MAP. 33 MAP. Among the most impoilant projections using tile idea of development is that devised by Mer- eator. In this piojeetiou a cylinder is assumed as tangent to the sphere at the equator, the axis ul' 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 Mercator'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. POLYCONIC PROJECTION. If a cone is placed tangent to the surface of the sphere, with its axis coincident with the axis of (he 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 case each parallel of latitude is a curved line concave to the pole, while the longitudes are straight lines converging toward the poles. A modified form of this projection known as the polyconic projection assumes that an infinite number of cones inclo.se the sphere. By 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 la( itudinal 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. Pr-ctic.l Methods. The construction of the necessary basic projections as a preliminary to the making of a map is now a very simple mat- ter, since the work is accomplished by merely laying oil' tabular values computed for the gen- eral use of map-makers. Tables for these pro- jections are easily obtained; tho.se computed and published by the United States Coast and Geo- detic Survey for various scales in meters and inches and by the Hyilrographic Office of the United States Navy Department are the most useful for the purpose. The preparation of an exact map presupposes a corresponding exact survey. For all maps of permanent value the survey must be based upon careful geodetic triangulations and levelings. For less exact work there are corresponding styles of maps, such as the plattings of sections and town- ships by the United States Land Office ; the general maps of the counties, compiled by county sur- veyors by the use of the pedometer and the sur- veyor's compass; the rapid military reconnais- sance in which the engineer officer, note-book in hand, sketches in such features as ma}' affect military operations ; the elab- orate maps of the United States Geological Survey, which undertake to give mi- nute details as to geology, mines, forests, and topog- raphy ; and the perfect hydro- graphic maps of the Coast and Geodetic Survey. The maps of the Coast and Geodetic Survey are luainly hydrographie in their char- acter. The original maps are projected on a polyconic base, and on this base the elaborate system of triangulations con- necting carefully measured base - lines is platted from the field notes by skillful draughtsmen. The main points of the coasts being thus indi- cated, the interlying areas of the triangles are worked in from the notes of surveys made by stadia, chain, or tape; and the hydrographie data obtained by careful soundings along definite lines are also entered. The base map thus prepared is reduced by hand to the scale of publication, and a finished map is prepared as a guide for the engraver. On this map the hydrography is indicated by uniform signs. The shoals and sandbars are represented by dots, close together along the shore and wider apart as they fall away into deeper waters. Lighthouses are indicated in their exact posi- tions, together with their bearings from im- portant points and their relation to channel entrances, etc. In short, all information re- lating to the hydrography of the seaboard is carefully marked by apjiropriate signs consis- tent on all the maps. From the finished map the engraver makes a tracing on hard gela- tin sheets, which he transfers in reverse to a copper plate from which the ultimate prints are obtained. In late years, in order to satisfy the increased demand for maps, a great deal of the hand reduction has been super- seded by photographic methods, and lithographs
