Elementary arithmetic, with brief notices of its history... by Robert Potts.

14

ON THE DIVISIONS AND MEASURES OF TIME,

consist of 355 days. But as 10 days were wanting to make the lunar
year correspond with the solar year of 365 days, he ordered in every
third year a month (called mensis intercalaris) to be inserted in the
calendar according to the discretion of the Pontifices, and by this
authority they made the years longer or shorter as was found from
circumstances most convenient. If Numa had retained the lunar year
of 354 days, and not added one day to the month of January, his
method of intercalation would have made the year as regular as
that of Julius Csesar. But by adding one day to the month of
January, each year deviated from the solar year one whole day too
much; and this irregularity he might have easily corrected by omitting
eight days of the intercalary month every eighth year. This, however, was not done, and the progression of all the months of the year
relative to the seasons continued to go onward.
The Decemviri about the year 452 B.c. ordered the month of February
to be reckoned next after the month of January, and.it has held this
position from that date down to the present time.
The method of arbitrary intercalation in course of time was calculated to produce confusion and disorder in the reckoning, so that the
months became removed from their proper seasons; the winter months
being carried back into the autumn, and the autumnal months into
the summer. This arrangement of the year, notwithstanding its
imperfections, was continued until the times of Julius Coesar, who
resolved to remedy the confusion by abolishing the cause of it, namely,
the arbitrary use of intercalation by the Pontifices. For this purpose,
with the aid of Sosigenes, an Egyptian astronomer in the year 707
A.u.0., or 47 B.C., he adjusted the year according to the course of the
sun, and assigned to each month the days they still retain. He found
that the reckoning of the months had receded from their proper
seasons, December coming on in September, and September in June.
In order to bring the seasons forward he found it necessary to devise
a year of fifteen months or 445 days (called the last year of confusion),
so as to make the ensuing year, 708 A.u..C., begin on the first day of
January, and so proceed regularly afterwards.
As the solar year consists of 365- days, Julius Csesar ordered that
the months should be reckoned, and the civil year regulated from
the course of the sun and not of the moon, and disposed of the 5 days
among the months, making them to consist, some of 30 days and some
of 31 days, except the month of February, which, in common years,
should still retain its number of 28 days. And to account for the
quarter of a day over 365 days, he calculated that the intercalation of
one day every four years in the month of February would bring the
new scheme into concert with the order of the seasons. This intercalary day followed the 6th of the Kalends of March in the Julian
Calendar, and was called bis-sextilis, the sixth day of the Kalends of
March twice reckoned. From this fact every fourth year has been
called bissextile, or leap year with us, one day having been passed or
leaped over without reckoning in the Julian Calendar. It would not,
lhowever, have been strictly correct to say, according to the Roman
mode of counting, that leap years had one day more than common
years. In leap year, when the month of February consists of 29 days,
both the 24th and 25th days of that month were marked in the Julian
Calendar as the sixth day before the Kalends of March, and these two
days were reckoned as one day, or one real day being leaped over,