when the car is moving at the highest supposed velocity; or, in other words, to give the inclined plane across the track, on which the wheels rest, an inclination such that the tendency of the wheels to slide towards the interior rail shall alone counteract the centrifugal force.

675. Sidings, &c. On single lines of railways short portions of a track, termed sidings, are placed at convenient intervals along the main track, to enable cars going in opposite directions to cross each other, one train passing into the siding and stopping while the other proceeds on the main track. On double lines arrangements, termed crossings, are made to enable trains to pass from one track into the other, as circumstances may require. The position of sidings and their length will depend entirely on local circumstances, as the length of the trains, the number daily, &c.

The manner generally adopted, of connecting the main track with a siding, or a crossing, is very simple. It consists (Fig. 161) in having two short lengths of the opposite rails of the main

track, where the siding or crossing joins it, moveable around one of their ends, so that the other can be displaced from the line of the main track, and be joined with that of the siding, or crossing, on the passage of a car out of the main track. These moveable portions of rails are connected and kept parallel by a long cross

Fig. 162-Represents a plan M, and section N, of a fixed crossing plate. The plate A is of cast-iron, with vertical ribs c, c, on the bottom, to give it the requisite strength. Wrought-iron bars a, a, placed in the lines of the two intersecting rails d, d, are firmly screwed to the plate; a sufficient space being left between them and the rails for the flanch of the wheel to pass.

bolt, to the end of which a vertical lever is attached to draw them forward, or shove them back.

At the point where the rails of the two tracks intersect, a castiron plate, termed a crossing-plate (Fig. 162) is placed to connect the rails. The surface of the plate is arranged either with grooves in the lines of the rails to admit the flanch of the wheel in passing, the tire running upon the surface of the plate; or wrought-iron bars are affixed to the surface of the plate for the same purpose.

The angle between the rails of the main tracks and those of a siding or crossing, termed the angle of deflection, should not be greater than 2° or 3°. The connecting rails between the straight portions of the tracks should be of the shape of an S curve, in order that the passage may be gradually effected.

676. Turn-plates. Where one track intersects another under a considerable angle, it will be necessary to substitute for the ordinary method of connecting them, what is termed a turn-plate, or turn-table. This consists of a strong circular platform of wood or cast-iron, moveable around its centre by means of conical rollers beneath it running upon iron roller-ways. Two rails are laid upon the platform to receive the car, which is transferred from one track to the other by turning the platform sufficiently to place the rails upon it in the same line as those of the track to be passed into.

677. Street-crossings. When a track intersects a road, or street, upon the same level with it, the rail must be guarded by cast-iron plates laid on each side of it, sufficient space being left between them and the rail for the play of the flanch. The top of the plates should be on a level with the top of the rail. Wherever it is practicable a drain should be placed beneath, to receive the mud and dust which, accumulating between the plates and rail, might interfere with the passing of the cars along the rails.

678. Gradients. From various experiments upon the friction of cars upon railways, it appears that the angle of repose is about, but that in descending gradients much steeper, the velocity due to the accelerating force of gravity soon attains its greatest limit and remains constant, from the resistance caused by the air.

The limit of the velocity thus attained upon gradients of any degree, whether the train descends by the action of gravity alone, or by the combined action of the motive power of the engine and gravity, can be readily determined for any given load. From calculation and experiment it appears that heavy trains may descend gradients of T, without attaining a greater velocity than about 40 or 50 miles an hour, by allowing them to run freely,

without applying the brake to check the speed. By the application of the brake, the velocity may be kept within any limit of safety upon much steeper gradients. The only question, then, in comparing the advantages of different gradients, is one of the comparative cost between the loss of power and speed, on the one hand, for ascending trains on steep gradients, and that of the heavy excavations, tunnels, and embankments, on the other, which may be required by lighter gradients.

In distributing the gradients along a line, engineers are generally agreed that it is more advantageous to have steep gradients upon short portions of the line, than to overcome the same difference of level by gradients less steep upon longer develop

ments.

679. In steep gradients, where locomotive power cannot be employed, stationary power is used, the trains being dragged up, or lowered, by ropes connected with a suitable mechanism, worked by stationary power placed at the top of the plane. The inclined planes, with stationary power, generally receive a uniform slope throughout. The portion of the track at the top and bottom of the plane, should be level for a sufficient distance back, to receive the ascending or descending trains. The axes of the level portions should, when practicable, be in the same vertical plane as that of the axis of the inclined plane.

Small rollers, or sheeves, are placed at suitable distances along the axis of the inclined plane, upon which the rope rests.

Within a few years back flexible bands of rolled hoop-iron have been substituted for ropes on some of the inclined planes of the United States, and have been found to work well, presenting more durability and being less expensive than ropes.

680. Tunnels. The great consumption of power by gravity, and the necessity therefore of either employing additional power, or of diminishing the load of locomotives in ascending steep gradients, have caused engineers to resort to excavations and embankments frequently of excessive dimensions, to obtain gradients upon which the ordinary loads on a level can be transported with a suitable degree of speed. The difficulty and cost of forming these works become in some cases so great, that it is found preferable to obtain the requisite gradient by carrying the road under ground by an excavation termed a tunnel.

The choice between deep cutting and tunnelling, will depend upon the relative cost of the two, and the nature of the ground. When the cost of the two methods would be about equal, and the slopes of the deep cut are not liable to slips, it is usually more advantageous to resort to deep cutting than to tunnelling. So much, however, will depend upon local circumstances, that the comparative advantages of the two methods can only be de

cided upon understandingly when these are known. Where any latitude of choice of locality is allowed, the nature of the soil, the length of the tunnel, that of the deep cuts by which it must be approached, and also the depths of the working and air shafts, must all be well studied before any definitive location is decided upon. In some cases it may be found, that a longer tunnel with shorter deep cuts will be more advantageous in one position, than a shorter tunnel with longer deep cuts in another. In others, the greater depth of working shafts may be more than compensated by obtaining a safer soil, or a shorter tunnel.

681. The operations in tunnelling will depend upon the nature of the soil. The work is commenced by setting out, in the first place, with great accuracy upon the surface of the ground, the profile line contained in the vertical plane of the axis of the tunnel. At suitable intervals along this line vertical pits, termed working shafts, are sunk to a level with the top, or crown of the tunnel. The shafts and the excavations, which form the entrances to the tunnel, are connected, when the soil will admit of it, by a small excavation termed a heading, or drift, usually five or six feet in width, and seven or eight feet in height, which is made along the crown of the tunnel. After the drift is completed, the excavation for the tunnel is gradually enlarged; the excavated earth is raised through the working shafts, and at the same time carried out at the ends. The dimensions and form of the cross section of the excavation, will depend upon the nature of the soil, and the object of the tunnel as a communication. In solid rock the sides of the excavation are usually vertical; the top receives an arched form; and the bottom is horizontal. In soils which require to be sustained by an arch, the excavation should conform as nearly as practicable to the form of cross section of the arch.

In tunnels through unstratified rocks, the sides and roof may be safely left unsupported; but in stratified rocks there is danger of blocks becoming detached and falling: wherever this is to be apprehended, the top of the tunnel should be supported by an arch.

Tunnelling in loose soils is one of the most hazardous operations of the miner's art, requiring the greatest precautions in supporting the sides of the excavations by strong rough framework, covered by a sheathing of boards, to secure the workmen from danger. When in such cases the drift cannot be extended throughout the line of the tunnel, the excavation is advanced only a few feet in each direction from the bottom of the working shafts, and is gradually widened and deepened to the proper form and dimensions to receive the masonry of the tunnel, which is immediately commenced below each working shaft, and is

carried forward in both directions towards the two ends of the tunnel.

682. Masonry of tunnels. The cross section of the arch of a tunnel (Fig. 163) is usually an oval segment, formed of arcs of

O

a

Fig. 163-Represents the general form of the cross section c of a brick arch for tunnels.

a, a, askew-back stone between the sides of the arch and the bottom inverted arch.

circles for the sides and top, resting on an inverted arch at bot tom. The tunnels on some of the recent railways in England are from 24 to 30 feet wide, and of the same height from the level of the rails to the crown of the arch. The usual thickness of the arch is eighteen inches. Brick laid in hydraulic cement is generally used for the masonry, an askew-back course of stone being placed at the junction of the sides and the inverted arch. The masonry is constructed in short lengths of about twenty fcet, depending, however, upon the precautions necessary to secure the sides of the excavation. As the sides of the arch are carried up, the frame-work supporting the earth behind is gradually removed, and the space between the back of the masonry and the sides of the excavation is filled in with earth well rammed. This operation should be carefully attended to throughout the whole of the backing of the arch, so that the masonry may not be exposed to the effects of any sudden yield ing of the earth around it.

683. The frame-work of the centres should be so arrangec that they may be taken apart and be set up with facility. The combination adopted will depend upon the size of the arch, and the necessity of supporting the sides as well as the top of the arch by the centre, during the process of the work.

684. The earth at the ends of the tunnel is supported by a retaining wall, usually faced with stone. These walls, termed the fronts of the tunnel, are generally finished with the usual