#Polyconic projection.# In plotting the original surveys it is essential that a projection be used which will for the area included on a survey sheet show the points in their correct relation both as to direction and distance. These conditions are substantially fulfilled by several projections, of which the polyconic is used in the United States. If a hollow cone were placed so that it would either be tangent to the earth's surface along one of the parallels of latitude or cut it along two parallels, and the points projected on to this cone, and the cone then unrolled and laid out flat, the result would be a conical projection, of which there are several variations. If successive tangent cones be used and each parallel of latitude be developed as the circumference of the base of a right cone tangent to the spheroid along that parallel, the result is the polyconic projection, which has been used for field sheets and for the large scale charts, as well as for the topographic maps of the United States. This projection has valuable qualities for moderate areas of the earth's surface, within which the scale is approximately uniform, areas retain nearly their true proportions, and great circles and consequently all bearings and directions are approximately straight lines. The parallels of latitude are arcs of circles with radiuses increasing as we recede from the pole; therefore they are not truly parallel and the length of the degree of latitude increases either side from the central meridian. The meridians converge toward the poles and become slightly curved as we recede from the central one; the longitude scale is everywhere correct, but the latitude scale is strictly correct only on the central meridian. The angles of intersection of parallels and meridians are right angles or nearly so. The polyconic projection is not used for very extensive areas of the earth's surface, as for instance a hemisphere. [Illustration: FIG. 24. GNOMONIC CHART OF NORTH PACIFIC OCEAN, SHOWING GREAT CIRCLE ROUTES YOKOHAMA TO PUGET SOUND, AND YOKOHAMA TO HONOLULU AND THENCE TO SAN FRANCISCO.]