Page:Lagrange - Œuvres (1867) vol. 1.djvu/725

de $3^{r{\acute {e}}v}4^{s}28^{\circ }6'0'',$ c’est-à-dire de $4\ 403\ 160'',$ d’où l’on trouve pour le mouvement séculaire de Saturne $4\ 398\ 126''.$

On aura donc

${\frac {h'}{h}}={\frac {4398126}{10926257}}=0{,}402528\,;$

d’où l’on tire

$a=0{,}545169.$

De là on trouvera

${\begin{alignedat}{2}{\mathfrak {A}}&=2{,}178104,\qquad &{\mathfrak {P}}&=\ \ 6{,}891711,\\{\mathfrak {B}}&=3{,}183228,&{\mathfrak {Q}}&=12{,}403290,\\{\mathfrak {C}}&=2{,}080116,&{\mathfrak {R}}&=\ \ 9{,}890764,\\{\mathfrak {D}}&=1{,}294032,&{\mathfrak {S}}&=\ \ 7{,}315770,\\\ldots &\ldots \ldots \ldots ,&\ldots &\ldots \ldots \ldots ,\end{alignedat}}$

et ensuite

${\begin{alignedat}{2}{\mathfrak {A}}_{2}=&-0{,}120125,&{\mathfrak {A}}'_{2}=&\ \ \ \quad 1{,}310407,\\{\mathfrak {A}}_{3}=&\ \quad 0{,}041029,&{\mathfrak {A}}'_{3}=&-\ \ 2{,}744209,\\{\mathfrak {A}}_{4}=&\ \quad 0{,}473042,&{\mathfrak {A}}'_{5}=&\ \ \ \quad 0{,}867697,\\{\mathfrak {B}}_{2}=&-0{,}143482,&{\mathfrak {B}}'_{2}=&\ \ \ \quad 4{,}793425,\\{\mathfrak {B}}_{5}=&-0{,}946083,\qquad &{\mathfrak {B}}'_{5}=&-\ \ 1{,}735395,\\\mathrm {p} \ \ \ =&\ \quad 3{,}997995,&\mathrm {p} _{1}\ =&-10{,}532304,\\\mathrm {q} \ \ \ =&\ \quad 8{,}300535,&\mathrm {q} _{1}\ =&-17{,}850234,\\\mathrm {r} \ \ \ =&\ \quad 7{,}306455,&\mathrm {r} _{1}\ =&-13{,}546971,\\{\mathfrak {P}}_{4}=&-0{,}232789,&{\mathfrak {P}}'_{4}=&-\ \ 3{,}488506,\\{\mathfrak {P}}_{7}=&-0{,}184498,&{\mathfrak {P}}'_{7}=&\ \ \ \quad 7{,}537649,\\{\mathfrak {Q}}_{5}=&\ \quad 0{,}700695,&{\mathfrak {Q}}'_{5}=&-\ \ 4{,}354384,\end{alignedat}}$

Donc, à cause de

$\mathrm {\frac {J}{I}} ={\frac {1}{1067}}=0,000\ 937\ 207$

et de

$\mathrm {\frac {J'}{I'}} ={\frac {1}{3021}}=0,000\ 331\ 016,$