BOOK Romans knew well, "that localities frequently influence victory more than courage and numbers."* VI. maps. Other branches of government equally require maps, especially consecrated to a particular object. Those of the waters and forests, for example, should always be consulted as a beacon in cultivation; and in this respect the states of Germany have hitherto had advantages over France. What Nautical a military map is for the ground, nautical maps are for the seas; they even interest the physical geographer, as they represent, though very imperfectly, the irregularities of the bottom of those basins covered with water which occupy so vast a portion of the globe. The rocks, reefs, sand-banks, scattered through the seas, are sub-marine mountains and hills; and a complete knowledge of them would throw great light on the geography of the terrestrial mountains. Unfortunately nature seems to forbid the hope of our ever completing that part of geography. Navigators," says a celebrated mariner, "can only answer for the routes they have made, or the soundings they have taken; and it is possible, that, on the finest seas they may have past close beside banks or shoals where there were no breakers (that is to say, whose existence was not betrayed by the foam of broken waves.") The maps of rivers present in detail all the branches of a stream, and all the circumstances of its course. They are comprised with nautical maps, under the general appellation of hydrographic. Scientific maps. 66 There are also maps of botany, mineralogy, geology, and even of zoology, the object of which is to show the geographical distribution of the productions of nature; there are some which their authors decorate with the name of historical, and which are intended to show the migrations of nations, and the changes of sovereignty; finally, there are few objects, the reduction of whose relations of locality * Veget. De Re Milit. iii. c. 26. La Perouse, Voy. ii. ch. ii. p. 54. Ritter, Cartes Physiques de l'Europe. VI. has not been attempted in the form of maps. But the com- BOOK position of these sorts of tables is subject to rules derived from sciences foreign to geography. ry maps. All maps are not intended to advance our knowledge by the publication of new details, or by greater exactness. Public instruction requires elementary maps, the merit of Elementawhich consists in rendering, in a faithful and complete manner, truths already known, and in which it were to be wished a system of engraving might be adopted, less elegant and less costly than what the refined taste of the public requires. The essential point in an elementary atlas, is not to display on a great scale maps full of details, and of minute exactness, but rather to exhibit, in a series of small but numerous maps, the complete assemblage of the principles of the science. After having duly reflected on his object, the designer has to collect and combine the details necessary to fill his map. ment of astrono servations. Good astronomical observations here hold, without dis- Employpute, the first rank; but how difficult is it to judge whether an observation be good! How many inconsiderate changes mical obhave been introduced into geography by the employment of longitudes badly observed or ill calculated! Above all, how many errors are owing to the careless use of the chronometer! We have indicted the different methods by which the astronomer assists in fixing the geographical positions of terrestrial places ;* but the value of an observation does not depend solely on the goodness of the method; to appreciate it we must know all the processes, and all the circumstances, and submit these details to a minute criticism, and to careful calculations. In a word, we must imitate the example of Oltmanns, in his Researches on the Observations of Humboldt. It is in studying the work of this geometer, that geographers may learn all the rules of sound criticism with respect to astronomical data. The true geographer ought to be almost an astronomer. Thus we every * Above, b. i. YOL. I. 17 Voyage De Humboldt, part. astron. BOOK where recognise that fraternal tie which unites all the sciences by rendering them necessary to each other! VI. Employ ment of The second and the richest source from which geographers draw the details of their maps, is triangulation; we have given an idea of it in speaking of the measurement of the earth of Picard.* When the position of a certain number of points has geodesical been fixed, either by astronomical observations, or trigonomeasures. metrical measures, it is easy to connect with these points the particular plans taken on the ground, and which exhibit the localities in detail. But, as the art of drawing plans on the ground depends in great part on principles foreign to geography, we shall content ourselves with indicating merely some practical means employed by geographers for constructing a topographical map from partial surveys. The reader who wishes for detailed instructions on trigonometrical subjects, cannot do better than to have recourse to the excellent Treatise on Geodesy by the learned and ingenious Puissant. When we wish to construct a map by connecting together plans taken separately, it is necessary that each of these plans should have at least two points in common with that to which it is to be joined; or, which comes to the same, there must be a line determined both in size and position in one which can be applied to a similar line in the other. Then, by drawing on the paper destined to form the general plan that directing line, so that there may be on each side a space proper for comprising each of the plans, it will be easy to refer to this general plan all the points that have been determined on the partial plans, by attaching them, by triangles, to any two points taken on the directing line, or combining them with any point, the position of which has been fixed. If there is to be a reduction, as almost always happens, the triangles of the topographical plan must be made similar to those formed on the basis of the surveys; but so that the sides of the Above, b. ii former may be to those of the latter in the relation which BOOK VI. When the sheets of the surveys are orientées, that is to say, when on each sheet the direction of the meridian, either the true or the magnetic, has been marked, the points of each plan are referred to the meridian, and to a perpendicular brought on that line by a point common to two contiguous plans. The distances are measured from all the points to each of these right lines parallel with the other; and, either preserving these distances as they were found, or reducing them in the relation required, they are brought on the meridian, and the perpendicular drawn in the topographical plan to represent those which are common to the collected plans. This method of constructing graphically Reduction by trellis, the general map after the plans of the surveys, has given rise to a mechanism of reduction known by the name of trellis; it is very convenient for bringing together the details of the map, but should not be used for fixing the position of the principal points. This operation consists in dividing the plans that are to be united in squares, by lines parallel and perpendicular to that which is common to those plans; the more these squares are multiplied, the better we perceive the place occupied in each square by the points and turns contained in it, the more easy also it is to refer them to the corresponding squares traced on the plan of reduction or of assemblage. Fig. 46. represents this operation. The leaves ABCD, EFGH, having for common lines the right lines CD and EF, are divided into squares, the sides of which are parallel and perpendicular to those right lines; the plan of assemblage a bf e, is divided in the same manner, with respect to the line c d, which represents the common right line, but the sides of each square are the halves of those of the plans ABCD, EFGH, so that the objects marked on these leaves are reduced on the plan of assemblage to a half of their former dimensions, and to a space which is only the quarter of that they first filled. To reproduce the design traced on each of the primitive plans, either it may be imitated at sight, in the cor VI. BOOK responding squares of the leaves ABCD, EFGH, or else, for more exactness, marks are made on each of the sides of the latter, and transferred to the others. If we wish to preserve exactly the designs that are to be copied, we may place upon them a very smooth piece of glass, and of equal transparency, on which squares are traced with a diamond, and afterwards two perpendicular lines are made to coincide together on those which are to serve for the assemblage of the collected plans, or on the points which determine them. Chorogra- After having thus formed the topographical plans by the phic maps, assemblage of the various plans of the surveys, chorographic maps are formed from them, not only by assembling the plans, but by submitting them likewise to the laws of the projection that has been adopted. For this purpose, the meridians and the parallels are traced on those plans in right lines, as those circles are when only a portion infinitely small is considered. The corresponding quadrilatcrals are also described on the frame of the map to be constructed, but conformably to the laws of the adopted projection; there is then nothing farther but to design in these quadrilaterals what is contained in the squares comprised between the meridians and the parallels of the topographical plans. If we wish for extreme precision, we take, with respect to the sides of the squares, the distances of the principal points inclosed in them; these distances are converted into subdivisions of the degrees of longitude, and similar ones are taken afterwards, setting out from the parallel and the meridian contiguous to the corresponding quadrilaterals on the map. Of plans not orientes, and without a scale. Two circumstances may stop the geographer in this operation. It may happen that the topographical plan may not be orienté, or having been so by the direction of the magnetic needle, only we do not know what was the declination of the compass at the time when the plan was taken and reduced, This element may be supplied when the plan contains two points, of which the respective position is known, for, by joining these two points by a right line, we have the angle which |