## Ellipsoids Sentence Examples

- 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. - 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. - 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**. - 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. - 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 of the two
**ellipsoids**made by x=o; or if aU - a? - 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. - 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. - 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. - 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. - The
**ellipsoids**(41) and (4~i) are reciprocal polars with respect to a sphere having 0 as centre. - The problem is identical with that of finding the common conjugate diameters of the
**ellipsoids**T(x, y, I) =const., V(x, y, 1) =const. - For example, all
**ellipsoids**referred to co-ordinates parallel to any three conjugate diameters are parallel projections of each other and of a sphere referred to rectangular co-ordinates. - Among his most remarkable works may be mentioned his ten memoirs on quantics, commenced in 1854 and completed in 1878; his creation of the theory of matrices; his researches on the theory of groups; his memoir on abstract geometry, a subject which he created; his introduction into geometry of the "absolute"; his researches on the higher singularities of curves and surfaces; the classification of cubic curves; additions to the theories of rational transformation and correspondence; the theory of the twenty-seven lines that lie on a cubic surface; the theory of elliptic functions; the attraction of
**ellipsoids**; the British Association Reports, 1857 and 1862, on recent progress in general and special theoretical dynamics, and on the secular acceleration of the moon's mean motion. - We have a memoir On the Attraction of Homogeneous
**Ellipsoids**, and the already mentioned memoir Allgemeine LehrsÃtze, on the theory of forces attracting according to the inverse square of the distance.