Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/112

mars et uranus.

$\alpha ={\frac {a'''}{a^{\rm {vi}}}}=0{,}07942807,$

d’où l’on a conclu

${\begin{aligned}b_{-{\frac {1}{2}}}^{(0)}&=2{,}00315565,\\b_{-{\frac {1}{2}}}^{(1)}&=-0{,}07936538.\end{aligned}}$

Ensuite,

${\begin{alignedat}{3}b_{\frac {1}{2}}^{(0)}&=2{,}003167,\qquad &b_{\frac {1}{2}}^{(1)}&=0{,}079617,\qquad &b_{\frac {1}{2}}^{(2)}&=0{,}004746,\\b_{\frac {1}{2}}^{(3)}&=0{,}000314,&b_{\frac {1}{2}}^{(4)}&=0{,}000022\,;\\\\{\frac {db_{\frac {1}{2}}^{(0)}}{d\alpha }}&=0{,}079995,&{\frac {db_{\frac {1}{2}}^{(1)}}{d\alpha }}&=1{,}007144,&{\frac {db_{\frac {1}{2}}^{(2)}}{d\alpha }}&=0{,}119822,\\{\frac {db_{\frac {1}{2}}^{(3)}}{d\alpha }}&=0{,}011982.\end{alignedat}}$

jupiter et saturne.

$\alpha ={\frac {a^{\rm {iv}}}{a^{\rm {v}}}}=0{,}54531725,$

d’où l’on a conclu

${\begin{aligned}b_{-{\frac {1}{2}}}^{(0)}&=2{,}1516824,\\b_{-{\frac {1}{2}}}^{(1)}&=-0{,}52421272.\end{aligned}}$

Ensuite,

${\begin{alignedat}{3}b_{\frac {1}{2}}^{(0)}&=2{,}1802348,\qquad &b_{\frac {1}{2}}^{(1)}&=0{,}6206406,\qquad &b_{\frac {1}{2}}^{(2)}&=0{,}2576379,\\b_{\frac {1}{2}}^{(3)}&=0{,}1179750,&b_{\frac {1}{2}}^{(4)}&=0{,}0565522,&b_{\frac {1}{2}}^{(5)}&=0{,}0278360,\\b_{\frac {1}{2}}^{(6)}&=0{,}0139345,&b_{\frac {1}{2}}^{(7)}&=0{,}0070481,&b_{\frac {1}{2}}^{(8)}&=0{,}0035837,\\b_{\frac {1}{2}}^{(9)}&=0{,}0018056,&b_{\frac {1}{2}}^{(10)}&=0{,}0008632,&b_{\frac {1}{2}}^{(11)}&=0{,}0003223\,;\end{alignedat}}$