Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/108

la terre et jupiter.

$\alpha ={\frac {a''}{a^{\rm {iv}}}}=0{,}19226461,$

d’où l’on a conclu

${\begin{aligned}b_{-{\frac {1}{2}}}^{(0)}&=\quad 2{,}01852593,\\b_{-{\frac {1}{2}}}^{(1)}&=-0{,}19137205.\end{aligned}}$

Ensuite,

${\begin{alignedat}{3}b_{\frac {1}{2}}^{(0)}&=2{,}018885,\qquad &b_{\frac {1}{2}}^{(1)}&=0{,}195003,\qquad &b_{\frac {1}{2}}^{(2)}&=0{,}028195,\\b_{\frac {1}{2}}^{(3)}&=0{,}004516,&b_{\frac {1}{2}}^{(4)}&=0{,}000779,&b_{\frac {1}{2}}^{(5)}&=0{,}000132,\\b_{\frac {1}{2}}^{(6)}&=0{,}000023\,;&&&&\\\\{\frac {db_{\frac {1}{2}}^{(0)}}{d\alpha }}&=0{,}200586,&{\frac {db_{\frac {1}{2}}^{(1)}}{d\alpha }}&=1{,}043204,&{\frac {db_{\frac {1}{2}}^{(2)}}{d\alpha }}&=0{,}297995,\\{\frac {db_{\frac {1}{2}}^{(3)}}{d\alpha }}&=0{,}070932,&{\frac {db_{\frac {1}{2}}^{(4)}}{d\alpha }}&=0{,}016369,&{\frac {db_{\frac {1}{2}}^{(5)}}{d\alpha }}&=0{,}003448,;\\\\{\frac {d^{2}b_{\frac {1}{2}}^{(0)}}{d\alpha ^{2}}}&=1{,}132355,&{\frac {d^{2}b_{\frac {1}{2}}^{(1)}}{d\alpha ^{2}}}&=0{,}466165,&{\frac {d^{2}b_{\frac {1}{2}}^{(2)}}{d\alpha ^{2}}}&=1{,}628667,\\{\frac {d^{2}b_{\frac {1}{2}}^{(3)}}{d\alpha ^{2}}}&=0{,}746681\,;&&&&\\\\{\frac {d^{3}b_{\frac {1}{2}}^{(0)}}{d\alpha ^{3}}}&=1{,}472714,&{\frac {d^{3}b_{\frac {1}{2}}^{(1)}}{d\alpha ^{3}}}&=2{,}874986,&{\frac {d^{3}b_{\frac {1}{2}}^{(2)}}{d\alpha ^{3}}}&=1{,}418830\,;\\\\b_{\frac {3}{2}}^{(0)}&=2{,}176460,&b_{\frac {3}{2}}^{(1)}&=0{,}619063,&b_{\frac {3}{2}}^{(2)}&=0{,}148198,\\b_{\frac {3}{2}}^{(3)}&=0{,}032439.&&&&\\\\\end{alignedat}}$

la terre et saturne.

$\alpha ={\frac {a''}{a^{\rm {v}}}}=0{,}10484520,$