Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 5.djvu/227

TABLE V. – Syzygies solsticiales.

${\begin{array}{|l|l|l|l|l|l|l|}\hline &\ (-1).&\ \ (0).&\ (+1).&\ (+2).&\ (+3).&\ (+4).\\\hline \\1807\ldots &41{,}030&43{,}040&44{,}745&45{,}545&43{,}830&41{,}575\\1808\ldots &41{,}365&44{,}260&46{,}075&45{,}920&44{,}875&42{,}535\\1809\ldots &41{,}195&44{,}140&46{,}885&45{,}945&45{,}610&43{,}334\\1810\ldots &41{,}942&45{,}481&46{,}623&46{,}487&45{,}425&41{,}242\\1811\ldots &40{,}695&44{,}163&45{,}159&45{,}736&45{,}219&43{,}284\\1812\ldots &42{,}058&44{,}759&45{,}932&45{,}478&43{,}474&40{,}904\\1813\ldots &41{,}733&44{,}867&45{,}821&44{,}845&43{,}302&39{,}784\\1814\ldots &40{,}380&43{,}665&45{,}767&45{,}050&44{,}017&41{,}264\\1815\ldots &40{,}045&43{,}043&45{,}129&44{,}834&43{,}289&40{,}867\\1816\ldots &40{,}830&42{,}390&44{,}090&43{,}850&41{,}640&39{,}620\\1817\ldots &39{,}440&42{,}720&44{,}380&43{,}880&41{,}910&40{,}120\\1818\ldots &39{,}474&42{,}400&43{,}575&44{,}145&42{,}048&39{,}468\\1819\ldots &39{,}457&41{,}030&42{,}733&42{,}325&41{,}268&38{,}261\\1820\ldots &38{,}320&40{,}990&42{,}222&42{,}454&41{,}208&39{,}029\\1821\ldots &39{,}220&42{,}130&42{,}160&41{,}825&41{,}225&38{,}055\\1822\ldots &38{,}194&41{,}824&43{,}357&43{,}524&42{,}532&39{,}470\\\\\hline \\{\text{Sommes}}\ldots &645{,}358&690{,}902&714{,}592&712{,}843&690{,}872&648{,}792\\\\\hline \end{array}}$

L’ensemble de ces hauteurs donne

${\begin{alignedat}{3}f\ \ =&645{,}358,&\qquad f'\ =&690{,}902,&\qquad f''=&714{,}592,\\f'''=&712{,}843,&f^{\text{ıv}}=&690{,}872,&f^{\mathrm {v} }=&648{,}792.\end{alignedat}}$

On trouve ainsi

${\begin{aligned}\zeta \ \ =&-11{,}08513,\\\zeta '\ =&\quad 55{,}86375,\\\zeta ''=&645{,}84780.\end{aligned}}$

L’expression $\zeta ''-{\frac {\zeta '^{2}}{4\zeta }}+\zeta \left(t+{\frac {\zeta '}{2\zeta }}\right)$ des valeurs de $f,f',\ldots$ devient

$716{,}2293-11{,}08515(t-2{,}51976)^{2},$