umnal equinox falls. But supposing
the instant of the sun's entering into the sign Libra to be very near
midnight, the small errors of the solar tables might render it doubtful to
which day the equinox really belonged; and it would be in vain to have
recourse to observation to obviate the difficulty. It is therefore
infinitely more commodious to determine the commencement of the year by a
fixed rule of intercalation; and of the various methods which might be
employed, no one perhaps is on the whole more easy of application, or
better adapted for the purpose of computation, than the Gregorian now in
use. But a system of 31 intercalations in 128 years would be by far the
most perfect as regards mathematical accuracy. Its adoption upon our
present Gregorian calendar would only require the suppression of the usual
bissextile once in every 128 years, and there would be no necessity for any
further correction, as the error is so insignificant that it would not
amount to a day in 100,000 years.

_Of the Lunar Year and Luni-solar Periods._--The lunar year, consisting of
twelve lunar months, contains only 354 days; its commencement consequently
anticipates that of the solar year by eleven days, and passes through the
whole circle of the seasons in about thirty-four lunar years. It is
therefore so obviously ill-adapted to the computation of time, that,
excepting the modern Jews and Mahommedans, almost all nations who have
regulated their months by the moon have employed some method of
intercalation by means of which the beginning of the year is retained at
nearly the same fixed place in the seasons.

In the early ages of Greece the year was regulated entirely by the moon.
Solon divided the year into twelve months, consisting alternately of
twenty-nine and thirty days, the former of which were called _deficient_
months, and the latter _full_ months. The lunar year, therefore, contained
354 days, falling short of the exact time of twelve lunations by about 8.8
hours. The first expedient adopted to reconcile the lunar and solar years
seems to have been the addition of a month of thirty days to every second
year. Two lunar years would thus contain 25 months, or 738 days, while two
solar years, of 3651/4 days each, contain 7301/2 days. The difference of 71/2
days was still too great to escape observation; it was accordingly proposed
by Cleostratus of Tenedos, who flourished shortly after the time of Thales,
to omit the biennary interc