Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 11.djvu/179

165

THÉORIE DE JUPITER ET DE SATURNE.

XXX.

Les valeurs précédentes de $a$ et de $a'$ donnent

${\frac {a}{a'}}=\alpha =0{,}545172\,;$

d’où j’ai conclu, par les formules de l’article XIV,

$b_{-{\frac {1}{2}}}^{(0)}=2{,}151600,\qquad b_{-{\frac {1}{2}}}^{(1)}=-0{,}524084.$

Ces valeurs m’ont donné les suivantes :

${\begin{alignedat}{2}b_{\frac {1}{2}}^{(0)}=&2{,}180130,&b_{\frac {1}{2}}^{(1)}=&0{,}620436\\b_{\frac {1}{2}}^{(2)}=&0{,}257489,&b_{\frac {1}{2}}^{(3)}=&0{,}117886\\b_{\frac {1}{2}}^{(4)}=&0{,}0565116,&b_{\frac {1}{2}}^{(5)}=&0{,}0278371\\b_{\frac {1}{2}}^{(6)}=&0{,}0139787,\qquad &b_{\frac {1}{2}}^{(7)}=&0{,}00714873\\b_{\frac {1}{2}}^{(8)}=&0{,}00376118\,;&\end{alignedat}}$

${\begin{alignedat}{2}{\frac {db_{\frac {1}{2}}^{(0)}}{d\alpha }}=&0{,}808367,&{\frac {db_{\frac {1}{2}}^{(1)}}{d\alpha }}=&1{,}482776,\\{\frac {db_{\frac {1}{2}}^{(2)}}{d\alpha }}=&1{,}104622,&{\frac {db_{\frac {1}{2}}^{(3)}}{d\alpha }}=&0{,}725968,\\{\frac {db_{\frac {1}{2}}^{(4)}}{d\alpha }}=&0{,}452687,&{\frac {db_{\frac {1}{2}}^{(5)}}{d\alpha }}=&0{,}274045,\\{\frac {db_{\frac {1}{2}}^{(6)}}{d\alpha }}=&0{,}162578,\qquad &{\frac {db_{\frac {1}{2}}^{(7)}}{d\alpha }}=&0{,}0946947\,;\end{alignedat}}$

${\begin{alignedat}{2}{\frac {d^{2}b_{\frac {1}{2}}^{(0)}}{d\alpha ^{2}}}=&2{,}873503,&{\frac {d^{2}b_{\frac {1}{2}}^{(1)}}{d\alpha ^{2}}}=&2{,}550988,\\{\frac {d^{2}b_{\frac {1}{2}}^{(2)}}{d\alpha ^{2}}}=&3{,}519366,&{\frac {d^{2}b_{\frac {1}{2}}^{(3)}}{d\alpha ^{2}}}=&3{,}532195,\\{\frac {d^{2}b_{\frac {1}{2}}^{(4)}}{d\alpha ^{2}}}=&2{,}994607,\qquad &{\frac {d^{2}b_{\frac {1}{2}}^{(5)}}{d\alpha ^{2}}}=&2{,}303625,\\{\frac {d^{2}b_{\frac {1}{2}}^{(6)}}{d\alpha ^{2}}}=&1{,}667085\,;\end{alignedat}}$