where the integrals only have to be extended over the ponderable body, but like in § 13, it should taken for the entire space enclosed by
.
At first, we replace
, etc. by the expressions (10), and, because of (I),
by
![{\displaystyle {\frac {\partial {\mathfrak {d}}_{x}}{\partial x}}+{\frac {\partial {\mathfrak {d}}_{y}}{\partial y}}+{\frac {\partial {\mathfrak {d}}_{z}}{\partial z}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/01409fe9272b07fb763188b0adcb47eb815ff4bc)
thus
|
(14)
|
Furthermore, a partial integration and application of (IV) and (II) gives (when we denote the direction constants of the perpendicular to
by
)
![{\displaystyle +\int {\mathfrak {H}}_{x}{\frac {\partial {\mathfrak {H}}_{x}}{\partial x}}\ d\ \tau .}](https://wikimedia.org/api/rest_v1/media/math/render/svg/139148f8b10a302ddfa3fbd8be3405a0b7cd4ede)
If we substitute this value into (14), then several terms occur, that can be completely integrated, and eventually by a simple transformation