A Popular Handbook of Astronomy
Library of Alexandria
The Sphere.—A sphere is a solid figure bounded by a surface which curves equally in all directions at every point. The rate at which the surface curves is called the curvature of the sphere. The smaller the sphere, the greater is its curvature. Every point on the surface of a sphere is equally distant from a point within, called the centre of the sphere. The circumference of a sphere is the distance around its centre. The diameter of a sphere is the distance through its centre. The radius of a sphere is the distance from the surface to the centre. The surfaces of two spheres are to each other as the squares of their radii or diameters; and the volumes of two spheres are to each other as the cubes of their radii or diameters. Distances on the surface of a sphere are usually denoted in degrees. A degree is 1/360 of the circumference of the sphere. The larger a sphere, the longer are the degrees on it. A curve described about any point on the surface of a sphere, with a radius of uniform length, will be a circle. As the radius of a circle described on a sphere is a curved line, its length is usually denoted in degrees. The circle described on the surface of a sphere increases with the length of the radius, until the radius becomes 90°, in which case the circle is the largest that can possibly be described on the sphere. The largest circles that can be described on the surface of a sphere are called great circles, and all other circles small circles. Any number of great circles may be described on the surface of a sphere, since any point on the sphere may be used for the centre of the circle. The plane of every great circle passes through the centre of the sphere, while the planes of all the small circles pass through the sphere away from the centre. All great circles on the same sphere are of the same size, while the small circles differ in size according to the distance of their planes from the centre of the sphere. The farther the plane of a circle is from the centre of the sphere, the smaller is the circle. By a section of a sphere we usually mean the figure of the surface formed by the cutting; by a plane section we mean one whose surface is plane. Every plane section of a sphere is a circle. When the section passes through the centre of the sphere, it is a great circle; in every other case the section is a small circle.