Page:Joseph Louis de Lagrange - Œuvres, Tome 5.djvu/307

${\begin{alignedat}{4}&&(2,0)=&0''{,}6581&(3,0)=&0''{,}3403&(4,0)=&0''{,}2073&(5,0)=&0''{,}0806\\&&&9{,}8182718,\ \ &&9{,}53181927,\ \ &&9{,}3166326,\ \ &&8{,}9060743,\\&&(2,1)=&14''{,}4116&(3,1)=&6''{,}9480&(4,1)=&0''{,}1312&(5,1)=&1''{,}5754\\&&&1{,}1587124,&&0{,}8418589,&&0{,}6160784,&&0{,}1974000,\\&&(2,3)=&1''{,}7724&(3,2)=&0''{,}4330&(4,2)=&0''{,}1482&(5,2)=&0''{,}0396\\&&&0{,}2485728,&&9{,}6364927,&&9{,}1707853,&&8{,}5974941,\\&&(2,4)=&0''{,}6760&(3,4)=&7''{,}4579&(4,3)=&6''{,}6908&(5,3)=&0''{,}8696\\&&&9{,}8299503,&&0{,}8726141,&&0{,}8254796,&&9{,}9393014,\\&&(2,5)=&0''{,}0182&(3,5)=&0''{,}0976&(4,5)=&0''{,}4223&(5,4)=&4''{,}1952\\&&&8{,}2596098,&&8{,}9893371,&&9{,}6256507,&&0{,}6227495,\\&&(2)=&17''{,}5363&(3)=&15''{,}2767&(4)=&11''{,}5999&\quad (5)=&6''{,}7603,\\&&&1{,}2439386,&&1{,}1840290,&&1{,}0644529,&&0{,}8299660.\end{alignedat}}$

Et si l’on détermine, d’après les éléments du n^o 26, les valeurs des variables $x'',y'',x''',\ldots ,s'',u'',s''',\ldots$ pour l’époque de 1700, on trouvera celles-ci.

Pour 1700:

${\begin{alignedat}{4}x''\ &=&\lambda ''\ \sin \varphi ''\ =&0{,}04572&y''\ &=&\lambda ''\ \cos \varphi ''\ =&-0{,}08099\\&&&8{,}6600670,\qquad \qquad &&&&\quad \ 8{,}9084081,\\x'''&=&\lambda '''\sin \varphi '''=&-0{,}01665&y'''&=&\lambda '''\cos \varphi '''=&0{,}00225&\\&&&\quad \ 8{,}2214213,&&&&7{,}3528905,\\x^{\scriptscriptstyle {\text{IV}}}&=&\lambda ^{\scriptscriptstyle {\text{IV}}}\sin \varphi ^{\scriptscriptstyle {\text{IV}}}=&-0{,}00561&y^{\scriptscriptstyle {\text{IV}}}&=&\lambda ^{\scriptscriptstyle {\text{IV}}}\cos \varphi ^{\scriptscriptstyle {\text{IV}}}=&0{,}00416\\&&&\quad \ 7{,}7489933,&&&&7{,}6185985,\\x^{\scriptscriptstyle {\text{V}}}\ &=&\lambda ^{\scriptscriptstyle {\text{V}}}\ \sin \varphi ^{\scriptscriptstyle {\text{V}}}\ =&-0{,}19660&y^{\scriptscriptstyle {\text{V}}}\ &=&\lambda ^{\scriptscriptstyle {\text{V}}}\ \cos \varphi ^{\scriptscriptstyle {\text{V}}}\ =&-0{,}06115&\\&&&\quad \ 9{,}2935821,&&&&\quad \ 8{,}7863982,\\s''\ &=&\theta ''\ \sin \omega ''\ =&0{,}02378&u''\ &=&\theta ''\ \cos \omega ''\ =&0{,}02186\\&&&8{,}3762126,&&&&8{,}3396176,\\s'''&=&\theta '''\sin \omega '''=&0,&u'''&=&\theta '''\cos \omega '''=&0,\\s^{\scriptscriptstyle {\text{IV}}}&=&\theta ^{\scriptscriptstyle {\text{IV}}}\sin \omega ^{\scriptscriptstyle {\text{IV}}}=&0{,}05691&u^{\scriptscriptstyle {\text{IV}}}&=&\theta ^{\scriptscriptstyle {\text{IV}}}\cos \omega ^{\scriptscriptstyle {\text{IV}}}=&0{,}01636\\&&&8{,}7552047,&&&&8{,}2137331,\\s^{\scriptscriptstyle {\text{V}}}\ &=&\theta ^{\scriptscriptstyle {\text{V}}}\ \sin \omega ^{\scriptscriptstyle {\text{V}}}\ =&0{,}08619&u^{\scriptscriptstyle {\text{V}}}\ &=&\theta ^{\scriptscriptstyle {\text{V}}}\ \cos \omega ^{\scriptscriptstyle {\text{V}}}\ =&0{,}08718&\\&&&8{,}9354332,&&&&8{,}9404024.\end{alignedat}}$