Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/135

109

SECONDE PARTIE. — LIVRE VI.

on peut donc négliger les inégalités de $\partial r''$ dont le coefficient est au-dessous de $\pm 0,000001.$ Nous négligerons les inégalités du mouvement de la Terre en longitude, au-dessous d’un quart de seconde.

Inégalités de la Terre indépendantes des excentricités.

$\partial \nu ''=(1+\mu ')\left\{{\begin{aligned}16'',&329870.\sin \ \ (n't-n''t+\varepsilon '-\varepsilon '')\\-18'',&567565.\sin 2(n't-n''t+\varepsilon '-\varepsilon '')\\-2'',&294582.\sin 3(n't-n''t+\varepsilon '-\varepsilon '')\\-0'',&695799.\sin 4(n't-n''t+\varepsilon '-\varepsilon '')\\-0'',&281511.\sin 5(n't-n''t+\varepsilon '-\varepsilon '')\\-0'',&132113.\sin 6(n't-n''t+\varepsilon '-\varepsilon '')\\-0'',&067984.\sin 7(n't-n''t+\varepsilon '-\varepsilon '')\\-0'',&037202.\sin 8(n't-n''t+\varepsilon '-\varepsilon '')\\\end{aligned}}\right\}$

$+(1+\mu ''')\left\{{\begin{aligned}1'',&318563.\sin \ \ (n'''t-n''t+\varepsilon '''-\varepsilon '')\\+10'',&750115.\sin 2(n'''t-n''t+\varepsilon '''-\varepsilon '')\\-0'',&664350.\sin 3(n'''t-n''t+\varepsilon '''-\varepsilon '')\\-0'',&145130.\sin 4(n'''t-n''t+\varepsilon '''-\varepsilon '')\\-0'',&048984.\sin 5(n'''t-n''t+\varepsilon '''-\varepsilon '')\\-0'',&019931.\sin 6(n'''t-n''t+\varepsilon '''-\varepsilon '')\\-0'',&009022.\sin 7(n'''t-n''t+\varepsilon '''-\varepsilon '')\\\end{aligned}}\right\}$

$+(1+\mu ^{\text{ıv}})\left\{{\begin{aligned}21'',&787201.\sin \ \ (n^{\text{ıv}}t-n''t+\varepsilon ^{\text{ıv}}-\varepsilon '')\\-8'',&253880.\sin 2(n^{\text{ıv}}t-n''t+\varepsilon ^{\text{ıv}}-\varepsilon '')\\-0'',&517808.\sin 3(n^{\text{ıv}}t-n''t+\varepsilon ^{\text{ıv}}-\varepsilon '')\\-0'',&051076.\sin 4(n^{\text{ıv}}t-n''t+\varepsilon ^{\text{ıv}}-\varepsilon '')\\\end{aligned}}\right\}$

$+(1+\mu ^{\mathrm {v} })\left\{{\begin{aligned}1'',&356204.\sin \ \ (n^{\mathrm {v} }t-n''t+\varepsilon ^{\mathrm {v} }-\varepsilon '')\\-0'',&342623.\sin 2(n^{\mathrm {v} }t-n''t+\varepsilon ^{\mathrm {v} }-\varepsilon '')\\-0'',&012792.\sin 3(n^{\mathrm {v} }t-n''t+\varepsilon ^{\mathrm {v} }-\varepsilon '')\\\end{aligned}}\right\}$

$\partial r''=(1+\mu ')\left\{{\begin{aligned}0,&0000015553\\-0,&0000060012.\cos(n't-n''t+\varepsilon '-\varepsilon '')\\+0,&0000171431.\cos 2(n't-n''t+\varepsilon '-\varepsilon '')\\+0,&0000027072.\cos 3(n't-n''t+\varepsilon '-\varepsilon '')\\+0,&0000009358.\cos 4(n't-n''t+\varepsilon '-\varepsilon '')\\+0,&0000004086.\cos 5(n't-n''t+\varepsilon '-\varepsilon '')\\+0,&0000002008.\cos 6(n't-n''t+\varepsilon '-\varepsilon '')\\\end{aligned}}\right\}$