ce qui donne
![{\displaystyle {\begin{alignedat}{2}b\sin \ \ \varpi =&\quad \,0{,}014861,\qquad &b\cos \ \ \varpi =&-0{,}011654,\\\sideset {^{1}}{}b\sin \sideset {^{1}}{}\varpi =&-0{,}023703,\qquad &\sideset {^{1}}{}b\cos \sideset {^{1}}{}\varpi =&-0{,}035746,\end{alignedat}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/26586f46e75b942116ab88090eaf4041b845d4bb)
Des deux valeurs de
et de
je conclus
![{\displaystyle \varpi =128^{\circ }6'\qquad }](https://wikimedia.org/api/rest_v1/media/math/render/svg/f9fef1047fa29471da4260bd1c40357d63c7679d)
et
![{\displaystyle \qquad b=0{,}018885\,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/db0da89df7723b5a0ace017e82b21bcb56f18590)
ensuite, des deux valeurs de
et de
je conclus
![{\displaystyle \sideset {^{1}}{}\varpi =33^{\circ }33'\qquad }](https://wikimedia.org/api/rest_v1/media/math/render/svg/5ebc80fced311dd52dc3b09e05890e7cd2935672)
et
![{\displaystyle \qquad \sideset {^{1}}{}b=-0{,}042891\,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/173c347996e771a91cf22434034d37c9bc1d3220)
enfin les équations
![{\displaystyle fb=(0,1)b-{\overline {(0,1)}}b',\qquad \sideset {^{1}}{^{1}}fb=(0,1)\sideset {^{1}}{}b-{\overline {(0,1)}}\sideset {^{1}}{}b'}](https://wikimedia.org/api/rest_v1/media/math/render/svg/92dc02ea7d2b651274b776c2a16f4fcb4d58401e)
donnent
![{\displaystyle b'=-0{,}047286,\qquad \sideset {^{1}}{}b'=-0{,}035808.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a17ad3fba2feb8d956ec0853a8c22df2b6a622db)
Si l’on nomme présentement
le nombre entier ou fractionnaire d’années écoulées depuis l’origine du mouvement, que je fixe au commencement de 1750, on aura
![{\displaystyle fu=22''{,}550x,\qquad \sideset {^{1}}{}fu=3''{,}888x\,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/28e41caee6a625cac055135cf0fdc2957825314d)
donc
![{\displaystyle {\begin{aligned}p\ =&\,\quad 0{,}018885\sin \left(22''{,}550x+128^{\circ }\ \ 6'\right)\\&-0{,}042891\sin \left(\ \ 3''{,}888x+\ \ 33^{\circ }33'\right),\\q\ =&\,\quad 0{,}018885\cos \left(22''{,}550x+128^{\circ }\ \ 6'\right)\\&-0{,}042891\cos \left(\ \ 3''{,}888x+\ \ 33^{\circ }33'\right),\\p'=&-0{,}047286\sin \left(22''{,}550x+128^{\circ }\ \ 6'\right)\\&-0{,}035808\sin \left(\ \ 3''{,}888x+\ \ 33^{\circ }33'\right),\\q'=&-0{,}047286\cos \left(22''{,}550x+128^{\circ }\ \ 6'\right)\\&-0{,}035808\cos \left(\ \ 3''{,}888x+\ \ 33^{\circ }33'\right)\,;\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d6cd6fa6dfa4bb8ba36bd3b87520311e4813c79e)
maintenant on a
![{\displaystyle \alpha ^{2}e^{2}=p^{2}+q^{2}\qquad }](https://wikimedia.org/api/rest_v1/media/math/render/svg/30fd0d4ad02f403c0df87ac09849d9c2170e0c7f)
et
![{\displaystyle \qquad \alpha e={\sqrt {p^{2}+q^{2}}}\,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bdd36a0a649ddfea4b45df2e9d39700badb7e55b)
d’où l’on conclura
![{\displaystyle \alpha e=}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d0946c2105935fe552902b03531fecc216aefbb4)
![{\displaystyle {\sqrt {(0{,}018885)^{2}+(0{,}042891)^{2}-2.0{,}018885.0{,}042891\cos(18''{,}662x+94^{\circ }33')}}\,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/33a2e4f38874cbc298fed43662bbb037f4dcecad)