Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/98

${\begin{alignedat}{3}{\frac {d^{3}b_{\frac {1}{2}}^{(0)}}{d\alpha ^{3}}}&=11{,}308703,\qquad &{\frac {d^{3}b_{\frac {1}{2}}^{(1)}}{d\alpha ^{3}}}&=12{,}06445,\qquad &{\frac {d^{3}b_{\frac {1}{2}}^{(2)}}{d\alpha ^{3}}}&=11{,}983424,\\{\frac {d^{3}b_{\frac {1}{2}}^{(3)}}{d\alpha ^{3}}}&=14{,}584366,&{\frac {d^{3}b_{\frac {1}{2}}^{(4)}}{d\alpha ^{3}}}&=16{,}067040,&{\frac {d^{3}b_{\frac {1}{2}}^{(5)}}{d\alpha ^{3}}}&=15{,}617274,\\{\frac {d^{3}b_{\frac {1}{2}}^{(6)}}{d\alpha ^{3}}}&=13{,}720218\,;&&&&\\\\{\frac {d^{4}b_{\frac {1}{2}}^{(2)}}{d\alpha ^{4}}}&=69{,}60594,&{\frac {d^{4}b_{\frac {1}{2}}^{(3)}}{d\alpha ^{4}}}&=82{,}36773,&{\frac {d^{4}b_{\frac {1}{2}}^{(4)}}{d\alpha ^{4}}}&=92{,}72610,\\{\frac {d^{4}b_{\frac {1}{2}}^{(5)}}{d\alpha ^{4}}}&=105{,}33962\,;&&\\\\b_{\frac {3}{2}}^{(0)}&=4{,}214154,&b_{\frac {3}{2}}^{(1)}&=3{,}035376,&b_{\frac {3}{2}}^{(2)}&=1{,}950536,\\b_{\frac {3}{2}}^{(3)}&=1{,}192372,&b_{\frac {3}{2}}^{(4)}&=0{,}708667,&b_{\frac {3}{2}}^{(5)}&=0{,}413762,\\b_{\frac {3}{2}}^{(6)}&=0{,}238807;&&\\\\{\frac {db_{\frac {3}{2}}^{(2)}}{d\alpha }}&=12{,}50630,&{\frac {db_{\frac {3}{2}}^{(3)}}{d\alpha }}&=9{,}76666,&{\frac {db_{\frac {3}{2}}^{(4)}}{d\alpha }}&=7{,}08399,\\{\frac {db_{\frac {3}{2}}^{(5)}}{d\alpha }}&=4{,}88781\,;&&\end{alignedat}}$

${\frac {d^{2}b_{\frac {3}{2}}^{(3)}}{d\alpha ^{2}}}=78{,}09476,\qquad {\frac {d^{2}b_{\frac {3}{2}}^{(3)}}{d\alpha ^{2}}}=67{,}14764.$

mercure et la terre.

$\alpha ={\frac {a}{a''}}=0{,}38709812,$

d’où l’on a conclu

${\begin{aligned}b_{-{\frac {1}{2}}}^{(0)}=&\quad 2{,}07565247,\\b_{-{\frac {1}{2}}}^{(1)}=&-0{,}37970591.\end{aligned}}$