Page:Joseph Louis de Lagrange - Œuvres, Tome 6.djvu/603

EXEMPLE II. N^o 42.

D’APRÈS LES OBSERVATIONS.

${\begin{array}{|c|}\hline \mathrm {PREMI{\grave {E}}RE\ CASE} .\\\hline {\begin{array}{llllllllll}&\quad 0^{\mathrm {s} }&\quad 2^{\mathrm {s} }10&\quad 4^{\mathrm {s} }20&\quad 7^{\mathrm {s} }&\quad 9^{\mathrm {s} }10&\quad 11^{\mathrm {s} }20&\quad 2^{\mathrm {s} }&\quad 4^{\mathrm {s} }10&\quad 6^{\mathrm {s} }20&\quad 9^{\mathrm {s} }\\&+\mathrm {7^{m}36^{s}} &-\mathrm {2^{m}48^{s}} &+\mathrm {4^{m}34^{s}} &-\mathrm {15^{m}33^{s}} &+\mathrm {3^{m}40^{s}} &+\mathrm {10^{m}31^{s}} &-\mathrm {3^{m}52^{s}} &+\mathrm {5^{m}49^{s}} &-\mathrm {13^{m}43^{s}} &-\mathrm {1^{m}12^{s}} \\&+\ \ 456&-168&+274&-933&+220&+631&-232&+349&-823&-\ \ 72\\&{\underline {+\ \ 881}}&{\underline {-616}}&{\underline {-457}}&{\underline {+305}}&{\underline {-181}}&{\underline {+860}}&{\underline {-360}}&{\underline {-657}}&{\underline {+358}}&{\underline {-237}}\\\mathrm {somme} .&+1337&-784&-183&-628&+39&+1491&-592&-308&-465&-309\end{array}}\\\hline \end{array}}$

${\begin{array}{|c|}\hline \mathrm {PREMI{\grave {E}}RE\ CASE} .\\\hline {\begin{array}{lllllllllll}&\quad 11^{\mathrm {s} }10&\quad 1^{\mathrm {s} }20&\quad 4^{\mathrm {s} }&\quad 6^{\mathrm {s} }10&\quad 8^{\mathrm {s} }20&\quad 11^{\mathrm {s} }&\quad 1^{\mathrm {s} }10&\quad 3^{\mathrm {s} }20&\quad 6^{\mathrm {s} }&\quad 8^{\mathrm {s} }10&\quad 10^{\mathrm {s} }20\\&+\mathrm {12^{m}52^{s}} &-\mathrm {3^{m}57^{s}} &+\mathrm {5^{m}58^{s}} &-\mathrm {10^{m}57^{s}} &-\mathrm {6^{m}0^{s}} &+\mathrm {14^{m}20^{s}} &-\mathrm {3^{m}1^{s}} &+\mathrm {5^{m}5^{s}} &-\mathrm {7^{m}37^{s}} &-\mathrm {10^{m}16^{s}} &+\mathrm {14^{m}41^{s}} \\&+772&-237&+\ \ 358&-\ \ 657&-360&+860&-181&+305&-457&-616&+881\\&{\underline {\qquad \ \ }}&{\underline {-\ \ 72}}&{\underline {-\ \ 823}}&{\underline {+\ \ 349}}&{\underline {-232}}&{\underline {+631}}&{\underline {+220}}&{\underline {-933}}&{\underline {+274}}&{\underline {-168}}&{\underline {+456}}\\\mathrm {diff} .\quad &+772&-165&+1181&-1006&-128&+229&-401&+1238&-731&-448&+425\\\end{array}}\\\hline \end{array}}$

${\begin{array}{|c|}\hline \mathrm {DEUXI{\grave {E}}ME\ CASE} .\\\hline {\begin{array}{llllllllllll}+\ \ 772&-2.8876173&{\underline {9.6023412}}&{\underline {0{,}40026}}&&&-1{,}23746&0.0925313&{\underline {9.6438769}}\\-\ \ 309&2.4899585&9.6023412&0{,}40026&9.2046824&0{,}16021&\quad 1{,}04031&0.0171628&9.9246315&0{,}84069&9.5685084&0{,}37026\\-\ \ 465&2.6654530&9.7798357&0{,}60233&9.3821769&0{,}24109&\quad 1{,}52886&0.184678&0.0918365&1{,}23543&9.7357134&0{,}54414\\-\ \ 308&2.4885507&9.6009354&0{,}39896&9.2032746&0{,}15969&-1{,}22546&0.0882993&9.9957680&0{,}99030&9.6396449&0{,}43616\\-\ \ 592&2.7723217&9.8847044&0{,}76684&9.4870456&0{,}30693&-0{,}05671&8.7536596&8.6611283&0{,}04582&8.3050052&0{,}02018\\+1491&3.1734776&0.2858603&1{,}93135&9.8882015&0{,}77304&-1{,}13817&0.0562072&9.9636759&0{,}91976&9.6075528&0{,}40509\\+\quad 39&1.5910646&8.7034473&0{,}05051&8.3057885&0{,}02022&\quad 0{,}51214&9.7093887&9.6168574&0{,}51386&9.2607343&0{,}18228\\-\ \ 698&2.7979596&9.9103423&0{,}81340&9.5126835&0{,}32560&\quad 1{,}92382&0.2841644&0.1916331&1{,}45465&9.8355100&0{,}68472\\-\ \ 183&2.2624511&9.3748338&0{,}23705&8.9771750&0{,}09488&-1{,}08833&0.0367606&9.9442293&0{,}87948\\-\ \ 784&2.8943161&0.0066988&1{,}01554&9.6090400&0{,}40648\\+1337&3.1261314&0.2385141&1{,}73186\\\end{array}}\\\hline \end{array}}$

${\begin{array}{|c|}\hline \mathrm {TROISI{\grave {E}}ME\ CASE} .\\\hline {\begin{array}{llllllllllll}-\ \ 165&2.217489.&{\underline {0.8517660}}&{\underline {7{,}15758}}&&&\quad 44{,}13394&1.6443727&{\underline {0.8002619}}\\+1181&3.0722499&0.8547660&7{,}15758&1.7095320&51{,}23091&-37{,}25772&1.5719163&9.9264436&0{,}84420&0.7267055&5{,}32973\\-1606&3.0025980&0.7851141&6{,}09697&1.6398801&43{,}63954&-10{,}26163&1.0112163&9.3664436&0{,}23251&0.1667055&1{,}46793\\-\ \ 128&2.1072100&9.8897261&0{,}77576&0.7444921&\ \ 5{,}55254&\quad \ \,6{,}72779&0.8278724&9.1830097&0{,}15944&9.9833616&0{,}96241\\+\ \ 229&2.3598355&0.1423516&1{,}38788&0.9971176&\ \ 9.93385&-\ \ 8{,}50418&0.9296326&9.2748599&0{,}18830&0.0751218&1{,}18884\\-\ \ 401&2.6031444&0.3856605&2{,}43030&1.2404265&17{,}39509&\ \ \ 46{,}84293&1.670640&0.0258713&1{,}06138&0.8261332&6{,}70090\\+1238&3.0927206&0.8752367&7{,}50303&1.7300027&53{,}70353&-26{,}92237&1.4301132&9.7853405&0{,}61002&0.5856024&3{,}85135\\-\ \ 731&2.8639174&0.6464335&4{,}43030&1.5011995&31{,}71025&-21{,}28845&1.3271441&9.6823714&0{,}48125\\-\ \ 448&2.6512780&0{,}4333941&2{,}71515&1.2885601&19{,}43390\\+\ \ 425&2.6283889&0.4109050&2{,}57575\end{array}}\\\hline \end{array}}$