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:
Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/109
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d’où l’on a conclu
b
−
1
2
(
0
)
=
2,005
50004
,
b
−
1
2
(
1
)
=
−
0,104
70094.
{\displaystyle {\begin{aligned}b_{-{\frac {1}{2}}}^{(0)}&=2{,}00550004,\\b_{-{\frac {1}{2}}}^{(1)}&=-0{,}10470094.\end{aligned}}}
Ensuite,
b
1
2
(
0
)
=
2,005
535
,
b
1
2
(
1
)
=
0,105
283
,
b
1
2
(
2
)
=
0,008
282
,
b
1
2
(
3
)
=
0,000
724
,
b
1
2
(
4
)
=
0,000
066
;
d
b
1
2
(
0
)
d
α
=
0,106
155
,
d
b
1
2
(
1
)
d
α
=
1,012
536
,
d
b
1
2
(
2
)
d
α
=
0,158
723
,
d
b
1
2
(
3
)
d
α
=
0,020
779
;
d
2
b
1
2
(
0
)
d
α
2
=
1,037
816
,
d
2
b
1
2
(
1
)
d
α
2
=
0,246
193
,
d
2
b
1
2
(
2
)
d
α
2
=
1,526
303
;
b
3
2
(
0
)
=
2,050
321
,
b
3
2
(
1
)
=
0,321
144
,
b
3
2
(
2
)
=
0,041
977.
{\displaystyle {\begin{alignedat}{3}b_{\frac {1}{2}}^{(0)}&=2{,}005535,\qquad &b_{\frac {1}{2}}^{(1)}&=0{,}105283,\qquad &b_{\frac {1}{2}}^{(2)}&=0{,}008282,\\b_{\frac {1}{2}}^{(3)}&=0{,}000724,&b_{\frac {1}{2}}^{(4)}&=0{,}000066\,;&&\\\\{\frac {db_{\frac {1}{2}}^{(0)}}{d\alpha }}&=0{,}106155,&{\frac {db_{\frac {1}{2}}^{(1)}}{d\alpha }}&=1{,}012536,&{\frac {db_{\frac {1}{2}}^{(2)}}{d\alpha }}&=0{,}158723,\\{\frac {db_{\frac {1}{2}}^{(3)}}{d\alpha }}&=0{,}020779\,;\\\\{\frac {d^{2}b_{\frac {1}{2}}^{(0)}}{d\alpha ^{2}}}&=1{,}037816,&{\frac {d^{2}b_{\frac {1}{2}}^{(1)}}{d\alpha ^{2}}}&=0{,}246193,&{\frac {d^{2}b_{\frac {1}{2}}^{(2)}}{d\alpha ^{2}}}&=1{,}526303\,;\\\\b_{\frac {3}{2}}^{(0)}&=2{,}050321,&b_{\frac {3}{2}}^{(1)}&=0{,}321144,&b_{\frac {3}{2}}^{(2)}&=0{,}041977.\end{alignedat}}}
la terre et uranus.
α
=
a
″
a
v
i
=
0,052
12866
,
{\displaystyle \alpha ={\frac {a''}{a^{\rm {vi}}}}=0{,}05212866,}
d’où l’on a conclu
b
−
1
2
(
0
)
=
2,001
35893
,
b
−
1
2
(
1
)
=
−
0,052
11095.
{\displaystyle {\begin{aligned}b_{-{\frac {1}{2}}}^{(0)}&=2{,}00135893,\\b_{-{\frac {1}{2}}}^{(1)}&=-0{,}05211095.\end{aligned}}}
Ensuite,
b
1
2
(
0
)
=
2,001
355
,
b
1
2
(
1
)
=
0,052
182
,
b
1
2
(
2
)
=
0,002
040
,
b
1
2
(
3
)
=
0,000
089
;
d
b
1
2
(
0
)
d
α
=
0,052
288
,
d
b
1
2
(
1
)
d
α
=
1,003
060
,
d
b
1
2
(
2
)
d
α
=
0,078
449.
{\displaystyle {\begin{alignedat}{3}b_{\frac {1}{2}}^{(0)}&=2{,}001355,\qquad &b_{\frac {1}{2}}^{(1)}&=0{,}052182,\qquad &b_{\frac {1}{2}}^{(2)}&=0{,}002040,\\b_{\frac {1}{2}}^{(3)}&=0{,}000089\,;\\\\{\frac {db_{\frac {1}{2}}^{(0)}}{d\alpha }}&=0{,}052288,&{\frac {db_{\frac {1}{2}}^{(1)}}{d\alpha }}&=1{,}003060,&{\frac {db_{\frac {1}{2}}^{(2)}}{d\alpha }}&=0{,}078449.\end{alignedat}}}