First, days of the month were not numbered incrementally, but rather counted down towards the next festive day, e.g., February 10 was “ante diem quartum Idus Februarias” (fourth prior day of the Ides of February). The Ides of February were February 13. 13 – 10 = 3, not 4. How does that compute? Well, Romans usually included both the first and last day in their reckoning of time periods. The liturgical calendar still calls the seven days following a major solemnity an “octave.” By this logic, if February 13 is the Ides of February, and February 12 is the “pridie Idus Februarias” (the prior day of the Ides of February), then February 11 is “ante diem tertium Idus Februarias” (third prior day of the Ides of February) and February 10 is “ante diem quartum Idus Februarias” (fourth prior day of the Ides of February).
Second, the intercalary or leap day in the Roman calendar was the “bissextile day,” i.e., the doubling of the sixth prior day of the Kalends of March: “ante diem bissextum Kalendas Martias” (February 24-25), followed by “ante diem quintum Kalendas Martias” (February 26).
Why February? March was the first month of the year, as the months still named after numerals attest: September, October, November and December were the 7th, 8th, 9th, and 10th months respectively because the first month was the month dedicated to Mars, the God of War.
Why the sixth day, though? Why not some other day? All the days after the Ides of February were counted down towards the Kalends of March. So why pick the sixth day? It was the convenient, placed somewhere within the countdown after the Ides of February towards the Kalends of March. If the intercalary day was perceived as a new special day (possibly unlucky rather than festive), then it was better not to place in the immediate vicinity of regular festive days, e.g., immediately after the Ides or immediately prior to the Kalends. In a leap year, taking the Kalends of March (March 1) as the center, February 24 is symmetrical to the Nones of March (March 7): there are six days preceding the Kalends, starting with the bissextile day, February 24, 25, 26, 27, 28, and 29, and there are six days following the Kalends, with the sixth being the Nones, March 2, 3, 4, 5, 6, and 7. There may have been additional reasons behind the choice of the sixth day.
By the way, the Bull of Gregory XIII, incipit “Inter gravissimas,” promulgating the Gregorian reform of the calendar, is dated, by our reckoning, on February 24, 1582, i.e., on the bissextile day preceding the year in which the reform was introduced. This was very clever considering that the reform largely focused on the modification of the leap-year rule (omitting 3 leap days every 400 years).
Read more about calendars on the VOF’s Faith and Science Archive: