tern 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.

When division-lines, on measures of great nicety, get too fine
to be read by the eye, we use the microscope. By its means we are
able to count 112,000 lines ruled on a glass plate within an inch.
The smallest object that can be seen by a keen eye makes an angle
of 40", but by putting six microscopes on the scale of the telescope
on the mural circle, we are able to reach an exactness of 0".1, or
1/3600 of an inch. This instrument is used to measure the declination
of stars, or angular [Page 64] distance north or south of the
equator. Thus a star's place in two directions is exactly fixed.
When the telescope is mounted on two pillars instead of the face of
a wall, it is called a transit instrument. This is used to determine
the time of transit of a star over the meridian, and if the transit
instrument is provided with a graduated circle it can also be used
for the same purposes as the mural circle. Man's capacity to measure
exactly is indicated in his ascertainment of the length of waves of
light. It is easy to measure the three hundred feet distance