Mécanique Céleste Vol.2

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sin. 2 è. [2120a] The integral in the first member must be a function of n, as in [137'", &z.c] ; and at the external surface, where n = 0, it becomes constant ; hence if we divide 131 522 FIGURE OF THE ATMOSPHERES [Méc. Cél, Putting R equal to the polar radius of the atmosphere, we shall have* [2121] c = - , therefore Equation /t of the sur- face of the t 2122 ] J = - + «»*. sin. 8 i.
pheie.
[2122] To obtain the ratio of the two axes of the atmosphere, we shall put R for the radius of its equa
...tor, and the preceding equation will give,t [2123] « R' 3 = 2 .
It The maximum '° U ato f r!i'i° The greatest possible value of R! is that which extends to the point where the radius to the polar . m t radium centrifugal force becomes equal to gravity. JNow in this casef -=g = «it, [2124] or v.R' 3 = l; consequently, R [2125] ~R = %' [2120c] [21206] the whole equation by im, and put — = «, it will become as in [2120], c being a constant quantity. At the equator, where sin. Ô = 1, and r = 1 [2119'"], the centrifugal force ?i 2 r .


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