. 



When this is done öQ reduces to 



and, taking into consideration (44) and (48), we find after division 

 by § 



ÖQ d/öQ \ ^ .d/öQ 

 — ^ h ^ («^«) ^— ^ 9ab,h + ^ {abe/ ) ^— gabjh 



-2 (abef) -^ ! ^ fv— 1 9ab, J =- - ^ {ab)Gabr'' ^ - (51) 



Ox e {O.Vf\agab, e/y ) 



In the second term of (44) we have interchanged here the indices 

 e and ƒ. 



If for shortness' sake we put, for e =\= h 



^1= :S{ab)^^ gab,h + 2{abf)-^- gabJh ~-:E{abf)-- (- \.^/.(52) 



^gab,e ^9ab,fe OX/\dgab, efj 



and for e=fh 



éj = - Q + 2{ab) — ^ gab,h + ^{abf) gabfh - 



^gab,h ^9nb,fh 



-2:{abf)--[—^)gab,h, (53) 



dxf\dgab,hfJ 



we may write 



2{é)^ = — 2{ab)Gabr'''^ (54) 



dXe 



The set of quantities el will be called the complex é and the set 

 of the four quantities which stand on the left hand side of (54) in 

 the cases /i = l, 2, 3, 4, the divergency of the complex.') It will 

 be denoted by div é and each of the four quantities separately by 



divh ^^ 



The equation therefore becomes 



divh^= — 2:{ab)Gab^r^>'' (55) 



1) Einstein uses the word "divergency" in a somewhat different sense. It seemed 

 desirable however to have a name for the left hand side of (54) and it was diffi- 

 cult to find a better one. 



