When, however, the locating passes from the lower ground, away up amongst the hills and mountain ranges, it becomes an intricate study whether it will be possible to lay out any line at all which may possess gradients and curves practicable for railway working. The question of property, population, or convenience of access, is here no longer the controlling influence, but in its stead there are the far more formidable natural difficulties to be overcome in working out a trackway to the inevitable summit level. The chief endeavour will be to gain length, and so reduce as much as possible the steepness of the gradients which at the best must necessarily be severe. In some of the 35 earlier mountain lines constructed abroad the system of _zigzags_ was introduced, as shown in Fig. 25. These _zigzags_ were laid out on ruling gradients, one above the other, on the sides of the mountain slopes with pieces of level at the apices, A, B, and C, on which the engine could be changed from one end of the train to the other. Although feasible in principle, the system entailed considerable loss of time in train-working, and was not unattended with risk. The more modern and simple method of working out the same idea is to connect the main zigzag lines by curves or _spirals_, thus rendering the route continuous and unbroken. By this arrangement the heavy work and delay in starting or stopping the train at the apices, A, B, and C, as shown on Fig. 25, is avoided, and the train can proceed continuously on its circuitous journey. Fig. 26 shows an instance of the zigzags and spirals, as carried out on an important railway abroad. To have made a direct line from D to E, the most difficult part of the route, would have involved a gradient of 1 in 11; but by constructing the spiral course, as shown, the length was more than trebled, and the gradient reduced to 1 in 35. Fig. 27 is another example of spiral zigzags in which advantage was taken to cut a short tunnel through a high narrow neck of rock at G, and then by skirting round the hill the line was taken over the top of the tunnel and along the side of the mountain to the summit tunnel at H. By this means the line from F to H was laid out to an average gradient of 1 in 42. Fig. 28 shows the Cumbres inclines on the Mexican Railway. The route had to be located through one of the rugged passes of the great Chain of the Andes, whose mountain-sides rise most abruptly from the lower plains, to the great upper-land plateau, some eight thousand feet above sea-level. The ground to be traversed was so steep and difficult that, even with the best available detours and greatest length that could be obtained, the result was an average continuous gradient of 1 in 25 for 12 miles. [Illustration: Fig. 25, 26, 27, 28, 29]