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presentation 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.
phical Plan Drawing," founded on this system of Major Lehman's, considers that between 10° and 35° of altitude the slope may be read by mere inspection within 1°; more accurately, indeed, than it can possibly be measured on the ground with a clinometer, or any portable contrivance of the sort. In Mr. Siborn's work contour lines are recommended to be drawn merely as a guide for the vertical strokes; but the system of tracing these horizontal lines at fixed vertical intervals, and drawing between the contours vertical strokes, without any reference to their thickness, but merely their direction, presents a far more easy mode of expressing correctly the actual surface of the ground, and infinitely more intelligible to those who have to make use of the plan. Indeed, if the contour lines are traced, at short vertical distances, either fixed or varying according to the nature of the ground, there is no occasion for the vertical strokes whatever, as these always cut the horizontal lines at right angles; this was the method recommended, wherever the ground was required to be shown very accurately, by the committee of French officers of engineers, appointed, in conjunction with some of the most scientific men of that period, to establish one general system of topographical plan drawing. The combined method of vertical lines and horizontal contours, at one fixed difference of level, is described in the German work alluded to, and also in Sir J. C. Smyth's "Topographical Memoir." From the vertical distance being a constant quantity, the angle formed by the slope of the ground is obtained by taking the length of the vertical line between any two of the contours in a pair of compasses, and applying it to a scale constructed upon a simple principle, self-evident from the figure. Above 45 the base, or "normal," becomes too short to be ap
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preciable if it has been constructed to suit moderate inclinations of the ground; and if on account of steep declivities the normal is increased in length, it becomes quite unmanageable on gentlyinclined surfaces.
By way of obviating this difficulty, and also making the same scale of normals still universally applicable, the vertical distance,
where required from the bold nature of particular slopes, is doubled or tripled, and these normals distinguished from others of the same length by being represented with thicker double or triple lines. This contrivance, the invention of Colonel Van Gorkum, is most highly extolled by Sir J. C. Smyth, in his "Topographical Memoir,” in which he strongly recommends the adoption, in the British service, of some part of the detail of this method of sketching ground, and proposes to omit the horizontal contours, but to take the angles of depression of the hills in sketching, and to represent their slopes, not over the whole plan, but occasionally on ground of the most importance, by normals of the proper length corresponding to such a vertical distance as may be judged best suited to the scale employed. On a scale of 4 inches to 1 mile, Colonel Van Gorkum fixes his perpendicular at 24 feet: Sir J. C. Smyth, in the memoir alluded to, has tabulated what he considers best adapted to the four scales in most general use; making it, at 6 inches to 1 mile, 22 feet; at 4 inches, 32 feet; at 2 inches, 66 feet; and at 1 inch, 132 feet. At 13°, in all these cases, he doubles the perpendicular, and at 50° triples it. With all deference to such authority, it is conceived that horizontal contour lines, traced at short known and generally equal vertical distances over the ground, afford ample data for the construction of sections in any required directions, even more accurate than a model of the features of the ground. The delineation of ground on the Ordnance Survey is now entirely effected on this system. The contours are traced with a spirit level or theodolite at different vertical intervals suited to the character of the surface, but averaging about 100 feet; these are interpolated with intermediate contour lines, traced with a water level, as being more expeditious, at the constant vertical distance of 25 feet. For the method of tracing these instrumental contour lines, see the chapter on Levelling, to which this subject more particularly belongs.
For representing the features of the country in a topographical plan, on a moderate scale, where the surface of the ground is not required to be determined with mathematical precision, the horizontal system of etching the hills, alluded to in page 34, is sufficiently accurate, and has the advantage of being generally intelli