Page:Joseph Louis de Lagrange - Œuvres, Tome 6.djvu/591

EXEMPLE I. N^o 41.

D’APRÈS LES OBSERVATIONS.

${\begin{array}{|c|}\hline \mathrm {PREMI{\grave {E}}RE\ CASE} .\\\hline {\begin{array}{llllllllll}&\quad 0^{\mathrm {s} }&\quad 2^{\mathrm {s} }10&\quad 4^{\mathrm {s} }20&\quad 7^{\mathrm {s} }&\quad 9^{\mathrm {s} }10&\quad 11^{\mathrm {s} }20&\quad 2^{\mathrm {s} }&\quad 4^{\mathrm {s} }10&\quad 6^{\mathrm {s} }20&\quad 9^{\mathrm {s} }\\&+7^{\mathrm {m} }36^{\mathrm {s} }&-2^{\mathrm {m} }48^{\mathrm {s} }&+4^{\mathrm {m} }34^{\mathrm {s} }&-15^{\mathrm {m} }33^{\mathrm {s} }&+3^{\mathrm {m} }40^{\mathrm {s} }&+10^{\mathrm {m} }31^{\mathrm {s} }&-3^{\mathrm {m} }52^{\mathrm {s} }&+5^{\mathrm {m} }49^{\mathrm {s} }&-13^{\mathrm {m} }43^{\mathrm {s} }&-1^{\mathrm {m} }12^{\mathrm {s} }\\&+456&-168&+274&-\ \ 933&+\ \ 220&+631&-232&+349&-\ \ 823&-\ \ 72\\&{\underline {-616}}&{\underline {-457}}&{\underline {+305}}&{\underline {-\ \ 181}}&{\underline {+\ \ 860}}&{\underline {-360}}&{\underline {-657}}&{\underline {+358}}&{\underline {-\ \ 237}}&{\underline {+772}}\\\mathrm {somme} .&-160&-625&+579&-1114&+1080&+271&-889&+707&-1060&+700\\\end{array}}\\\hline \end{array}}$

${\begin{array}{|c|}\hline \mathrm {PREMI{\grave {E}}RE\ CASE} .\\\hline {\begin{array}{lllllllllll}&\quad 11^{\mathrm {s} }10&\quad 1^{\mathrm {s} }20&\quad 4^{\mathrm {s} }&\quad 6^{\mathrm {s} }10&\quad 8^{\mathrm {s} }20&\quad 11^{\mathrm {s} }&\quad 1^{\mathrm {s} }10&\quad 3^{\mathrm {s} }20&\quad 6^{\mathrm {s} }&\quad 8^{\mathrm {s} }10\\&+12^{\mathrm {m} }52^{\mathrm {s} }&-3^{\mathrm {m} }57^{\mathrm {s} }&+5^{\mathrm {m} }58^{\mathrm {s} }&-10^{\mathrm {m} }57^{\mathrm {s} }&-6^{\mathrm {m} }0^{\mathrm {s} }&+14^{\mathrm {m} }20^{\mathrm {s} }&-3^{\mathrm {m} }1^{\mathrm {s} }&+5^{\mathrm {m} }5^{\mathrm {s} }&-7^{\mathrm {m} }37^{\mathrm {s} }&-10^{\mathrm {m} }16^{\mathrm {s} }\\&+772&-237&+358&-657&-360&+860&-181&+305&-457&-\ \ 616\\&{\underline {-\ \ 72}}&{\underline {-823}}&{\underline {+349}}&{\underline {-232}}&{\underline {+631}}&{\underline {+220}}&{\underline {-933}}&{\underline {+274}}&{\underline {-168}}&{\underline {+\ \ 456}}\\\mathrm {diff} .\quad \ \ &+844&+586&+\quad 9&-425&-991&+640&+752&+\ \ 31&-289&-1072\\\end{array}}\\\hline \end{array}}$

${\begin{array}{|c|}\hline \mathrm {DEUXI{\grave {E}}ME\ CASE} .\\\hline {\begin{array}{llllllllll}+\ \ 700&2.8450980&{\underline {9.7111996}}&{\underline {0{,}51428}}&-1{,}23123&0.0903392&{\underline {9.5121772}}&{\underline {0{,}32522}}\\-1060&3.0253059&0.1802079&1{,}51428&9.8914075&0{,}77877&+2{,}26485&0.3550395&0.2647003&1{,}83950&9.7768775&0{,}59824\\+\ \ 707&2.8494194&0.0043214&1{,}01000&9.7155210&0{,}51943&-0{,}74400&9.8715729&9.7812337&0{,}60427&9.2934109&0{,}19652\\-\ \ 889&2.9489018&0.1038038&1{,}27000&9.8150034&0{,}65314&-0{,}47196&9.6739052&9.5835660&0{,}38332&9.0957432&0{,}12466\\+\ \ 271&2.439693&9.5838713&0{,}38714&9.2990709&0{,}19910&+0{,}41083&9.6136621&9.5233229&0{,}33367&9.0355001&0{,}10853\\+1080&3.0384238&0.1883258&1{,}54286&9.8995254&0{,}79346&-1{,}55156&0.1907685&0.1004293&1{,}26017&9.6126065&0{,}40983\\-1114&3.0468852&0.2017872&1{,}59143&9.9129868&0{,}81844&+2{,}05890&0.3136353&0.2232961&1{,}67223&9.7354733&0{,}54384\\+\ \ 579&2.7626786&9.9175806&0{,}82714&9.6287802&0{,}42539&-0{,}13939&9.1432316&9.0528924&0{,}11295\\-\ \ 625&2.7958800&9.9507820&0{,}89286&9.6619816&0{,}45918\\-\ \ 160&2.2041200&9.3590220&0{,}22857\\\end{array}}\\\hline \end{array}}$

${\begin{array}{|c|}\hline \mathrm {TROISI{\grave {E}}ME\ CASE} .\\\hline {\begin{array}{llllllllll}+\ \ 844&2.9263424&{\underline {9.4852812}}&{\underline {0{,}30569}}&-1{,}22290&0.0873909&{\underline {9.7288892}}&{\underline {0{,}53566}}\\+\ \ 586&2.7678976&9.8415552&0{,}69431&9.3268364&0{,}21224&-0{,}19402&9.2878465&9.2004556&0{,}15865&8.9293448&0{,}08498\\+\ \ \quad 9&0.9542425&8.0279001&0{,}01066&7.5131813&0{,}00326&+1{,}31744&0.1197209&0.0323300&1{,}07730&9.7612192&0{,}57706\\-\ \ 425&2.6283889&9.7020465&0{,}50355&9.1873277&0{,}15393&+0{,}10419&9.0178260&8.9304351&0{,}08519&8.6593243&0{,}04563\\-\ \ 991&2.9960737&0.0697313&1{,}17417&9.5550125&0{,}35893&+0{,}05137&8.7107096&8.6233187&0{,}04201&8.3522079&0{,}02250\\+\ \ 640&2.8061800&9.8798376&0{,}75829&9.3651188&0{,}23180&-1{,}06739&0.0283232&9.9409323&0{,}87284&9.6698215&0{,}46755\\+\ \ 752&2.8762178&9.9448754&0{,}89100&9.4351566&0{,}27237&-0{,}55981&9.7480406&9.6606497&0{,}45777&9.3895389&0{,}24521\\+\quad 31&1.4913617&8.5650193&0{,}03673&8.0503005&0{,}01123&+1{,}33808&0.1264721&0.0390812&1{,}09416\\-\ \ 289&2.4608978&9.5345554&0{,}34242&9.0198366&0{,}10467\\-1072&3.0301948&0.1038524&1{,}27014\\\end{array}}\\\hline \end{array}}$