Maps are representations, commonly upon flat surfaces, of all or parts of the earth's surface. The scale of a map is the relation which distances on the map bear to distances upon the area rep resented. They may be expressed in terms of miles or kilometers on the ground to an inch on the map, or by a fraction, as 1 rao:ozr or 1:100,000 in which the numerator refers to the distance on the map, and the denominator to that on the ground, both being expressed in the same units, as feet, meters, or miles. A third method is by the 'bar scale,' in which actual measure ments are drawn on the map, and marked with the distances which they represent in nature.
Maps may be in accordance with the kind of information which they present. Thus there are geological, climatic, and statistical maps. The maps considered here, however, are those only which represent the topographical features prop er, the streams and other bodies of water, the relief of the country, its mountains, valleys, and plains, and the culture or the works of man, the cities, roads, railroads, boundaries, etc. Re stricted to this definition, maps may be classified as: (1) Plans, which are upon large scales and represent limited areas, such as a city or town ship; (2) topographic maps, upon smaller scales, say from one to eight miles to an inch and cover ing much larger areas; and (3) geographic maps, upon smaller scales, and representing areas of States, countries, or continents. The distinction between them cannot be sharply drawn, although mainly one of scale, but it is a useful one. An other distinction may be made in maps, between the original maps, made directly from surveys, which are known as mother maps, and those derived or compiled from them.
The earth having a spherical surface and the map a plane surface, it is obvious that no map can be a strictly accurate reproduction, since there must always be error in the transfer_ Various methods of projection, from the spherical to the plane surface, are in use, some applicable to one form of map, some to another. Among them are the following: The orthographic, which is often used in the projection of a hemisphere, on a very small scale. Here the points on the hemisphere are supposed to be projected by means of parallel lines at right angles to the plane of projection, which is that of the great circle bounding the hemisphere Here the eye is supposed to be at an infinite distance above the plane of projection.
In the stereographic projection the eye is sup posed to be at the earth's surface opposite the area to be projected, the plane of projection being that of a great circle midway between them. The intersection of lines with this plane, drawn from the view-point to points to be reproduced, gives their positions. This also is used only for maps on small scales.
A third projection, also used only with small scales, is the globular projection. Here the view point is placed on a perpendicular to the plane of projection, and at a distance outside the earth equal to the radius x 1/1/2, the plane of projec tion being similarly a great circle.
The projections in common use for geographic maps upon the larger scales and for topographic maps are the various forms of conical projections, and especially the polyconic, upon which the mother maps of nearly all nations are being made. The simple conical projection is made by assuming that the portion of the earth to be represented is wrapped in a cone, tangent to the earth at the mid-latitude of the area, its axis being the earth's axis, and its apex being on the prolonged axis. On this cone are projected by
radial lines points on the sphere, and when the cone is unrolled they will appear on the flat sur face. This projection is correct only on the middle parallel, and the distortion increases rapidly as the area increases. By combining many such cones, the distortion is greatly reduced, and the polyconic or many-cone projection is that In most general use for topographic maps.
A modification of the conical projection, known as the secant cone, is sometimes employed. Here the elements of the cone, instead of being tangent to the earth, cut it at two points, the cone being partly within and partly without the earth.
Mercator's projection, which is universally used in sailing charts,.is supposed to be constructed on a cylinder, circumscribing the earth at the equa tor. Points on the earth are projected on the cylinder by radial lines from the earth's centre, and the cylinder then unrolled. Here the merid ians are drawn as straight lines, parallel to one another, instead of converging as on the earth, and the spaces between the parallels are increased in the same proportion as are those between the meridians. Thus the scale of the chart increases from the equator toward the poles in the ratio of the tangent of the latitude. Because the me ridians and parallels are represented as parallel straight lines, sailing courses are also represented by straight lines, a fact which renders the projec tion of special value to mariners.
The contents of topographic maps are common ly classed in three groups: Hydrography, includ ing streams, lakes, and other water bodies; relief, the mountains, valleys, plains, etc.; and culture, or works of man, boundaries, cities, roads, rail ways, etc. The first of these groups is often rep resented in blue ink, the second in brown, and the last in black. These are the colors employed by the United States Geological Survey on its mother maps.
The relief has been represented on maps in various ways, but upon modern maps only two methods are employed, which may be charac terized as the pictorial method and the contour method. In the first, a pictorial effect of hill shading is produced, either by the artistic use of crayon or water-color, or by drawing fine lines, parallel to the direction of slope of the ground, closest and heaviest where the slopes are steepest. When well done this hachure method produces fine pictorial effects, but it is expensive, and crayon is more commonly used at present.
The most modern method of representing relief and that which is growing into the widest use is the contour method. Here relief is shown by lines of equal altitude above the sea. These lines are drawn at right angles to the slope, and each line being everywhere at a certain height, the map shows the altitude of all parts of the region represented. Thus a contour map is a map of three dimensions, while other maps are of two dimensions only. Upon steep slopes the contours are, of course, near one another, and upon gentle slopes are far apart, and thus contours produce an effect like that of shading, but much inferior pictorially to that produced by hachures or cray on. See MAP.