Prolate meaning

The cases of greatest practical importance are those of a sphere (which is an ellipsoid with three equal axes) and an ovoid or prolate ellipsoid of revolution.

An experiment was devised by Lord Kelvin for demonstrating this, in which the difference of steadiness was shown of a copper shell filled with liquid and spun gyroscopically, according as the shell was slightly oblate or prolate.

ZUy2BB0 Bll; reducing, when the liquid extends to infinity and B 3 =0, to = xA o' _ - zUy 2B o so that in the relative motion past the body, as when fixed in the current U parallel to xO, A 4)'=ZUx(I+Bo), 4)'= zUy2(I-B o) (6) Changing the origin from the centre to the focus of a prolate spheroid, then putting b 2 =pa, A = A'a, and proceeding to the limit where a = oo, we find for a paraboloid of revolution P B - p (7) B = 2p +A/' Bo p+A y2 i =p+A'- 2x, (8) p+?

The ellipsoid is the only shape for which a and (3 have so far been determined analytically, as shown already in § 44, so we must restrict our calculation to an egg-shaped bullet, bounded by a prolate ellipsoid of revolution, in which, with b =c, Ao= fo (a2 + X)V [4(a2+X)(b +X)2]-J0 2(a2 +X)3/2(b2+X), (13) Ao+2Bo = I, (t4) _ B 0 t - A 0 I a?I-A0' Q I - Bo I-{- A o I-?

In the extreme case when e=1, the prolate ellipsoid becomes a long thin rod, and then the capacity is given by C 1 = a/log e 2a/b (io), which is identical with the formula (2) already obtained.