gente avec la normale (6) au même point, c’est-à-dire, l’angle d’incidence, on aura
![{\displaystyle \operatorname {Sin} .\theta ={\frac {\sqrt {\left(Q{\frac {\operatorname {d} z}{\operatorname {d} t}}-R{\frac {\operatorname {d} y}{\operatorname {d} t}}\right)^{2}+\left(R{\frac {\operatorname {d} x}{\operatorname {d} t}}-P{\frac {\operatorname {d} z}{\operatorname {d} t}}\right)^{2}+\left(P{\frac {\operatorname {d} y}{\operatorname {d} t}}-Q{\frac {\operatorname {d} x}{\operatorname {d} t}}\right)^{2}}}{\sqrt {\left(P^{2}+Q^{2}+R^{2}\right)\left\{\left({\frac {\operatorname {d} x}{\operatorname {d} t}}\right)^{2}+\left({\frac {\operatorname {d} y}{\operatorname {d} t}}\right)^{2}+\left({\frac {\operatorname {d} z}{\operatorname {d} t}}\right)^{2}\right\}}}}.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e4fccc3eb2920599fe3eec12aea1f74e6f8973b0)
(10)
Mais, si l’on représente par
la vîtesse absolue de la molécule au point
ce qui donnera
![{\displaystyle v^{2}=\left({\frac {\operatorname {d} x}{\operatorname {d} t}}\right)^{2}+\left({\frac {\operatorname {d} y}{\operatorname {d} t}}\right)^{2}+\left({\frac {\operatorname {d} z}{\operatorname {d} t}}\right)^{2},\qquad }](https://wikimedia.org/api/rest_v1/media/math/render/svg/9b0a211720c43459732ab44d0f4c1d27c7e9c99e)
(11)
la vîtesse, dans le sens du plan tangent en
à la surface (4) de densité constante, sera
en substituant donc, dans son expression, pour
et
leurs valeurs, cette vîtesse deviendra
![{\displaystyle {\frac {\sqrt {\left(Q{\frac {\operatorname {d} z}{\operatorname {d} t}}-R{\frac {\operatorname {d} y}{\operatorname {d} t}}\right)^{2}+\left(R{\frac {\operatorname {d} x}{\operatorname {d} t}}-P{\frac {\operatorname {d} z}{\operatorname {d} t}}\right)^{2}+\left(P{\frac {\operatorname {d} y}{\operatorname {d} t}}-Q{\frac {\operatorname {d} x}{\operatorname {d} t}}\right)^{2}}}{\sqrt {P^{2}+Q^{2}+R^{2}}}}\,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fae307c3180845eabe7597d083c75ed3127fd627)
et il faudra que la différentielle de cette composante, en y traitant
comme constans, puisqu’on reste dans le plan tangent, soit nulle ; ce qui donnera, pour deuxième équation du mouvement de la molécule,
![{\displaystyle \left.{\begin{aligned}&\left(Q{\frac {\operatorname {d} z}{\operatorname {d} t}}-R{\frac {\operatorname {d} y}{\operatorname {d} t}}\right)\left(Q{\frac {\operatorname {d} ^{2}z}{\operatorname {d} t^{2}}}-R{\frac {\operatorname {d} ^{2}y}{\operatorname {d} t^{2}}}\right)\\\\+&\left(R{\frac {\operatorname {d} x}{\operatorname {d} t}}-P{\frac {\operatorname {d} z}{\operatorname {d} t}}\right)\left(R{\frac {\operatorname {d} ^{2}x}{\operatorname {d} t^{2}}}-P{\frac {\operatorname {d} ^{2}z}{\operatorname {d} t^{2}}}\right)\\\\+&\left(P{\frac {\operatorname {d} y}{\operatorname {d} t}}-Q{\frac {\operatorname {d} x}{\operatorname {d} t}}\right)\left(P{\frac {\operatorname {d} ^{2}y}{\operatorname {d} t^{2}}}-Q{\frac {\operatorname {d} ^{2}x}{\operatorname {d} t^{2}}}\right)\end{aligned}}\right\}=0.\quad }](https://wikimedia.org/api/rest_v1/media/math/render/svg/58612de20df33c8b0afe0117ed4bc680fdcc4773)
(12)