Thus we see (comp. § 58) that at a distance from the attracting sphere decreases proportionally to . Further it is to be noticed that on account of the indefiniteness pointed out in § 58, there remains some uncertainty as to the distribution of the energy over the space, but that nevertheless the total energy of the gravitation field
has a definite value.
Indeed, by the integration the last terra of (111) vanishes. After multiplication by this term becomes namely
The integral of this expression is 0 because (comp. §§ 57 and 58) is continuous at the surface of the sphere and vanishes both for and for .
We have thus
where the value (107) can be substituted for . If e.g. the density is everywhere the same all over the sphere, we have at an internal point
and at an external point
From this we find
§ 61. The general equation (99) found for can be transformed in a simple way. We have namely
and we may write (§ 54) for the last term. Hence