Page:Annales de mathématiques pures et appliquées, 1818-1819, Tome 9.djvu/129

123

DU 7 DE SEPTEMBRE 1820.

Premier Tableau.

Résultats communs aux deux villes de Montpellier et de Strasbourg.

${\begin{array}{|l|r|r|r|r|}\hline {\text{Temps vrai de Paris.}}&1^{h}.\ 0^{m}.\,\ 0^{s}.\quad &2^{h}.\ 0^{m}.\,\ 0^{s}.\quad \\\hline {\text{Long. ☉}}&164^{\circ }.\,45'.\,12''{,}8&164^{\circ }.\,47'.\,38''{,}6\\{\text{Long. ☾}}&164\,\ .\,17\ .\ 44\,\ {,}1&164\,\ .\,47\ .\ 11\,\ {,}3\\{\text{Latit. ☾}}=\lambda &0\,\ .\,47\ .\ 24\,\ {,}2&0\,\ .\,44\ .\ 42\,\ {,}4\\{\text{Parall. horisont. (☾-☉)}}=\varpi &0\,\ .\,53\ .\ 39\,\ {,}7&0\,\ .\,53\ .\ 39\,\ {,}6\\{\text{Ascension dro. ☉}}&165\ .\,57\ .\ 45\,\ \quad &166\ .\ \ \ 0\,.\,\ \ 0\,\ \quad \\\hline \end{array}}$

${\begin{array}{|l|r|r|}\hline {\text{Temps vrai de Paris.}}&3^{h}.\ 0^{m}.\,\ 0^{s}.\quad &4^{h}.\ 0^{m}.\,\ 0^{s}.\quad \\\hline {\text{Long. ☉}}&164^{\circ }.\,50'.\ \,\,4''{,}4&164^{\circ }.\,52'.\,30''{,}2\\{\text{Long. ☾}}&165\,\ .\ 16\,.\,38\,\ {,}4&165\,\ .\ 46\,.\,\ \ 5\,\ {,}5\\{\text{Latit. ☾}}=\lambda &0\,\ .\ 44\,.\,42\,\ {,}4&0\,\ .\ 39\,.\,18\,\ {,}7\\{\text{Parall. horisont. (☾-☉)}}=\varpi &0\,\ .\ 53\,,\,39\,\ {,}6&0\,\ .\ 53\,.\,39\,\ {,}4\\{\text{Ascension dro. ☉}}&166\ .\,\ \ 2\,.\,15\,\ \quad &166\ .\,\ \ 4\,.\,30\,\ \quad \\\hline \end{array}}$

Aplatissement de la terre $={\frac {1}{320}}.$

Demi-diamètre du soleil $=0^{\circ }.15'.54''{,}8.$

Parall. de long.

$=\Pi =a+a^{2}\operatorname {Cot} .({\text{☾}}-\mathrm {N} )\operatorname {Sin} .1''+a^{3}\left[\operatorname {Cot} .^{3}({\text{☾}}-\mathrm {N} )-{\tfrac {1}{3}}\right]\operatorname {Sin} .^{2}1''+\ldots$

$a={\frac {\operatorname {Sin} .\varpi \operatorname {Sin} .h\operatorname {Sin} .({\text{☾}}-\mathrm {N} )}{\operatorname {Cos} .\lambda \operatorname {Sin} .1''}}.$

Parall. de latit.

$=\pi =a'+a'^{2}\operatorname {Tang} .(x+\lambda )\operatorname {Sin} .1''+a'^{3}\left[\operatorname {Tang} .^{2}(x+\lambda )-{\tfrac {1}{3}}\right]\operatorname {Sin} .^{2}1''+\ldots$

$=a''+a''(a''-\lambda )\operatorname {Tang} .x\operatorname {Sin} .1''+a''\lambda \left(a''-{\tfrac {3}{2}}\lambda -a''\operatorname {Tang} .^{2}x\right)\operatorname {Sin} .^{2}1''$

$+a''^{3}\left(\operatorname {Tang} .^{2}x-{\tfrac {1}{3}}\right)\operatorname {Sin} .^{2}1''$

$a'={\frac {\operatorname {Sin} .\varpi \operatorname {Cos} .h\operatorname {Cos} .(x+\lambda )}{\operatorname {Cos} .x\operatorname {Sin} .1''}}\,;\qquad a''=\operatorname {Sin} .\varpi \operatorname {Cos} .h\operatorname {Cot} .1''\,;$

$\operatorname {Tang} .x=\operatorname {Tang} .h\operatorname {Cos} .\left({\text{☾}}-\mathrm {N} +{\frac {1}{2}}\Pi \right){\rm {{S{\acute {e}}c}.{\frac {1}{2}}\Pi .}}$