LXXVI.
Soit pour le premier satellite (ces formules s’appliquent également aux trois autres, suivant les remarques des Articles IX et XIII)
![{\displaystyle {\begin{aligned}\mathrm {L} _{1}\ =&g_{1}-2\mu _{1}\mathrm {H} _{1}-{\frac {\chi _{2}}{1+n\chi _{1}}}{\breve {\Gamma }}(a_{1},a_{2})-{\frac {\chi _{3}}{1+n\chi _{1}}}{\breve {\Gamma }}(a_{1},a_{3})-{\frac {\chi _{4}}{1+n\chi _{1}}}{\breve {\Gamma }}(a_{1},a_{4})\\&-{\frac {1}{2}}{\frac {\mathrm {K} _{1}}{1+n\chi _{1}}}+{\frac {1}{5}}{\frac {\varkappa _{1}}{1+n\chi _{1}}},\\\mathrm {M} _{1}^{2}=&3\mu _{1}^{2}-2f_{1}-nf_{1}\left[\chi _{2}{\breve {\Pi }}(a_{1},a_{2})+\chi _{3}{\breve {\Pi }}(a_{1},a_{3})+\chi _{4}{\breve {\Pi }}(a_{1},a_{4})+{\frac {1}{2}}\mathrm {K} _{1}+{\frac {1}{5}}\varkappa _{1}\right],\\\mathrm {N} _{1}^{2}\,=&\mu _{1}^{2}\\+&nf_{1}\left[\chi _{2}{\overset {\backsim }{\Gamma }}(a_{1},a_{2})+\chi _{3}{\overset {\backsim }{\Gamma }}(a_{1},a_{3})+\chi _{4}{\overset {\backsim }{\Gamma }}(a_{1},a_{4})+{\frac {3}{2}}\mathrm {K} _{1}+{\frac {2}{5}}\varkappa _{1}\right]+2n\mu _{1}f_{1}\mathrm {H} _{1}.\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/19467210fa56856575b9089aae3887543eba4d53)
Supposons de plus (Articles XXXVI et XXXVIII)
![{\displaystyle {\begin{aligned}\theta _{1}=&-{\frac {\chi _{2}}{1+n\chi _{1}}}\left[\Xi _{1}(a_{1},a_{2})\cos(u_{2}-u_{1})t+\Xi _{2}(a_{1},a_{2})\cos 2(u_{2}-u_{1})t+\ldots \right]\\&-{\frac {\chi _{3}}{1+n\chi _{1}}}\left[\Xi _{1}(a_{1},a_{3})\cos(u_{3}-u_{1})t+\Xi _{2}(a_{1},a_{3})\cos 2(u_{3}-u_{1})t+\ldots \right]\\&-{\frac {\chi _{4}}{1+n\chi _{1}}}\left[\Xi _{1}(a_{1},a_{4})\cos(u_{4}-u_{1})t+\Xi _{2}(a_{1},a_{4})\cos 2(u_{4}-u_{1})t+\ldots \right]\\&-{\frac {\mathrm {K} _{1}}{1+n\chi _{1}}}\gamma _{1}\sin 2(m-\mu _{1})t,\\\\\vartheta _{1}=&{\frac {\chi _{2}}{1+n\chi _{1}}}\left[\Phi _{1}(a_{1},a_{2})\sin(u_{2}-u_{1})t+\Phi _{2}(a_{1},a_{2})\sin 2(u_{2}-u_{1})t+\ldots \right]\\+&{\frac {\chi _{3}}{1+n\chi _{1}}}\left[\Phi _{1}(a_{1},a_{3})\sin(u_{3}-u_{1})t+\Phi _{2}(a_{1},a_{3})\sin 2(u_{3}-u_{1})t+\ldots \right]\\+&{\frac {\chi _{4}}{1+n\chi _{1}}}\left[\Phi _{1}(a_{1},a_{4})\sin(u_{4}-u_{1})t+\Phi _{2}(a_{1},a_{4})\sin 2(u_{4}-u_{1})t+\ldots \right]\\+&{\frac {\mathrm {K} _{1}}{1+n\chi _{1}}}\gamma _{1}\sin 2(m-\mu _{1})t,\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/78349be95eebb4ac7582061c3d05b532638e4cc1)
et faisons 
(nous verrons bientôt la raison de ces substitutions). Les équations de l’Article XXXIII se changeront en
