THEORY OF MAP CONSTRUCTION. As it is im possible to make the surface of a sphere conform with a plane, the problem of representing por known as Mercator, who invented the first de veloped projection and published a map of the world (1569) ; Ortelius, the publisher of an atlas. Thratrum Orb is Terra rum (1570) ; and Blaeu (died 1638), author of Atlas Norus. Ilo mann (died 1724) issued the first school atlas, At/as Seholastieus. i\lercator's projection prac tically revolutionized the method of map-making, as it solved for the navigator the complex prob lems involving the relations of courses and dis tances to latitude and longitude.
flans of the earth's surface upon a map can be solved with only approximate accuracy. The solution may be approached by various methods which lead to results more or less valuable for particular purposes. Among these methods are the orthographic and stereographic projections of Hipparchus, the gnomic projection of Thalee, and the globular or equidistant projection devised by Niceolisi. These projections, which are based upon the relative positions of the eye and the plane of projection, are best adapted for the representation of hemispheres and are seldom used in mapping small areas.
The orthographic projection assumes that the eye is placed at an infinite distance. so that all lines leading from it to the object are parallel. The plane of projection is at right angles to the line of sight and every point upon the hemi sphere is referred to the plane by a perpendicular let fall on it. In this projection the central portions of the hemisphere are faithfully repre sented, but near the circumference the areas be come greatly diminished and the relative angular directions are greatly changed.
The stereographic projection is obtained when the surfaces are touch larger than on the globe; hut. I In 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 1 of the sphere at a distance --- times the radios 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 objects are not represented with their true outlines, but the relative dimensions are fairly well preserved. An equidistant method for polar projections of the sphere is employed in the meteorological charts of the Northern and Southern hemispheres frequently used by the 'United Mates Weather Bureau.
Modern maps upon large scales are constructed by so-called projections which are actually de r..lopinonts of projections. Development is ren dered possible by the substitution of a cylindrical or conical surface for the ordinary plane of projection. the eye occupying an arbitrary posi tion when not assumed at the centre of the sphere. The surface of the cylinder or cone is developed subsequently in a plane. Various re sults may he obtained by changing the place at which the cone or cylinder is tangent to the 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 eentral 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 COUP lying partly within and partly without the sphere, projections are obtained which are known as equal surface projections and whieh are valuable for the construetion of maps exhibiting stalls deal information and for celestial charts.