par suite
![{\displaystyle \lambda =\lambda _{0}+\mathrm {M} \tau \cot .\lambda _{0}\operatorname {tang} .\mathrm {L} ''\,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7763b294cb2ee260e3305f1998483051cdf92c46)
et comme
il s’ensuit qu’en éliminant
au moyen de sa valeur on a, au même degré de précision,
![{\displaystyle \cos .\lambda '={\frac {\sin .\lambda '}{\sin .\lambda _{0}}}\left(1-\mathrm {M} \tau \cot .^{2}\lambda _{0}\operatorname {tang} .\mathrm {L} ''\right).}](https://wikimedia.org/api/rest_v1/media/math/render/svg/54680192eef86bd1bf4db2df0816c393e3b49100)
Désignant également par
ce que devient
lorsque
on aura
et
![{\displaystyle \cos .\sigma '=\cos .\sigma '_{0}-\mathrm {M} \tau \cos .\sigma '_{0}\cot .^{2}\lambda _{0}\operatorname {tang} .\mathrm {L} '',}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a186b7c2e78fff058e8acfeffb0753df33a5a323)
de là
![{\displaystyle \sigma '=\sigma '_{0}+\mathrm {M} \tau \cos .\sigma '_{0}\cot .\sigma '_{0}\operatorname {tang} .\mathrm {L} ''.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1ed14c025c13ca2aa52156a622218cd047aee571)
D’un autre côté, à cause de
on trouve, en substituant pour
sa valeur ci-dessus,
![{\displaystyle \sin .\sigma ''={\frac {\cot .\mathrm {V} ''}{\operatorname {tang} .\lambda _{0}}}\left(1-\mathrm {M} \tau \operatorname {cosec} .^{2}\lambda _{0}\operatorname {tang} .\mathrm {L} ''\right)\,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/282910fb6891c846edf42050b733ce71b76460a3)
et si
représente
lorsque
on aura
![{\displaystyle \sin .\sigma ''_{0}=\cot .\mathrm {V} ''\cot .\lambda _{0}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/43503be0d5089fea180adb98b66dab8a687848ab)
![{\displaystyle \sin .\sigma ''=\sin .\sigma ''_{0}-\mathrm {M} \tau \operatorname {tang} .\mathrm {L} ''\operatorname {cosec} .^{2}\lambda _{0}\sin .\sigma ''_{0}\,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/58c9c0a41b336ecf7afbae9e48151f0ab605259d)
par suite
![{\displaystyle \sigma ''=\sigma ''_{0}-\mathrm {M} \tau \operatorname {tang} .\mathrm {L} ''\operatorname {cosec} .^{2}\lambda _{0}\operatorname {tang} .\sigma ''_{0}.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6ef20fbd1c3fc93533b9574c0f211fa84af2c4bf)
Concluons de là que
![{\displaystyle {\begin{aligned}&\sin .2\sigma '=\sin .2\sigma '_{0}+2\mathrm {M} \tau \cot .^{2}\lambda _{0}\operatorname {tang} .\mathrm {L} ''\cot .\sigma '_{0}\cos .2\sigma '_{0}\\&\sin .2\sigma ''=\sin .2\sigma ''_{0}-2\mathrm {M} \tau \operatorname {cosec} .^{2}\lambda _{0}\operatorname {tang} .\mathrm {L} ''\operatorname {tang} .\sigma ''_{0}\cos .2\sigma ''_{0},\\&\mathrm {A} ^{(1)}=\mathrm {A} ^{(1)}-2\mathrm {M} \tau \operatorname {cosec} .^{2}\lambda _{0}\operatorname {tang} .\mathrm {L} ''\left[\operatorname {tang} .\sigma ''_{0}\cos .2\sigma ''_{0}\right.\\\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5ba9e587f6134d1bbc5fa85997600bc1e2a03262)
![{\displaystyle \left.+\cos .^{2}\lambda _{0}\cot .\sigma '_{0}\cos .2\sigma '_{0}\right],}](https://wikimedia.org/api/rest_v1/media/math/render/svg/728904fa68e8345bd229c3c5a3e8f836589eac84)