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positions of the principal points in all great cities of the country
are known, and can be laid down on maps.

The world has always had to depend on astronomy for all its knowledge
concerning times and seasons. The changes of the moon gave us the first
month, and the year completes its round as the earth travels in its
orbit. The results of astronomical observation are for us condensed
into almanacs, which are now in such universal use that we never think
of their astronomical origin. But in ancient times people had no
almanacs, and they learned the time of year, or the number of days in
the year, by observing the time when Sirius or some other bright star
rose or set with the sun, or disappeared from view in the sun's rays.
At Alexandria, in Egypt, the length of the year was determined yet more
exactly by observing when the sun rose exactly in the east and set
exactly in the west, a date which fixed the equinox for them as for us.
More than seventeen hundred years ago, Ptolemy, the great author of The
Almagest, had fixed the length of the year to within a very few
minutes. He knew it was a little less than 365 1/2 days. The dates of
events in ancient history depend very largely on the chronological
cycles of astronomy. Eclipses of the sun and moon sometimes fixed the
date of great events, and we learn the relation of ancient calendars to
our own through the motions of the earth and moon, and can thus measure
out the years for the events in ancient history on the same scale that
we measure out our own.

At the present day, the work of the practical astronomer is made use of
in our daily life throughout the whole country in yet another way. Our
fore-fathers had to regulate their clocks by a sundial, or perhaps by a
mark at the corner of the house, which showed where the shadow of the
house fell at noon. Very rude indeed was this method; and it was
uncertain for another reason. It is not always exactly twenty-four
hours between two noons by the sun, Sometimes for two or three months
the sun will make it noon earlier and earlier every day; and during
several other months later and later every day. The result is that, if
a clock is perfectly regulated, the sun will be sometimes a quarter of
an hour behind it, and sometimes nearly the same amount before it. Any
effort to keep the clock in accord with this changing sun was in vain,
and so the time of day was always uncertain.

Now, however, at some of the principal obse