ellipsoids's Usage Examples:

During forty years the resources of analysis, even in the hands of d'Alembert, Lagrange and Laplace, had not carried the theory of the attraction of ellipsoids beyond the point which the geometry of Maclaurin had reached.

Legendre shows that Maclaurin's theorem with respect to confocal ellipsoids is true for any position of the external point when the ellipsoids are solids of revolution.

The potential of such a shell at any internal point is constant, and the equi-potential surfaces for external space are ellipsoids confocal with the ellipsoidal shell.

well-known theorem in attractions that if a shell is made of gravitative matter whose inner and outer surfaces are similar ellipsoids, it exercises no attraction on a particle of matter in its interior.

- a of the two ellipsoids made by x=o; or if aU - a?

The continuity is secured if the liquid between two ellipsoids X and X 11 moving with the velocity U and 15 1 of equation (II), is squeezed out or sucked in across the plane x=o at a rate equal to the integral flow of the velocity I across the annular area a l.

A system of confocal ellipsoids is taken y2 (3) a 2 +X b 2 +X c2 + A= I, and a velocity function of the form = x1 P, (4) where 4' is a function of X only, so that 4) is constant over an ellipsoid; and we seek to determine the motion set up, and the form of >G which will satisfy the equation of continuity.

Legendre, in 1783, extended Maclaurin's theorem concerning ellipsoids of revolution to the case of any spheroid of revolution where the attracted point, instead of being limited to the axis or equator, occupied any position in space; and Laplace, in his treatise Theorie du mouvement et de la figure elliptique des planetes (published in 1784), effected a still further generalization by proving, what had been suspected by Legendre, that the theorem was equally true for any confocal ellipsoids.

The magnetometric method, except when employed in connexion with ellipsoids, for which the demagnetizing factors are [[[Magnetic Measurements]] accurately known, is generally less satisfactory for the exact determination of induction or magnetization than the ballistic method.

These, together with values of nt 2 N for cylindrical rods, and of N and m 2 N for ellipsoids of revolution, are given in the following useful table (loc. cit.

Synonyms:

two-dimensional figure, plane figure,

Antonyms:

three-cornered, square, prolate,