is of gentle slope and the section of considerable length, it is usual to exaggerate the vertical heights for the purpose of rendering the undulations of the surface perceptible, which necessarily produces a distorted representation of the ground. The horizontal scale is usually made an aliquot part of the vertical, that the proportions between them may be at once obvious. Scales of 25, 50, 100 or 150 feet to one inch*, are appropriate for the latter, according to the degree of detail required in the section; and the horizontal scale may be fromto of either of them; or even a less proportion if the section is of great length, and the ground generally flat, as in the figure below, plotted from the specimen of a levelling field-book in page 87.

The horizontal line from which the vertical distances are set off, may be either on a level with one end, or some one point of the section; or a datum line may be drawn any number of feet above or below this line, exceeding the sum of all the vertical heights: this latter arrangement makes all the dimensions reduced for plotting either plus or minus. Laying off intermediate horizontal and vertical distances, should be avoided in plotting sections; the former ought always to be measured from the commencement of the section, with as few interruptions as the length of the line will allow; and the latter from the datum line. Both horizontal and vertical distances should, particularly in a working section, be written legibly on the drawing.

Trial sections that have been run for the purpose of ascertaining the best of several routes for a railroad, canal, or other work, should invariably be all plotted on the same scale and paper, and from the same datum line; and commencing at, and having refe

* The plotting scales, already alluded to, are very convenient for laying down sections; and Mr. Holtzapffell's cardboard Engine-Divided Scales will be found useful where a variety of scales are often required; from their method of construction, they can be sold at the low price of nine shillings a dozen, of all descriptions in general use.

By this

rence to, the same points as bench-marks. arrangement their comparison by the eye is facilitated. Cross or transverse sections are sometimes plotted above, and sometimes below the longitudinal section: and if only extending a few feet to the right and left, they are occasionally plotted on the line of section: but, if numerous, this last method causes a confused appearance in the drawing.

A method of combining plan and section has lately been introduced by Mr. Macneil, for the purpose of giving a popular representation of the quantity of excavation and embankment at any part of the section of a line of railway, the direction of which is shown on the outline plan of the country through which it passes by a thick black line, supposed to represent a vertical section of the rail. From the accurate section previously drawn, the heights of the embankments and depths of excavation at the different parts of the line are transferred to this datum line on the plan; and these quantities being tinted

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with different colours, or, if engraved, represented the one with vertical, and the other with horizontal lines, show at a glance the general relative proportions of cutting or embankment, as in the annexed figure.

The dark line in both figures represents the surface of the railroad or embankment.

To those unaccustomed to the use of sections, this simple contrivance by which they are rendered intelligible is particularly useful, and has been ordered to be adopted in all plans for railways submitted to the House of Commons. Of course it is only intended to give a general idea of the quantity of work on any line of road, railroad, or canal, and to be explanatory of the report and estimate.

The section which has always to accompany this species of plan must be plotted on a scale, the horizontal distances being not less than 4 inches to 1 mile, and the vertical not less than 100 feet to 1 inch. A line must also be drawn on the section representing the upper surface of the rails. At each change of inclination the height above some datum plane must be shown, and also the rates of the slopes, and the distances for which these gradients are maintained. The height of the railway over or under any turnpike road, navigable river, canal, or other railway, is likewise to be marked at the crossing. A variety of precautions and regulations are enforced by the "Standing Orders" relative to the construction of railways; and there are numerous other details connected with them, for which reference must be made to some of the numerous excellent practical works devoted solely to this branch of civil engineering.

Numerous transverse sections are required for computing the relative proportions of embankment and excavation* on any work, which operation is much facilitated by the use of Mr. Macneil's ingenious tables, calculated upon the "Prismoidal Formula,” which shows the cubic content of any prism to be equal to the area of each end + four times the middle area, multiplied by the length and divided by 6; whereas the common methods of taking

* Of the greatest possible consequence, both for the sake of avoiding unnecessary expense, and of laying out the work to the best advantage, valuable information upon this subject will be found in Mr. Macneil's work.

half the sums of the extreme heights for a mean height, or of taking half the sum of the extreme areas for a mean area, are both erroneous; the first giving too large a result, and the second too little.

Mr. Haskoll also gives very useful tables for the calculation of the areas of cross sections in the 2nd vol. of his "Engineer's Railway Guide;" a book containing full information upon all subjects connected with the laying out and construction of railway works.

The last description of levelling by the spirit-level to be noticed, is the method of tracing instrumentally horizontal sections termed "contours," either round a group of isolated features of ground for the formation of plans for drainage, sanitary, railway, or other engineering purposes-models or plans of comparison for military works, &c.; or over a whole tract of country with the view of giving a mathematical representation of the surface of the ground in connection with a national, or other extensive and accurate survey.

As regards the first of these, the tracing instrumental contour lines round any limited feature, or group of features of ground, the manner of proceeding is very simple. The site must be first carefully examined, and those slopes that best define the configuration of the surface, particularly the ridge and watercourse lines, marked out by rods or long pickets at such distances apart as may appear suited to the degree of minutiæ required, and the variety in the undulations of the ground. Where no such marked sensible lines exist, the rods must be placed where they can most readily be observed, being necessary as guides for the levelling staff during the subsequent operations. An accurate survey of the ground on which the positions of these rods are shown is then to be made. This should be laid down upon a scale proportioned to the purposes for which the plan is required, and to the vertical interval by which the contour lines are to be separated.

The scale for towns that has been adopted on the Ordnance Survey is 88 feet to 1 inch, which is sufficiently large for most engineering and municipal works, but can be increased to 40 or 50 feet for illustrating projects for drainage, or for the supply of water by pipes, &c. Estates are generally laid down upon a scale of 3 or 4 chains to 1 inch. For the larger scales the contour

lines may be traced at equidistant vertical intervals of from 2 to 10 feet, where the scale of the plan varies from 50 to 500 feet to 1 inch. This plan of the ground should be in the hands of the surveyor on commencing his contouring, as it will be of considerable assistance during the operation; and it is also desirable that sections should be run from the level of some fixed plane of comparison along the principal and best-defined lines marked out by the rods alluded to, leaving pickets at the vertical intervals assigned to the contours. These pickets serve as tests of the accuracy of the work as it progresses and as starting points for fresh contours. The staff is now to be held at one of the pickets; the spirit-level (or theodolite used as a spirit-level) being so placed as to command the best general view of the line of level, and adjusted so that its axis may, when horizontal, cut the staff; and the vane (for a levelling staff of this description is required) raised or lowered till it is intersected by the cross wires of the instrument. The staff with the vane kept to this height is then shifted to a point about the same level between the next row of ranging rods not more than 12 or 15 chains distant from the spirit level, on account of the correction that would otherwise be required for the curvature of the earth (about of an inch in 10 chains), and moved up and down the slope till the vane again coincides with the wires, when another picket is driven. This process is continued until it is found necessary to move the level to carry on the contour line to the extent required.

The same operation of course takes place with the contours above and below that first laid out; and where any bench-marks or points, the level of which can be of importance, come within the scope of the spirit-level, they should be invariably determined.

Where the vertical interval is small, the pickets upon more than one line of contours can often be traced without shifting the position of the instrument, if the levelling staff is of sufficient length. Too much should not however, be attempted at one time.

With regard to the second division of this subject, the tracing instrumental contours in connection with a national survey, the best instructions that can be given is a brief outline of the mode at present followed on the Ordnance Survey.

The ground between each of the trigonometrical stations is care