Sphere, a surface of which every point is equally distant from a definite point known as the centre. It may be described by the rotation of a semicircle (or circle) about its diameter. From every aspect a sphere has the same appearance. Every plane section is a circle—a great circle if the cutting plane contains the centre of the sphere, a small circle in all other cases. The shortest line that can be drawn on the surface so as to join any two points must be an arc of the great circle passing through these two points. If is the radius of the sphere its volume is and its surface is . These are intimately related to the volume and curved portion of the surface of the circumscribing cylinder, whose height is equal to the diameter of the sphere. The volumes are as two to three, and the surface areas, so defined, are equal.
Spheroid is a species of Ellipsoid (q.v.), and is represented by the same equation. If an ellipse be made to revolve round one of its axes, the curved outline of the ellipse describes the spheroid. Should the major or longer axis be the axis of revolution the spheroid is said to be prolate, but if the minor or shorter axis, oblate. The Earth (q.v.) is very approximately an oblate spheroid.
Spherometer is an instrument for measuring the sphericity of portions of spherical surfaces—for example, lenses. It rests on three pointed legs, whose points form an equilateral triangle. Midway between these is a fourth leg, which can be screwed up or down as desired through a distance measured by the number of turns given to it. After the spherometer is adjusted on any spherical surface till the four legs are all in contact with the surface it is lifted on to a plane surface and the middle leg screwed up or down until the four legs all lie on the plane. Thus we measure the height of the segment whose base is the circle passing through the equilateral triangle mentioned above, and can by a simple calculation find the radius of the spherical surface. The instrument may also be applied to measure the thicknesses of plates small enough to be pushed within the legs.