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Page 20
Suppose a telescope, fixed to a mural circle, to revolve on an axis,
as in Fig. 21; point it horizontally at a star; [Page 61] turn it up
perpendicular to another star. Of course the two stars are 90�
apart, and the graduated scale, which is attached to the outer edge
of the circle, shows a revolution of a quarter circle, or 90�, But a
perfect accuracy of measurement must be sought; for to mistake the
breadth of a hair, seen at the distance of one hundred and
twenty-five feet, would cause an error of 3,000,000 miles at the
distance of the sun, and immensely more at the distance of the
stars. The correction of an inaccuracy of no greater magnitude than
that has reduced our estimate of the distance of our sun 3,000,000
miles.
[Illustration: Fig. 21.--Mural Circle.]
Consider the nicety of the work. Suppose the graduated scale to
be thirty feet in circumference. Divided into 360�, each would
be one inch long. Divide each degree into 60', each one is 1/60
of an inch long. It takes good eyesight to discern it. But each
minute must be [Page 62] divided into 60", and these must not only
be noted, but even tenths and hundredths of seconds must be
discerned. Of course they are not seen by the naked eye; some
mechanical contrivance must be called in to assist. A watch loses
two minutes a week, and hence is unreliable. It is taken to a
watch-maker that every single second may be quickened 1/20160 part
of itself. Now 1/20000 part of a second would be a small interval of
time to measure, but it must be under control. If the temperature of
a summer morning rises ten or twenty degrees we scarcely notice it;
but the magnetic tastimeter measures 1/5000 of a degree.
Come to earthly matters. In 1874, after nearly twenty-eight years'
work, the State of Massachusetts opened a tunnel nearly five miles
long through the Hoosac Mountains. In the early part of the work
the engineers sunk a shaft near the middle 1028 feet deep. Then the
question to be settled was where to go so as to meet the approaching
excavations from the east and west. A compass could not be relied
on under a mountain. The line must be mechanically fixed. A little
divergence at the starting-point would become so great, miles away,
that the excavations might pass each other without meeting; the
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.
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 between
the crests of storm-waves in the wide Atlantic; easy to measure the
different wave-lengths of the different tones of musical sounds. So
men measure the lengths of the undulations of light. The shortest is
of the violet light, 154.84 ten-millionths of an inch. By the
horizontal pendulum Professor Root has made 1/36000000 of an inch
apparent.
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