891 
and equation (27) becomes finally 
02 EE Rae 
Bas 40 Rip sis: OF ha A, Ae ee BE) 
j Ow 1 Ow; 
This equation is identical with ErNsTEIN’s equation (22), which 
he obtained by variation of the g””’s. The variation performed in 
this paper does therefore not give new equations for the field. It 
shows however clearly that the expressions (23) for © also hold 
for the general theory of relativity. 
Finally the formulae may still be specialized for an adiabatic 
fluid. For such a fluid (comp. Herrerorz § 10) @ is only a function 
of the quantity 
a A eS 9 
ei ee == ———— 32 
0 Le EE), . . ( 2) 
da VS 9,,30740 34 
NC) 
which gives the relation between the volume when in rest and the 
normal volume. We thus have according to (11) 
= 736 740 
a, [3 
“7 3 
A13 
W_gD Ee lt ME 
B ly (i eee eae a V Sgosaag. en Ta (33) 
fs : 
The tension-energy tensor may be calculated most simply in, its 
contravariant form. By doing this we obtain. 
a a le he ct ye ee (34) 
D049; ; DE goganass 
where, as in HeRGLOTZ’s article, 
02 
denotes the scalar pressure. By performing once respectively twice 
a mixed multiplication with the covariant fundamental tensor we 
(35) 
obtain the expressions for % and 3, 
mass when in rest. If therefore, we assume Vv —g = 1, the obtained 
expressions agree with those given by HiNsrrIN *). 
Leiden, Nov. 24 1916. 
') A. Erster, Die Grundlage der allgemeinen Relativitätstheorie, § 19, Ann. d. 
Phys. 49, 1916, p. 769. 
Lé 
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