Land Surveying and Levelling, pp. 194, 195. NOTE THE POSITION OF CONTOUR POINTS IN THE FIELD IS FIXED DURING LEVELLING BY LATHS laterally or at right angles from the larger ranges, will generally be found to have the most gradual and regular slope. Hence the datum pegs for checking the contour levels in the process of setting out can best be fixed at such points. When running a line similar to a contour for setting out a gradient, the assistance of a chain is required to arrive approximately at relative distance. Two men are, therefore, engaged to chain continuously over the line marked out by the laths, following by eye the irregular course so indicated as near as possible. Suppose that the object of the contour is to subsequently set out a gradient of 1 in 1,000. The follower at the chain reports to the surveyor at the insertion of every fifth arrow, indicating 500 links with the use of a foot chain, or at every 7 chains (497 feet) with the use of a Gunter's chain. The surveyor then either reduces or increases the reading to be taken upon the staff by 0'50, according as he is ascending or descending a gradient. It is not necessary to alter the reading for determining the position of these points more frequently than at intervals of, say, half a foot, because the line afterwards ranged out for adoption when marked out either as a straight line or set out as a regular curve, is not likely to approach nearer to the line of levels so found than six inches when taken as a longitudinal section. As regards the origin of contour lines, Mr. J. Butler Williams, in his treatise on Practical Geodesy, states that "the idea of employing horizontal lines for the representation of forms suggested itself as early as 1742 to Philippe Buache, when observing the horizontal marks left on the land by the gradual subsidence of the waters of an inundation. But he only aimed at tracing them as lines of equal soundings on hydrographical charts. Thirty-three years later, Ducarla proposed to adapt imaginary lines, following the same law, to the representation of the features of ground; and in 1782, Dupain-Triel in arranging the method into a system, recommended that the lines should generally be vertically equidistant. However, owing to the want of precise data and accurate outline maps, the principle was not fully carried out until of late years, when these vertically equidistant horizontal lines, which we shall call normal contours, came to be determined in the field by means of the theodolite, spirit level, or other instrument. These normal contours have been adopted in the French cadastre since 1818." The Ordnance Surveyors employed a 5-in. theodolite for contouring with the aid of a contouring staff 8 ft. long figured upon one face only, and provided with a sliding vane. which was fixed at the required height by a clamp at the back of the staff. The visibility of points upon a site to be seen from one another is sometimes an important question. This depends mainly upon the general convexity or concavity of the intervening ground, and may best be determined by a longitudinal section taken between the points under review, but in the absence of such section, it may be judged by a glance at a plan showing the intervening contours, bearing in mind that when the contour lines which were run at the higher level appear closer together than those which were run at the lower level, the 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. The plan of the proposed reservoir shows contours at heights having an interval of 5 ft. between them. The 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 |