degree the place of a relievo; and lines drawn on a plane which has but two dimensions may produce the same effect as a model in relievo, if the extent of ground represented is not too great, and if it is thoroughly known in all its parts. But the difficulties are almost insurmountable when the horizontal projection embraces a hilly country of a surface of several thousand square leagues. In the most inhabited region of Europe, for example, in France, Germany, or England, the plains which are the seat of cultivation are only elevated, in general, a hundred*, or two hundred metres above one another. Their absolute heights are too inconsiderable to have any sensible influence on the climate‡. Hence an accurate knowledge of these elevations is much less interesting to the cultivator than to the naturalist;and hence also, in the maps of Europe, the geographers merely indicate the most elevated chains *About 328 feet. Trans. + About 656 feet. Trans. The interior of Spain presents a very striking exception; the soil of the Castiles in the environs of Madrid being six hundred metres of absolute elevation (about 1960 feet). See my memoir on the configuration of the soil of Spain, inserted in the itinerary of M. Alexandre de Laborde, T. I. p. CXLVII, From the data contained in that memoir, the small geological map attached to the interesting Rapport sur l'importation des Merinos, par M. Poyféré de Céré, 1809, was drawn up. It is to be regretted, however, that this map was not drawn up in all its parts according to the same scale of elevation. CLVI. of mountains. But in the equinoxial region of the new continent, particularly in the kingdoms of New Grenada, Quito, and Mexico, the temperature of the atmosphere, its state of dryness or humidity, the kind of cultivation followed by the inhabitants, all depend on the enormous elevation of the plains which stretch along the ridges of the Cordilleras. The geological constitution of these countries is an object equally importantfor the statesman and the naturalist; from whence it follows that the imperfection of our graphical methods is much more sensible in a map of New Spain than in a map of France. Hence, to give a complete idea of the countries examined by me, of which the soil possesses so extraordinary a configuration, I have been compelled to recur to methods hitherto unattempted by geographers, because the most simple ideas are usually those which occur the last. I have represented whole countries, vast extents of territory in vertical projections, in the manner in which the section of a mine or canal is drawn*. The principles on which similar physical views ought to be constructed are detailed in my Essay on geological pasigraphy. As * The first attempt made by me in this way was the physical map of the river de la Madaleine, engraved, in 1801, against my will at Madrid. See my Recueil d'Observations astronomiques, vol. i. p. 370. the places of which it is important to know the absolute height are rarely to be found on the same line, the section is composed of several planes, which differ in their direction, or rather of one plane which exhibits the average parallel line of direction on which the perpendiculars fall. In the last case the distances exhibited by the physical map differ from the absolute distances, particularly when the mean direction of the points whose height and position have been determined deviates considerably from the direction of the plane of projection. In sections of whole countries, as in sections of canals, the scale of distances cannot be equal to the scale of elevations. If we were to attempt to give the same magnitude to these scales, we should be forced either to make the drawings of an immoderate length, or to adopt a scale of elevation so small that the most remarkable inequalities of the soil would become insensible. I have indicated on the plate by two arrows the heights which the Chimborazo and the city of Mexico would have, if the physical view were subjected to the same standard in all its dimensions. We see that in this case an elevation of 500 metres* would not occupy in the drawing more than the space of a millimetre f. But in employing for itinerary distances the scale of * About 1640 feet. Trans. elevations exhibited in the plates VI, VII, VIII, which is nearly 270 metres to the centimetre†, a plate would be requisite of more than 15 metres in length, to represent the extent of country comprised between the meridians of Mexico and Vera Cruz! Hence from this inequality of scales, my physical maps, as well as the sections of canals and roads, drawn up by engineers, do not exhibit the true declinations of the soil, but these declinations, according to the nature of the projections employed, appear more rapid in the designs than they are in nature§. This inconvenience is increased if the plains of a great elevation are of very small extent, or if they are separated by deep and narrow vallies. It is from the proportion which the scales of distance and elevation bear to one another that the effect produced by the section of a country principally depends. I shall not enter here into a minute discussion of the principles followed by me in this kind of map. Every graphical method should be subject to rules, and it appeared to me so much the more necessary to point out some of these rules in this place, as the imitations of my views recently published are arbitrary projections on planes abounding with curves, of which nothing * About 885 feet. Trans. About 55 feet. Trans. § See my Essai sur la geographie des plantes, p. 53. indicates the direction in relation to the great circles of the sphere. Physical maps in vertical projections can only be constructed on knowing, for the points through which the plan of projection passes, the three coordinates of longitude, latitude, and elevation above the level of the ocean; and it is only in uniting barometrical measurements with the results of astronomical observations, that the section of a country can be drawn. This kind of projec tion will become more frequent in proportion as travellers shall addict themselves more assiduously to barometrical observations. But few provinces of Europe at this day offer the necessary materials for constructing views analogous to those published by me of equinoxial America. The construction of the sections, plates VI, VII, VIII, are absolutely uniform. The scales are the same in all the three views; the scales of distance are to those of height nearly as one to twentyfour. The three maps indicate the nature of the rocks which compose the surface of the soil. This knowledge is interesting to agriculturists; and it is also useful to engineers employed in constructing roads or canals. I have been blamed for not exhibiting in these sections the superposition or situation of the secondary or primitive strata, their inclination or their direction. I had particular reasons for not indicating these phenomena. I possess in my |