the centre subtended by a chord 100 feet long. For example, if on any curve a chord 100 feet long subtends an angle of 5° at the centre, that curve is known as a five-degree curve. In profile the centre line is composed of a combination of level or horizontal lines and of inclined lines or grades ascending or descending from the horizontal. Grades are designated either by stating the number of feet of rise or fall in a horizontal length of line of 100 feet or of one mile. For example, a grade having a rise of one foot in a horizontal length of line of 100 feet is known as a 1 per cent. grade. The same grade defined in terms of feet rise per mile of length would be known as a grade of 52.8 feet per mile. When two grade lines meet or when a grade line and a level meet the junction is marked by an angle more or less abrupt. This angle is always replaced by a vertical curve which is convex upward at a summit and concave at a valley.
Roadbed Construction. The first task in the building of a railway is the construction of the roadbed or permanent way. In its broadest meaning the permanent way of a railway comprises all structure upon which track is laid, but the term is often given a more limited application which excludes culverts, trestles, viaducts, bridges, etc.; the broader application of the term will be chosen here. The actual work of construction of the roadbed of a railway begins with the clearing of the right of way. This right of way is a strip of land usually 100 feet wide, or 50 feet each side of the centre line of the road, and the clearing from it of all obstructions is obviously necessary before the work of actual construction can be begun. The amount of clearing required varies according to the natural conditions; on an open prairie section it is merely nominal, but in thickly wooded country, where trees have to be felled and their stumps pulled up, it forms quite an item in the expense of construction. As soon as the right of way is cleared, the work of excavation and embankment construction is begun. In locating the road the engineer has settled upon certain stretches and grades which are right lines and which define the top surface of the roadbed. The lines of these levels and grades in some places cut the natural surface of the ground and in other places they lie above the ground surface so that the roadbed has to be filled in. So far as he can do so without sacrificing more important things, the engineer endeavors to make the adjacent cuts and fills balance each other; that is, he tries to arrange the grades so that the material excavated from the cuts will be sufficient in quantity to construct the adjacent fills or embankments. When this desirable end cannot be accomplished the extra earth necessary for the embankments is secured by excavating pits called burrow pits at points convenient to the embankment to be built. Sometimes also it is preferable to take the material from burrow pits even where the amount of cuttings is more than enough to form the fills, since it is less expensive to do this than to haul the material excavated from the cuts to the points where it is required for embankment construction. A cut is simply a trench whose bottom is at the plane of the grade line and somewhat wider than the required roadbed, and whose sides slope upward and away from the track to the ground surface at greater or less angles, determined by the slope at which the material will stand without sliding. The natural slope of different materials runs from a nearly vertical plane in firm rock to planes as flat as one foot rise in a horizontal distance of four feet, or technically defined, a slope of one on four. Slopes of 1 on 1½ or 1 on 2 are perhaps the most common. Evidently the width of the cut at its top will depend upon its depth and the slope of the sides; it may easily reach 100 feet. When it exceeds this width it becomes necessary for the engineer to figure upon the desirability of sustaining the sides of the cut by retaining walls (see Retaining Wall), or perhaps to consider the substitution of a tunnel for an open cut. Cuts are always made with a bottom width enough wider than the roadbed to allow a ditch to be built at each side to carry away the water from rain or melted snow which runs down or seeps through the side slopes.
The excavation of cuts is accomplished by any of the ordinary means of earth and rock excavation. For earth excavation the steam shovel (q.v.) is the tool most commonly employed. A fill may be described as the reverse of a cut; in fact, were it possible to take out a cut in a single solid piece and to deposit this piece on the ground bottom side up, it would serve as a fill. The manner of constructing a fill is to deposit the material from cuts and burrow pits along the line until an embankment is formed whose top is at grade and somewhat wider than the required roadbed and whose sides slope downward and outward at angles depending upon the natural shape of the material. Care is taken to make the embankments solid, since they must carry heavy trains, and to construct them so that the water falling on them will drain away as soon as possible. Usually there is not much attempt to use selected material, except for the upper section on top of which the track ballast will come. Fills, and, more particularly, deep fills, are often constructed by building a rough timber trestle onto which the material cars are run and their contents dumped until the trestle is entirely buried in an embankment of earth. Often also a trestle is at first built to carry the trains with the intention of filling it in afterwards. This hastens the construction and cheapens the first cost of the road, thus allowing the owners to begin operations and to earn money while the final embankment awaits some convenient time for its construction. The method of constructing embankments by filling in trestles is often resorted to in order to carry the roadbed across morasses of swampy ground.
It often happens that the problem of carrying an embankment across a morass is one of the most difficult which falls to the lot of the railway engineer. Where streams have to be crossed it is necessary to provide openings in the embankment for their passage. For small streams these openings are provided by means of culverts (see Culvert) and in the case of large streams bridges are built. (See Bridge.) Bridges or viaducts are also employed to carry the road across gorges and deep valleys. Where the contrary condition exists and the engineer is called upon to carry his line over ridges or mountains where an open cut is not possible, because of its size and cost, and a direct climb is not practicable, because of the steep grades, he either resorts to the construction of a tunnel or of a switchback. The conditions which call for a
