V. parts, and carry through the corresponding points of divi- BOOK sion, ellipses representing the meridians. This projection has some resemblance with the orthographic, but is more easy to trace; it disfigures the countries infinitely less, and gives the spaces in their just proportions. jection. We may consider as an arbitrary alteration of this pro- Alteration portional projection, the method of which the idea is attri- of this probuted by Vaugondy to G. de L'Isle,* but which is indicated in more ancient authors. It consists in dividing the principal meridian, the equator, and the circumference of the map into equal parts, and then carrying through the points of division, curves representing the meridian and parallels. Arrowsmith's maps of the world are traced according to this method, which has nothing particularly recommendable. The operations of Cassini, to determine the figure of the Projection earth by the measure of the degrees of the meridian, and of Cassini, the parallels, gave rise to a very important kind of projection, being that according to which the great map of France, the finest geographical work ever executed, is constructed.‡ When it was attempted to measure a degree of longitude, the difficulty was experienced of tracing exactly on the earth a parallel to the equator. In fact, if, by a line directed by means of vertical pegs, and perpendicular to the meridian of a place, we determine a series of points, it is evident that, supposing the earth spherical, they will belong to the great circle determined by the vertical plane, drawn perpendicularly to the meridian in question, and which, on the earth, answers to the celestial circle, named first vertical. The parallel soon separates from this circle, which it only touches at the point where it cuts the meridian. In a spheroid, the curve perpendicular to the meridian has a double curvature, and an inquiry into its properties has occupied several geometers. The meridian and its perpendiculars being the lines most * R. Vaugondy, Instit. Geogr. 324. Puissant, Topogr. 133. Fournier, Hydrogr. 1. xiv. ch. 30. Cassini, Acad. des Sciences, 1745. V. BOOK easily traced by astronomical and geodesical operations, it is to the meridian of the observatory at Paris and to its perpendiculars that the points of the map of France are immediately referred: their latitudes and longitudes were only concluded à posteriori, and by calculation.* Properties of this projection. To form an idea of the manner in which this projection. represents the terrestrial spaces, we must observe, that the great circles perpendicular to the meridian, (supposing the earth spherical,) all cut each other at the poles of this meridian, and consequently converge towards each other, while, on the map, where the same meridian is a right line, they become parallel among themselves. It thence results that the portions determined by two circles perpendicular to the meridian are represented by rectangles of the same length, but broader towards the extremities. Thus their distances and their areas can be measured immediately on the map of France only by approximation; and though the extent in longitude is not considerable enough for the convergence of the perpendiculars to the meridian to induce an important error, we must be cautious in the employment of this projection, which is only excellent for the immediate assemblage of trigonometrical surveys. Several German geometers have calculated formulas and tables to render its use more sure, and correct its errors.‡ Spindle of It is to arbitrary developments of the globe that we must the terres- refer the construction of the spindles, which are traced on trial globe, paper, to cover globes that are not very large. The surface of the globe is divided into 12 or 18 parts, according to the size of its diameter, by drawing meridians, of 30 to 30°, or of 20 to 20°. The space comprehended between two of those meridians, having very little curve in the direction of its breadth, may be considered as forming part of a cylindrical surface circumscribed to the sphere, accord * Du Sejour, Traité Analytique des Mouvemens apparens des Corps celestes, t. ii., and the Description Geometrique de la France, by Cassini. † They extend in the extremities of Cassini's France to 150 toises in 40,000 Barbié du Bocage. Topog. Mem. du Depot de la Guerre, 1, 23. Zach, Correspond, V. ing to the meridian which divides it into two equal parts. BOOK This meridian is developed, and by carrying perpendicularly (like ordinates) on each side the semi-breadths of the portions of parallels comprehended between the meridians which terminate the spindle, we obtain the form of the latter. Sometimes it is truncated at the two extremities at 15 or 20 degrees from the poles, and these two zones or spherical domes are traced apart, considering them as if they were flat. This process is only an approximative mechanism, which facilitates the fabrication of globes, and deserves no farther notice. Let us only express our wish that some able mechanician would invent the means of giving more exactness to the engraving of globes, at the same time that the advantage of the multiplication of copies is preserved. Choice of projections BOOK VI. Continuation of the Theory of Geography. Continuation and end of the Theory of Geographical Maps. Of the choice and assemblage of Details. In vain would geometry have taught us so many and such ingenious methods of tracing maps in a manner conformable to the wants of geography, if we could only insert in these pictures of the globe incomplete images of the differcnt countries. All our projections would then be only what the rules of perspective are to a sign-painter. It is the novelty, the exactness, and richness of details, which distinguish a learned map from those unformed sketches, the contrivance of which is confided to ignorance. To compose a good map, we must know how to choose, and to assemble the details which form its merit. The first object of consideration for the designing geoof the scale. grapher is to determine the kind and the object of his map. Is it general? does it embrace a vast portion of the world? He chooses a large paper, and employs a projection such as the different modified conical projections, which hardly alters the configurations. Does he wish to construct a map of the world, destined for the studies of astronomical geography? He uses the horizontal stereographic projection. Is it to be applied to physical geography? He prefers the development of it on a single meridian, placing the new continent to the right, not to interrupt the connexion of the continents. In special maps, where an empire or province is traced, the choice of the projection seems more indifferent, because the defects of all the methods diminish when the map embraces only a small portion of the surface of the globe. Neverthe VI. less there are advantages and inconveniences which flow BOOK from the nature of projections, and which we have indicated in the preceding book; there may be also one projection which, with respect to the paper, will oblige the geographer to admit into his map more countries foreign to his principal object than another; but it is essential to avoid such projections, because they diminish the scale of the map; that is to say, the proportion between the image and the object represented. Mariners who point their route on maps, say, instead of great and small scale, great and small point, an expression properly applied only to reduced maps. cal maps. The impossibility of admitting into a map, even of very great dimensions, all the details relative to topography, necessitates a choice among those details, which, however, it is impossible to subject to general rules. One map is des- Political tined to shew the political limits of states, and the boun- and physidaries of provinces, with their chief towns; another is destined to shew the chains of mountains and the branches of rivers; and these two classes still admit of sub-divisions. A military map is, in reality, only a perfect and Military detailed topography; the warrior should find in it every maps. road in which he can advance, either with artillery, or only with his musket; every ford in a river, every defile by which he can turn the position of an enemy; in a word, these maps should exhibit all the localities which can influence his operations; the number of good military maps is therefore very limited. It is in great part to the excellence of those supplied by the Depot de la Guerre, that the French armies owe their successes. A learned geometer, deeply skilled in the art of war,* had made a list of the French generals, in which he estimated their talents; opposite an illustrious name was often this note, He is well acquainted with the map. The importance of geographical studies for the leaders of armies was felt by the ancients, and the * M. Carnot. Comp. Zach. Corresp. Astron. i. 520. |