between A and C, and we cannot go over it; we can measure its
distance as easily as if we could. Set a table four feet by eight
out-doors (Fig. 25); so arrange it that, looking along one end, the
line of sight just strikes a tree the other side of the river. Go to
the other end, and, looking toward the tree, you find the line of
sight to the tree falls an inch from the end of the table on the
farther side. The lines, therefore, approach each other one inch in
every four feet, and will come together at a tree three hundred and
eighty-four feet away.

[Illustration: Fig. 25.--Measuring Distances.]

[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.