Fig. 2.

29. Fig. 2 shows a broken ridge a a a from which the water flows in both directions; and in general, the sources of streams point towards the higher lands.

Fig. 3.

30. If it be required to join the points A and D by railroad, (fig. 3.) it may be better to pass at once from A through B and C, than to go by the streams F E, F′ E′. By the latter route the road would ascend all of the way from A to E; and descend from E′ to D. By the first if it requires steep gradients to rise from A to B, and to fall from C to D, still if the section B C is a plateau, and if the rise between A and B and A and E is the same, by grouping the grades at B and C we may so adapt the motive power, as to take the same train from A to D without breaking. The general arrangement of grades by the line A B C D is then as fig. 4; and A F E E′ F′ D, as in fig. 5. The saving in this case is by length, as the same amount of power is required to overcome a given ascent.

Fig. 4.

Fig. 5.