=261. Mountain Locations of Railroad Lines.=—The skill of the civil engineer is sometimes severely taxed in making mountain locations of railroads. Probably no more skilful engineering work of this kind has ever been done than in the crossings of the Rocky Mountains and the Sierras in this country by trans-continental railroad lines, although more striking examples of railroad location for short distances may perhaps be found in Europe or other countries. The main problem in such cases is the making of distance in order to attain a desired elevation without exceeding maximum grades, such as those which have already been given. Most interesting engineering expedients must sometimes be resorted to. One of the oldest of these is the switchback plan shown in Fig. 6. This is probably the simplest procedure in order to make distance in attaining elevation. The line is run up the side of a mountain at its maximum grade as far in one direction as it may be desirable to go. It then runs back on itself a short distance before being diverted so as to pass up another grade in the reverse direction. This zigzagging of alignment may obviously be made to attain any desired elevation and so overcome the summit of a mountain range. The old switchback coal road near Mauch Chunk, Pa., is one of the oldest and more famous instances of the method, which has many times been employed in other locations. [Illustration: FIG. 7.] A more striking method, perhaps, is that of loops by which the direction of a line or motion of a train on it is continuous. Distance is made by a judicious use of the topography of the locality so as to run the line as far up the side of the valley as practicable and then turn as much as a semicircle or more, sometimes over a bridge structure and sometimes in tunnel, so as to give further elevation by running either on the opposite side of the valley or on the same. A succession of loops or other curves suitably located will give the distance desired in order to reach the summit. =262. The Georgetown Loop.=—Fig. 7 shows one of these spiral or loop locations on the Georgetown branch of the Union Pacific Railroad in Colorado. It is a well-known and prominent instance of railroad location of this kind. On the higher portion of this loop system included in the figure there is a viaduct on a curve which crosses the line 75 feet above the rail below it and 90 feet above the water. This location is a specimen of excellent railroad engineering. The length of line shown in the figure, including the spiral, is 8½ miles, and it cost $265,000 per mile exclusive of the bridges.