electromagnetic system; for this purpose we must use the equations 

 (45) and (46) (1915) or in E[nstein's notation, which we shall follow 

 here, ') 



V- = — h-^ 2: {a)x^\'^a'r' (39) 



and for b =1 



1b= :S (a)x^\rpa'c' (60) 



ab 



The set of quantities i,^ might be called the stress-energy -complex 

 (comp. § 38). As for a change of the system of coordinates the 

 transformation formulae for X are similar to those by which tensors 

 are defined, we can also speak of the stress-energy -tensor. We have 

 namely 



V-g^ c ]/-g 



§ 41. The equations for the gravitation tield are now obtained 

 (comp. §§13 and 14, 1915) from the condition that 



dp fhdS-^^ö fQdS = (61) 



for all variations dg^f, which vanish at the boundary of the field 

 of integration together with their first derivatives. The index ip in 

 the first term indicates that in the variation of L the quantities i|^a6 

 must be kept constant. 



If we suppose L to be expressed in the quantities g"^ and if (42), 

 (45) and (48) are taken into consideration, we find from (61) that 

 at each point of the field-figure 



-^(«^) (^) ^r' + ^ ^(«^) G«'^ ^0"^ = . . (62) 



If now in the first term we put 



1) The notations J.^^, v}/^^ and vl»'^ (see (27), (^29) and § 11, 1915), will however 

 be preserved though they do not correspond to those of Einstein. As to 

 formulae (59) and (60) it is to be understood that if p and q are two of the 

 numbers ] , 2, 3, 4, p' and q' denote the other two in such a way that the order 

 p q p' q' is obtained from 1 2 3 4 by an even number of permutations of two 

 ciphers. 



If Xi, X2, a:3, Xi are replaced by x, y, z, t and if for the stresses the usual 

 notations Xx, Xy, etc., are used (so that e.g. for a surface element da perpendicular 

 to the axis of .x, Xx is the first component of the force per unit of surface which 

 the part of the system situated on the positive side of dr exerts on the opposite 

 part) then %i^ = Xx,1r= Xy,e\.Q,. Further —X\^, — ïgS — Ï3'* are the components 

 of the momentum per unit of volume and %^^, J^^^ j^s the components of the 

 energy-current. Finally %^'^ is the energy per unit of volume. 



