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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.”


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."




THE Mountain Barometer presents a method of determining comparative altitudes not susceptible of so much accuracy as those already described, but far more expeditious when applied to isolated stations separated from each other by considerable distances. It is also capable of being used extensively by one individual; and the observations, if performed with care, will in most cases give results very near the truth. The instrument, as made at present, is very portable, though liable to injury in travelling if the proper precautions are not invariably taken, the most essential of which is that of always carrying the cistern inverted, and in this position tightening the screw at the bottom of the cistern to prevent the oscillations of the mercury breaking the tube. In barometers considered of the best construction, and which are the most expensive, the surface of the mercury in the cistern is brought by a screw to the zero of the instrument, which marks the height at which it stood there when the scale was first graduated†. In others, not furnished with the means of effecting this adjustment, and in which the cistern is entirely enclosed from view, an allowance must be made to reduce the reading on the scale to what it would have been if the mercury in the cistern had been adjusted to zero. It is


* Mr. Howlett remarks that, in barometers where the bottom of the cistern is formed by a leather bag, the mercury should be forced up nearly to the top of the tube by the bottom screw, whilst the instrument is held upright. It should then be carefully inverted, in which position it must always be carried. When required for use, it should again be placed upright before the pressure of the screw against the bag is relaxed; otherwise the bag is liable to be burst.

+ It is doubtful if this is any advantage: a barometer of this kind takes a long time to adjust and read; and as a tangent to the surface of the mercury is required, both in the tube and the cistern, there is more chance of error in the observation.

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