nces.]

[Illustration: Fig. 26.--Measuring Elevations.]

The next process is to measure the height or magnitude of objects
at an ascertained distance. Put two pins in a stick half an inch
apart (Fig. 26). Hold it up two feet from the eye, and let the
upper pin fall in line with your eye and the top of a distant church
steeple, and the lower pin in line with the bottom of the church and
your eye. If the church is three-fourths of a mile away, it must
be eighty-two feet high; if a mile away, it must be one hundred
and ten feet high. For if two lines spread [Page 68] one-half an
inch going two feet, in going four feet they will spread an inch,
and in going a mile, or five thousand two hundred and eighty feet,
they will spread out one-fourth as many inches, viz., thirteen
hundred and twenty--that is, one hundred and ten feet. Of course
these are not exact methods of measurement, and would not be correct
to a hair at one hundred and twenty-five feet, but they perfectly
illustrate the true methods of measurement.

Imagine a base line ten inches long. At each end erect a perpendicular
line. If they are carried to infinity they will never meet: will
be forever ten inches apart. But at the distance of a foot from
the base line incline one line toward the other 63/10000000 of
an inch, and the lines will come together at a distance of three
hundred miles. That new angle differs from the former right angle
almost infinitesimally, but it may be measured. Its value is about
three-tenths of a second. If we lengthen the base line from ten
inches to all the miles we can command, of course the point of
meeting will be proportionally more distant. The angle made by
the lines where they come together will be obviously the same as
the angle of divergence from a right angle at this end. That angle
is called the parallax of any body, and is the angle that would
be made by two lines coming from that body to the two ends of any
conventional base, as the semi-diameter of the earth. That that
angle would vary according to the various distances is easily seen
by Fig. 27.

[Illustration: Fig. 27.]

Let O P be the base. This would subtend a greater angle seen from
star A than from star B. Let B be far enough away, and O P would
become invisible, and B [Page 69] would have no parallax for that
base. Thus the moon has a parallax of 57" with the semi-equatorial
diameter of the earth for a base. And the sun has a parallax 8".85
on the same base.