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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
gible. In addition to the sketch of the ground, a representation of the geological features of the country can be given, without at all interfering with or confusing the sketch, by tracing on the back of the paper the divisions of the geological features, the different portions of which are afterwards coloured according to the conventional system of distinguishing the several various formations on geological maps. On holding the sketch against the light these divisions appear clearly visible, though in any other position of the paper they are not in the least perceptible. Geological sections should also be shown on the margin of the sketch, having reference to lines drawn across it*.
The inclination of such slopes as are of peculiar moment are measured with a "Clinometer," and the angles written either on the slopes themselves or as references. This little instrument can be made by cutting a small quadrant out of pasteboard and roughly graduating the arc. A small shot, suspended by a piece of silk, forms the plummet; and independently of its use in measuring vertical angles, it is of great assistance in tracing level. lines in sketching the contours. The instrument sold under this name is made with a spirit level; but the substitute, as described above, answers the purpose equally well, and moreover, from its
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being made merely of pasteboard, fits into the pocket of the sketching portfolio.
The slopes most necessary to note on a military sketch are those which relate to the facilities of ascent for artillery, cavalry, and infantry. According to the "Aide Mémoire," a slope of about
60°, or of 4 to 7, is inaccessible for infantry.
45°, or of 1 to 1, difficult.
If 30°, about 7 to 4, inaccessible for cavalry.
4 to 1, inaccessible for wheel carriages.
5o, 12 to 1, easy for carriages.
The leading features of ground are the summit ridges of hills (sometimes termed the water-shed lines), and the lowest parts of the valleys, down which the rain finds its way to the nearest rivers
* The geological part of the Ordnance Survey is now quite distinct from the geodesical.
or pools, called water-course lines. These two directing lines, if traced with care, will alone give some idea of the surface of the country, and assist materially in sketching the hills, particularly if drawn on the horizontal system, as the contour lines always cut the ridges and all lines of greatest inclination at right angles. It is a very common error, in first beginning to sketch ground, to regard hills as isolated features, as they often appear to the eye. Observation, and a slight practical knowledge of geology, inevitably produce more enlarged ideas respecting their combinations; and analogy soon points out where to expect the existence of fords, springs, defiles, and other important features incidental to peculiar formations. Thus appearances that at one time presented nothing but confusion and irregularity, will, as the eye becomes more experienced, be recognised as the results of general and known laws of nature.
The representation of the outline of the hills, and their relative command, is also materially assisted in a topographical plan, and more particularly in a military reconnaissance, by a few outline sketches taken from spots where the best general views can be obtained. A series of these topographical sketches running along the length of a range of hills, and a few taken perpendicular to this direction, supply in some degree the place of longitudinal and transverse sections; and give, in addition to the information communicated by a mere section, a general idea of the nature of the surrounding country.
A good judgment of distances is indispensable in sketching ground, even in filling up the interior of a survey, and more particularly in a reconnaissance, where there has not been either time or means for accurate measurement and triangulation. Practising for a few days will enable an officer to estimate with tolerable accuracy the length and average quickness of his ordinary pace, as also that of his horse (as on a rapid reconnaissance he must necessarily be mounted); and the habit of guessing distances, which can afterwards be verified, will tend to correct his eye. A micrometical scale in the eye-piece of his field telescope, with a corresponding table of distances, is also a very useful auxiliary; and the gradual
* See description of Dr. Brewster's micrometical telescope, in Dr. Pearson's Practical Astronomy, vol. ii.