Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/105

vénus et jupiter.

$\alpha ={\frac {a'}{a^{\rm {iv}}}}=0{,}13907116,$

d’où l’on a conclu

${\begin{aligned}b_{-{\frac {1}{2}}}^{(0)}&=2{,}00968215,\\b_{-{\frac {1}{2}}}^{(1)}&=-0{,}13873412.\end{aligned}}$

Ensuite,

${\begin{alignedat}{3}b_{\frac {1}{2}}^{(0)}&=2{,}009778,\qquad &b_{\frac {1}{2}}^{(1)}&=0{,}140092,\qquad &b_{\frac {1}{2}}^{(2)}&=0{,}014623,\\b_{\frac {1}{2}}^{(3)}&=0{,}001695,&b_{\frac {1}{2}}^{(4)}&=0{,}000206,&b_{\frac {1}{2}}^{(5)}&=0{,}000026\,;\\\\{\frac {db_{\frac {1}{2}}^{(0)}}{d\alpha }}&=0{,}142160,&{\frac {db_{\frac {1}{2}}^{(1)}}{d\alpha }}&=1{,}022206,&{\frac {db_{\frac {1}{2}}^{(2)}}{d\alpha }}&=0{,}212046,\\{\frac {db_{\frac {1}{2}}^{(3)}}{d\alpha }}&=0{,}036783,&{\frac {db_{\frac {1}{2}}^{(4)}}{d\alpha }}&=0{,}006111\,;&&\\\\{\frac {d^{2}b_{\frac {1}{2}}^{(0)}}{d\alpha ^{2}}}&=1{,}067532,&{\frac {d^{2}b_{\frac {1}{2}}^{(1)}}{d\alpha ^{2}}}&=0{,}325869,&{\frac {d^{2}b_{\frac {1}{2}}^{(2)}}{d\alpha ^{2}}}&=1{,}575190,\\{\frac {d^{2}b_{\frac {1}{2}}^{(3)}}{d\alpha ^{2}}}&=0{,}533951\,;\\\\b_{\frac {3}{2}}^{(0)}&=2{,}089736,&b_{\frac {3}{2}}^{(1)}&=0{,}432801,&b_{\frac {3}{2}}^{(2)}&=0{,}075054.\end{alignedat}}$

vénus et saturne.

$\alpha ={\frac {a'}{a^{\rm {v}}}}=0{,}07583790,$

d’où l’on a conclu

${\begin{aligned}b_{-{\frac {1}{2}}}^{(0)}&=2{,}00287673,\\b_{-{\frac {1}{2}}}^{(1)}&=-0{,}07578334.\end{aligned}}$