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.
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.
Gnomonic projection. In this projection the eye is assumed to be at the center of the earth and the features are projected upon a plane tangent to some point on the earth's surface. It is practicable to use this projection for oceanic areas, and it has the very important quality that every straight line on it represents a great circle of the earth. To obtain the great circle or shortest course between two points it is therefore only necessary to draw a straight line between the points on a gnomonic chart. Because of the great distortion near the edges this projection is not otherwise adapted to navigational use, and it is employed only to mark out the general course, and sufficient points are then transferred to a mercator chart. The gnomonic chart is therefore useful in supplementing the mercator chart, supplying its deficiencies as to convenience in marking out great circle courses. The great circle course can be derived not only more easily and quickly from the gnomonic chart than by computation, but the chart is also to be preferred because the course marked out on it will show at once if any obstruction, as an island or danger, is met or too high a latitude is reached. A modified or composite course can readily be laid out on a gnomonic chart.
FIG. 25. NORTH POLAR CHART ON ARBITRARY PROJECTION.
Arbitrary projection. The few charts published of the polar regions are sometimes on an arbitrary projection, in which the meridians are straight lines radiating from the pole and the parallels are equidistant circles with the pole as center. The latitude scale is uniform. At some distance from the pole the longitude scale becomes very much distorted, but the projection is a practicable and convenient one for the immediate polar regions. Gnomonic and conical projections are also used for the polar charts, differing little from the foregoing for moderate areas.
Scales. Charts are published on a variety of scales to suit different needs of navigation, and the usual classification depends on scale. In addition to the ocean charts covering a single ocean in either one or several sheets and intended for navigation on the high seas, there are for our Atlantic coast the following series:
Sailing charts, scale about 11200000, for general coastwise navigation.
General coast charts, scale 1400000, for local coastwise navigation.