GLOBE, a round or spherical body, more usually called a sphere, bounded by one uniform convex surface, every point of which is equally distant from a point within, called its centre. Euclid defines the globe or sphere, to be a solid figure described by the revolution of a semi-cir cle about its diameter, which remains unmoved. Also, its axis is the fixed line or diameter about which the semi-circle revolves ; and its centre is the same with that of the revolving semi-circle, a diame ter of it being any right line that passes through the centre, and terminated both ways by the superficies of the sphere.
Euclid, at the end of the twelfth book, skews that spheres are to one another in the triplicate ratio of their meters, that is, their solidities are to onos.another as the cubes of their diameters. And Archimedes determines the real magni tudes and measures of the surfaces and solidities of spheres and their segments, in his treatise " De Sphxra et Cylindro :" viz. 1. That the superficies of any globe is equal to four times a great circle of it. 2. That any sphere is equal to two-thirds of its circumscribing cylinder, or of the cylinder of the same diameter and alti tude. 3. That the curve surface of the segment of a globe, is equal- to the circle whose radius is the line drawn from the vertex of the segment to the circum ference of the base. 4. That the content
of a solid sector of the globe is equal to a cone whose altitude is the radius, of the globe, and its base equal to the curve superfices or the base of the sector, with many other properties. And from hence are easily deduced these practical rules for the surfaces and solidities of globes and their segments ; viz 1. "For the Sur face of a globe," multiply the square of the diameter by 3.1416; or multiply the diameter by the circumference. 2. " For the Solidity of a Globe," multiply the cube of the diameter by .5236 (viz. one sixth of 3.1416) ; or multiply the surface by one-sixth of the diameter. 3. " For the surface of a Segment," multiply the diameter of the globe by the altitude of the segment, and the product again by 3.1416. 4. "For the Solidity of a Segment," multiply the square of the diameter of the globe by the difference between three times that diameter and twice the alti tude of the segment, and the pro duct again by .5236, or one-sixth of 3.1416.
Hence, if d denote the diameter of the globe, c the circumference, a the altitude of any segment, and p = 3.1416 ; then The surface. The solidity: In the globe pi' =cc14. pd3 In the segment pcP X 3d-2a See Al.EXSURATION.