Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/102

Ensuite,

${\begin{alignedat}{3}b_{\frac {1}{2}}^{(0)}&=2{,}000823,\qquad &b_{\frac {1}{2}}^{(1)}&=0{,}040610,\qquad &b_{\frac {1}{2}}^{(2)}&=0{,}001236,\\b_{\frac {1}{2}}^{(3)}&=0{,}000042,&b_{\frac {1}{2}}^{(4)}&=0{,}000001,&&\,;\\\\{\frac {db_{\frac {1}{2}}^{(0)}}{d\alpha }}&=0{,}040662,&{\frac {db_{\frac {1}{2}}^{(1)}}{d\alpha }}&=1{,}001841,&{\frac {db_{\frac {1}{2}}^{(2)}}{d\alpha }}&=0{,}060919\,;\\\\{\frac {db_{\frac {1}{2}}^{(3)}}{d\alpha }}&=0{,}003085\,;&&&\\\\{\frac {d^{2}b_{\frac {1}{2}}^{(0)}}{d\alpha ^{2}}}&=1{,}003904,&{\frac {d^{2}b_{\frac {1}{2}}^{(1)}}{d\alpha ^{2}}}&=0{,}091840,&{\frac {d^{2}b_{\frac {1}{2}}^{(2)}}{d\alpha ^{2}}}&=1{,}469188.\end{alignedat}}$

mercure et uranus.

$\alpha ={\frac {a}{a^{\rm {vi}}}}=0{,}02017895,$

d’où l’on a conclu

${\begin{aligned}b_{-{\frac {1}{2}}}^{(0)}&=2{,}00020360,\\b_{-{\frac {1}{2}}}^{(1)}&=-0{,}02017792.\end{aligned}}$

Ensuite,

$b_{\frac {1}{2}}^{(0)}=2{,}000182,\qquad b_{\frac {1}{2}}^{(1)}=0{,}020183,\qquad b_{\frac {1}{2}}^{(2)}=0{,}000306\,;$

${\frac {db_{\frac {1}{2}}^{(0)}}{d\alpha }}=0{,}020196,\qquad {\frac {db_{\frac {1}{2}}^{(1)}}{d\alpha }}=1{,}000913.$

vénus et la terre.

$\alpha ={\frac {a'}{a''}}=0{,}72333230,$

d’où l’on a conclu

${\begin{aligned}b_{-{\frac {1}{2}}}^{(0)}&=2{,}27159162,\\b_{-{\frac {1}{2}}}^{(1)}&=-0{,}67226315.\end{aligned}}$