arising at intermediate places, and as these will not usually lie exactly on the direct line, deviations from straightness will be rendered necessary. In the second place, except in the unlikely event of all the places on-the selected route lying at the same elevation, a line that is perfectly level is a physical impossibility; and from engineering considerations, even one with uniform gradients will be impracticable on the score of cost, unless the surface of the country is extraordinarily even. In these circumstances the constructor has two broad alternatives between which to choose. On the one hand he may make the line follow the natural inequalities of the ground as nearly as may be, avoiding the elevations and depressions by curves; or on the other he may aim at making it as nearly straight and level as possible by taking it through the elevations in cuttings or tunnels and across the depressions on embankments or bridges. He will incline to the first of these alternatives when cheapness of first cost is a desideratum, but, except in unusually favourable circumstances, the resulting line, being full of sharp curves and severe gradients, will be unsuited for fast running and will be unable to accommodate heavy traffic economically. If, however, cost within reasonable limits is a secondary consideration and the intention is to build a line adapted for express trains and for the carriage of the largest volume of traffic with speed and economy, he will lean towards the second. In practice every line is a compromise between these two extremes, arrived at by carefully balancing a large number of varying factors. Other things being equal, that route is best which will serve the district most conveniently and secure the highest revenue; and the most favourable combination of curves and gradients is that by which the annual cost of conveying the traffic which the line will be called on to carry, added to the annual interest on the capital expended in construction; will be made a minimum.
Cuttings and Embankments.—A cutting, or cut, is simply a trench dug in a hill or piece of rising ground, wide enough at the bottom to accommodate one or more pairs of rails, and deep enough to enable the line to continue its course on the level or on a moderate gradient. The slopes of the sides vary according to the nature of the ground, the amount of moisture present, &c. In solid rock they may be vertical; in gravel, sand or common earth they must, to prevent slipping, rise 1 ft. for 1 to 1½ or 2 ft. of base, or even more in treacherous clay. In soft material the excavation may be performed by mechanical excavators or “steam navvies,” while in hard it may be necessary to resort to blasting. Except in hard rock, the top width of a cutting, and therefore the amount of material to be excavated, increases rapidly with the depth; hence if a cutting exceeds a certain depth, which varies with the particular circumstances, it may be more economical, instead of forming the sides at the slope at which the material of which they are composed will stand, to make them nearly vertical and support the soil with a retaining wall, or to bore a tunnel. An embankment-bank, or fill, is the reverse of a cutting, being an artificial mound of earth on which the railway is taken across depressions in the surface of the ground. An endeavour is made so to plan the works of a railway that the quantity of earth excavated in cuttings shall be equal to the quantity required for the embankments; but this is not always practicable, and it is sometimes advantageous to obtain the earth from some source close to the embankment rather than incur the expense of hauling it from a distant cutting. As embankments have to support the weight of heavy trains, they must be uniformly firm and well drained, and before the line is fully opened for traffic they must be allowed time to consolidate, a process which is helped by running construction or mineral trains over them.
An interesting case of embankment and cutting in combination was involved in crossing Chat Moss on the Liverpool & Manchester railway. The moss was 4½ m. across, and it varied in depth from 10 to 30 ft. Its general character was such that cattle could not stand on it, and a piece of iron would sink in it. The subsoil was composed principally of clay and sand, and the railway had to be carried over the moss on the level, requiring cutting, and embanking for upwards of 4 m. In forming 277,000 cub. yds. of embankment 670,000 yds. of raw peat were consumed, the difference being occasioned by the squeezing out of the water. Large quantities of embanking were sunk in the moss, and, when the engineer, George Stephenson, after a month’s vigorous operations, had made up his estimates, the apparent work done was sometimes less than at the beginning of the month. The railway ultimately was made to float on the bog. Where embankment was required drains about 5 yds. apart were cut, and when the moss between them was dry it was used to form the embankment. Where the way was formed on the level, drains were cut on each side of the intended line, and were intersected here and there by cross drains, by which the upper part of the moss was rendered dry and firm. On this surface hurdles were placed, 4 ft. broad and 9 long, covered with heath, upon which the ballast was laid.
Bridges.—For conveying small streams through embankments, channels or culverts are constructed in brickwork or masonry. Larger rivers, canals, roads, other railways and sometimes deep narrow valleys are crossed by bridges (q.v.) of timber, brick, stone, wrought iron or steel, and many of these structures rank among the largest engineering works in the world. Sometimes also a viaduct consisting of a series of arches is preferred to an embankment when the line has to be taken over a piece of flat alluvial plain, or when it is desired to economize space and to carry the line at a sufficient height to clear the streets, as in the case of various railways entering London and other large towns. In connexion with a railway many bridges have also to be constructed to carry public roads and other railways over the line, and for the use of owners or tenants whose land it has cut through (“accommodation bridges”). In the early days of railways, roads were often taken across the line on the level, but such “level” or “grade” crossings are now usually avoided in the case of new lines in populous countries, except when the traffic on both the road and the railway is very light. In many instances old level crossings have been replaced by over-bridges with long sloping approaches; in this way considerable expenditure has been involved, justified, however, by the removal of a danger to the public and of interruptions to the traffic on both the roads and the railways. In cases where the route of a line runs across a river or other piece of water so wide that the construction of a bridge is either impossible or would be more costly than is warranted by the volume of traffic, the expedient is sometimes adopted of carrying the wagons and carriages across bodily with their loads on train ferries, so as to avoid the inconvenience and delay of transshipment. Such train ferries are common in America, especially on the Great Lakes, and exist at several places in Europe, as in the Baltic between Denmark and Sweden and Denmark and Germany, and across the Straits of Messina.
Gradients.—The gradient or grade of a line is the rate at which it rises or falls, above or below the horizontal, and is expressed by stating either the horizontal distance in which the change of level amounts to 1 ft., or the amount of change that would occur in some selected distance, such as 100 ft., 1000 ft. or r m. In America a gradient of 1 in 100 is often known as a 1% grade, one of 2 in 100 as a 2% grade, and so on; thus a 0·25% grade corresponds to what in England would be known as a gradient of 1 in 400. The ruling gradient of a section of railway is the steepest incline in that section, and is so called because it governs or rules the maximum load that can be placed behind an engine working over that portion of line. Sometimes, however, a sharp incline occurring on an otherwise easy line is not reckoned as the ruling gradient, trains heavier than could be drawn up it by a single engine being helped by an assistant or “bank” engine; sometimes also “momentum” or “velocity” grades, steeper than the ruling gradient, are permitted for short distances in cases where a train can approach at full speed and thus surmount them by the aid of its momentum. An incline of 1 in 400 is reckoned easy, of 1 in 200 moderate and of 1 in 100 heavy. The ruling gradient of the Liverpool & Manchester railway was fixed at 1 in 900, excepting the inclines at Liverpool and at Rainhill summit, for working which special provision was made; and I. K. Brunel laid out the Great Western for a long distance