Il ne reste plus qu’à substituer pour φ 1 , φ 2 , φ 3 , φ 4 {\displaystyle \varphi _{1},\varphi _{2},\varphi _{3},\varphi _{4}} et ψ {\displaystyle \psi } leurs valeurs μ 1 t + n y 1 , μ 2 t + n y 2 , μ 3 t + n y 3 , μ 4 t + n y 4 {\displaystyle \mu _{1}t+ny_{1},\mu _{2}t+ny_{2},\mu _{3}t+ny_{3},\mu _{4}t+ny_{4}} et m t + n J ; {\displaystyle mt+n\mathrm {J} \,;} ce qui est très-facile, car il n’y aura qu’à changera, φ 1 , φ 2 , φ 3 , φ 4 , ψ {\displaystyle \varphi _{1},\varphi _{2},\varphi _{3},\varphi _{4},\psi } en μ 1 t , μ 2 t , {\displaystyle \mu _{1}t,\mu _{2}t,} μ 3 t , μ 4 t , m t , {\displaystyle \mu _{3}t,\mu _{4}t,mt,} et ajouter ensuite aux expressions de R , {\displaystyle \mathrm {R} ,} et Q , {\displaystyle \mathrm {Q} ,} les quantités suivantes
et
Pour trouver les valeurs de R 2 , Q 2 , P 2 , {\displaystyle \mathrm {R_{2},Q_{2},P_{2}} ,} il ne faudra qu’ajouter un trait
![{\displaystyle {\begin{aligned}&+n{\frac {{\mathfrak {S}}_{4}}{\mathbb {Z} \!^{\upsilon }}}{\frac {\mathbb {Z} \!^{\upsilon }}{a_{1}^{2}}}z_{1}\left[a_{1}^{3}\Gamma (a_{1},a_{4})+a_{1}^{3}\Gamma _{1}(a_{1},a_{4})\cos(\varphi _{4}-\varphi _{1})+\ldots \right]\\&+n{\frac {a_{1}^{3}}{\alpha ^{3}}}{\frac {\circledast }{\mathbb {Z} \!^{\upsilon }}}{\frac {\mathbb {Z} \!^{\upsilon }}{a_{1}^{2}}}z_{1}\\&-n{\frac {{\mathfrak {S}}_{2}}{\mathbb {Z} \!^{\upsilon }}}{\frac {\mathbb {Z} \!^{\upsilon }}{a_{1}^{2}}}z_{2}\left[a_{1}^{2}a_{2}\Gamma (a_{1},a_{2})-{\frac {a_{1}^{2}}{a_{2}^{2}}}+a_{1}^{2}a_{2}\Gamma _{1}(a_{1},a_{2})\cos(\varphi _{2}-\varphi _{1})+\ldots \right]\\&-n{\frac {{\mathfrak {S}}_{3}}{\mathbb {Z} \!^{\upsilon }}}{\frac {\mathbb {Z} \!^{\upsilon }}{a_{1}^{2}}}z_{3}\left[a_{1}^{2}a_{3}\Gamma (a_{1},a_{3})-{\frac {a_{1}^{2}}{a_{3}^{2}}}+a_{1}^{2}a_{3}\Gamma _{1}(a_{1},a_{3})\cos(\varphi _{3}-\varphi _{1})+\ldots \right]\\&-n{\frac {{\mathfrak {S}}_{4}}{\mathbb {Z} \!^{\upsilon }}}{\frac {\mathbb {Z} \!^{\upsilon }}{a_{1}^{2}}}z_{4}\left[a_{1}^{2}a_{4}\Gamma (a_{1},a_{4})-{\frac {a_{1}^{2}}{a_{4}^{2}}}+a_{1}^{2}a_{4}\Gamma _{1}(a_{1},a_{4})\cos(\varphi _{4}-\varphi _{1})+\ldots \right]\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c5cd5bda41f97b832d41686f3a7406bff63f2813)
et 
leurs valeurs 
et 
ce qui est très-facile, car il n’y aura qu’à changera, 
en 
et ajouter ensuite aux expressions de 
et 
les quantités suivantes
![{\displaystyle {\begin{aligned}&n{\frac {{\mathfrak {S}}_{2}}{\mathbb {Z} \!^{\upsilon }}}{\frac {\mathbb {Z} \!^{\upsilon }}{a_{1}^{2}}}(y_{2}-y_{1})\left[{\breve {\Gamma }}_{1}(a_{1},a_{2})\sin(\mu _{2}-\mu _{1})t+2{\breve {\Gamma }}_{2}(a_{1},a_{2})+\ldots \right]\\+&n{\frac {{\mathfrak {S}}_{3}}{\mathbb {Z} \!^{\upsilon }}}{\frac {\mathbb {Z} \!^{\upsilon }}{a_{1}^{2}}}(y_{3}-y_{1})\left[{\breve {\Gamma }}_{1}(a_{1},a_{3})\sin(\mu _{3}-\mu _{1})t+2{\breve {\Gamma }}_{2}(a_{1},a_{3})+\ldots \right]\\+&n{\frac {{\mathfrak {S}}_{4}}{\mathbb {Z} \!^{\upsilon }}}{\frac {\mathbb {Z} \!^{\upsilon }}{a_{1}^{2}}}(y_{4}-y_{1})\left[{\breve {\Gamma }}_{1}(a_{1},a_{4})\sin(\mu _{4}-\mu _{1})t+2{\breve {\Gamma }}_{2}(a_{1},a_{4})+\ldots \right]\\+&n{\frac {a_{1}^{3}}{\alpha ^{3}}}{\frac {\circledast }{\mathbb {Z} \!^{\upsilon }}}{\frac {\mathbb {Z} \!^{\upsilon }}{a_{1}^{2}}}(\mathrm {J} -y_{1})\times 3\sin 2(m-\mu _{1})t,\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/be0fd9f402344dfb0d623e741b7517e90a9f5141)
![{\displaystyle {\begin{aligned}-&n{\frac {{\mathfrak {S}}_{2}}{\mathbb {Z} \!^{\upsilon }}}{\frac {\mathbb {Z} \!^{\upsilon }}{a_{1}^{2}}}(y_{2}-y_{1})\left[{\widehat {\Gamma }}_{1}(a_{1},a_{2})\cos(\mu _{2}-\mu _{1})t+2{\widehat {\Gamma }}_{2}(a_{1},a_{2})+\ldots \right]\\-&n{\frac {{\mathfrak {S}}_{3}}{\mathbb {Z} \!^{\upsilon }}}{\frac {\mathbb {Z} \!^{\upsilon }}{a_{1}^{2}}}(y_{3}-y_{1})\left[{\widehat {\Gamma }}_{1}(a_{1},a_{3})\cos(\mu _{3}-\mu _{1})t+2{\widehat {\Gamma }}_{2}(a_{1},a_{3})+\ldots \right]\\-&n{\frac {{\mathfrak {S}}_{4}}{\mathbb {Z} \!^{\upsilon }}}{\frac {\mathbb {Z} \!^{\upsilon }}{a_{1}^{2}}}(y_{4}-y_{1})\left[{\widehat {\Gamma }}_{1}(a_{1},a_{4})\cos(\mu _{4}-\mu _{1})t+2{\widehat {\Gamma }}_{2}(a_{1},a_{4})+\ldots \right]\\+&n{\frac {a_{1}^{3}}{\alpha ^{3}}}{\frac {\circledast }{\mathbb {Z} \!^{\upsilon }}}{\frac {\mathbb {Z} \!^{\upsilon }}{a_{1}^{2}}}(\mathrm {J} -y_{1})\times 3\cos 2(m-\mu _{1})t.\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/74dcaacd05a578f272ecd605f11ab52e2adb76c3)
il ne faudra qu’ajouter un trait
