Page:The New International Encyclopædia 1st ed. v. 13.djvu/46

* 3)IAF. 32 representation of hemispheres and are seldom used in mapping small areas. The orthographic projection assumes that the eye is placed at an inlinite distance, so that all lines leading from it to the object are paralh-l. The plane of projection is at right angles to the line of sight and every point upon the herai- MAP. GNOMIC PEOJECTION. (On plane o( the Equator.) sphere is referred to the plane hy a perpendicular let fall on it. In this projection the central portions of the hciiiisphcri' arc faithfully rc]ne- sented. tnit near 1lic circiiinfcrcnce the areas Ix'- come greatly diniiiiisluHl and tlie relative angular directions are greatly changed. The stereographic projection is obtained when the surfaces are much larger than on the globe; but. on the other hand, the relative positions of objects that are near together are well preserved. The gnomic projection assumes that the eye is placed at the centre of a sphere while the plane of projection is tangent to its surface. The globular or equidistant projection was de- signed to correct, as much as possible, the con- traction of the orthographic and the expansion of the stereographic projections. In this method the eye is supposed to be placed along the diameter of the sphere at a distance — = times the radius above the surface, and the plane of projection is perpendicular to the diameter. In this con- struction all circles on the sphere become ellipses, and ol>jects are not represented with their true outlines, but the relative dimensions are fairly well preserved. An eciuidistant method for polar projections of the sphere is employed in the meteorological charts of the Northern and Southern hemispheres frequently used by the United States Weather Bureau. Modern maps upon large scales are constructed by so-called projections which arc actually dv- rilopmenls of projections. Development is ren- dered possible by the substitution of a cylindrical or conical surface for the ordinary plane of [irojection, the eye occupying an arbitrary posi- tion when not assmned at the centre of the >phere. The surface of the cylinder or cone is developed subsequently in a plane. Various re- sults may be obtainecl by changing the place at which the cone or cylinder is tangent to the 160 180 160 140 120 100 80 40 20 20 40 60 80 100 120 140 160 MBRCATOB 8 PROJECTION. the eye is placed at any point on the surface of the sphere and the line of sight to any point on the opposite hemisphere is prolonged until it in- tersects the plane of projection tangent to the hemisphere. By this method the central portion of the map is enlarged relative to the correspond- ing surface of the globe, and in the outer zones sphere, while by substituting for the tangent cylinder or cone a secant cylinder or cone lying partly within ami partly without the sphere, projections arc obtained which are known as equal surface |)rojections and which are valuable for the construction of maps exhibiting statis- tical information and for celestial charts.