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.
BAROMETRICAL LEVELLING.
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.
| Barom. | Attached Therm. | Detached Therm. | |
|---|---|---|---|
| Upper Station, | 29.75 | 28.5 | 27.9 |
| Lower Station, | 26.80 | 36.8 | 36.3 |
| Latitude 46° N. | |||
| We have by table A, against the bar. point, | 29.75, | 6108.6 |
| also by table A, against the bar. point, | 26.80, | 5276.6 |
| The difference | 832.0 | |
| Diff. of attached therm. 36.8°- 28.5° = 8.3° | (table B) | -12.2 |
| 819.8 | ||
| Double the sum of detached thermometers multiplied by 1 1000 of 819.8 is | ||
| 2(27.9 + 36.3) × .8198 = | + 105.3 | |
| 925.1 | ||
| Correction (see table C) for lat. 46° N. and approximate height 925.1 | + 3.1 | |
| 928.2 | ||
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