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MAP PROJECTIONS]
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MAP


Maps of Newfoundland, orographical as well as geological, scale 1: 1, 584,200, have been published.

In the United States a “geological survey ” was organized in 1879, under Clarence King as director, whose successor, Major ]. W. Powell, rightly conceived that it was necessary to produce good topographical maps before a geological survey could be pursued with advantage. It is under his wise guidance that the survey has attained its present eliiciency. It is based upon a triangulation by the U.S. Coast and Geodetic Survey. The maps of the more densely peopled parts of the Union are published on a scale of 1:62, 500, and those of the remainder of the country on half or a quarter of that scale. The hills are shown by contours at intervals of IO or 100 ft. The details given are considered sufficient to admit of the selection of general routes for railways or other public works. The survey progresses at the rate of about 40,000 sq. m. annually, and in course of time it will supersede the map of the separate states, based on older surveys. A “ reconnaissance ” map of Alaska (on a scale of 1: 250,000) was published in 1908. In Mexico the surveys are in charge of a comision geograficaexploradora attached to the secret aria de Fomento, but only Central about 140 sheets of a Carta general on a scale of A, ,, e, ,, c, , 1:100,000 have been published. There are also a map of the state of S. Luis Potosi (1:250,000), of the environs of Puebla (1: 50,000) and a Carta general de la republic mexicana (1: 250,000).

A useful map of Central America has been published by the topographical section of the British general staff on a scale of 1:170,300. Of great value for cartographical work is a careful survey, carried out by American engineers (1897-1898), for a continental railway running along the west coast from Mexico to Chile. In South America, in proportion to the area ofethe country, only few surveys of a thoroughly scientific nature have been made, and it is therefore satisfactory that the service géographique of the French army should be publishing, since 1900, a map of the entire continent on a scale.of 1: 1,000,000. Colombia is but inadequately represented by rough maps. For Colombia we have F. L. Vergara y Velasco's Atlas de geograja colombiana (1906-1908); Ecuador is fairly well represented by Th. Wolf (1892) and Hans Meier (1907); in the case of Peru we still largely depend upon Paz Soldan's Atlas geograjca (1865-1867) and A. Raimondi's Mapa del Peru (1:500,000) based upon surveys made before 1869. Sir Martin Conway's “Map of the Andes of La Paz” (1:600,000; 1900) as well as Major P. H. Fawcett's survey of the Brazilian boundary (1906-1907) are welcome additions to our knowledge of Bolivia. In Chile a comision topogratico was appointed as long ago as 1848, but the map produced under its auspices by Professor F. Pissis (1: 250,000, 1870-1877), leaves much to be desired. Since that time, however, valuable maps have been published by an Ojicina de mensura de tierras, by a seccion de geograja y minas connected with the department of public works, by the Ojicina hidrograjica, and more especially in connexion with surveys necessitated by the boundary disputes with Argentina, which were settled by arbitration in 1899 and 1902. The surveys which led to the latter were conducted by Sir Thomas Holdich.,

In Venezuela a commission for producing a plana militar or military map of the country was appointed by General Castro in 1904, but little progress seems to have been made, and meantime we are dependent upon a revised edition of A. Codazzi's map of 1840 which was published in 1884. In Brazil little or nothing is done by the central government, but the progressive states of Sao Paulo and Mines Geraes have commissars geographicos e geologicos engaged in the production of topographical maps. Valuable materials have likewise been acquired by several river surveys including those of the Amazonas by Azevedo and Pinto (1862-1864) and W. Chandless (1862-186Q) and of the Rio Madeira by Colonel G. Earl Church and Keller-Leuzinger (1869-1875). The proposal of a committee presided over by the Marshal H. de Beaurepaire-Rohan (1876) to prepare a map of Brazil on a scale of 1:200,000 has never been acted upon, and in the meantime we are dependent upon works like the Atlas do imperio do Brazil by Mendes de Almeida (1868) or the maps in our general atlases.

In Argentina an official geographical institute was established in 1879, but neither A. Seelstrang's Atlas (1886-1892) nor H. Hoskold's Mapa topograjica (1:2,000,000; London, 1895), which were published by it, nor any of the numerous provincial maps are based upon scientific surveys.

It need hardly be said that hydro graphic surveys have been of great service to compilers of maps. There are few coast-lines, frequented by shipping, which have not yet been surveyed in a definite manner. In this work the British hydro graphic office may justly claim the credit of having contributed the chief share. Great Britain has likewise taken the lead in those deep-sea explorations which reveal to us the configuration of the sea-bottom, and enable us to construct charts of the ocean bed corresponding to the contoured maps of dry land yielded by topographical surveys. (E. G. R.)

MAP PROIECTIONS

In the construction of maps, one has to consider how a portion of spherical surface, or a configuration traced on a sphere, can be represented on a plane. If the area to be represented bear a very small ratio to the Whole surface of the sphere, the matter is easy: thus, for instance, there is no difficulty in making a map of a parish, for in such cases the curvature of the surface does not make itself evident. If the district is larger and reaches the size of a county, as Yorkshire for instance, then the curvature begins to be sensible, and one requires to consider how it is to be dealt with. The sphere cannot be opened out into a plane like the cone or cylinder; consequently in a plane representation of configurations on a sphere it is impossible to retain the desired proportions of lines or areas or equality of angles. But though one cannot fulfil all the requirements of the case, we may fulfil some by sacrificing others; we may, for instance, have in the representation exact 'similarity to all very small portions of the original, but at the expense of the areas, which will be quite misrepresented. Or we may retain equality of areas if we give up the idea of similarity. It is therefore usual, excepting in special cases, to steer a middle course, and, by making compromises, endeavour to obtain a representation which shall not involve large errors of scale.

A globe gives a perfect representation of the surface of the earth; but, practically, the necessary limits to its size make it impossible to represent in this manner the details of countries. A globe of the ordinary dimensions serves scarcely any other purpose than to convey a clear conception of the earth's surface as a whole, exhibiting the figure, extent, position and general features of the continents and islands, with the intervening oceans and seas; and for this purpose it is indeed absolutely essential and cannot be replaced by any kind of map. The construction of a map virtually resolves itself into the drawing of two sets of lines, one set to represent meridians, the other to represent parallels. These being drawn, the filling in of the outlines of countries presents no difficulty. The first and most natural idea that occurs to one as to the manner of drawing the circles of latitude and longitude is to draw them according to the laws of perspective. Perhaps the next idea which would occur would be to derive the meridians and parallels in some other simple geometrical way.

Cylindrical Equal Area Projection.-Let us suppose a model of the earth to be enveloped by a cylinder in such a way that the cylinder touches the equator, and let the plane of each parallel such as PR be prolonged to intersect the cylinder in the circle pr. Now unroll the cylinder and the projection will appear as in fig. 2. The whole world is now represented as a rectangle, each parallel is a straight line, and its total length is the same as that of the equator, the distance of each parallel from the equator is sinl (where l is the ' F12 I latitude and the radius of the model earth is taken as unity). The meridians are parallel straight lines spaced at equal distances.