(2)
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et les formules (2), (5) du même paragraphe donneront
(3)
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les valeurs de
![{\displaystyle {\begin{array}{llllll}\mathrm {L} ,&\mathrm {M} ,&\mathrm {N} ,&\mathrm {P} ,&\mathrm {Q} ,&\mathrm {R} ,\\\mathrm {L} _{_{'}},&\mathrm {M} _{_{'}},&\mathrm {N} _{_{'}},&\mathrm {P} _{_{'}},&\mathrm {Q} _{_{'}},&\mathrm {R} _{_{'}},\end{array}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3dd4d847320c9af300862c0176f35b71a015d173)
étant déterminées par les formules symboliques
![{\displaystyle {\begin{aligned}\mathrm {L} \,&=\mathbf {S} m\left[f(\mathrm {r} )+\mathrm {\frac {x^{2}}{r}} \operatorname {D} _{\mathrm {r} }f(\mathrm {r} )\right]\Delta -\mathbf {S} m_{_{'}}\left[\operatorname {f} (\mathrm {r} _{_{'}})+\mathrm {\frac {x_{_{'}}^{2}}{r_{_{'}}}} \operatorname {D} _{\mathrm {r} _{_{'}}}\operatorname {f} (\mathrm {r} _{_{'}})\right],{\text{ etc.}}\\\mathrm {P} \,&=\mathbf {S} m\mathrm {\frac {yz}{r}} \operatorname {D} _{\mathrm {r} }f(\mathrm {r} )\Delta -\mathbf {S} m_{_{'}}\mathrm {\frac {y_{_{'}}z_{_{'}}}{r_{_{'}}}} \operatorname {D} _{\mathrm {r} _{_{'}}}\operatorname {f} (\mathrm {r} _{_{'}})\Delta ,{\text{ etc.}}\\\mathrm {L} _{_{'}}&=\mathbf {S} m_{_{'}}\left[\operatorname {f} (\mathrm {r} _{_{'}})+\mathrm {\frac {x_{_{'}}^{2}}{r_{_{'}}}} \operatorname {D} _{\mathrm {r} _{_{'}}}\operatorname {f} (\mathrm {r} _{_{'}})\right](1+\Delta _{_{'}}),{\text{ etc.}}\\\mathrm {P} _{_{'}}&=\mathbf {S} m_{_{'}}\mathrm {\frac {y_{_{'}}z_{_{'}}}{r_{_{'}}}} \operatorname {D} _{\mathrm {r} _{_{'}}}\operatorname {f} (\mathrm {r} _{_{'}})(1+\Delta _{_{'}}),{\text{ etc.}}\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/05b278f112c34b8cbc44e6e90e2d06b83bd4d9e2)
maintenant on pose, comme dans le paragraphe précédent,
![{\displaystyle u=\operatorname {D} _{x},\qquad v=\operatorname {D} _{y},\qquad w=\operatorname {D} _{z},}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a9b1ac8ceae3c48766f11e90a11ee8750586beb8)
![{\displaystyle \iota =x\operatorname {D} _{x}+y\operatorname {D} _{y}+z\operatorname {D} _{z},\qquad \iota _{_{'}}=x_{_{'}}\operatorname {D} _{x}+y_{_{'}}\operatorname {D} _{y}+z_{_{'}}\operatorname {D} _{z},}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ddafb828c0222b8233c79cd3656b828937cd3c84)
alors, en ayant égard aux formules symboliques
![{\displaystyle \Delta =e^{\iota }-1,\qquad 1+\Delta _{_{'}}=e^{\iota _{_{'}}},}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d0e7e3886b9c4c8347bd9d3a0a940309e202ea09)
et en posant d’ailleurs
(4)
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(5)
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