is required for the successful application of definite formulae to the problem. For example, what is a safe speed at a given curve for an engine, truck or coach having the load equally distributed over the wheels may lead to either climbing or overturning if the load is shifted to a diagonal position. An ill-balanced load also exaggerates “plunging,” and if the period of oscillation of the load happens to agree with the changes of contour or other inequalities of the track vibrations of a dangerous character, giving rise to so-called “sinuous” motion may occur.
In general it is not curvature, but change of curvature, that presents difficulty in the laying-out of a line. For instance, if the curve is of S-form, the point of danger is when the train enters the contra-flexure, and it is not an easy matter to assign the best super elevation at all points throughout the double bend. Closely allied to the question of safety is the problem of preventing jolting at curves; and to obtain easy running it is necessary not merely to adjust the levels of the rails in respect to one another, but to tail off one curve into the next in such a manner as to avoid any approach to abrupt lateral changes of direction. With increase of speeds this matter has become important as an element of comfort in passenger traffic. As a first approximation, the centre-line of a railway may be plotted out as a number of portions of circles, with intervening straight tangents connecting them, when the abruptness of the changes of direction will depend on the radii of the circular portions. But if the change from straight to circular is made through the medium of a suitable curve it is possible to relieve the abruptness, even on curves of comparatively small radius. The smoothest and safest running is, in fact, attained when a “transition,” “easement” or “adjustment” curve is inserted between the tangent and the point of circular curvature.
For further information see the following papers and the discussions on them: “Transition Curves for Railways,” by James Glover, Proc. Inst. C.E. vol. 140, part ii.; and “High Speed on Railway Curves,” by J. W. Spiller, and “A Practical Method for the Improvement of Existing Railway Curves,” by W. H. Shortt, Proc. Inst. C.E. vol. 176, part ii.
Gauge.—The gauge of a railway is the distance between the inner edges of the two rails upon which the wheels run. The width of 4 ft. 8½ in. may be regarded as standard, since it prevails on probably three-quarters of the railways of the globe. In North America, except for small industrial railways and some short lines for local traffic, chiefly in mountainous country, it has become almost universal; the long lines of 3 ft. gauge have mostly been converted, or a third rail has been laid to permit interchange of vehicles, and the gauges of 5 ft. and more have disappeared. A considerable number of lines still use 4 ft. 9 in., but as their rolling stock runs freely on the 4 ft. 8½ in. gauge and vice versa, this does not constitute a break of gauge for traffic purposes. The commercial importance of such free interchange of traffic is the controlling factor in determining the gauge of any new railway that is not isolated by its geographical position. In Great Britain railways are built to gauges other than 4 ft. 8½ in. only under exceptional conditions; the old “broad gauge” of 7 ft. which I. K. Brunel adopted for the Great Western railway disappeared on the 20th–23rd of May 1892, when the mainline from London to Penzance was converted to standard gauge throughout its length. In Ireland the usual gauge is 5 ft. 3 in., but there are also lines laid to a 3 ft. gauge. On the continent of Europe the standard gauge is generally adopted, though in France there are many miles of 4 ft. 9 in. gauge; the normal Spanish and Portuguese gauge is, however, 5 ft. 5¾ in., and that of Russia 5 ft. In France and other European countries there is also an important mileage of metre gauge, and even narrower, on lines of local or secondary importance. In India the prevailing gauge is 5 ft. 6 in., but there is a large mileage of other gauges, especially metre. In the British colonies the prevailing gauge is 3 ft. 6 in., as in South Africa, Queensland, Tasmania and New Zealand; but in New South Wales the normal is 4 ft. 8½ in. and in Victoria 5 ft. 3 in., communication between different countries of the Australian Commonwealth being thus carried on under the disadvantage of break of gauge. Though the standard gauge is in use in Lower Egypt, the line into the Egyptian Sudan was built on a gauge of 3 ft. 6. in., so that if the so-called Cape to Cairo railway is ever completed, there will be one gauge from Upper Egypt to Cape Town. In South America the 5 ft. 6 in. gauge is in use, with various others.
Mono-Rail Systems.—The gauge may be regarded as reduced to its narrowest possible dimensions in mono-rail lines, where the weight of the trains is carried on a single rail. This method of construction, however, has been adopted only to a very limited extent. In the Lartigue system the train is straddled over a single central rail, elevated a suitable distance above the ground. A short line of this kind runs from Ballybunnion to Listowel in Ireland, and a more ambitious project on the same principle, on the plans of Mr F. B. Behr, to connect Liverpool and Manchester, was sanctioned by Parliament in 1901. In this case electricity was to be the motive-power, and speeds exceeding 100 m. an hour were to be attained, but the line has not been built. In the Langen mono-rail the cars are hung from a. single overhead rail; a line on this system works between Barmen and Elberfeld, about 9 m., the cars for a portion of the distance being suspended over the river Wupper. In the system devised by Mr Louis Brennan the cars run on a single rail laid on the ground, their stability being maintained by a heavy gyrostat revolving at great speed in a vacuum.
Permanent Way.—When the earth-works of a line have been completed and the tops of the embankments and the bottoms of the cuttings brought to the level decided upon, the next step is to lay the permanent way, so-called probably in distinction to the temporary way used during construction. The first step is to deposit a layer of ballast on the road-bed or “formation,” which often slopes away slightly on each side from the central line to facilitate drainage. The ballast consists of such materials as broken stone, furnace slag, gravel, cinders or earth, the lower layers commonly consisting of coarser materials than the top ones, and its purpose is to provide a firm, well-drained foundation in which the sleepers or cross ties may-be embedded and held in place, and by which the weight of the track and the trains may be distributed over the road-bed. Its depth varies, according to the traffic which the line has to bear, from about 6 in. to 1 ft. or rather more under the sleepers, and the materials of the surface layers are often chosen so as to be more or less dustless. Its width depends on the numbers of tracks and their gauge; for a double line of standard gauge it is about 25 ft., a space of 6 ft. (“six-foot way”) being left between the inner rails of each pair in Great Britain (ng. 8), and a rather larger distance in America (fig. 9), where the over-hang of the rolling stock is greater. The intervals between the sleepers are filled in level with ballast, which less commonly is also heaped up over them, especially at the projecting ends.