cuttings. In both cases it is beneath the level of the rails (by which term is always understood the upper surface of the rails) to the extent of the depth of the ballast and permanent way.

The width of the earthworks at formation level depends on the number of lines of way, the gauge of the railway, the length of the sleepers, the slopes of the ballast, and the width of the side ditches where these are re

quired. The formation width is generally greater in cuttings than it is on embankments, in order to afford space for side ditches, and the width varies, as the side ditches require to be more capacious in certain situations and in certain soils than in others. A cess of about ten or

twelve feet is usually provided at the top of cuttings and at the foot of embankments to afford space for fences and ditches. Figs. 11 and 12 are sections of a double

line of railway, and show the formation level and the cess ordinarily given in England. Fig. 13 is a section of a rock cutting for a single line of railway, and shows on one side the slope used for shaley rock, and on the other side the slope for limestone rock. In both cases it is supposed that a depth of about eight feet of soft soil is superimposed on the rock.

Where rock is encountered it is important, on account of the expense of rock excavation, to reduce the width of the cuttings in order to minimise the amount of rock to be excavated; and the formation width is often less in rock cuttings than elsewhere. To reduce the width of

rock cuttings the ballast may be arranged as will be explained further on, and one side ditch may be used instead of two side ditches, the water being taken across the cutting by transverse drains at frequent intervals. The earth to be removed to make the slopes of a cutting is a quantity independent of what may be the formation width, and thus, inasmuch as the flat slopes of ordinary earthwork cuttings have much larger cubical dimensions than have the steep slopes of rock cuttings, a reduction of the for

mation width of earthwork cuttings does not produce nearly the percentage of saving on the whole quantity of earthwork that a similar reduction of width does in rock cuttings.

In considering the relative cost of a cutting and tunnel, the width of the railway and the nature of the soil are important elements in the calculation. A tunnel for a single line costs more than half as much as a tunnel for a double line; but it is to be remembered that a tunnel saves not only the excavation of the central part of the cutting but also the excavation of the slopes, and that the amount of earth contained in the slopes of a cutting-which in a deep cutting in soft earth form the greater part of the excavation-is the same whatever the formation width may be. In rock of a soft character tunnelling is easy, as little timbering is required and blasting is unnecessary; while some of the most expensive of known tunnels are those which have been made through soft soil and London clay, for, though such soil is easily excavated, it is frequently extremely treacherous, and very strong timbering is necessary. Thus, before pronouncing definitely on the depth at which tunnelling becomes economical, we require very exact knowledge of the whole of the strata lying between the surface of the ground and the level of rails. This knowledge will enable us not only to estimate the amount of earthwork saved by tunnelling, but will afford the requisite data to enable us to estimate the probable cost of the brickwork or stonework of the tunnel itself.

The internal dimensions, cross-sections and thickness of tunnels, premising that they must be sufficiently large to accommodate the engines and rolling stock, should be designed with regard to the nature of the soil and the position which the tunnel is to occupy. Thus where the

strain due to the nature of the earth and the position of the tunnel is mainly vertical, the shape is made elliptical,

with the major axis vertical, as shown in Fig. 14; where there is little vertical strain, and where there is but little height available, as in the case of a metropolitan tunnel

beneath a street, the shape is made elliptical, with the major axis horizontal, as shown in Fig. 15. In this case,

and in the case of a tunnel through rock (Fig. 16), that shape is adopted which accommodates most conveniently the trains which have to pass through it. A nearly cylindrical form is probably best in a material such as London clay, which may almost be said to press equally in all directions. Tunnels through the side of a hill, when the pressure on one side is not perfectly balanced by the pressure on the other side, are works requiring great care and special precautions, not only to prevent the

sides being damaged, but also to prevent the stability of the hill-side itself being disturbed.

Tunnels ought always to be made in a straight line if possible, so that an engine-driver can see through the tunnel from one end to the other when it is free from steam. Ventilation is a most troublesome matter in heavily worked tunnels. In one instance in England, viz. the Liverpool and Edge Hill Tunnel, resort has been of necessity had to artificial ventilation by means of a fan worked by a stationary engine in a large shaft near the centre of the tunnel. There is no doubt that in