448 
In In In == TE, ISN, GG HOCH), 
In gij (—=4, j=4) we now have to go only up to the terms 
of the first order inclusive, in 9,4, Joy Js, up to the terms of order 
14, in g,, up to the terms of order 2. As the quantities 9,,, 4.4, Jaa 
may be considered to arise from the motions of the bodies that 
produce the field (viz. by the changes that arise consequently in the 
field: of the first order), we wil suppose that 9,,,4,,.9,, only contain 
terms of order 13 (or higher). We consequently put 
i jig +B (I=E4 IES) , gaan + 2° 0;4(7=]=4) © naaar eB ast? raa 
gi=aei+xpis , g4=att + ho" , gh=ai4+2p+27 744 
For all values of 7 and j the quantities «;; and a’ represent the 
values of g;;and g in the case of absence of any gravitating body. 
As to the differential coefficients of these quantities a differentiation 
with respect to z,, 7,, 2, will not change their order, a differentiation 
with respect to 2,, however, will raise their order by 
In the equations of the field 
2 Gij — 221; + za jT a) AE Ten oe. ete 
il 0 (27 il) jon) ij} ml 
EE KeS 8) DEN | fads id, 
| se |) | =r MGE 
ij Et serie ij ij =? Win Ogjn _ Ògij 
| l = = é ga | ij i (# T Ou; vt) i 
Putting 
EET ml 
n a : Ow; Ow; O2n 
tel 
the left hand member is 
0 
2G;;=—22| — 
J I En 
where 
woh 
and giving to 
a corresponding meaning (putting gij = aij + 28: j + #2 613 + #°yij 
for all values of 7 and j, so that many of the 3; ;, 9; ; and 7; ; become 
zero), we get 
ij ij ij ij 
Be | flees (alm + 2Blr Hala on 4+ x7 y!n) (« | + ls | al + x° | ul ), 
n ng Nn ls nl, 
ied 
and so, omitting terms of higher than the second order, we obtain 
Wy smell] A ated a ade eel 
l Ll Ie Aan n n 2 tf, 
2. We now proceed to the calculation of the terms of the first 
