Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/179

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SECONDE PARTIE. — LIVRE VI.

$+\left(1+\mu ^{\mathrm {v} }\right)\left\{{\begin{aligned}&\,\quad 65'',961045.\sin \ \ \left(n^{\mathrm {v} }t-n^{\text{vı}}t+\varepsilon ^{\mathrm {v} }-\varepsilon ^{\text{vı}}\right)\\&-13'',027691.\sin 2\left(n^{\mathrm {v} }t-n^{\text{vı}}t+\varepsilon ^{\mathrm {v} }-\varepsilon ^{\text{vı}}\right)\\&-\ \ 2'',660850.\sin 3\left(n^{\mathrm {v} }t-n^{\text{vı}}t+\varepsilon ^{\mathrm {v} }-\varepsilon ^{\text{vı}}\right)\\&-\ \ 0'',754350.\sin 4\left(n^{\mathrm {v} }t-n^{\text{vı}}t+\varepsilon ^{\mathrm {v} }-\varepsilon ^{\text{vı}}\right)\\&-\ \ 0'',247564.\sin 5\left(n^{\mathrm {v} }t-n^{\text{vı}}t+\varepsilon ^{\mathrm {v} }-\varepsilon ^{\text{vı}}\right)\\&-\ \ 0'',089294.\sin 6\left(n^{\mathrm {v} }t-n^{\text{vı}}t+\varepsilon ^{\mathrm {v} }-\varepsilon ^{\text{vı}}\right)\\&-\ \ 0'',033731.\sin 7\left(n^{\mathrm {v} }t-n^{\text{vı}}t+\varepsilon ^{\mathrm {v} }-\varepsilon ^{\text{vı}}\right)\\&-\ \ 0'',012801.\sin 8\left(n^{\mathrm {v} }t-n^{\text{vı}}t+\varepsilon ^{\mathrm {v} }-\varepsilon ^{\text{vı}}\right)\end{aligned}}\right\},$

$\partial r^{\text{vı}}=\left(1+\mu ^{\text{ıv}}\right)\left\{{\begin{aligned}&\quad 0,0063473160\\&+0,0048914790.\cos \ \ \left(n^{\text{ıv}}t-n^{\text{vı}}t+\varepsilon ^{\text{ıv}}-\varepsilon ^{\text{vı}}\right)\\&+0,0000236184.\cos 2\left(n^{\text{ıv}}t-n^{\text{vı}}t+\varepsilon ^{\text{ıv}}-\varepsilon ^{\text{vı}}\right)\\&+0,0000030669.\cos 3\left(n^{\text{ıv}}t-n^{\text{vı}}t+\varepsilon ^{\text{ıv}}-\varepsilon ^{\text{vı}}\right)\\&+0,0000005044.\cos 4\left(n^{\text{ıv}}t-n^{\text{vı}}t+\varepsilon ^{\text{ıv}}-\varepsilon ^{\text{vı}}\right)\end{aligned}}\right\}$

$+\left(1+\mu ^{\mathrm {v} }\right)\left\{{\begin{aligned}&\quad 0,0023641285\\&+0,0035433901.\cos \left(n^{\mathrm {v} }t-n^{\text{vı}}t+\varepsilon ^{\mathrm {v} }-\varepsilon ^{\text{vı}}\right)\\&+0,0004061682.\cos 2\left(n^{\mathrm {v} }t-n^{\text{vı}}t+\varepsilon ^{\mathrm {v} }-\varepsilon ^{\text{vı}}\right)\\&+0,0000889425.\cos 3\left(n^{\mathrm {v} }t-n^{\text{vı}}t+\varepsilon ^{\mathrm {v} }-\varepsilon ^{\text{vı}}\right)\\&+0,0000255870.\cos 4\left(n^{\mathrm {v} }t-n^{\text{vı}}t+\varepsilon ^{\mathrm {v} }-\varepsilon ^{\text{vı}}\right)\end{aligned}}\right\}.$

Inégalités dépendantes de la première puissance des excentricités.

$\partial \nu ^{\text{vı}}=\left(1+\mu ^{\text{ıv}}\right)\left\{{\begin{aligned}&-\,\ 3'',807443.\sin \left(n^{\text{ıv}}t+\varepsilon ^{\text{ıv}}-\varpi ^{\text{vı}}\right)\\&+\,\ 3'',887493.\sin \left(2n^{\text{ıv}}t-n^{\text{vı}}t+2\varepsilon ^{\text{ıv}}-\varepsilon ^{\text{vı}}-\varpi ^{\text{ıv}}\right)\\&-11'',224270.\sin \left(2n^{\text{vı}}t-n^{\text{ıv}}t+2\varepsilon ^{\text{vı}}-\varepsilon ^{\text{ıv}}-\varpi ^{\text{vı}}\right)\\&-\,\ 0'',685175.\sin \left(2n^{\text{vı}}t-n^{\text{ıv}}t+2\varepsilon ^{\text{vı}}-\varepsilon ^{\text{ıv}}-\varpi ^{\text{ıv}}\right)\end{aligned}}\right\}$

$+\left(1+\mu ^{\mathrm {v} }\right)\left\{{\begin{aligned}&-4'',328267.\sin \left(n^{\mathrm {v} }t+\varepsilon ^{\mathrm {v} }-\varpi ^{\text{vı}}\right)\\&-0'',663139.\sin \left(n^{\mathrm {v} }t+\varepsilon ^{\mathrm {v} }-\varpi ^{\text{vı}}\right)\\&-0'',678358.\sin \left(2n^{\mathrm {v} }t-n^{\text{vı}}t+2\varepsilon ^{\mathrm {v} }-\varepsilon ^{\text{vı}}-\varpi ^{\text{vı}}\right)\\&-2'',712230.\sin \left(2n^{\mathrm {v} }t-n^{\text{vı}}t+2\varepsilon ^{\mathrm {v} }-\varepsilon ^{\text{vı}}-\varpi ^{\text{vı}}\right)\\&-\left(135'',961650-t.0'',000761\right)\sin \left(2n^{\text{vı}}t-n^{\mathrm {v} }t+2\varepsilon ^{\text{vı}}-\varepsilon ^{\mathrm {v} }-\varpi ^{\text{vı}}\right)\\&+\left(462'',369642-t.0'',025635\right)\sin \left(2n^{\text{vı}}t-n^{\mathrm {v} }t+2\varepsilon ^{\text{vı}}-\varepsilon ^{\mathrm {v} }-\varpi ^{\text{vı}}\right)\\&+7'',673429.\sin \left(3n^{\text{vı}}t-2n^{\mathrm {v} }t+3\varepsilon ^{\text{vı}}-2\varepsilon ^{\mathrm {v} }-\varpi ^{\text{vı}}\right)\\&-5'',069294.\sin \left(3n^{\text{vı}}t-2n^{\mathrm {v} }t+3\varepsilon ^{\text{vı}}-2\varepsilon ^{\mathrm {v} }-\varpi ^{\mathrm {v} }\right)\\&+1'',304718.\sin \left(4n^{\text{vı}}t-3n^{\mathrm {v} }t+4\varepsilon ^{\text{vı}}-3\varepsilon ^{\mathrm {v} }-\varpi ^{\text{vı}}\right)\\&-0'',869752.\sin \left(4n^{\text{vı}}t-3n^{\mathrm {v} }t+4\varepsilon ^{\text{vı}}-3\varepsilon ^{\mathrm {v} }-\varpi ^{\mathrm {v} }\right)\\&+0'',390410.\sin \left(5n^{\text{vı}}t-4n^{\mathrm {v} }t+5\varepsilon ^{\text{vı}}-4\varepsilon ^{\mathrm {v} }-\varpi ^{\text{vı}}\right)\end{aligned}}\right\},$

$\partial r^{\text{vı}}=\left(1+\mu ^{\mathrm {v} }\right)\left\{{\begin{aligned}&+0,0016092001.\cos \left(2n^{\text{vı}}t-n^{\mathrm {v} }t+2\varepsilon ^{\text{vı}}-\varepsilon ^{\mathrm {v} }-\varpi ^{\text{vı}}\right)\\&+0,0061835858.\cos \left(2n^{\text{vı}}t-n^{\mathrm {v} }t+2\varepsilon ^{\text{vı}}-\varepsilon ^{\mathrm {v} }-\varpi ^{\text{vı}}\right)\end{aligned}}\right\}.$