24 



with respect to r are indicated bj accents, we have according 

 to (40) and (101) 



i\ II II 



U U V u w 



G,, =r--l— I — 1 ^ __1^ 4- 

 1— A'l^V 2r 4v' ^ 4 



11 



Vlü 



liy 4u'' ^vw 



,'a 



?f ?« M V V W W 10 



u 2n^ 2uv ivio 2iv 4w' 

 u'w' v'lv' w" w'^ 

 2uv 4v* 2v 4mo 

 (?rtj^ = 0, for a =1= 6 . 

 So we have found the left hand sides of the tield equations (65). 

 Before considering these equations more closely we shall introduce 

 the simplification that the ^,,^'8 are very little different from the 

 normal values (100). For these latter we have 



u = r' , ï;= 1 , to = c' (102) 



and therefore we now put 



u = r^ (1 + A) , V = 1 -\r ii , w = c^ (1 + I') . . (103) 

 The quantities X, ft, v, which depend on r, will be regarded as 

 infinitely small of the first order and in the field equations we 

 shall neglect quantities of second and higher orders. 

 Then we may write for (t^ etc. 



G,, = -i— {k + 2rA' 4- ir^A" -IX- ir(i' + ^rv'), 



1— '^1 

 G,, = {l-w,'){X + 2rX' + irU" - (I - ir(i' + lrv% 



r r 



G,^ = -c'f^v' 4- hy 



On the right hand-sides of the field equations (65) we may take 

 for gab the normal value ; moreover we shall take for Tab and T 

 the values which hold for a system of incoherent material points. 

 We ma}' do so if we assume no other internal stresses but those 

 caused by the mutual attractions; these stresses may be neglected 

 in the present approximation. 



As we supposed the attracting matter to be at rest we have 

 according to (10), (16) and (15) (1915) lo^ = lu^ = w^ = 0, w^ = q, 



7^1 = U^ = U^ =: 0, a^ = C*(), P = CQ. 



In the notations we are now using we have further, according 



to (23) (1915), 



