In Mexico the surveys are in charge of a comision geografica-exploradora attached to the secretaria de Fomento, but only about 140 sheets of a Carta general on a scale of Central America. 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 republica 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 of the 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 geografia 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 geografica (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 topografica 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 Oficina de mensura de tierras, by a seccion de geografia y minas connected with the department of public works, by the Oficina hidrografica, 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 plano 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 São Paulo and Mines Gerães have commissãos 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 (1862-1869) and of the Rio Madeira by Colonel G. Earl Church and Keller-Leuzinger (1860-1875). 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 topografica (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 hydrographic 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 hydrographic 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 Projections
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.