D O C . 9 E N E R G Y C O N S E RVAT I O N 6 1
By explicit calculation of the I convinced myself that the surface integral over
an “infinitely distant”
sphere10
which includes the origin of the coordinates, and
which appears in the spatial integration of the first three terms of the expression,
does indeed vanish (at least in the special case of uniformly distributed matter).
With this choice of coordinates, too, the gravitational field, in this case, contributes
nothing to the energy of the world.
Translator’s Notes
{1} The misprint “Sinnenelement” in the German original has been read and translated
here as “line element.”
{2} “ ” has been corrected to “ .”
{3} “ ” in the third term of the first integral on the left side has been corrected here
to “ .”
10
I.e., over a surface with an infinitely large .
U
σ
ν
x2
1
x2
2
x2
3
+ + R2
=
R
∂Uσ-
1
∂x1
-----------
∂Uσ-
2
∂x2
-----------
∂Uσ-
3
∂x3
-----------
∂U
4
∂x4
------------σ
+ + +
tσν ( )1
tν
σ)1 (
nx2
nx3