Among the most important projections using the idea of development is that devised by :Mer cator. in this projection a cylinder is assumed as tangent to the sphere at the equator, the axis of the former being coincident with that of the latter. The eye is supposed to be placed at the centre of the sphere and the lines of sight passing through points on the surface of the sphere are prolonged until they intersect the circumscribing cylinder. On developing (unrolling) the cylinder in a plane the projected meridians become paral lel and equidistant straight lines which are inter sected at right angles by parallel straight lines representing latitudes.. The defects of Mereator's projection relate to scale and area. The scale is correct only on the equator, from which north ward and southward the successive parallels of latitude increase in distance from each other in the ratio of the tangent of the latitude, attaining an infinite value at the poles. This increase of the latitudes, together with the parallelism of the meridians, produces such an exaggeration of areas as to make the map of little use for any purpose except that of navigation.
If a cone is placed tangent to the surface of the sphere, with its axis coincident with the axis of the latter, the surface of the sphere may be pro jected from the centre of the cone, which can then be unrolled or developed on a plane. In this ease each parallel of latitude is a curved line concave to the pole, while the longitudes are straight lines converging toward the poles. A mollified form of this projection known as the polyconic projection assumes that an infinite number of cones inclose the sphere. lly this method each parallel of latitude is developed by its own cone and determines the value of its own longitudinal intervals. This method, devised by Hassler. the former superintendent of the United States Coast. and Geodetic Survey, is the most perfect of all projections for mapping areas not exceeding a latitudinal amplitude of more than 40°, as it preserves an almost absolutely uniform scale over the entire map. It has been universally adopted for the construction of maps of land areas on large scales.