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ground must be concave, and that when the contour lines at the higher level appear further apart than the contour lines at the lower level, the ground must be convex.

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The plan of the proposed reservoir shows contours at heights having an interval of 5 ft. between them. The

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altitudes are supposed to range between 50 and 100 ft. Watersheds are indicated by a salient or outward bend in a contour line; watercourses by a re-entering bend in the contour line. The vertical interval at which the contours are to be levelled having been decided, a line of section is taken (sometimes called "the initial line "), upon which pegs, as temporary bench marks, are fixed near the level of each contour, and in running the required contours the instrument is set up so that the telescope, when levelled, may intersect the levelling staff which is held upon the initial point, or top of each contour peg, in order to arrive at the reduced level to be read upon the staff for tracing the required contour, as explained above.

The areas of the contours can be best arrived at with the use of a planimeter, as described upon pages 155, 156. In carrying the tracer round, care must be taken to observe whether the disc M has performed an entire revolution, in which case 10 must be added to the unit in the last reading taken by the instrument. The diagram indicates the method of calculating the area enclosed by the top bank contour. In this case the enclosure being large it is divided into three parts, and one side being straight, a triangle is formed in the centre, the area of which can be most accurately calculated in the ordinary way by multiplying the base by half the height, as it would be waste of time to go round the boundary of any regular geometrical form with the planimeter. The two adjoining enclosures to the triangle being irregular in outline are more accurately determined by the planimeter than by drawing "give-and-take lines" in the usual way. (See page 197.)

The subjoined table gives a systematic method of drawing up the statement of capacities. (See page 200.)

There are two principal modes of expressing the nature of hill and valley on a plan. The vertical system is largely employed in France and Prussia, and also in England when the scale is very small and the maps are to be engraved; and in this method it is assumed that the lines represent the course which the rills of water would take in descending from the water-sheds to the lower levels. It may be used simply for the expression of ground when the relative

thickness or distance of the lines apart have no especial meaning beyond depicting the folds and irregularities of the ground; or the lines and distances may be constructed according to a scale of shade, as in German military maps, where the relative thickness denotes the angle of the slope

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as well as its form. Thus Lehman's scale of shade com mences with fine lines at 5°, and proceeds in increasing thicknesses of line, every 5°, up to 45°, which being practically impassable is represented as composed of very thick black lines extremely close to one another.

The horizontal method may be considered as but an extension of the principle of contouring, as the space between the chief contours is filled in with horizontal lines, preserving a rough parallelism to them. These hachures are not, however, continuous, as this would tend to make the drawing too smooth and even, and destroy the irregularity of work produced by drawing them in sets or groups of various lengths, which, moreover, tends to produce a nearer resemblance to the roughness of the actual surface.

Lieut.-Colonel William Paterson, Professor at the Royal Military College, Sandhurst, in his "Notes on Military Surveying and Reconnaissance," thus describes the different theories of expressing ground upon paper: "There are three principal and distinct methods of expressing hills upon paper. The first method is to suppose a sheet of light in parallel rays to fall upon ground from directly above it. Wherever the ground is level, the appearance will be white; when it slopes, the rays falling obliquely on the surface will give a dark appearance; and as it becomes more precipitous, it will of course be still darker. This is the theory of the style of drawing which is done with a brush and successive shades of indian ink or other tint. In the second method, a volume of water is supposed to fall on a hill. Wherever the slopes are gentle, the water will run off in small thin rills, diverging as they descend; in the abrupt slopes, it will rush down in large broad streams. This is the theory of the vertical system; only to avoid stiffness, the lines are broken into a series of successive strokes, not following one another down the hills. In the third method, the hills may be imagined as inundated with water, and that every time the water falls, a certain fixed number of feet, a mark is run round the surface of the ground at the upper edge of the water. According to the steepness of the falls, the lines, to an eye placed

immediately above them, will appear close or far apart. This is called the contour or horizontal system, and is applied in field sketching; the strokes being broken instead of being carried continuously round, and the effect of the shading increased by making them thicker, as well as closer on the steeper slopes, and lighter, longer, and wider apart on the more gentle declivities." (See also remarks upon pages 120-122.)

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