one close at hand and one at a distance, so as to
give a line pointing exactly to the rising spot of the sun on the
horizon, as at Stonehenge. They recorded the number of days which
elapsed before the longest day again appeared, and they marked also
the division of that period by the two events of equally long sunlight
and darkness--the spring and the autumn "equinox." It is obvious that
if they took 365 days roughly as the period of revolution they would
(owing to the odd hours and minutes left out) get about a day wrong in
four years, and it was the business of the priests--even in ancient
Rome the pontiffs were charged with this duty--to make the correction
add the missing day, and proclaim the chief days of the year--the
shortest day, the longest day, and the equinox-days of equal halves of
sunshine and darkness. In ancient China, if the State astronomer made
a wrong calculation in predicting an eclipse he was decapitated.

It is easy to understand how it became desirable to recognise more
convenient divisions of the year than the four quarters marked by the
solstices and the equinoxes. Various astronomical events were studied,
and their regular recurrence ascertained, and they were used for this
purpose. But the most obvious natural timekeeper to make use of,
besides the sun, was the moon. The moon completes its cycle of change
on the average in 29-1/2 days. It was used by every man to mark the
passage of the year, and its periods from new moon to new moon were
called, as in our language, "months" or "moons," and divided into
quarters. It is, however, an awkward fact that twelve lunar months
give 354 days, so that there are eleven days left over when the solar
year is divided into lunar months. The attempt to invent and cause the
adoption of a system which shall regularly mark out the year into the
popular and universally recognised "moons," and yet shall not make the
year itself, so built up, of a length which does not agree with the
true year recorded by the return of the rising sun to exactly the same
spot on the horizon after 365 days and a few hours, has been
throughout all the history of civilised man, and even among
prehistoric peoples, a matter of difficulty. It has led to the most
varied and ingenious systems, entrusted to the most learned priests
and state officers, and mostly so complicated as to break down in the
working, until we come to the great clear-headed man Julius Caesar.

In the very earliest