Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/106

Ensuite,

${\begin{alignedat}{3}b_{\frac {1}{2}}^{(0)}&=2{,}002886,\qquad &b_{\frac {1}{2}}^{(1)}&=0{,}076002,\qquad &b_{\frac {1}{2}}^{(2)}&=0{,}004323,\\b_{\frac {1}{2}}^{(3)}&=0{,}000273,&b_{\frac {1}{2}}^{(4)}&=0{,}000018\,;&&\\\\{\frac {db_{\frac {1}{2}}^{(0)}}{d\alpha }}&=0{,}076331,&{\frac {db_{\frac {1}{2}}^{(1)}}{d\alpha }}&=1{,}006490,&{\frac {db_{\frac {1}{2}}^{(2)}}{d\alpha }}&=0{,}114267,\\{\frac {db_{\frac {1}{2}}^{(3)}}{d\alpha }}&=0{,}011085,;&&&\\\\{\frac {d^{2}b_{\frac {1}{2}}^{(0)}}{d\alpha ^{2}}}&=1{,}019629,&{\frac {d^{2}b_{\frac {1}{2}}^{(1)}}{d\alpha ^{2}}}&=0{,}172510,&{\frac {d^{2}b_{\frac {1}{2}}^{(2)}}{d\alpha ^{2}}}&=1{,}419950\,;\\\\b_{\frac {1}{2}}^{(0)}&=2{,}026116,&b_{\frac {1}{2}}^{(1)}&=0{,}229988,&b_{\frac {1}{2}}^{(2)}&=0{,}021791.\end{alignedat}}$

vénus et uranus.

$\alpha ={\frac {a'}{a^{\rm {vi}}}}=0{,}03770634,$

d’où l’on a conclu

${\begin{aligned}b_{-{\frac {1}{2}}}^{(0)}&=2{,}00071095,\\b_{-{\frac {1}{2}}}^{(1)}&=-0{,}03769964.\end{aligned}}$

Ensuite,

${\begin{alignedat}{3}b_{\frac {1}{2}}^{(0)}&=2{,}000712,\qquad &b_{\frac {1}{2}}^{(1)}&=0{,}037725,\qquad &b_{\frac {1}{2}}^{(2)}&=0{,}001067,\\b_{\frac {1}{2}}^{(3)}&=0{,}000034\,;&&&&\\\\{\frac {db_{\frac {1}{2}}^{(0)}}{d\alpha }}&=0{,}716690,&{\frac {db_{\frac {1}{2}}^{(1)}}{d\alpha }}&=1{,}000829,&{\frac {db_{\frac {1}{2}}^{(2)}}{d\alpha }}&=0{,}056634.\end{alignedat}}$

la terre et mars.

$\alpha ={\frac {a''}{a'''}}=0{,}65630030,$

d’où l’on a conclu

${\begin{aligned}b_{-{\frac {1}{2}}}^{(0)}&=2{,}22192172,\\b_{-{\frac {1}{2}}}^{(1)}&=-0{,}61874262.\end{aligned}}$