Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/232

en négligeant les quantités qui restent de l’ordre $m^{5}$ après les intégrations,

${\frac {3m'u'^{3}}{2h^{2}u^{3}}}\cos(2v-2v')={\frac {3m^{2}}{2a_{\text{ı}}}}$

$\times \left\{{\begin{aligned}&\left(1+e^{2}+{\frac {1}{4}}wg^{2}-{\frac {5}{2}}e'^{2}\right)\cos(2v-2mv)\\&-m{\frac {3+4m}{2}}e\left(1+{\frac {1}{2}}e^{2}-{\frac {5}{2}}e'^{2}\right)cos(2v-2mv-cv+\varpi )\\&-m{\frac {3-4m}{2}}ecos(2v-2mv+cv-\varpi )\\&+{\frac {7}{2}}e'cos(2v-2mv-c'mv+\varpi ')\\&-{\frac {1}{2}}e'\cos(2v-2mv+c'mv-\varpi ')\\&-{\frac {21(1+2m)}{4}}ee'\cos(2v-2mv-cv-c'mv+\varpi +\varpi ')\\&-{\frac {21(1-2m)}{4}}ee'\cos(2v-2mv+cv-c'mv-\varpi +\varpi ')\\&+{\frac {3+2m}{4}}ee'\cos(2v-2mv-cv+c'mv+\varpi -\varpi ')\\&+{\frac {3-2m}{4}}ee'\cos(2v-2mv+cv+c'mv-\varpi -\varpi ')\\&+{\frac {17}{2}}e'^{2}\cos(2v-2mv-2c'mv+2\varpi ')\\&+m{\frac {6+15m+8m^{2}}{4}}e^{2}\cos(2cv-2v+2mv-2\varpi )\\&+m{\frac {6-15m+8m^{2}}{4}}e^{2}\cos(2cv+2v-2mv-2\varpi )\\&+{\frac {3+2m}{8}}wg^{2}\cos(2gv-2v+2mv-2\theta )\\&+{\frac {3-2m}{8}}wg^{2}\cos(2gv+2v-2mv-2\theta )\\&-{\frac {3(2+m)}{8}}ewg^{2}\cos(2v-2mv-2gv+cv+2\theta -\varpi )\end{aligned}}\right\}$

Le terme ${\frac {9m'u'^{4}}{8h^{2}u^{4}}}cos(v-v')$ de l’expression de $-{\frac {1}{h^{2}}}{\frac {\partial {\rm {Q}}}{\partial u}}-{\frac {s}{h^{2}u}}{\frac {\partial {\rm {Q}}}{\partial s}}$