Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/153

Pareillement, les coefficients des inégalités dépendantes de $\varpi ^{\rm {v}}$ ont $e^{\rm {v}}$ pour multiplicateur ; en nommant donc ${\rm {B}}e^{\rm {v}}$ l’un de ces coefficients, sa variation sera ${\rm {B}}e^{\rm {v}}{\frac {\delta e^{\rm {v}}}{e^{\rm {v}}}},$ et l’on verra dans la suite que

$\delta e^{\rm {v}}=-t.1''{,}984469.$

Cela posé, on trouve

$\delta v^{\rm {iv}}=\left(1+\mu ^{\rm {v}}\right)\left\{{\begin{aligned}&26''{,}569412.\sin \left(n^{\rm {v}}t+\varepsilon ^{\rm {v}}-\varpi ^{\rm {iv}}\right)\\&29''{,}914770.\sin \left(n^{\rm {v}}t+\varepsilon ^{\rm {v}}-\varpi ^{\rm {v}}\right)\\-&(427''{,}078201+t.0''{,}0141929)\\&\ \ \ \qquad \qquad .\sin \left(2n^{\rm {v}}t-n^{\rm {iv}}t+2\varepsilon ^{\rm {v}}-\varepsilon ^{\rm {iv}}-\varpi ^{\rm {iv}}\right)\\+&(174''{,}796601-t.0''{,}0096906)\\&\ \ \ \qquad \qquad .\sin \left(2n^{\rm {v}}t-n^{\rm {iv}}t+2\varepsilon ^{\rm {v}}-\varepsilon ^{\rm {iv}}-\varpi ^{\rm {v}}\right)\\-&(137''{,}224760+t.0''{,}0045603)\\&\ \ \ \qquad \qquad .\sin \left(3n^{\rm {v}}t-2n^{\rm {iv}}t+3\varepsilon ^{\rm {v}}-2\varepsilon ^{\rm {iv}}-\varpi ^{\rm {iv}}\right)\\+&(262''{,}168424-t.0''{,}0145351)\\&\ \ \ \qquad \qquad .\sin \left(3n^{\rm {v}}t-2n^{\rm {iv}}t+3\varepsilon ^{\rm {v}}-2\varepsilon ^{\rm {iv}}-\varpi ^{\rm {v}}\right)\\+&24''{,}460840.\sin \left(4n^{\rm {v}}t-3n^{\rm {iv}}t+4\varepsilon ^{\rm {v}}-3\varepsilon ^{\rm {iv}}-\varpi ^{\rm {iv}}\right)\\-&48''{,}239570.\sin \left(4n^{\rm {v}}t-3n^{\rm {iv}}t+4\varepsilon ^{\rm {v}}-3\varepsilon ^{\rm {iv}}-\varpi ^{\rm {v}}\right)\\+&\ \ 3''{,}233695.\sin \left(5n^{\rm {v}}t-4n^{\rm {iv}}t+5\varepsilon ^{\rm {v}}-4\varepsilon ^{\rm {iv}}-\varpi ^{\rm {iv}}\right)\\-&\ \ 8''{,}585382.\sin \left(5n^{\rm {v}}t-4n^{\rm {iv}}t+5\varepsilon ^{\rm {v}}-4\varepsilon ^{\rm {iv}}-\varpi ^{\rm {v}}\right)\\+&\ \ 1''{,}256948.\sin \left(6n^{\rm {v}}t-5n^{\rm {iv}}t+6\varepsilon ^{\rm {iv}}-2\varepsilon ^{\rm {iv}}-\varpi ^{\rm {v}}\right)\\-&\ \ 2''{,}818833.\sin \left(6n^{\rm {v}}t-5n^{\rm {iv}}t+6\varepsilon ^{\rm {v}}-2\varepsilon ^{\rm {iv}}-\varpi ^{\rm {v}}\right)\\+&\ \ 0''{,}460731.\sin \left(7n^{\rm {v}}t-6n^{\rm {iv}}t+7\varepsilon ^{\rm {v}}-6\varepsilon ^{\rm {iv}}-\varpi ^{\rm {iv}}\right)\\-&\ \ 1''{,}004913.\sin \left(7n^{\rm {v}}t-6n^{\rm {iv}}t+7\varepsilon ^{\rm {v}}-6\varepsilon ^{\rm {iv}}-\varpi ^{\rm {v}}\right)\\-&16''{,}074450.\sin \left(2n^{\rm {iv}}t-n^{\rm {v}}t+2\varepsilon ^{\rm {iv}}-\varepsilon ^{\rm {v}}-\varpi ^{\rm {iv}}\right)\\-&\ \ 1''{,}758450.\sin \left(2n^{\rm {iv}}t-n^{\rm {v}}t+2\varepsilon ^{\rm {iv}}-\varepsilon ^{\rm {v}}-\varpi ^{\rm {v}}\right)\\+&39''{,}742746.\sin \left(3n^{\rm {iv}}t-2n^{\rm {v}}t+3\varepsilon ^{\rm {iv}}-2\varepsilon ^{\rm {v}}-\varpi ^{\rm {iv}}\right)\\-&\ \ 1''{,}087650.\sin \left(3n^{\rm {iv}}t-2n^{\rm {v}}t+3\varepsilon ^{\rm {iv}}-2\varepsilon ^{\rm {v}}-\varpi ^{\rm {v}}\right)\\+&\ \ 3''{,}973709.\sin \left(4n^{\rm {iv}}t-3n^{\rm {v}}t+4\varepsilon ^{\rm {iv}}-3\varepsilon ^{\rm {v}}-\varpi ^{\rm {iv}}\right)\\-&\ \ 0''{,}533617.\sin \left(4n^{\rm {iv}}t-3n^{\rm {v}}t+4\varepsilon ^{\rm {iv}}-3\varepsilon ^{\rm {v}}-\varpi ^{\rm {v}}\right)\\+&\ \ 1''{,}100702.\sin \left(5n^{\rm {iv}}t-4n^{\rm {v}}t+5\varepsilon ^{\rm {iv}}-4\varepsilon ^{\rm {v}}-\varpi ^{\rm {iv}}\right)\\-&\ \ 0''{,}256755.\sin \left(5n^{\rm {iv}}t-4n^{\rm {v}}t+5\varepsilon ^{\rm {iv}}-4\varepsilon ^{\rm {v}}-\varpi ^{\rm {v}}\right)\end{aligned}}\right\}$

$+\left(1+\mu ^{\rm {vi}}\right)\left\{{\begin{aligned}&0''{,}381191.\sin \left(n^{\rm {vi}}t+\varepsilon ^{\rm {vi}}-\varpi ^{\rm {iv}}\right)\\-&0''{,}726050.\sin \left(n^{\rm {vi}}t+\varepsilon ^{\rm {vi}}-\varpi ^{\rm {vi}}\right)\\-&1''{,}645307.\sin \left(2n^{\rm {vi}}t-n^{\rm {iv}}t+2\varepsilon ^{\rm {vi}}-\varepsilon ^{\rm {iv}}-\varpi ^{\rm {iv}}\right)\\+&0''{,}316891.\sin \left(2n^{\rm {vi}}t-n^{\rm {iv}}t+2\varepsilon ^{\rm {vi}}-\varepsilon ^{\rm {iv}}-\varpi ^{\rm {vi}}\right)\\-&0''{,}394947.\sin \left(3n^{\rm {vi}}t-2n^{\rm {iv}}t+3\varepsilon ^{\rm {vi}}-2\varepsilon ^{\rm {iv}}-\varpi ^{\rm {vi}}\right)\end{aligned}}\right\}$