27. The general topography of a country may be ascertained by reference to State maps, where such exist, and when not, by riding over the district. The direction and size of watercourses, will show at once the position of summits.

28. Water flowing as in fig. 1, indicates a fall from B to E; and also traverse slopes from a a and c c to d d.

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.

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.

31. Valleys generally rise much faster near their source, than at any point lower down; also the width increases as we approach the debouch. Fig. 6 shows the cross sections of a valley from its source to the mouth.

32. In the case of parallel valleys running in the same direction, the form will be as in fig 7. Let 1 2, 1 2, etc., represent a datum level, or a horizontal plane passing through the lowest point. The line a b, shows the height of the bottom at B; c d that at D, e f that at E, and g h that at C. The broken lines i, k, l, m, n, show the general form of the land. Now by the route m m m m, from A to F, we have the profile m m m m, fig. 8, by n n n n, the profile n n n n, and by o o o, the profile o o o.

33. In the case of parallel valleys running in opposite directions, as in fig. 9, we have the form there shown; and the profiles corresponding to the several lines are shown in fig. 10. As we should always adopt the line giving the least rise and fall, other things being equal, it is plain which line on the plan we must follow.

34. In passing from A to B, figs. 11 and 12, by the several lines c, d, e, f, we have the profiles shown at c, d, e, f, from which it appears, that the nearer we cross to the heads of streams, the less is the difference of heights.

35. If we wish to go from A to B, fig. 12 (a), we should of course take first the straight line; but being obliged to avoid the hill C, on arriving at d, we should not try to recover that line at e, but proceed at once to B. Also as we are obliged to pass through d, we ought to go directly to d and not by the way of c; and the same idea is repeated between A and d; the last line being A b d B. Few rules can be given in the choice of routes. Practice only will enable the engineer to find the best location for a railroad.

36. The relative height of summits, the rate of fall of streams, and absolute elevation, within a few feet, may be easily, rapidly, and cheaply found by the barometer. This also affords an excellent check upon subsequent levelling operations. The results thus obtained depend upon the physical property, that the density of the air decreases as the square of the height.

37. The barometer is a glass tube, partly filled with mercury, having a vacuum in the upper part. By it the exact density of the air at any point is determined. Accompanying are two thermometers; one attached, showing the temperature of the barometer; the other detached, showing the atmospheric temperature.

38. Knowing now the manner of finding the density of the air at any two points, and also the relation between density and height, the operation of levelling by the barometer is very simple.

The modus operandi is as follows, (see tables A, B, C, and D):—

Let us have the notes.

Final correction by table D. The barometer at the lower station being 26.80, and the tabular number against 27.56 being 0.22, that for 26.80 will be 0.31, and we have

which add to 928.2 and we have as the final height

The tables above referred to, are those of Mr. Oltman, and are considered as the most convenient and reliable of any published.