grade must also rise toward the central shaft, and fall in working
away from it; but the lines were fixed with such infinitesimal
accuracy that, when the one going west from the eastern portal and
the one going east from the shaft met in the heart of the mountain,
the western line was only one-eighth of an inch too high, and
three-sixteenths of an inch too far north. To reach this perfect
result they had to triangulate from the eastern portal to distant
[Page 63] mountain peaks, and thence down the valley to the central
shaft, and thus fix the direction of the proposed line across the
mouth of the shaft. Plumb-lines were then dropped one thousand and
twenty-eight feet, and thus the line at the bottom was fixed.

Three attempts were made--in 1867, 1870, and 1872--to fix the exact
time-distance between Greenwich and Washington. These three separate
efforts do not differ one-tenth of a second. Such demonstrable results
on earth greatly increase our confidence in similar measurements
in the skies.

[Illustration: Fig. 22.]

A scale is frequently affixed to a pocket-rule, by which we can
easily measure one-hundredth of an inch (Fig. 22). The upper and
lower line is divided into tenths of an inch. Observe the slanting
line at the right hand. It leans from the perpendicular one-tenth
of an inch, as shown by noticing where it reaches the top line. When
it reaches the second horizontal line it has left the perpendicular
one-tenth of that tenth--that is, one-hundredth. The intersection
marks 99/100 of an inch from one end, and one-hundredth from the
other.