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Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/102
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Ensuite,
b
1
2
(
0
)
=
2,000
823
,
b
1
2
(
1
)
=
0,040
610
,
b
1
2
(
2
)
=
0,001
236
,
b
1
2
(
3
)
=
0,000
042
,
b
1
2
(
4
)
=
0,000
001
,
;
d
b
1
2
(
0
)
d
α
=
0,040
662
,
d
b
1
2
(
1
)
d
α
=
1,001
841
,
d
b
1
2
(
2
)
d
α
=
0,060
919
;
d
b
1
2
(
3
)
d
α
=
0,003
085
;
d
2
b
1
2
(
0
)
d
α
2
=
1,003
904
,
d
2
b
1
2
(
1
)
d
α
2
=
0,091
840
,
d
2
b
1
2
(
2
)
d
α
2
=
1,469
188.
{\displaystyle {\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.
α
=
a
a
v
i
=
0,020
17895
,
{\displaystyle \alpha ={\frac {a}{a^{\rm {vi}}}}=0{,}02017895,}
d’où l’on a conclu
b
−
1
2
(
0
)
=
2,000
20360
,
b
−
1
2
(
1
)
=
−
0,020
17792.
{\displaystyle {\begin{aligned}b_{-{\frac {1}{2}}}^{(0)}&=2{,}00020360,\\b_{-{\frac {1}{2}}}^{(1)}&=-0{,}02017792.\end{aligned}}}
Ensuite,
b
1
2
(
0
)
=
2,000
182
,
b
1
2
(
1
)
=
0,020
183
,
b
1
2
(
2
)
=
0,000
306
;
{\displaystyle b_{\frac {1}{2}}^{(0)}=2{,}000182,\qquad b_{\frac {1}{2}}^{(1)}=0{,}020183,\qquad b_{\frac {1}{2}}^{(2)}=0{,}000306\,;}
d
b
1
2
(
0
)
d
α
=
0,020
196
,
d
b
1
2
(
1
)
d
α
=
1,000
913.
{\displaystyle {\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.
α
=
a
′
a
″
=
0,723
33230
,
{\displaystyle \alpha ={\frac {a'}{a''}}=0{,}72333230,}
d’où l’on a conclu
b
−
1
2
(
0
)
=
2,271
59162
,
b
−
1
2
(
1
)
=
−
0,672
26315.
{\displaystyle {\begin{aligned}b_{-{\frac {1}{2}}}^{(0)}&=2{,}27159162,\\b_{-{\frac {1}{2}}}^{(1)}&=-0{,}67226315.\end{aligned}}}