Levelling with Aneroid. The aneroid barometer has been fully described in Chapter III., and it is necessary only to explain its manipulation in the field. The larger the size, the more satisfactory the observations. The surveyor should provide himself with an accurate plan or map of the district through which he proposes to take the levels, and at the points of observation he should mark with a small dot, and place letters as A, B, C, &c, so that he may identify their relative positions from his note-book in which he records the readings. The temperature at starting should be noted, and the index or zero of the movable scale "should be set to where the hand of the instrument points." "On ascending a mountain the hand travels backward, and as each division represents 100 ft. (on the movable scale), an approximate indication of the ascent is thus readily obtained." The aneroid should be held perfectly horizontal and gently tapped during an observation. "Subtract the reading at the lower station from that at the upper station; the difference is the height in feet." Cross Sections. - Cross-sections in their general acceptance mean a line of levels taken at right angles to the longitudinal section at every chain, or oftener if necessary. Their length is regulated by circumstances; for railways from 1 to 5 chains on each side, at points right and left at all changes of contour. They are set out either with a cross-staff or preferably an optical square. The most satisfactory and accurate method is to treat the sections at each chain as consecutive members-0, 1, 2, 3, 4, &c., starting at the commencement of the longitudinal section—and looking in direction of its termination to treat all observations, either of height or distance, as being right or left of the centre line (or line of section), as in Fig. 246, and having set out three sight lines, commence to measure from the centre, right, and left in each separate case, noting any irregularity in the surface of the ground. These measurements should be personally made by the surveyor, who should be provided with a quantity of pieces of white paper (about 1 in. square), upon which he should write the number of the cross-section, the measurement in feet (all cross-sections should be measured in feet), and after these particulars have been carefully written upon a piece of paper, it should be placed in a slit of some twigs of trees, pointed at the other end, and stuck in the ground at the point observed. Thus, as in Fig. 247, it will be observed that the cross-section is at M.CH. 0 .01 (no miles, 1 chain), and on the right-hand side there are five points, a, b, c, d, e, of 10 ft., 25 ft., 39 ft., 58 ft., and 66 ft. from the centre, whilst on the left there are also five points, ƒ, g, h, j, k, of 4 ft., 16 ft. 6 ins., 30 ft., 59 ft., and 66 ft. respectively. Take the point b on the right and g on the left, they would be marked on the paper, as in Figs. 248 and 249, No. 1 section, 25 ft. right and 16 ft. 6 in. left. The chief advantages claimed by this process is, that not only does the surveyor personally superintend these preliminary operations, but after a series of eight or a dozen cross-sections have been set out and measured all the higher points of the series may be taken from one point, so that the change of instrument is minimised. The staff-holder, who should be properly instructed as to his duties, proceeds to each of the points, and holding the staff thereat, he picks up the ticket, and at a signal from the surveyor he reads out in a clear, loud voice, "Crosssection number one, fifteen feet 6 inches left," the surveyor booking this repeats it, and if correct the ticket should be destroyed, so as not to be taken again. In conclusion, I recommend the surveyor to make his assistants thoroughly understand their duties and his requirements, and, by a code of signals mutually understood, a great deal of satisfactory work may be accomplished in almost dumb show. CHAPTER X. CONTOURING. CONTOURING is the art of delineating upon a plan a series of lines which represent certain altitudes parallel with the horizon, or, in other words, "lines of intersection of a hill by a horizontal plane." The simplest illustration is the high and low water marks along the sea-shore, where the fringe of seaweed marks the extreme boundary of high water, and its zig-zag outline is due to the water finding out the inequalities of the level of the shore, so that whatever form this fringe may take, all round the coast of this "sea-girt island will be found a line representing one uniform level parallel with the horizon. Another and very primitive illustration: if varying quantities of different coloured liquids, commencing with the lightest colours in the largest quantities, were poured into some basin-shaped vessel whose sides would absorb some of the colours, so as to leave the mark of its highest level, and smaller quantities of colour of graduating darkness were successively poured in and emptied out, the defined lines made by those different colours would represent concentric circles on the sides of the basin, whose distance apart would be governed by the varying quantities of the different coloured liquids, and these lines would be the contours of the sides of the vessel. Vertical Intervals and Horizontal Equivalents.-It is the province of the modern surveyor to practically show upon his plane these lines of contour. The known difference of height thereof are called the vertical intervals, and their VERTICAL INTERVAL SLOPE HORIZONTAL EQUIVALENT distance apart upon the survey are termed the horizontal equivalents, as will be seen by Fig. 250. In Figs. 251 and 252 we have a simple illustration of contour lines upon the truncated cone (Fig. 251) at points A, B, C, D, E, F, G, H, which in plan are represented by the concentric circles in Fig. 252, so that in the former case the relative height of в over ▲, c over в, &c., represent the vertical intervals, whilst in Fig. 252 the distance of B from A, C from в, &c., are the horizontal equivalents. Fig. 250. In Figs. 253 and 254 we have examples of the form contour lines will show on plan whose planes are projected from a section of irregularity. The contours will occur in smaller horizontal dis HYPOTENUSAL ALLOWANCE. 201 tance, in proportion to the steepness of the ground. The contour lines in Fig. 253, besides giving the relative altitudes, explain the form and flexure of every slope, thus a A' and в B' (Fig. 253) show the exact concavity and convexity of the slopes a a', в B' in Fig. 254. Now these vertical intervals are to be determined by two methods; 1st by angular observations, 2nd by means of levelling. SLOPE HORIZONTAL EQUIVALENT 10 B Hypotenusal Allowance.-We will briefly consider the first system. It has been shown in the chapter on chain surveying, that in chaining up the slope of a hill it is necessary to make an allowance for hypotenusal measurements by observing the angle which the slope makes with the horizon; and in the inverse ratio, by the same process, it is possible to calculate the difference of level between points on a hillside by finding the natural sine of the angle of slope. To take a simple illustration, suppose, as in Fig. 255, Iwe have a slope forming an angle of 10 deg. with the horizon, and it is desired to establish at c a point whose height above B shall be 25 ft. By measuring 143.96 ft. from a along the slope we shall at c get this point, whose horizontal equivalent is 141.78 ft. In Fig. 256 we have an instance of the slope of a hill taking three different forms of flexure, as at C, D, and E, where the slopes are relatively 10°, 35°, and 65° with the horizon. We have seen that, requiring a vertical interval of 25 ft. between ▲ and o with the first angle of 10°, the horizontal equivalent will be 141.78 ft.; for the second angle of 35° with the same altitude the horizontal equivalent will be 35.70 ft., whilst the hypotenusal measurement Fig. 255. C D PARALLEL WITH HORIZON d D65 PARALLEL WITH HORIZON from c to D will be 43.58 ft.; and in the case of the third slope of 65°, with a vertical interval also of 25 ft., the horizontal equivalent DE will be 11.65 ft., and the distance along the slope from D to E 27.56. It may be well that I should explain how the foregoing results have been obtained. The natural cotangent of the angle of slope in the case of 10° is 5.6713, and this multiplied by the vertical interval 25 ft. gives a result of 141.78 as the horizontal equivalent. Next, if the natural secant of 10° or 101543 be now multiplied |