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 important for 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 places of which

*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 astro

nomiques, vol. i. p. 370.

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 diffe 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 millimetref. But in employing for itinerary dis

tances the scale of elevations exhibited in the plates VI, VII, VIII, which is nearly 270 metres* to the centimetref, a plate would be requisite of more han 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 indicates

§ See my Essai sur la geographie des plantes, p. 53.

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 coordinate 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 projection. 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 twenty-four. 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

itineraries all the necessary geological materials for forming what are usually called mineralogical maps. A great number of these materials were published by me in my recent work on the measurement of the Cordillera of the Andes; but on mature examination I adopted the resolution of separating entirely the geological sections which display the superposition of rocks from the physical views which indicate inequalities of surface. It is very difficult, I had almost said impossible, to construct a geological section of an extensive country, if this section must be subjected to a scale of elevation. A stratum of gypsum of one metre* thick is often more interesting to a geologist than an enormous mass of amygdaloid or porphyry; for the existence of these very slender strata, and the manner in which they lie, throw light on the relative antiquity of formations. How then shall we trace the section of entire provinces, if the magnitude of the scale is to be such as to exhibit masses so inconsiderable? How shall we indicate in a narrow valley, in that of Papagayo, for example, (Plate v11.) in a space of one or two millimetres of breadth, which the valley occupies in the drawing, the different formations which repose on one another? Those who have reflected on graphical methods, and endeavoured to improve

* 39.371 inches. Trans.

A millimetre contains .03937 of an inch. Trans.