Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 5.djvu/237

TABLE XI. — Quadratures solsticiales.

${\begin{array}{|l|c|c|c|c|}\hline &\ \ (0).&\ (1).&\ (2).&\ (3).\\\hline \\1807\ldots \ldots &28{,}720&26{,}495&25{,}310&27{,}135\\1808\ldots \ldots &28{,}910&25{,}765&25{,}145&27{,}120\\1809\ldots \ldots &28{,}950&26{,}863&24{,}840&25{,}815\\1810\ldots \ldots &29{,}586&25{,}750&26{,}477&27{,}910\\1811\ldots \ldots &29{,}319&26{,}445&25{,}943&28{,}034\\1812\ldots \ldots &28{,}106&25{,}837&25{,}823&27{,}705\\1813\ldots \ldots &26{,}584&24{,}908&26{,}234&28{,}684\\1814\ldots \ldots &27{,}196&24{,}431&25{,}500&28{,}384\\1815\ldots \ldots &25{,}720&24{,}787&25{,}285&28{,}224\\1816\ldots \ldots &26{,}870&25{,}500&24{,}900&28{,}370\\1817\ldots \ldots &25{,}640&24{,}100&25{,}370&28{,}930\\1818\ldots \ldots &26{,}607&24{,}713&24{,}853&26{,}769\\1819\ldots \ldots &26{,}611&24{,}677&24{,}304&26{,}574\\1820\ldots \ldots &26{,}934&24{,}412&23{,}709&26{,}226\\1821\ldots \ldots &27{,}355&25{,}180&24{,}415&26{,}430\\1822\ldots \ldots &28{,}047&25{,}014&24{,}204&26{,}036\\\\\hline \\{\text{Sommes}}\ldots &\quad 441{,}215&\quad 404{,}877\quad &\quad 402{,}312\quad &\quad 438{,}376\quad \\\\\hline \end{array}}$

L’ensemble de ces hauteurs donne

$f=441{,}215,\quad f'=404{,}877,\quad f''=402{,}3l2,\quad f'''=438{,}376,$

d’où l’on tire

$\zeta =18{,}1005,\qquad \zeta '=-55{,}4097,\qquad \zeta ''=441{,}4578.$

L’expression

$\zeta t^{2}+\zeta 't+\zeta ''$

devient ainsi

$399{,}0524+18{,}1005(t-1{,}53062)^{2},$

ce qui donne, par un calcul semblable à celui que nous venons de faire