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+?
With A' =0 over the surface of the paraboloid; and then' = ZU[y 2 - pJ (x2 + y2) + px ]; (9) =-2U p [1/ (x2 + y2)-x]; (io) 4, = - ZUp log [J(x2+y2)+x] (II) The relative path of a liquid particle is along a stream line 1,L'= 2Uc 2, a constant, (12) = /,2 3, 2 _ (y 2 _ C 2) 2 2 2 2' - C2 2 x 2p(y2 - c2) /' J(x2 +y 2)= py ` 2p(y2_c2)) (13) a C4; while the absolute path of a particle in space will be given by dy_ r - x _ y 2 - c2 dx_ - y - 2py y 2 - c 2 = a 2 e -x 1 46.
A rotifer may be regarded as typically a hemisphere or half an oblate spheroid or paraboloid with a mouth somewhere on the flat end ("disk" or "corona"), which bears a usually double ciliated ring, the outer zone the "cingulum," and inner the "trochus".
Foucault invented in 1857 the polarizer which bears his name, and in the succeeding year devised a method of giving to the speculum of reflecting telescopes the form of a spheroid or a paraboloid of revolution.
Showed that, if the large mirror were a segment of a paraboloid of revolution whose focus is F, and the small mirror an ellipsoid of revolution whose foci are F and P respectively, the resulting image will be plane and undistorted.
The surface of the large mirror should be a paraboloid of revolution, that of the small mirror a true optical plane.
Take the pole of each face of such a polyhedron with respect to a paraboloid of revolution, these poles will be the vertices of a second polyhedron whose edges are the conjugate lines of those of the former.
If we project both polyhedra orthogonally on a plane perpendicular to the axis of the paraboloid, we obtain two figures which are reciprocal, except that corresponding lines are orthogonal instead of parallel.
46) is made entirely of glass, and is in the form of a paraboloid, having on the top a spherical hole, of such a curvature that all entering rays, r r' r", parallel to the axis, after their reflection on the surface of the paraboloid, traverse the spherical surface perpendicularly and unite in F, the centre of the sphere.
Another form of the paraboloid condenser, also due to Wenham, has a plane surface on the upper side.
- Siedentopf's Paraboloid Condenser.