on aura ainsi
![{\displaystyle {\begin{aligned}x&={\frac {\mathrm {K} }{a^{2}}}\left({\frac {1}{2}}\sin ^{2}\nu -\cos ^{2}\nu \right)(1-\cos at)\\&+{\frac {\mathrm {K} \sin ^{2}\nu }{2a^{2}-8m^{2}}}\left[\cos(2mt-2\varpi )-\cos 2\varpi \cos at-{\frac {2m}{a}}\sin 2\varpi \sin at\right]\\z&={\frac {2\mathrm {K} \sin \nu \cos \nu }{a^{2}-m^{2}}}\left[\cos(mt-\varpi )-\cos \varpi \cos at-{\frac {m}{a}}\sin \varpi \sin at\right],\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/33e46f860b02ecd00a6e41d6ecf9896dbf684a76)
ce qui donne
![{\displaystyle {\begin{aligned}u&={\frac {\mathrm {K} }{a^{2}}}\sin 2\theta \left({\frac {1}{2}}\sin ^{2}\nu -\cos ^{2}\nu \right)(1-\cos at)\\&+{\frac {\mathrm {K} \sin ^{2}\nu }{2a^{2}-8m^{2}}}\sin 2\theta \left[\cos(2mt-2\varpi )-\cos 2\varpi \cos at-{\frac {2m}{a}}\sin 2\varpi \sin at\right]\\&+{\frac {2\mathrm {K} \sin \nu \cos \nu }{a^{2}-m^{2}}}\cos 2\theta \left[\cos(mt-\varpi )-\cos \varpi \cos at-{\frac {m}{a}}\sin \varpi \sin at\right]\\v&={\frac {\cos \theta }{\sin \theta }}{\frac {2\mathrm {K} \sin \nu \cos \nu }{a^{2}-m^{2}}}\left[\sin(mt-\varpi )+\sin \varpi \cos at-{\frac {m}{a}}\cos \varpi \sin at\right]\\&+{\frac {\mathrm {K} \sin ^{2}\nu }{a^{2}-4m^{2}}}\left[\sin(2mt-2\varpi )+\sin 2\varpi \cos at-{\frac {2m}{a}}\cos 2\varpi \sin at\right]\\y&={\frac {6l\mathrm {K} \sin \nu \cos \nu }{a^{2}-m^{2}}}\sin 2\theta \left[\cos(mt-\varpi )-\cos \varpi \cos at-{\frac {m}{a}}\sin \varpi \sin at\right]\\&+{\frac {3l\mathrm {K} \sin ^{2}\nu }{a^{2}-4m^{2}}}\sin ^{2}\theta \left[\cos(2mt-2\varpi )-\cos 2\varpi \cos at-{\frac {2m}{a}}\sin 2\varpi \sin at\right]\\&-{\frac {l\mathrm {K} }{a^{2}}}\left({\frac {1}{2}}\sin ^{2}\nu -\cos ^{2}\nu \right)(1+3\cos 2\theta )(1-\cos at)\,;\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/03c1866edbd33d14d4fe3280b6d8fc5a9ac6aa2d)
telles seraient les valeurs de 
et 
si la planète n’avait aucun mouvement de rotation.
Si l’on suppose l’astre attirant au-dessus du pôle ou à l’origine de l’angle 
on aura le cas que M. d’Alembert a traité dans ses excellentes Recherches sur la cause des vents ; dans ce cas, 
partant on a
