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employed on a reconnaissance; and as they can always be carried without inconvenience about his person, or strapped in front of his saddle, he need never be driven to the necessity of sketching entirely without their assistance, though the practice of doing so occasionally is decidedly of service, as it teaches him to make use of his eyes, and tends to make him a good judge both of linear and angular measurement *.
Sketching such parts of the interior detail as have a decidedly marked outline is comparatively easy, but the delineation of ground, so as to represent the various slopes of the hills and irregularities of the surface, is far more difficult; and methods have been adopted both on the Continent and in this country, as systems for expressing these features, giving not merely a general idea of their character, but a mathematical representation of their various complicated inclinations; so that the angle of every slope might be evident from a. mere inspection of the drawing, or measured from a scale; and, consequently, furnishing data for constructing sections of the ground in any required direction. This degree of perfection would of course be most desirable in military.sketches, as well as in finished topographical plans, but the labour and difficulty attending the execution will always prevent its general application, excepting in surveys of a national character, or of limited detached portions of ground.
The two methods in general use for representing with a pen or pencil the slopes of the ground are known as the vertical and the horizontal. In the first of these the strokes of the pencil follow the course that water would take in running down these slopes; in the second (which is comparatively of late introduction) they represent horizontal lines traced round them, such as would be shown on the ground by water flooding the country at the different stages of its progressive altitude. This last is the mode now generally practised, and it certainly produces a more correct re
* A protractor (for want of a better) can be made by folding a square or rectangular piece of paper into three, 3 0 which, when doubled, divides the edge into six portions of fifteen degrees each; these can be again divided into three parts, by which angles of five degrees can be laid down, or even approximately observed, the intermediate degrees being judged by the eye.
presentatlon of the general character and features of the ground than the vertical method *. Neither of them, however, when sketched by the eye, between fixed points and measured lines, aspires to the mathematical accuracy which is obtained by tracing with a theodolite or spirit level, horizontal contour lines at equidistant vertical distances over the surface of the ground, the method of doing which will be treated of in the chapter upon Levelling. Systems have also been introduced into Germany, founded upon a proposal by Major Lehman, for representing the slopes of the ground by a scale of shade consisting of a combination of vertical and horizontal lines, but they have not been adopted in this country. The light in Major Lehman's system, as is generally the case in describing ground with a pen, is supposed to descend in vertical rays, and the illumination received by each slope is diminished in proportion to its divergence from the plane of the horizon. As vertical rays falling upon a plane inclined at an angle of 45° are reflected horizontally, this slope, which is considered the greatest that is ever required to be shown, is also considered the maximum in the scale of shade, and is represented by perfect black. A horizontal plane reflects all rays upwards, and is, therefore, represented at the other end of the scale by perfect white; and the intermediate degrees being divided into nine parts, show the proportion of black in the lines to the white spaces intervening between them for every 5°; which at 5° is 1 to 8; at 10°, 2 to 7; at 15°, 3 to 6, &c. Figure 1 will explain the construction of this scale, and the thickness of the strokes drawn on this principle must be copied till the hand becomes habituated to their formation. In sketching ground the inclinations must be measured or estimated, if the eye is experienced enough to be trusted, and are to be represented by lines of a proportional thickness. To this system is to be objected its extreme difficulty of execution, as well as that of estimating correctly by the eye the angle intended to be represented by the thickness of the lines; though Mr. Siborn, who published a work in 1822 on “ Topogra
* Very good specimens of both these styles of sketching hills are to be found in Mr. Burr's “ Practical Surveying.” The vertical is best adapted to a military sketch if pressed for time, as, however roughly it may be scratched down, a good general idea of the ground is conveyed.