Julian Calendar - Leap Year Error

Leap Year Error

Although the new calendar was much simpler than the pre-Julian calendar, the pontifices initially added a leap day every three years, instead of every four. According to Macrobius, the error was the result of counting inclusively, so that the four-year cycle was considered as including both the first and fourth years; perhaps the earliest recorded example of a fence post error. After 36 years, this resulted in three too many leap days. Augustus remedied this discrepancy by restoring the correct frequency. He also skipped three leap days over 12 years in order to realign the year. Once this reform was complete, intercalation resumed in every fourth year and the Roman calendar was the same as the Julian proleptic calendar.

The historic sequence of leap years in this period is not given explicitly by any ancient source, though Scaliger established that the Augustan reform was instituted in 8 BC. Several solutions have been proposed, which are summarised in the following table. The table shows for each solution the implied proleptic Julian date for the first day of Caesar's reformed calendar (Kal. Ian. AUC 709) and the first Julian date in which the Roman calendar date matches the proleptic Julian calendar after the completion of Augustus' reform.

Scaliger's proposal is the most widely accepted solution. It closely matches Macrobius' description and results in a calendar year and leap year cycle which exactly matches the proleptic Julian calendar at the time of Caesar's reform, except for his belief that the first reformed year, 45 BC, was not a leap year. Although some scholars, including Mommsen, support Ideler's view that 45 BC was a leap year, Brind'Amour has proved that there was only one bissextile day before 41 BC.

All proposals which end the triennial cycle before 9 BC are provably incorrect. The Asian calendar reform decreed by the proconsul Paullus Fabius Maximus aligned the calendar of the Asian province to the Roman calendar with a New Year falling on Augustus' birthday. It cannot have taken effect any earlier than 9 BC, and the decree states that the first reformed year was a leap year in a triennial cycle.

In 1999, an Egyptian papyrus was published that gives an ephemeris table for 24 BC with both Roman and Egyptian dates. While the Egyptian and lunar synchronisms match the Roman dates on the proleptic Julian calendar, they do not match them on any previously proposed solution for the triennial cycle. One suggested resolution of this problem, which matches the data of the papyrus, is a new triennial sequence, in which the triennial leap years started in 44 BC and ended in 8 BC, with leap years resuming in AD 4.