Page:Mémoires de l’Académie des sciences, Tome 3.djvu/291

On aura ainsi les quatre équations suivantes :

$411^{\mathrm {m} }{,}359=63{,}546581.1{,}022486.2\mathrm {A} '.{\frac {\mathrm {L'} }{r^{'3}}}+63{,}632467.2\mathrm {A} .{\frac {\mathrm {L} }{r^{3}}}$

$-3{,}333442.2(\mathrm {A'-B} ).1{,}022486.{\frac {\mathrm {L'} }{r^{'3}}}-4{,}685805.2(\mathrm {A-B} ).{\frac {\mathrm {L} }{r^{3}}};\quad (1)$

$367^{\mathrm {m} }{,}468=56{,}879696.1{,}022486.2\mathrm {A} '.{\frac {\mathrm {L'} }{r^{'3}}}+54{,}260856.2A.{\frac {\mathrm {L} }{r^{3}}}$

$+3{,}333442.2(\mathrm {A'-B} ).1{,}022486.{\frac {\mathrm {L'} }{r^{'3}}}+4{,}685805.2(\mathrm {A-B} ).{\frac {\mathrm {L} }{r^{3}}};\quad (2)$

${\begin{aligned}160^{\mathrm {m} }{,}850=56{,}962913.&0{,}977514.2\mathrm {A} '.{\frac {\mathrm {L'} }{r^{'3}}}-63{,}635484.2\mathrm {A} .{\frac {\mathrm {L} }{r^{3}}}\\+&3{,}267165.0{,}977514.2(A'-B).{\frac {\mathrm {L'} }{r^{'3}}};\\+&4{,}667171.2(\mathrm {A-B} ).{\frac {\mathrm {L} }{r^{3}}};\quad (3)\end{aligned}}$

$203^{\mathrm {m} }{,}948=63{,}497242.0{,}977514.2\mathrm {A} '.{\frac {\mathrm {L'} }{r^{'3}}}-54{,}301142.2\mathrm {A} .{\frac {\mathrm {L} }{r^{3}}}$

$-3{,}267165.0{,}977514.2(\mathrm {A'-B} ).{\frac {\mathrm {L'} }{r^{'3}}}-4{,}667171.2(\mathrm {A-B} ).{\frac {\mathrm {L} }{r^{3}}};\quad (4)$

Dans toutes ces équations, les valeurs ${\frac {\mathrm {L'} }{r^{'3}}}$ et ${\frac {\mathrm {L} }{r^{3}}}$ sont relatives aux moyennes distances de la lune et du soleil à la terre.

Le système $+(1)+(2)$ des équations précédentes, donne

$778^{\mathrm {m} }{,}708=120{,}426277.1{,}022486.2\mathrm {A} '.{\frac {\mathrm {L'} }{r^{'3}}}+117{,}893323.2\mathrm {A} .{\frac {\mathrm {L} }{r^{3}}};\quad (5)$

Le système des équations $+(3)+(4),$ donne

$364^{\mathrm {m} }{,}798=120{,}460155.0{,}977514.2\mathrm {A} '.{\frac {\mathrm {L'} }{r^{'3}}}-117{,}936626.2\mathrm {A} .{\frac {\mathrm {L} }{r^{3}}};\quad (6)$

De ces deux équations, on tire

$2\mathrm {A} '.{\frac {\mathrm {L'} }{r^{'3}}}=4^{\mathrm {m} }{,}74788;\qquad 2\mathrm {A} .{\frac {\mathrm {L} }{r^{3}}}=1^{\mathrm {m} }{,}64658.$