d’où l’on tire
![{\displaystyle y_{\mu }=}](https://wikimedia.org/api/rest_v1/media/math/render/svg/167d5a2d591170b7768a7f1f77b71fa42ef9d987)
![{\displaystyle {\frac {2}{m}}\left[\mathrm {S} _{1}\sin {\frac {\mu \varpi }{2m}}+\mathrm {S} _{2}\sin {\frac {2\mu \varpi }{2m}}+\mathrm {S} _{3}\sin {\frac {3\mu \varpi }{2m}}+\ldots +\mathrm {S} _{m-1}\sin {\frac {(m-1)\mu \varpi }{2m}}\right].}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1afee133c81e9b9873ab7d4c60fded2bd89d05e5)
Voilà donc quelle doit être l’expression générale des
qui dénotent les espaces parcourus par chacun des corps dans un temps quelconque
27. Pour connaître plus clairement la nature de l’équation trouvée, on y substituera les valeurs des quantités
du no 23, ce qui donnera finalement la formule
![{\displaystyle {\begin{aligned}y_{\mu }&={\frac {2}{m}}\mathrm {P} _{1}\sin {\frac {\mu \varpi }{2m}}\ \ \cos \left(2t{\sqrt {e}}\sin {\frac {\varpi }{4m}}\right)\\&+{\frac {2}{m}}\mathrm {P} _{2}\sin {\frac {2\mu \varpi }{2m}}\cos \left(2t{\sqrt {e}}\sin {\frac {2\varpi }{4m}}\right)\\&+{\frac {2}{m}}\mathrm {P} _{3}\sin {\frac {3\mu \varpi }{2m}}\cos \left(2t{\sqrt {e}}\sin {\frac {3\varpi }{4m}}\right)\\&\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \\&+{\frac {2}{m}}\mathrm {P} _{m-1}\sin {\frac {(m-1)\mu \varpi }{2m}}\cos \left[2t{\sqrt {e}}\sin {\frac {(m-1)\varpi }{4m}}\right]\\&+{\frac {1}{m{\sqrt {e}}}}{\frac {\mathrm {Q} _{1}\sin {\cfrac {\mu \varpi }{2m}}\ \ \sin \left(2t{\sqrt {e}}\sin {\cfrac {\varpi }{4m}}\right)}{\sin {\cfrac {\varpi }{4m}}}}\\&+{\frac {1}{m{\sqrt {e}}}}{\frac {\mathrm {Q} _{2}\sin {\cfrac {2\mu \varpi }{2m}}\sin \left(2t{\sqrt {e}}\sin {\cfrac {2\varpi }{4m}}\right)}{\sin {\cfrac {2\varpi }{4m}}}}\\&+{\frac {1}{m{\sqrt {e}}}}{\frac {\mathrm {Q} _{3}\sin {\cfrac {3\mu \varpi }{2m}}\sin \left(2t{\sqrt {e}}\sin {\cfrac {3\varpi }{4m}}\right)}{\sin {\cfrac {3\varpi }{4m}}}}\\&\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \\&+{\frac {1}{m{\sqrt {e}}}}{\frac {\mathrm {Q} _{m-1}\sin {\cfrac {(m-1)\mu \varpi }{2m}}\sin \left(2t{\sqrt {e}}\sin {\cfrac {(m-1)\varpi }{4m}}\right)}{\sin {\cfrac {(m-1)\varpi }{4m}}}}\,;\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/08972bd0343ab8aa0aa35288f3a8e804689200bc)
les quantités
et
dépendent de la première