![{\displaystyle \Delta y'=b\Delta _{0}+\nu a\Delta _{0}+\lambda \left(c\Delta _{0}-b^{2}{\frac {\operatorname {d} \Delta _{0}}{\operatorname {d} c}}\right)-\mu ab{\frac {\operatorname {d} \Delta _{0}}{\operatorname {d} c}}+b{\frac {\operatorname {d} \Delta _{0}}{\operatorname {d} c}}+Z.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/75e38024502277bab65dfbcc75b5e21402387757)
Au moyen de ces valeurs, nous trouverons, en employant la transformation indiquée par l’équation (11),
![{\displaystyle \iiint \Delta \operatorname {d} x'\operatorname {d} y'\operatorname {d} z'=\iiint \Delta \operatorname {d} a\operatorname {d} b\operatorname {d} c=\iiint \Delta _{0}\operatorname {d} a\operatorname {d} b\operatorname {d} c+Z\iiint {\frac {\Delta _{0}}{\operatorname {d} c}}\operatorname {d} a\operatorname {d} b\operatorname {d} c}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6650d9964d005e64281fa00d83113a89f328f2cf)
![{\displaystyle +\mu \iiint a{\frac {\Delta _{0}}{\operatorname {d} c}}\operatorname {d} a\operatorname {d} b\operatorname {d} c-\lambda \iiint b{\frac {\Delta _{0}}{\operatorname {d} c}}\operatorname {d} a\operatorname {d} b\operatorname {d} c\,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7fb79e4c0df34de59e291e9d7f21da918e7f695c)
![{\displaystyle \iiint \Delta x'\operatorname {d} x'\operatorname {d} y'\operatorname {d} z'=\iiint \Delta x'\operatorname {d} a\operatorname {d} b\operatorname {d} c=\iiint a\Delta _{0}\operatorname {d} a\operatorname {d} b\operatorname {d} c+Z\iiint a{\frac {\Delta _{0}}{\operatorname {d} c}}\operatorname {d} a\operatorname {d} b\operatorname {d} c}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6ce7fd65a3b6161e7261321e1828262a0d46d2bb)
![{\displaystyle +\nu \iiint b\Delta _{0}\operatorname {d} a\operatorname {d} b\operatorname {d} c-\mu \iiint \left(c\Delta _{0}-a^{2}{\frac {\operatorname {d} \Delta _{0}}{\operatorname {d} c}}\right)\operatorname {d} a\operatorname {d} b\operatorname {d} c-\lambda \iiint ab{\frac {\operatorname {d} \Delta _{0}}{\operatorname {d} c}}\operatorname {d} a\operatorname {d} b\operatorname {d} c\,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b96e04d626987aeaf5e49e7e27c4652a96ee5af2)
![{\displaystyle \iiint \Delta y'\operatorname {d} x'\operatorname {d} y'\operatorname {d} z'=\iiint \Delta y'\operatorname {d} a\operatorname {d} b\operatorname {d} c=\iiint b\Delta _{0}\operatorname {d} a\operatorname {d} b\operatorname {d} c+Z\iiint b{\frac {\Delta _{0}}{\operatorname {d} c}}\operatorname {d} a\operatorname {d} b\operatorname {d} c}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fd8497feb8a85f9540ef583082771ec6ee3ef796)
![{\displaystyle -\nu \iiint a\Delta _{0}\operatorname {d} a\operatorname {d} b\operatorname {d} c+\lambda \iiint \left(c\Delta _{0}-b^{2}{\frac {\operatorname {d} \Delta _{0}}{\operatorname {d} c}}\right)\operatorname {d} a\operatorname {d} b\operatorname {d} c+\mu \iiint ab{\frac {\operatorname {d} \Delta _{0}}{\operatorname {d} c}}\operatorname {d} a\operatorname {d} b\operatorname {d} c.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5e1f3b1e06bebd68d8c09ace2364c2b50f1a1c38)
Maintenant on doit observer que
sont les valeurs de
qui auraient lieu dans le cas d’équilibre, et que, conséquemment, on doit avoir identiquement (10)
![{\displaystyle {\begin{aligned}&\iiint \Delta _{0}\operatorname {d} a\operatorname {d} b\operatorname {d} c=m,\\\\&\iiint a\Delta _{0}\operatorname {d} a\operatorname {d} b\operatorname {d} c=0,&\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9846330f29095d27c8ae4dfd93fad3427c4b837c)