intermediate contours filled in by the eye; to perform which with tolerable accuracy, with the assistance of the instrumental contours previously marked by pickets on the ground, becomes, after a little practice, an operation of no great difficulty. Even in surveys where the delineation of the surface of the ground is to be represented entirely by sketching on the horizontal system, as described in page 60, a few distant instrumental contours very much facilitate the work, and give it a character of truth and certainty that could not otherwise be looked for. Fig. 1, Plate 8, illustrates the method of tracing and surveying the contour lines when the operation is carried on between the separate secondary triangles on an extensive survey. As has been remarked however, there is no necessity for following this system of working rigidly within the boundary lines of these triangles, as bench-marks established at any convenient spots out of the direct line connecting two trigonometrical stations, answer just as well for checks upon the progress of the work, and for datum points from whence to commence, and upon which to close the work. Supposing, for instance, the altitudes of the trigonometrical points B, C, D, had been previously ascertained to be respectively 625, 570, and 282 feet above the level of the sea, and that the instrumental contours were required to be marked at equal vertical intervals of 50 feet above that level. Starting from either of these points, say C, in the direction of C B, mark the level of the nearest line of contours, which in this case would be 20 feet below C; and then the points where every difference of altitude of 50 feet would cut the line C B (500, 450, &c.). On arriving at B a check is at once obtained upon the section that has just been run; and the error, if any, can be corrected upon the spot. The other sides of the triangle, B D and DC, are then levelled in the same manner; the connection of the corresponding contour lines cutting each of them traced out by the spirit-level; and their position in plan laid down, either by traversing, or by reference to points and lines already surveyed and plotted. The places of many of these contour pickets can generally be ascertained whilst the levelling is in progress, by measuring their distances from the instrument, and observing the angles made by them and the trigonometrical or other known points. For this and other methods of obtaining their positions in the readiest manner, no fixed directions can be given, as they must vary in different localities; and nothing but practice will render a surveyor capable of availing himself of the many opportunities he will constantly meet with of simplifying his operations by the exercise of a little forethought and judgment. If, instead of confining the process of contouring within triangles, the altitudes of any points, a, b, c, d, &c., had been determined by levelling, and given to the surveyor as his starting points; he has only to level from one of them to the required altitude of the nearest contour line, either above or below him, and then proceed to carry this level round the hill features as in contouring isolated surveys. In very hilly or broken ground this system would appear preferable to that of working within the limits of regular figures, as the whole operation is made to depend more upon the marked natural features of the country. It is hardly necessary to enumerate the advantages of a system of horizontal contours, traced thus accurately upon the plans of a national survey. Not only can the best general lines of directions for roads, canals and railways; conduits for the supply of water; drainage pipes, &c., be ascertained without the trouble and expense of trial sections; but accurate sections, for whatever purpose required, may be traced to any extent across the country in all directions. Had this system been adopted on the Ordnance Survey of England, twenty years ago, an incalculable saving would have been effected on all the trial lines run to ascertain the best practicable directions for the railways that now intersect this country. Another use to which contour lines traced round any limited extent of ground can be applied, is the formation of models for military or other purposes; though the contour plan itself affords far more accurate data for reference than can be obtained from the model, the dimensions of which being derived from the plan, are, like all copies, more liable to be vitiated by errors than the originals. To construct these models an outline of the plan is pasted upon a flat board of seasoned wood or other material, the points at which all the vertical heights have been determined being marked upon the orthographic projection. Vertical standards of copper, zinc, or any other metal, are then inserted into the board at these points, and cut off at the proper heights. The level of the board forms the lowest horizontal plane-that of the sea at low water, if the ground to be represented is contiguous to the coast;—and the tops of the highest set of rods the superior plane of contours. The intervals between these pieces of wire are filled in with composition or modelling clay, which is worked carefully to the level of the tops of the rods, and with a small flattening tool or the hand, moulded so as to represent as nearly as possible the irregularities of the surface of the ground; which representation will be more or less perfect in proportion to the smallness of the vertical intervals between the successive series of contours. In some cases, particularly when the scale of the model is small, and the character of the country of slight elevation, it is found desirable to increase the vertical scale, making it some multiple of the horizontal; but this of course produces an unreal and more or less exaggerated representation of the ground. Where the contours have been run at considerable vertical intervals, and the surface sketched by the eye between them, the sketch will be found of much assistance in shaping the surface of the model. From this model, if a mould in plaster of Paris is made, any required number of casts can be taken, which if properly prepared with isinglass or size, may be coloured, and have delineated on their surfaces, references, boundary lines, &c., for geological purposes. These models are eminently useful, but they should be made of small detached pieces, representing the different divisions and characters of the strata. By the aid of a contoured plan, many problems can likewise be worked out without the aid of vertical sections; from among others the five following are selected as of practical utility* :— 1. To find the direction of the slope and the inclination of a plane passing through three given points A B C, not in the same straight line.-Fig. 2, Plate 8. Divide the line A C, joining the highest and lowest of the given points, so that the two parts may bear the same proportion to each * These problems are taken from a paper on Contour Plans and Defilade, by Captain Harness, extracted principally from the "Mémorial du Génie." H other as the numbers expressing the difference of level between the third point and each of the other two; that is, make AD: DC :: A~B:B~C; D will then be on the same level as B; and D B will be a horizontal of the plane required. 2. To find the scale of a plane which shall pass through two given points and have a given inclination. This inclination determines the interval in plan between the contours passing through the two given points. With one of these points as a centre, and that interval as radius, describe a circle, the tangent drawn to which from the other point is a horizontal of the plane required. If the distance between the points is less than the necessary interval between the contours, this problem is of course impossible; and when possible it admits of two solutions. 3. To find what part of a given surface is elevated above a given plane. The intersection of the horizontals of the plane with the contour lines at corresponding levels of the surface above, denotes, as seen in Fig. 3, the portion of the surface rising above the plane. 4. To find the intersection of two planes. Produce until they meet two or more contours, having corresponding levels of each; the line joining the points of meeting will be that of intersection. If the contours of the two planes be parallel, their intersections, being a horizontal of each plane, will be known if one point in it be found. 5. To find in a plane, given by its scale of slope, a straight line, which, passing through a given point in the plane, shall have a given inclination less than that of the plane (Fig. 4). Trace a contour of the plane having any convenient difference of level above or below this point. With that point as a centre, and with the base due, with the required inclination of the line to the assumed difference of level as a radius, describe an arc cutting that contour. The line drawn through their intersections and the given point will have the required inclination. By the above problem a road up the side of a hill represented by contours, can be traced so as not to exceed in any part a given inclination. The application of contours to the object of defilading a work to secure its interior from fire (almost the first use to which they were applied) can hardly be entered upon here. The subject is fully treated by many French authors on fortification; and extracts from Captain Noizet's paper, in the "Mémorial du Génie,” will be found in the sixth volume of the Royal Engineers' Professional Papers*. The method of measuring altitudes by the barometer and the temperature of boiling water is reserved for the next chapter. * See also the chapter upon Defilade in Captain Macaulay's "Field Fortification," |