Page:Mémoires de l’Académie des sciences, Tome 10.djvu/759

${\begin{alignedat}{2}\log .{\frac {1}{4}}\varepsilon ^{2}=&5.02532\\\log .\mathrm {M} =&1.65351-\\\log .(\sigma ''_{0}-\sigma '_{0})=&3.89600\\\operatorname {l} .\cos .^{2}\lambda _{0}=&{\underline {9.34596}}\\&9.92079-&\ldots \ldots \ldots \ldots \ldots \ldots &9.92079-\\\operatorname {l} .\cot .\mathrm {Z} =&0.06594-&\log .(\sigma ''_{0}-\sigma '_{0})=&3.89600\\\operatorname {l} .\cot .^{2}\lambda _{0}=&9.45492&\operatorname {l} .\sin .1''=&4.19612\\\operatorname {l} .\sin .(\sigma ''_{0}-\sigma '_{0})=&8.08909&\operatorname {l} .\cot .\mathrm {Z} =&{\underline {0.06594-}}\\{\text{c}}.\log .\sin .\sigma ''_{0}=&0.20662&&8.07885+\\{\text{c}}.\log .\sin .\sigma '_{0}=&{\underline {0.19994}}&=&+0''{,}01199\\&7.93730+&&{\underline {+0{,}00866}}\\=&+0''{,}008656\qquad &4^{\text{e}}{\text{ et }}5^{\text{e}}{\text{ termes}}=&{\underline {+0{,}02065}}\\\end{alignedat}}$

Récapitulation.

${\begin{aligned}&\varphi =0^{\text{g}}{,}7033''{,}490\\&\quad +\qquad 12\ \ {,}002\\&\quad -\ \ \ \qquad 0\ \ {,}002\\&{\underline {\,\quad +\quad \qquad 0\ \ {,}021}}\\&\omega =0{,}7045''{,}511=\omega ''-\omega '.\end{aligned}}$

La valeur de $\omega$ étant trouvée, on aura celle de $z'$ au moyen de l’équation (E); c’est-à-dire que

${\begin{aligned}\log .\sin .\omega =&8.0440228\\{\text{c}}.\log .{\text{dénomin}}.=&{\underline {1.8907827-}}\\\operatorname {l} .\operatorname {tang} .z'=&9.9348055-=-45^{\text{g}}{,}2395''{,}07\\&\;\qquad \qquad z'=154{,}7604{,}93\end{aligned}}$

Partant

$\mathrm {V} '=200^{\text{g}}-z'=45^{\text{g}}{,}2395''{,}07.$

Ensuite on trouvera, à l’aide des relations

$\cos .\lambda =\cos .\lambda '\sin .z'\,;\qquad \cos .\sigma '={\frac {\sin .\lambda '}{\sin .\lambda }}\,;\qquad \cos .\sigma ''={\frac {\sin .\lambda ''}{\sin .\lambda }}\,;$

les valeurs suivantes :