Page:Joseph Louis de Lagrange - Œuvres, Tome 5.djvu/263

${\begin{alignedat}{2}(3,0){\frac {\theta \ \ \ \cos \omega \ \ \ }{\operatorname {tang} \mathrm {I} }}=&-0''{,}0123m&(3,0)\theta \ \ \ \sin \omega \ \ \ =&0''{,}0139m\\&\quad \ \ \,8{,}0904581,\qquad \qquad \qquad &&\ \ 8{,}1422893,\\(3,1){\frac {\theta '\ \ \cos \omega '\ \ }{\operatorname {tang} \mathrm {I} }}=&-0''{,}0485m'&(3,1)\theta '\ \ \sin \omega '\ \ =&0''{,}1586m'\\&\quad \ \ \,8{,}6859252,&&\ \ 9{,}2004031,\\(3,2){\frac {\theta ''\ \cos \omega ''\ }{\operatorname {tang} \mathrm {I} }}=&0''{,}0218m''&(3,2)\theta ''\ \sin \omega ''\ =&0''{,}0103m''\\&\ \ 8{,}3381540,&&\ \ 8{,}0127053,\\(3,4){\frac {\theta ^{\scriptscriptstyle {\text{IV}}}\cos \omega ^{\scriptscriptstyle {\text{IV}}}}{\operatorname {tang} \mathrm {I} }}=&0''{,}2808m^{\scriptscriptstyle {\text{IV}}}&(3,4)\theta ^{\scriptscriptstyle {\text{IV}}}\sin \omega ^{\scriptscriptstyle {\text{IV}}}=&0''{,}4244m^{\scriptscriptstyle {\text{IV}}}\\&\ \ 9{,}4483909,&&\ \ 9{,}6278188,\\(3,5){\frac {\theta ^{\scriptscriptstyle {\text{V}}}\ \cos \omega ^{\scriptscriptstyle {\text{V}}}\ }{\operatorname {tang} \mathrm {I} }}=&0''{,}0196m^{\scriptscriptstyle {\text{V}}}&(3,5)\theta ^{\scriptscriptstyle {\text{V}}}\ \sin \omega ^{\scriptscriptstyle {\text{V}}}\ =&0''{,}0084m^{\scriptscriptstyle {\text{V}}}\\&\ \ 8{,}2917832,&&\ \ 7{,}9247703.\end{alignedat}}$

27. De là j’ai eu les résultats que voici.

Mouvements annuels des aphélies.

${\begin{aligned}{\frac {d\varphi \ \ \ }{dt}}=&15''{,}9951m'+0''{,}0006m''+0'',0010m'''+0''{,}0007m^{\scriptscriptstyle {\text{IV}}},\\{\frac {d\varphi '\ \ }{dt}}=&6''{,}5601m+0''{,}0021m''+0''{,}0089m''+0''{,}0060m^{\scriptscriptstyle {\text{IV}}}+0''{,}0002m^{\scriptscriptstyle {\text{V}}},\\{\frac {d\varphi ''\ }{dt}}=&0''{,}6955m+12''{,}3083m'+1''{,}9211m'''+0''{,}7027m^{\scriptscriptstyle {\text{IV}}}+0''{,}0208m^{\scriptscriptstyle {\text{V}}},\\{\frac {d\varphi '''}{dt}}=&0''{,}1914m+6''{,}7938m'+1''{,}5461m''+5''{,}1969m^{\scriptscriptstyle {\text{IV}}}-0''{,}41651m^{\scriptscriptstyle {\text{V}}},\\{\frac {d\varphi ^{\scriptscriptstyle {\text{IV}}}}{dt}}=&0''{,}0812m+6''{,}3758m'+1''{,}1854m''-5''{,}0579m'''-4''{,}3043m^{\scriptscriptstyle {\text{V}}},\\{\frac {d\varphi ^{\scriptscriptstyle {\text{V}}}\ }{dt}}=&0''{,}0795m+1''{,}5599m'+0''{,}0408m''+0''{,}8391m'''+4''{,}1412m^{\scriptscriptstyle {\text{IV}}}.\end{aligned}}$