Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 4.djvu/133

$\delta v'=m\left\{{\begin{alignedat}{3}&-&6951''&{,}1660.\sin &(nt-n't+\varepsilon -\varepsilon ')\\&-&52''&{,}6315.\sin 2&(nt-n't+\varepsilon -\varepsilon ')\\&-&10''&{,}5253.\sin 3&(nt-n't+\varepsilon -\varepsilon ')\\&-&3''&{,}3448.\sin 4&(nt-n't+\varepsilon -\varepsilon ')\\&-&1''&{,}2969.\sin 5&(nt-n't+\varepsilon -\varepsilon ')\end{alignedat}}\right\}$

$+m''\left\{{\begin{alignedat}{3}&&184''&{,}5172.\sin &(n''t-n't+\varepsilon ''-\varepsilon ')\\&-&12108''&{,}9920.\sin 2&(n''t-n't+\varepsilon ''-\varepsilon ')\\&-&68''&{,}8828.\sin 3&(n''t-n't+\varepsilon ''-\varepsilon ')\\&-&15''&{,}7643.\sin 4&(n''t-n't+\varepsilon ''-\varepsilon ')\\&-&5''&{,}2597.\sin 5&(n''t-n't+\varepsilon ''-\varepsilon ')\\&-&2''&{,}0814.\sin 6&(n''t-n't+\varepsilon ''-\varepsilon ')\end{alignedat}}\right\}$

$+m'''\left\{{\begin{alignedat}{2}&&12''&{,}3755.\sin &(n'''t-n't+\varepsilon '''-\varepsilon ')\\&-&10''&{,}8356.\sin 2&(n'''t-n't+\varepsilon '''-\varepsilon ')\\&-&1''&{,}0646.\sin 3&(n'''t-n't+\varepsilon '''-\varepsilon ')\end{alignedat}}\right\}$

$+0''{,}5881.\sin(2n't-2{\rm {M}}t+2\varepsilon '-2{\rm {E),}}$

$\delta r'=m\left\{{\begin{aligned}&-0{,}00044608\\&+0{,}05069318.\cos \ \ (nt-n't+\varepsilon -\varepsilon ')\\&+0{,}00059197.\cos 2(nt-n't+\varepsilon -\varepsilon ')\\&+0{,}00014002.\cos 3(nt-n't+\varepsilon -\varepsilon ')\\&+0{,}00004784.\cos 4(nt-n't+\varepsilon -\varepsilon ')\\&+0{,}00001928.\cos 5(nt-n't+\varepsilon -\varepsilon ')\end{aligned}}\right\}$

$+m''\left\{{\begin{aligned}&0{,}00006497\\+&0{,}00073255.\cos \ \ (n''t-n't+\varepsilon ''-\varepsilon ')\\-&0{,}08670960.\cos 2(n''t-n't+\varepsilon ''-\varepsilon ')\\-&0{,}00063398.\cos 3(n''t-n't+\varepsilon ''-\varepsilon ')\\-&0{,}00016685.\cos 4(n''t-n't+\varepsilon ''-\varepsilon ')\\-&0{,}00006067.\cos 5(n''t-n't+\varepsilon ''-\varepsilon ')\end{aligned}}\right\}$