Projection

Projection is the representation on any surface of objects or figures as they appear to the eye of an observer. It thus includes Perspective (q.v.), and is most simply illustrated by the shadow of an object thrown by a candle on a wall; the shadow being the projection and the place of the light the position of the eye. The theory of projections is of great importance, both in mathematics and geography, being, in the former case, perfectly general in its application, while in the latter only the projection of the sphere is required. Projections of the sphere are of various kinds, depending upon the position and distance of the eye from the sphere, and the form of the surface on which the projection is thrown; thus we have the orthographic, stereographic, globular, conical, and cylindrical or Mercator's projections, all of which are treated of under the article MAP. Another projection frequently employed is the gnomonic. In the gnomonic projection the eye is supposed to be situated at the centre of the sphere, and the surface on which the projection is thrown is a plane surface which touches the sphere at any one point (called the principal point). It is evident that a map constructed on the gnomonic projection is sensibly correct only for a circular area whose circumference is at a small angular distance from the principal point. From the position of the eye in the gnomonic projection (which is not suited for representing large portions of the earth's surface) it follows that all great circles or portions of great circles of the sphere are represented by straight lines, for their planes pass through the eye. The gnomonic projection derives its name from its connection with the mode of describing a gnomon or Dial (q.v.). The gnomonic and stereographic projection of crystals is described and illustrated at CRYSTALLOGRAPHY.