Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/272

coefficients ${\rm {A}}_{2}^{(0)},{\rm {A}}_{1}^{(1)},{\rm {A}}_{2}^{(2)},\ldots$ J’ai supposé, conformément aux phénomènes des marées, la masse de la Lune ${\frac {1}{58{,}7}}$ de celle de la Terre. Cela posé, les équations entre ces coefficients, trouvées dans les n^os 10 et 14, deviennent

${\begin{aligned}{\rm {A_{2}^{(0)}=}}&0{,}00723508-0{,}005001814.\left({\rm {B_{1}^{(0)}-B_{2}^{(1)}}}\right),\\{\rm {A_{1}^{(1)}=}}&0{,}204044-0{,}0660894.{\rm {A_{2}^{(0)}-0{,}0480577.\left({\rm {B_{2}^{(5)}-{\rm {B_{2}^{(6)}}}}}\right),}}\\{\rm {A_{2}^{(2)}=}}&-0{,}00372953,\\{\rm {A_{2}^{(3)}=}}&-0{,}000315160-0{,}00449610.{\rm {B_{1}^{(9)},}}\\{\rm {A_{2}^{(4)}=}}&0{,}0289026-0{,}00564793.{\rm {B_{1}^{(10)},}}\\{\rm {A_{1}^{(6)}=}}&-0{,}193315+0{,}104996.{\rm {A_{1}^{(1)}+0{,}372796.A_{1}^{(9)},}}\\{\rm {A_{1}^{(7)}=}}&0{,}538027+0{,}0334044.{\rm {A_{1}^{(1)}+0{,}135144.A_{1}^{(8)},}}\\{\rm {A_{1}^{(8)}=}}&-0{,}0908432+0{,}139071.{\rm {A_{1}^{(1)}-0{,}280299.A_{1}^{(7)},}}\\{\rm {A_{1}^{(9)}=}}&0{,}0791193+1{,}055799.{\rm {A_{1}^{(1)}+0{,}270902.A_{1}^{(6)},}}\\{\rm {A_{2}^{(10)}=}}&0{,}00285368-0{,}00415018.{\rm {B_{0}^{(11)},}}\\{\rm {A_{1}^{(11)}=}}&0{,}366100-0{,}0172338.{\rm {A_{1}^{(1)}-0{,}259744.A_{2}^{(10)}-0{,}324680.(A_{1}^{(1)})^{2},}}\\{\rm {A_{2}^{(12)}=}}&0{,}00265066,\\{\rm {A_{1}^{(13)}=}}&0{,}0523335-1{,}555935.{\rm {B_{1}^{(0)}-0{,}220276.{\rm {A_{2}^{(12)},}}}}\\{\rm {A_{2}^{(14)}=}}&-0{,}0129890,\\{\rm {A_{0}^{(15)}=}}&-0{,}1007403+0{,}0385084.{\rm {A_{1}^{(1)}+2{,}09016.A_{1}^{(13)}}}\\&-1{,}022473.{\rm {A_{1}^{(16)}-36{,}11032.\left(B_{2}^{(3)}-B_{1}^{(0)}B_{2}^{(5)}\right),}}\\{\rm {A_{1}^{(16)}=}}&0,114623+0{,}166591.{\rm {A_{0}^{(15)}-5{,}07811.B_{2}^{(4)},}}\\{\rm {A_{1}^{(17)}=}}&-0{,}121028+0{,}937593.{\rm {A_{2}^{(0)}-0{,}000031563.A_{0}^{(18)}}}\\&-0{,}139767.\left({\rm {B_{2}^{(14)}+B_{2}^{(15)}}}\right),\\{\rm {A_{0}^{(18)}=}}&1{,}208124+1{,}018700.{\rm {A_{1}^{(17)}-5{,}074801.A_{1}^{(19)},}}\\{\rm {A_{1}^{(19)}=}}&-0{,}121295+0{,}675879.{\rm {A_{1}^{(17)}+0{,}183834.A_{0}^{(18)},}}\\{\rm {B_{1}^{(0)}=}}&0{,}0287031-0{,}0574772.{\rm {A_{2}^{(0)}+0{,}000432665.A_{1}^{(1)},}}\\{\rm {B_{2}^{(1)}=}}&-0{,}00000236395,\\{\rm {B_{2}^{(2)}=}}&-0{,}00564433+0{,}0048210.{\rm {B_{1}^{(0)},}}\\{\rm {B_{2}^{(3)}=}}&0{,}0166486+0{,}0166486.{\rm {A_{1}^{(1)}-0{,}0165194.B_{1}^{(0)},}}\end{aligned}}$