The line representing the formation of the railway, i.e., the bottoms of the cuttings or the tops of the banks, or the "road bed," is drawn on the section in red ink, the surface line being in black ink, as also the datum line. Blue vertical lines are drawn upwards from the datum line, extending as far as the surface or formation line, as the case may be, at every chain, and every 10 chains is numbered along the datum line. All chainages should be in miles and chains.

Fixing Gradients on Working Section.-The gradient line will be limited by the ruling gradient, and the gradients on the Parliamentary plans together with the limits of vertical deviation. It is drawn on the section so as to equalise the cuttings and embankments as much as possible, consistently with at the same time getting economical and uniform working gradients. A good method of fixing the gradient line is to use a piece of fine thread stretched tight, moving it up or down until the cuttings and banks are as nearly as may be judged by the eye equalised. Transparent set squares are also useful for this. In laying down the gradients it should be remembered that the slopes of the embankments will generally be much flatter than the slopes of the cuttings, and that the banks are wider at the top than the formation widths of the cuttings. Thus a rock cutting may have slopes of to 1 or nearly vertical, while the adjacent embankment may have slopes of 1 to 1, and this is to be allowed for in equalising cuttings and banks on the section.

It should also be remembered that there is shrinkage to be allowed for in the case of earth embankments, while rock expands in bulk when put into bank.

Levels on Working Section.-Having thus decided upon the gradient line, which will be considerably influenced by the necessity of crossing roads on the level and by the headroom required for bridges, the levels at each change of gradient are next to be figured on near the datum line, and the gradients calculated out and printed on in red ink, as 1 in 100, 1 in 50, and so on. The changes of gradient should as far as possible be selected at even chains, and should be indicated by red in place of blue vertical lines ruled up from the datum line.

The level of the surface of the ground at each chain should be figured on alongside the vertical blue line at the chain to which

Q

it refers, next to the datum line and in black ink; the level of the formation of the railway calculated from the gradient should be figured on at each chain next above the ground level, and in red ink; finally, the difference between the two, being the depth of cutting or height of bank, as the case may be, should be figured above the formation level, in red ink when cutting, and in blue ink when bank.

Cuttings and Banks on Working Section. - The spaces included between the ground line and the formation line of the railway, being the cuttings or banks as the case may be, should be coloured red.

A blue line representing the surface of the rails is also often. drawn on parallel to the formation line.

New Works and Existing Details on Working Section. All new works, such as bridges, culverts, pipes, &c., should be described in writing above the section at the points where they occur in red ink, all existing details, such as roads, streams, &c., being similarly described in black ink.

The setting out and the preparation of the general plan and section as above described may be said to complete the surveying work proper, the preparation of the detail working drawings of bridges, culverts, accommodation works, &c. &c., the specification and bill of quantities, coming under the head of the engineer's work.

Examples of Working Plan and Working Section of Railway taken from actual practice.-Figs. 170 and 171, Plates IX. and X., are examples of the general working plan and working section of a railway actually constructed, executed as described in this chapter.

Ruling Gradients.-The ruling gradient is the steepest gradient which occurs oftenest on the line. The considerations which fix the ruling gradient are

1. Train load.

2. Speed.

3. Power and weight of locomotive and train resistance.

1. Train Load. The train load must be fixed from local considerations of traffic, extent of rolling stock, &c. Ordinary 10 ton coal waggons, built for use over main lines to railway

companies' regulations, will weigh about 6 tons each empty. Composite six compartment passenger carriages will weigh about 12 tons each empty.

2. Speed. The most economical speed for goods is 20 miles per hour.

3. Locomotive Power and Train Resistance. The tractive power of a locomotive is given by

where D = diameter of cylinder in inches.

P= mean pressure of steam in cylinders in lbs. per square inch.

L= length of stroke in inches.

w = diameter of driving wheel in inches.

T= tractive force in lbs.

The tractive power is, however, limited by the adhesion of the locomotive drivers to the rails. In ordinary English weather the adhesion of a locomotive may be taken at 450 lbs. per ton of weight on drivers, or about one-fifth. When the tractive power developed by the cylinders exceeds the adhesion, the adhesion must be taken as the tractive power. In addition to the tractive power the boiler capacity is a dominant factor in determining the working load which a locomotive will take.

The resistance of a train on the level may be found from the following formulæ :—

where T = weight of train in tons; v = velocity in miles per hour; A = area of frontage of train in square feet; B = volume of train in cubic feet; R = resistance in lbs. on a level. As compared with experiment, equations (2) and (3) give results too high for low speeds.

The average train resistance may be taken at about 10 lbs. per ton at about 20 miles per hour, on the level.

In addition to the above train resistance on the level, the resistance due to gravity in ascending an incline must be cal

culated upon.

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Let G = gradient, so that inclination of gradient,

Let G = gradient, so that

G