|
(113)
|
where we must give the values 1, 2, 3 to
and
.
The gravitation energy lying within a closed surface consists therefore of two parts, the first of which is
|
(114)
|
while the second can be represented by surface integrals. If namely
are the direction constants of the normal drawn outward
|
(115)
|
In the case of the infinitely feeble gravitation field represented by
(§ 57) both expressions
and
contain quantities of the first order, but it can easily be verified that these cancel each other in the sum, so that, as we knew already, the total energy is of the second order.
From
and the equations of § 32 we find namely
|
(116)
|
so that we can write
|
|
The factor
is of the first order. Thus, if we confine ourselves to that order, we may take for all the other quantities these normal values. Many of these are zero and we find
|
(117)
|
Here we must take
;
, while we remark that for
the expression between brackets vanishes. For
the integral becomes
do, which after summation with respect to
gives
|
(118)
|
representing the normal to the surface. If
and
differ from each other, while neither of them is equal to 4, we can deduce from (110) and (109)