![{\displaystyle \left({\frac {\operatorname {d} x}{\operatorname {d} t}}\right)^{2}=4k^{2}\left({\frac {x-a}{p}}\right)^{2}+A,\quad \left({\frac {\operatorname {d} y}{\operatorname {d} t}}\right)^{2}=4k^{2}\left({\frac {y-b}{q}}\right)^{2}+B,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1988ebefb1fc3eaa25c1c66e3c51fa25b66b706a)
![{\displaystyle \left({\frac {\operatorname {d} z}{\operatorname {d} t}}\right)^{2}=4k^{2}\left({\frac {z-c}{r}}\right)^{2}+C\,;\quad }](https://wikimedia.org/api/rest_v1/media/math/render/svg/3fb0f3fdb42d9cd2991602960f9e11aab46b7594)
(18)
étant trois constantes arbitraires.
Pour les déterminer, supposons que la molécule soit partie de l’origine, avec la vîtesse
dans une direction faisant avec les axes des
des angles respectivement égaux à
; nous aurons ainsi
![{\displaystyle V^{2}\operatorname {Cos} .^{2}\alpha =4k^{2}{\frac {a^{2}}{p^{2}}}+A,\quad V^{2}\operatorname {Cos} .^{2}\beta =4k^{2}{\frac {b^{2}}{q^{2}}}+B,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/82e7eef514f5922a7b856ca1c3de010f6808ff0d)
![{\displaystyle V^{2}\operatorname {Cos} .^{2}\gamma =4k^{2}{\frac {c^{2}}{r^{2}}}+C\,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d71b3682bf15d1d1441b7d69fba875436f04c6fa)
en retranchant ces équations des précédentes, il viendra, en transposant,
![{\displaystyle \left.{\begin{aligned}\left({\frac {\operatorname {d} x}{\operatorname {d} t}}\right)^{2}&=4k^{2}\left({\frac {x-a}{p}}\right)^{2}+V^{2}\operatorname {Cos} .^{2}\alpha -4k^{2}{\frac {a^{2}}{p^{2}}},\\\\\left({\frac {\operatorname {d} y}{\operatorname {d} t}}\right)^{2}&=4k^{2}\left({\frac {y-b}{q}}\right)^{2}+V^{2}\operatorname {Cos} .^{2}\beta -4k^{2}{\frac {b^{2}}{q^{2}}},\\\\\left({\frac {\operatorname {d} z}{\operatorname {d} t}}\right)^{2}&=4k^{2}\left({\frac {z-c}{r}}\right)^{2}+V^{2}\operatorname {Cos} .^{2}\gamma -4k^{2}{\frac {c^{2}}{r^{2}}}\,;\end{aligned}}\right\}\quad }](https://wikimedia.org/api/rest_v1/media/math/render/svg/aed78488540e2b241792316ac122e479039ddb93)
(19)
d’où on tirera
![{\displaystyle \left.{\begin{aligned}\operatorname {d} t&={\frac {\operatorname {d} x}{\sqrt {4k^{2}\left({\frac {x-a}{p}}\right)^{2}+V^{2}\operatorname {Cos} .^{2}\alpha -4k^{2}{\frac {a^{2}}{p^{2}}}}}},\\\\\operatorname {d} t&={\frac {\operatorname {d} y}{\sqrt {4k^{2}\left({\frac {y-b}{q}}\right)^{2}+V^{2}\operatorname {Cos} .^{2}\beta -4k^{2}{\frac {b^{2}}{q^{2}}}}}},\\\\\operatorname {d} t&={\frac {\operatorname {d} z}{\sqrt {4k^{2}\left({\frac {z-c}{r}}\right)^{2}+V^{2}\operatorname {Cos} .^{2}\gamma -4k^{2}{\frac {c^{2}}{r^{2}}}}}}\,;\end{aligned}}\right\}\quad }](https://wikimedia.org/api/rest_v1/media/math/render/svg/bf4e41188631f3b72e80559957271f4a607e8381)
(20)