Map (Lat. Mappa), a representation of a portion of the earth's surface, or of the celestial sphere, upon a plane. Its object is to present to the eye the bearings of objects upon the surface from each other, and their relative distances apart, as nearly correct as may be. But this can be done with accuracy only upon a globe, the surface of which is similar to that of the earth itself. Various plans, however, have been devised by which in the more convenient form of plane sheets true delineations of the surface are presented, reference being had to the principles upon which these maps are constructed. By the method called projection, the rules of perspective are applied to the delineation of objects upon the surface according to four principal modes. In the method of projection called orthographic, the eye is supposed to be at an infinite distance from the sphere, so that the rays of light coming from every point of the hemisphere opposite to it may be considered as parallel to one another. The sphere is intersected through its centre by a plane perpendicular to these. rays, and it is upon this plane that the objects are projected, as their shadows might be cast upon it from the sun through a transparent medium.

Objects near the centre of the plane would by this method be delineated in nearly correct proportions; but in receding from this, as the rays strike more obliquely npon the surface of the sphere, their projection becomes more and more distorted, and the parallels of latitude or meridians of longitude (as the eye is placed opposite the pole or the equator) are drawn more and more closely together. - In the stereographic projection, the eye is supposed to be placed at the surface of the sphere, and the surface to be delineated is the opposite hemisphere or a portion of it, of which the inner or concave side is presented to the eye. The plane upon which the objects are projected is supposed to be transparent, and placed so as to pass through the centre of the earth, its surface perpendicular to the line passing from the eve to the centre. In this method the meridians and parallels intersect each other as thev do upon the globe; and though there is distortion increasing from the centre, it is less than by some of the other methods.

The stereographic method is much used for the maps of the world drawn in two hemispheres; and the meridian of 20° W. from Greenwich is usually selected for the plane of projection, because this throws the two great continental divisions of the earth into their respective hemispheres. - In the central or gnomic projection, the eye is supposed to be at the centre of the earth, and the objects upon the surface are projected upon a plane which is a tangent to its surface. This method is obviously applicable to maps of a limited extent only; and except for maps of the polar regions, where the parallels of latitude are concentric circles, and the meridians are straight lines, they are troublesome to execute on account of the irregular curves the parallels assume. - In the globular projection, the eye is supposed to be at a distance from the sphere equal to the sine of 45o; or, the diameter being 200, this distance is 70.7. In order, however, that the meridians may intersect the equator at equal distances, the distance for the eye is generally fixed at 59 1/2, the diameter being 200. Maps are also constructed in which the meridians are represented by arcs of circles cutting the equatorial diameter at equal distances, and the parallels by arcs of circles cutting the polar diameter at equal distances.

These maps are not projections, and founded upon no geometrical principle which can be of service in their use; nevertheless they give a very good representation of the forms and relations of areas, and are of very simple construction. They are called globular maps, but must not be confounded with maps constructed upon the principle of globular projection, mentioned above. - Another method of map making is based upon the principle called development, which is a mode of projecting the forms upon the surface of the earth upon the inner surface of a cone or of a cylinder, which is supposed to envelop the earth and touch it only around the circle which is to be the middle latitude of the map. The points on the earth's surface being projected by other lines drawn through them from the centre, the inner surface of the cone or cylinder is afterward supposed to be unrolled or developed, and thus present the various objects upon a plane surface. Those situated nearest the middle latitude will he most correctly represented. In the use of the cylinder the latitude circles and meridians appear a- parallel straight lines, and thus most correctly represent for nautical purposes the angles at which they are cut by objects moving over the .surface on any other lines.

This principle is in part the foundation of the projection known as Mercator's, and applied by him to chart. for navigators, in which the correct hearings of objects upon the surface are of more importance to determine than the true figures of countries. - Still other principles are employed in constructing maps, according to the special purposes for which they are designed. In maps of small areas, the figure of the earth may be neglected, and the positions and forms of bodies be represented as if the surface were itself a plane. Some have special objects in view, as the delineation of the coast lines, channels, shoals, reefs, lighthouses, etc, hence called hydrographic maps or charts; others are intended to show the political divisions of states, counties, and towns; and others, designated topographical maps, to represent the natural features of a country, as its mountains, hills, rivers, plains, etc, for all of which certain conventional signs are adopted. Maps have also been constructed to represent the courses of the winds and of oceanic currents over the surface of the earth; to designate the position of the isothermal lines; to indicate the geological formations found in different regions; and others to indicate the flora and the fauna of different countries.

In the construction of geographical maps covering large areas, the principal places are located according to their latitudes and longitudes, and the lines of coasts and of countries, roads, etc, are plotted from the most exact surveys that have been made. Those which have been conducted under government patronage have furnished the materials for the best maps, and these are constantly improving as new materials are collected. Of the United States, the most complete maps are those of the state of Massachusetts made by order of the legislature, of the coast survey under the general government, Whitney's survey map of California, and Clarence King's survey map of the 42d parallel. The great lakes, more especially on the Canadian side, have been surveyed and mapped with great accuracy by Lieut. Bayfield of the royal army. Maps of the Spanish provinces in America have been made by the Spanish hydrographical depot in Madrid; and Brazil and other South American states have executed maps of their territories. - The ancient Egyptians had some knowledge of maps, as Sesostris caused the territories he possessed and had conquered to be represented upon tablets for the instruction of his people; and the Israelites appear to have acquired the same knowledge, from the record, in Josh, xviii. (6 of a map of the country being ordered by that lawgiver.

The first ma]) of the world, as known to the ancients, is said to have been made by Anaximander the Milesian. Herodotus makes mention of maps constructed by the Persians in the time of Darius, and of one by Aristagoras of Miletus. Eratosthenes introduced the lines of latitude and longitude, and the use of these was established by Hipparchus upon a mathematical principle. Still, for want of exact surveys, and owing to the dependence of geographers upon the reports of travellers and their itine-raria picta, or painted itineraries, the maps afterward made were extremely inaccurate. Even those of Strabo and Ptolemy, of which those of the latter were for centuries the chief authorities in geography, contained most extravagant errors, such as giving to the Mediterranean 1,400 miles greater length than belonged to it; and what is equally extraordinary, some of their gross exaggerations were continued in all the maps from that period down to the commencement of the 18th century. The system upon which Ptolemy's maps were drawn was that of stereographic projection. After the discovery of America, the early maps representing the position of the new world relative to the old were exceedingly inaccurate.

In one published in Venice in 1546 Asia and America are joined together in lat. 38°. The great difficulty was in determining the true longitude of places; and until this could be done there was no means of avoiding such errors. In 1700 De Lisle published a new map of the world, and others of Europe, Asia, and Africa, founded on comparatively accurate astronomical observations, and in them the errors introduced from the maps of the ancients were first corrected. The true system of map making may be considered as at that time established. - Maps were first engraved on metal by Biickink and Schweyn-heim in 1478, and on wood by Holl in 1482. An " Essay toward a Circumstantial History of Maps," by Hauber, was published in Ulm in 1724. A historical account of the art is also given in a series of lectures by J. G. Kohl, published in the report of the Smithsonian institution for 1856-7. See also Santaran, Essni sur la cartographie pendant le moyen age (3 vols., Paris, 1849-'52).