ce qui donnera, en intégrant,
![{\displaystyle \left.{\begin{aligned}t+D&={\frac {p}{2k}}\operatorname {Log} .\left\{2k{\frac {x-a}{p}}+{\sqrt {4k^{2}\left({\frac {x-a}{p}}\right)^{2}+V^{2}\operatorname {Cos} .^{2}\alpha -4k^{2}{\frac {a^{2}}{p^{2}}}}}\right\},\\\\t+E&={\frac {q}{2k}}\operatorname {Log} .\left\{2k{\frac {y-b}{q}}+{\sqrt {4k^{2}\left({\frac {y-b}{q}}\right)^{2}+V^{2}\operatorname {Cos} .^{2}\beta -4k^{2}{\frac {b^{2}}{q^{2}}}}}\right\},\\\\t+F&={\frac {r}{2k}}\operatorname {Log} .\left\{2k{\frac {z-c}{r}}+{\sqrt {4k^{2}\left({\frac {z-c}{r}}\right)^{2}+V^{2}\operatorname {Cos} .^{2}\gamma -4k^{2}{\frac {c^{2}}{r^{2}}}}}\right\},\end{aligned}}\right\}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c0fa82cde27719915b4220c51c741cc8702fbf97)
(21)
étant trois nouvelles constantes arbitraires.
Pour les déterminer, fixons l’origine des temps au passage de la molécule par l’origine des coordonnées ; alors
devront être nuls en même temps que
ce qui donnera
![{\displaystyle {\begin{aligned}D&={\frac {p}{2k}}\operatorname {Log} .\left(-2k{\frac {a}{p}}+V\operatorname {Cos} .\alpha \right),\\\\E&={\frac {q}{2k}}\operatorname {Log} .\left(-2k{\frac {b}{q}}+V\operatorname {Cos} .\beta \right),\\\\F&={\frac {r}{2k}}\operatorname {Log} .\left(-2k{\frac {c}{r}}+V\operatorname {Cos} .\gamma \right)\,;\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0e13bd75fba1e3360d7f84a1d116bf4f2ee7d0fc)
d’où, en retranchant,
![{\displaystyle \left.{\begin{aligned}t&={\frac {p}{2k}}\operatorname {Log} .{\frac {2k{\frac {x-a}{p}}+{\sqrt {4k^{2}\left({\frac {x-a}{p}}\right)^{2}+V^{2}\operatorname {Cos} .^{2}\alpha -4k^{2}{\frac {a^{2}}{p^{2}}}}}}{V\operatorname {Cos} .\alpha -2k{\frac {a}{p}}}},\\\\t&={\frac {q}{2k}}\operatorname {Log} .{\frac {2k{\frac {y-b}{q}}+{\sqrt {4k^{2}\left({\frac {y-b}{q}}\right)^{2}+V^{2}\operatorname {Cos} .^{2}\beta -4k^{2}{\frac {b^{2}}{q^{2}}}}}}{V\operatorname {Cos} .\beta -2k{\frac {b}{q}}}},\\\\t&={\frac {r}{2k}}\operatorname {Log} .{\frac {2k{\frac {z-c}{r}}+{\sqrt {4k^{2}\left({\frac {z-c}{r}}\right)^{2}+V^{2}\operatorname {Cos} .^{2}\gamma -4k^{2}{\frac {c^{2}}{r^{2}}}}}}{V\operatorname {Cos} .\gamma -2k{\frac {c}{r}}}}\,;\end{aligned}}\right\}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4127216690826532282d746acffba4b4b22e9a39)
(22)