On the attractions of homogeneous ellipsoids / [Sir James Ivory].

  • Ivory, James, Sir, 1765-1842.
Date:
1809
Catalogue details

Licence: Public Domain Mark

Credit: On the attractions of homogeneous ellipsoids / [Sir James Ivory]. Source: Wellcome Collection.

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    consequence of the equation of the solid, R is a function of the angles p and q: therefore, making p only variable, we shall have — dy = j (2) sin.p + R cos. jcos. q.dp: then, because y must be constant when z varies, we must make — dz = { (|f) sin- P + R cos./.} sin. q.dp + { (^) sin. q + R cos. q | sin. p . dq, 0 = {(f) s‘n-/> + R cos,/.} cos. q.dp + {ff) cos. q - R sin. q j sm. p . dq. and by exterminating dp, we get _ d% =- R shl- P • dv. cos. q and hence, by substitution, r(?) A- = ,ff\ R cos.p sin. *p + cos. *p si n./> j dp . dq; the fluent to be taken from p = 0, to p = -p and from q = 0, q = Stet. The transformed formula for cannot be integrated, un¬ less we substitute, in place of R, the function of the angles p and q, that is equal to it. Now, x = R co s.p, y =3 b - R sin./> cos. q, z = c — R sin.p sin. q: let these values be substituted in the equation of the solid, £ + £ + .2. - A* ‘ k'z i A* — A ’ and, for the sake of simplicity, let
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