gles to the true direction of the plumb-line or the force of
gravity. Its direction is therefore a little different at two different
places on the surface, and the change can be measured by its effect on
the apparent direction of a star seen by reflection from the surface.

It is true that a considerable distance on the earth's surface will
seem very small in its effect on the position of a star. Suppose there
were two stars in the heavens, the one in the zenith of the place where
you now stand, and the other in the zenith of a place a mile away. To
the best eye unaided by a telescope those two stars would look like a
single one. But let the two places be five miles apart, and the eye
could see that there were two of them. A good telescope could
distinguish between two stars corresponding to places not more than a
hundred feet apart. The most exact measurements can determine distances
ranging from thirty to sixty feet. If a skilful astronomical observer
should mount a telescope on your premises, and determine his latitude
by observations on two or three evenings, and then you should try to
trick him by taking up the instrument and putting it at another point
one hundred feet north or south, he would find out that something was
wrong by a single night's work.

Within the past three years a wobbling of the earth's axis has been
discovered, which takes place within a circle thirty feet in radius and
sixty feet in diameter. Its effect was noticed in astronomical
observations many years ago, but the change it produced was so small
that men could not find out what the matter was. The exact nature and
amount of the wobbling is a work of the exact astronomy of the present
time.

We cannot measure across oceans from island to island. Until a recent
time we have not even measured across the continent, from New York to
San Francisco, in the most precise way. Without astronomy we should
know nothing of the distance between New York and Liverpool, except by
the time which it took steamers to run it, a measure which would be
very uncertain indeed. But by the aid of astronomical observations and
the Atlantic cables the distance is found within a few hundred yards.
Without astronomy we could scarcely make an accurate map of the United
States, except at enormous labor and expense, and even then we could
not be sure of its correctness. But the practical astronomer being able
to determine his latitude and longitude within fifty yards, t