First, for Line: It has been explained that the permissible deviation of the center line of the track on either side of the center line of the tunnel was 6 in. Had the metal lining been invariably of the true diameter, it would have been necessary to survey only one side of the tunnel; this would have given a line parallel to the center line, and might have been plotted as such; then, by setting off 6 in. on either side of this line, there would have been obtained a pair of parallel lines within which the center line of the track must lie. Owing to variations in the diameter of the tunnel, however, such a method was not permissible, and therefore the following process was used:
When running the survey lines through the tunnel (which were the center lines used in driving the shields), offsets were taken to the inner edges of the flanges of the metal lining, both on the north and south sides, at axis level at each 25-ft. interval. On the plat on which the survey lines were laid down, and at each point surveyed, a distance was laid off to north and south equal to the following distances:
Offset, as measured in the tunnel to north (or south), minus 10.08 ft.
This 10.08 ft. (or 10 ft, 1 in.) represents 10 ft. 7 in., the true radius to inside of iron, minus 6 in., the permissible lateral deviation of the track from the axis of the tunnel.
The result of this process was two lines, one on either side of the survey lines, not parallel to it or to each other, but approaching each other when the horizontal diameter was less than the true diameter, receding from each other when the diameter was more, and exactly 12 in. apart when the diameter was correct. As long as the center line of the track lay entirely within these two limiting lines, the condition that the concrete arch should not be 6 in. less in thickness than the standard 2 ft. was satisfied, and in order to arrive at the final line, the longest possible tangents that would be within these limits were adopted as the final lines; and, as the survey lines were those used in driving the tunnel shields (that is, the lines to which it was intended that the track should be built), the amount by which the new lines thus obtained deviated from the survey lines was a measure of the deviation of the finally adopted track and concrete line from the original contract lines.
Next, for Grades: The considerations for grade were very similar to those for line. If the vertical diameter of the tunnel had been true at each 25-ft. interval surveyed, it would have been correct to plot the elevations of the crown (or invert) as a longitudinal section of the tunnel, and to have set up over those points others 6 in. above (as the metal lining could have been 6 in. lower than the standard section, which is equivalent to the track being an equal amount higher), and below these crown or invert elevations others 3 in. lower (as the metal lining could be 3 in. higher).
Then, by joining the points 6 in. above in one line and those 3 in. below in another, there would have been obtained lines of limitation between which the track grades must lie. However, as the tunnel diameter was not uniformly correct, a modification of this method had to be made, as in the case of the line determination, the principle, however, remaining the same.
The elevations were taken on the inner edges of the circumferential flanges of the metal lining, not only in the bottom, but also in the top, of the tunnel, at each 25-ft. interval; then, for the upper limit of the track at each such interval the following was plotted:
Elevation of inner edge of flange at top, minus 16.58 ft.
This 16.58 ft. (or 16 ft. 7 in.) was obtained thus: The standard height from the top of the rail to the inner edge of the iron flange is 17 ft. 1 in., but, as the track may be 6 in. above the standard or normal, the minimum height permissible is 16 ft. 7 in. For the lower limit of track at each 25-ft. interval the following was plotted: