Page:Annales de mathématiques pures et appliquées, 1817-1818, Tome 8.djvu/349

333

DE SOLEIL.

${\begin{array}{r|r}{\text{Longit. du soleil.}}&{\text{Angle horaire.}}\\\hline {\text{Pour }}0{\text{ heure}}\ 164^{\circ }.42'.41''+\ \ \ 0''&165^{\circ }.55'.30''+\ 0^{\circ }.0'.\ 0'',\\1{\text{ heure }}\ 164\ .42\ \,.41\,\ +146\ &165\ \ .55\ .30\,\ +15\ .2\ .15\,\ ,\\2{\text{ heures}}\ 164\ .42\ \,.41\,\ +292\ &165\ \ .55\ .30\,\ +30\ .4\ .30\,\ ,\\3{\text{ heures}}\ 164\ .42\ \,.41\,\ +438\ &165\ \ .55\ .30\,\ +45\ .6\ .45\,\ ,\\4{\text{ heures}}\ 164\ .42\ \,.41\,\ +584\ &165\ \ .55\ .30\,\ +60\ .9\ .\ \,0\,\ .\end{array}}$

5. Longitude de la lune.

$\left.{\begin{array}{rl}\mathrm {Le\,6,\,{\grave {a}}\,midi} \,152^{\circ }.\ 0'.32&=547232''\\\mathrm {{\grave {a}}\,minuit} \,157\ .54\,.39\ &=586479\ \\\mathrm {Le\,7,\,{\grave {a}}\,midi} \,163\ .48\,.17\ &=589697\ \\\mathrm {{\grave {a}}\,minuit} \,169\ .41\,.40\ &=610900\ \end{array}}\right|\left.{\begin{aligned}&21247''\\&21218\ \\&21203\ \end{aligned}}\right|\left.{\begin{aligned}&-29''\\&-15\ \end{aligned}}\right|+14''.$

${\begin{array}{rr}\mathrm {Il\,en\,r{\acute {e}}sulte} \qquad a=&547232'',\\\Delta a=&21247\ ,\\2\Delta ^{2}a=&-29\ ,\\6\Delta ^{3}a=&+14\ ;\\\end{array}}$

donc

6 Long. lunaire $=3283392''+127597''t-129''t^{2}14''t^{3}.$