Fig. 38.
102. As an example of laying out work with regard to heights, take the case of fig. 38. Let the grade of the centre line be one in 100, the angle of obliquity 45°, the width of bridge twenty feet, and span on the skew one hundred feet. Required the elevations of the points a, b, c, d.
| Assume the height of (2) as | 100.00 |
| That of (3) will be | 99.00 |
| b being 10 ft. back of 2 is 0.1 ft. higher than 2, or | 100.10 |
| and d 0.1 feet less than (2) or | 99.90 |
| also a = 99.00 + 0.10, or | 99.10 |
| and c = 99.00 – 0.10, or | 98.90 |
TUNNELS.
103. The maintaining a correct centre line through tunnels is generally considered difficult. The fixing of the line in deep shafts requires great care, owing to the short distance between the only two fixed points, that can be transferred from the surface to the bottom of the pit. This is a matter of manual skill and of instrumental manipulation. There is no difficulty in aligning the upper ends of two plumb-lines; and the lower ones will certainly be governed by their position. The following method has been found to answer every purpose.
Let the opening of the shaft be ten feet in diameter. Place two horizontal bars at right angles to the road across the opening, upon which slide blocks holding the upper end of the plumb-lines. Adjust these lines, at the surface, with a transit; and when fixed, place iron pins at the point marked by the plumbs at the bottom of the shaft. Upon these pins fix the exact centres. For keeping the line in the shaft headings, a straight rod, with steel points at each end, should be used, which being placed upon the iron centre pins, fixes the centre line of the tunnel. When the tunnel is curved, the line should be laid off by offsets from the tangent to the curve at the shaft.
By this method points at ten feet distance may be fixed within 1
100 of an inch, a difference of which would cause an error of ⅒ of an inch per one hundred, or an inch per thousand feet.
CHAPTER VI.
EARTHWORK.
FORM OF RAILROAD SECTIONS.
104. The reader is presumed to be acquainted with the manner of finding the areas and cubes of simple geometric figures and bodies. The following fifteen figures show the forms which may be taken by the cross section of a railroad in cutting; for embankment invert the same. They are easily separable into simple figures.