scope, 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 deg.
apart, and the graduated scale, which is attached to the outer edge
of the circle, shows a revolution of a quarter circle, or 90 deg., 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 deg., 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 eas