mathematical accuracy, the first attempts at which were made by Major Lehman, an officer in the Saxon service, whose system met with great encouragement in Germany; but though subsequently much improved, does not appear likely to be adopted in any other country.

The light (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, shows the proportion of black in the lines, to the white spaces intervening between them for every 5o; which at 5o is 1 to 8; at 10o 2 to 7; at 15o 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 "Topographical 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 1o, 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

"Militairisches Zeichnen und Aufnchmen."-Berlin, 1829.

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; and this was the method recommended, wherever the ground is 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," as it is technically termed

15 20 30 45

by the authors who have written on the subject, becomes too short to be appreciable, 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 gently inclined 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," where 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

The sketching of the ground on the Ordnance Survey of Ireland is actually commenced, partially, on this system; horizontal lines being traced at certain vertical distances, and the intermediate space filled in by the eye.

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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 four inches to one mile, Colonel Van Gorkum fixes his perpendicular at twenty-four 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 six inches to one mile, twenty-two feet; at four inches, thirty-two feet; at two inches, sixty-six feet; and at one inch, one hundred and thirty-two feet. At 13o 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, and even for a model of the features of the ground.*

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 intelligible. In addition to the sketch of the ground, a representation of the geological features of the country is given by several of the gentlemen who fill in the outline plan of the ordnance survey, without at all interfering with, or confusing the sketch. On the back of the paper are traced the divisions of the geological features, and these different portions are 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 are also shown on the margin of the sketch, having reference to lines drawn across it.

The inclination of such slopes as are of peculiar moment should be 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

For the method of tracing these contour lines, see page 91.