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THÉORIE DE JUPITER ET DE SATURNE.
dans la supposition de
![{\displaystyle {\begin{aligned}{\frac {\delta r}{a}}=&\quad \ \ \ 3{,}921972e\ \cos(2n't-nt+2\varepsilon '-\varepsilon -\varpi )\\&-\ \ 1{,}936758e'\cos(2n't-nt+2\varepsilon '-\varepsilon -\varpi '),\\\delta v=&\quad \ 46{,}831183e\ \,\sin(2n't-nt+2\varepsilon '-\varepsilon -\varpi )\\&-16{,}383921e'\,\sin(2n't-nt+2\varepsilon '-\varepsilon -\varpi ')\,;\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2af8f41082b3b97718da759866d9a7ada06fb08a)
dans la supposition de ![{\displaystyle i=3,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/600808eb6cfe65dbbfec764b2e11724514aeab3e)
![{\displaystyle {\begin{aligned}{\frac {\delta r}{a}}=&\quad \ \,\ 6{,}179689e\ \cos(3n't-2nt+3\varepsilon '-2\varepsilon -\varpi \ )\\&-10{,}384318e'\cos(3n't-2nt+3\varepsilon '-2\varepsilon -\varpi '),\\\delta v=&\quad \ 15{,}042550e\ \,\sin(3n't-2nt+3\varepsilon '-2\varepsilon -\varpi \ )\\&-24{,}582706e'\,\sin(3n't-2nt+3\varepsilon '-2\varepsilon -\varpi ')\,;\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a66ef08f508e37deafb0ebc5f75de9e288448c9c)
dans la supposition de ![{\displaystyle i=4,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/949d982776d5290a7eae3a33d3be42dc47b9d74d)
![{\displaystyle {\begin{aligned}{\frac {\delta r}{a}}=&-1{,}689958e\ \cos(4n't-3nt+4\varepsilon '-3\varepsilon -\varpi \ )\\&+2{,}781392e'\cos(4n't-3nt+4\varepsilon '-3\varepsilon -\varpi '),\\\delta v=&-2{,}681615e\ \,\sin(4n't-3nt+4\varepsilon '-3\varepsilon -\varpi \ )\\&+4{,}521536e'\,\sin(4n't-3nt+4\varepsilon '-3\varepsilon -\varpi ').\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7390481abced752ccbf0174d6d62a71ff0a8345f)
Je n’ai pas poussé plus loin les approximations relatives aux valeurs positives de
parce que les termes suivants sont presque insensibles.
En faisant successivement
on trouve, dans la supposition de
![{\displaystyle {\begin{aligned}{\frac {\delta r}{a}}=&-0{,}777084e\ \cos(2nt-n't+2\varepsilon -\varepsilon '-\varpi \ )\\&-0{,}102748e'\cos(2nt-n't+2\varepsilon -\varepsilon '-\varpi '),\\\delta v=&\quad \ 1{,}762156e\ \,\sin(2nt-n't+2\varepsilon -\varepsilon '-\varpi \ )\\&+0{,}165032e'\,\sin(2nt-n't+2\varepsilon -\varepsilon '-\varpi ')\,;\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d83a4513855a4f8ffdccc3feb7ea8209172f151c)
dans la supposition de ![{\displaystyle i=-2,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/07fdd5614b4c9b8a8c32474f5e88a8ff658821a4)
![{\displaystyle {\begin{aligned}{\frac {\delta r}{a}}=&\quad \ 1{,}807069e\ \cos(3nt-2n't+3\varepsilon -2\varepsilon '-\varpi \ )\\&-0{,}075906e'\cos(3nt-2n't+3\varepsilon -2\varepsilon '-\varpi '),\\\delta v=&-4{,}357375e\ \,\sin(3nt-2n't+3\varepsilon -2\varepsilon '-\varpi \ )\\&+0{,}102055e'\,\sin(3nt-2n't+3\varepsilon -2\varepsilon '-\varpi ').\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2a9a45308164470447a8957804979db1bed54243)
Les suppositions suivantes donnent des résultats insensibles.