![{\displaystyle \delta \,a=-\mathrm {H} _{0}\int \left({\frac {d\Omega '}{da'}}dt\iint \Omega 'dt^{2}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b07ae45994d95c91e0ad5ac2649fe252498407de)
![{\displaystyle {\begin{aligned}-\mathrm {H} _{0}\int &\left[{\frac {d^{2}\Omega }{da^{'2}}}\int {\frac {d\Omega }{da}}dt-{\frac {d^{2}\Omega }{da'da}}\int {\frac {d\Omega }{da'}}dt+{\frac {d^{2}\Omega }{da'db'}}\int {\frac {d\Omega }{db}}dt\right.\\&\quad \left.-{\frac {d^{2}\Omega }{da'db}}\int {\frac {d\Omega }{db'}}dt+{\frac {d^{2}\Omega }{da'dc'}}\int {\frac {d\Omega }{dc}}dt-{\frac {d^{2}\Omega }{da'dc}}\int {\frac {d\Omega }{dc'}}dt\right]dt,\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b4ca537f4e3efa1135394364de8f1f40cf5fa696)
![{\displaystyle \delta \,a'=\mathrm {H} _{0}\int \left({\frac {d\Omega '}{da}}dt\iint \Omega 'dt^{2}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e8d92ac2475aad71883f86da17bc746b2f547c97)
![{\displaystyle {\begin{aligned}-\mathrm {H} _{0}\int &\left[{\frac {d^{2}\Omega }{da^{2}}}\int {\frac {d\Omega }{da'}}dt-{\frac {d^{2}\Omega }{dada'}}\int {\frac {d\Omega }{da}}dt+{\frac {d^{2}\Omega }{dadb}}\int {\frac {d\Omega }{db'}}dt\right.\\&\quad \left.-{\frac {d^{2}\Omega }{dadb'}}\int {\frac {d\Omega }{db}}dt+{\frac {d^{2}\Omega }{dadc}}\int {\frac {d\Omega }{dc'}}dt-{\frac {d^{2}\Omega }{dadc'}}\int {\frac {d\Omega }{dc}}dt\right]dt\,;\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bb308b1480028b3a2c69e92899321105d865a09d)
nous n’écrivons pas les valeurs de
qui se déduisent de celles de
par de simples changemens de lettres.
Dans tous ces termes du premier et du second ordre, il faudra faire
et considérer
etc., comme des constantes absolues. En les substituant, ainsi qu’il vient d’être dit, dans la valeur de
on trouve
![{\displaystyle {\frac {d^{2}\rho }{dt^{2}}}=n\mathrm {H_{0}H_{1}} \Omega ''\iint \left(\Omega 'dt^{2}\int \Omega 'dt\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c8ad5c5a48fce2906abadba76778447f6eaae428)
![{\displaystyle +\mathrm {H} _{0}^{3}\left[\Omega ''\iint \left(\Omega ''dt^{2}\iint \Omega 'dt^{2}\right)+{\frac {1}{2}}\Omega '''\left(\iint \Omega 'dt^{2}\right)^{2}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/91ce62b4ac95030d99c240b196757bfe79a09631)
![{\displaystyle +\mathrm {H} _{0}^{2}\left([da',da]-[da,da']+[db',db]-[db,db']+[dc',dc]-[dc,dc']\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2856c50187512fad26003a851f8cc976c5a3d549)