Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 4.djvu/138

${\begin{alignedat}{3}(0,\ 1)=&m'\ .&39826''&{,}00,\qquad &{\begin{array}{|c|}\hline 0,\ 1\\\hline \end{array}}=&m'\ .29516''{,}02,\\(0,\ 2)=&m''\,.&5205''&{,}05,&{\begin{array}{|c|}\hline 0,\ 2\\\hline \end{array}}=&m''\,.2511''{,}39,\\(0,\ 3)=&m'''.&767''&{,}12,&{\begin{array}{|c|}\hline 0,\ 3\\\hline \end{array}}=&m'''.213''{,}46\,;\\\\(1,\ 0)=&m\ \ .&31573''&{,}71,&{\begin{array}{|c|}\hline 1,\ 0\\\hline \end{array}}=&m\ \ .23400''{,}04,\\(1,\ 2)=&m''\,.&19566''&{,}65,&{\begin{array}{|c|}\hline 1,\ 2\\\hline \end{array}}=&m''\,.14469''{,}66,\\(1,\ 3)=&m'''.&1804''&{,}18,&{\begin{array}{|c|}\hline 1,\ 3\\\hline \end{array}}=&m'''.790''{,}56\,;\\\\(2,\ 0)=&m\ \ .&3267''&{,}32,&{\begin{array}{|c|}\hline 2,\ 0\\\hline \end{array}}=&m\ \ .1576''{,}46,\\(2,\ 1)=&m'\ .&15492''&{,}62,&{\begin{array}{|c|}\hline 2,\ 1\\\hline \end{array}}=&m'\ .11456''{,}90,\\(2,\ 3)=&m'''.&5886''&{,}85,&{\begin{array}{|c|}\hline 2,\ 3\\\hline \end{array}}=&m'''.3995''{,}03\,;\\\\(3,\ 0)=&m\ \ .&363''&{,}09,&{\begin{array}{|c|}\hline 3,\ 0\\\hline \end{array}}=&m\ \ .101''{,}03,\\(3,\ 1)=&m'\ .&1077''&{,}15,&{\begin{array}{|c|}\hline 3,\ 1\\\hline \end{array}}=&m'\ .471''{,}99,\\(3,\ 2)=&m''\,.&4438''&{,}87,&{\begin{array}{|c|}\hline 3,\ 2\\\hline \end{array}}=&m''\,.3012''{,}37\,;\end{alignedat}}$

Les équations (V) du n^o 17 deviennent ainsi

$0=(g-553878''{,}78.\mu -103''{,}27-39826''{,}00.m'-5205''{,}05.m''$

$-767''{,}12.m''')h$

$+29516''{,}02.m'h'+2511''{,}39.m''h''+213''{,}46.m'''h'''$

$+{\frac {\left({\begin{aligned}&-(688803''.m+436089''.m')m'h\\&+(250103''.m+158343''.m'-213931''.m'')m'h'\\&+78234''.m'm''h''\end{aligned}}\right)}{\left(1+{\cfrac {g}{3001300''}}\right)^{2}}}$

$0=(g-109003''{,}20.\mu -207''{,}29-31573''{,}71.m-19566''{,}65.m''$

$-1804''{,}18.m''')h'$

$+23400''{,}04.mh+11469''{,}66.m''h''+790''{,}56.m'''h'''$

$+{\frac {(226503''{,}.m+143201''{,}.mm'-196037''.m'')mh}{\left(1+{\cfrac {g}{3001300''}}\right)^{2}}}$

$-{\frac {\left({\begin{aligned}&82242''.m^{2}+52068''.mm'-140696''.mm''\\&+94603''.m'm''+60174''.m''^{2}\end{aligned}}\right)h'}{\left(1+{\cfrac {g}{3001300''}}\right)^{2}}}$

$+{\frac {-25726''.m+34596''.m'+22518''.m''}{\left(1+{\cfrac {g}{3001300''}}\right)^{2}}}$