Page:Joseph Louis de Lagrange - Œuvres, Tome 5.djvu/454

${\begin{alignedat}{2}(3)=&0{,}080402\qquad \qquad &\log .\quad &8{,}9052669,\\(4)=&0{,}023346&&8{,}3682125,\\\ldots \ldots &\ldots \ldots \ldots &&\ldots \ldots \ldots \ldots ,\end{alignedat}}$

ensuite

${\begin{alignedat}{2}r''[r'',r^{\scriptscriptstyle {\text{V}}}]\ \,=&1{,}016747\qquad \qquad &\log .\quad &0{,}0072129,\\r''[r'',r^{\scriptscriptstyle {\text{V}}}]_{1}=&0{,}260461&&9{,}4157422,\\r''[r'',r^{\scriptscriptstyle {\text{V}}}]_{2}=&0{,}049762&&8{,}6968923,\\r''[r'',r^{\scriptscriptstyle {\text{V}}}]_{3}=&0{,}010533&&8{,}0225428,\\r''[r'',r^{\scriptscriptstyle {\text{V}}}]_{4}=&0{,}002286&&7{,}3590238,\\\ldots \ldots \ldots \ldots &\ldots \ldots \ldots &&\ldots \ldots \ldots ,\end{alignedat}}$

enfin

${\begin{alignedat}{2}2r''{\frac {d[r'',r^{\scriptscriptstyle {\text{V}}}]}{dr''}}\ \,=&-2{,}103063\qquad \qquad &\log .\quad &{\overline {0}}{,}3228523,\\2r''{\frac {d[r'',r^{\scriptscriptstyle {\text{V}}}]_{1}}{dr''}}=&-1{,}068583&&{\overline {0}}{,}0288080,\\2r''{\frac {d[r'',r^{\scriptscriptstyle {\text{V}}}]_{2}}{dr''}}=&-0{,}304298&&{\overline {9}}{,}4832991,\\2r''{\frac {d[r'',r^{\scriptscriptstyle {\text{V}}}]_{3}}{dr''}}=&-0{,}085746&&{\overline {8}}{,}9332139,\\2r''{\frac {d[r'',r^{\scriptscriptstyle {\text{V}}}]_{4}}{dr''}}=&-0{,}024125&&{\overline {8}}{,}3824673,\\\ldots \ldots \ldots \ldots \ldots &\ldots \ldots \ldots \ldots &&\ldots \ldots \ldots .\end{alignedat}}$

19. Or, $n$ étant égal à $1-{\frac {1}{z^{\frac {3}{2}}}},$ on aura

$n=-6{,}809280\,;$

et ces substitutions donneront la formule

$-\mathrm {T} ^{\scriptscriptstyle {\text{V}}}\left[0{,}247740\sin(p''-p^{\scriptscriptstyle {\text{V}}})-0{,}022278\sin 2(p''-p^{\scriptscriptstyle {\text{V}}})-\ldots \right].$

La masse $\mathrm {T} ^{\scriptscriptstyle {\text{V}}}$ de Mercure a été déterminée dans la Théorie des variations séculaires de ${\frac {1}{2025810}}$ (n^o 14, seconde Partie) ; en la multipliant par