This differed from the solar year by ten whole days and a fraction; but to restore the coincidence, Numa ordered an additional or intercalary month to be inserted every second year between the 23d and 24th of February, consisting of twenty-two and twenty-three days alternately, so that four years contained 1465 days, and the mean length of the year was consequently 366-1/4 days, so that the year was then too long by one day.
As the error amounted to twenty-four days in as many years, it was ordered that every third period of eight years, instead of containing four intercalary months, two of twenty-two and two of twenty-three days, amounting in all to ninety days, should contain only three of those months of twenty-two days each, amounting to sixty-six days, thereby suppressing twenty-four days in as many years, reducing the mean length of the year to 365-1/4 days.
Had the intercalations been regularly made the concurrence of the solar and the civil year would have been preserved very nearly. But its regulation was left to the pontiffs, who, to prolong the term of a magistracy or hasten an annual election, would give to the intercalary month a greater or less number of days, and consequently the calendar was thrown into confusion, so that in the time of Julius Cæsar there was a discrepancy between the solar and the civil year of about three months; the winter months being carried back into autumn and the autumnal into summer.
A table of the order and the names of the planets in the Egyptian astronomy illustrating the origin of the names of the days of the week:
---------+---------+--------+-------+-------+----------+------- Saturn, |Jupiter, |Mars, |Sun, |Venus, |Mercury, |Moon, Saturday.|Thursday.|Tuesday.|Sunday.|Friday.|Wednesday.|Monday. ---------+---------+--------+-------+-------+----------+------- 1 | 2 | 3 | 4 | 5 | 6 | 7 8 | 9 | 10 | 11 | 12 | 13 | 14 15 | 16 | 17 | 18 | 19 | 20 | 21 22 | 23 | 24 | 1 | 2 | 3 | 4 5 | 6 | 7 | 8 | 9 | 10 | 11 12 | 13 | 14 | 15 | 16 | 17 | 18 19 | 20 | 21 | 22 | 23 | 24 | 1 2 | 3 | 4 | 5 | 6 | 7 | 8 9 | 10 | 11 | 12 | 13 | 14 | 15 16 | 17 | 18 | 19 | 20 | 21 | 22 23 | 24 | 1 | 2 | 3 | 4 | 5 6 | 7 | 8 | 9 | 10 | 11 | 12 13 | 14 | 15 | 16 | 17 | 18 | 19 20 | 21 | 22 | 23 | 24 | 1 | 2 3 | 4 | 5 | 6 | 7 | 8 | 9 10 | 11 | 12 | 13 | 14 | 15 | 16 17 | 18 | 19 | 20 | 21 | 22 | 23 24 | 1 | 2 | 3 | 4 | 5 | 6 7 | 8 | 9 | 10 | 11 | 12 | 13 14 | 15 | 16 | 17 | 18 | 19 | 20 21 | 22 | 23 | 24 | 1 | 2 | 3 4 | 5 | 6 | 7 | 8 | 9 | 10 11 | 12 | 13 | 14 | 15 | 16 | 17 18 | 19 | 20 | 21 | 22 | 23 | 24 ---------+---------+--------+-------+-------+----------+-------