ELLIP'SIS I Lat., from CI:. .i22r/e4c, ellei 11 11'1111 in grammar and to signify the omission of a sword 11001'9 .11 ry ("qpre,tion senleitcr in its usual form. The ohjcrt of ellipsis is brevity and ELLIP'SOID ifrow (A:. 172 1 olar.
ifb)4. (?.r111). .\ 1:1I1(1 of bounded by a surface of the second order, the spheroid being a special case. The latter has a peculiar interest because the form of the earth is spheroidal. The Cartesian equation of an ellip soid referred to its centre as origin, and its axes y2 ,2 as axes of coordinates (q.v.) is+=+ =- a- 1,2 ,2 where a, b, c are the semi-axes. By giving the value 0 successively to y, z, the equations of three ellipses are obtained, which are the sec tions of the ellipsoid, made by the respective co ordinate planes. If any two of the quantities a, b, c are equal, one of the three sections is a circle. and the ellipsoid becomes an ellipsoid of revol u ion. The surface formed by the revolu
tion of an ellipse about its major axis is called a prolate spheroid, and that formed by the revo lution about the minor axis is called an oblate spheroid. the latter being the general form of the earth. The term is often applied to the solid inclosed by the surface above defined. Ellipsoids play an important part in the theory of inertia. If on any line / through the origin 0, a length OP he laid off, inversely proportional to the square root of the moment of inertia I of the line with respect to the given mass m, the locus of the point P will be a quadric surface called the ellipsoid of inertia or moment& ellipsoid of the point O. The polar reciprocal (see POLE AND POLAR) of the momental ellipsoid with respect to a certain sphere is called the ellipsoid of gyration or the reciprocal ellipsoid.