structural:expansion
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. There are accounts of this in Solinus, Pliny, Ammianus, Suetonius, and Censorinus.

Macrobius gives the following account of the introduction of the Julian calendar:

Caesar's regulation of the civil year to accord with his revised measurement was proclaimed publicly by edict, and the arrangement might have continued to stand had not the correction itself of the calendar led the priests to introduce a new error of their own; for they proceeded to insert the intercalary day, which represented the four quarter-days, at the beginning of each fourth year instead of at its end, although the intercalation ought to have been made at the end of each fourth year and before the beginning of the fifth.This error continued for thirty-six years by which time twelve intercalary days had been inserted instead of the number actually due, namely nine. But when this error was at length recognised, it too was corrected, by an order of Augustus, that twelve years should be allowed to pass without an intercalary day, since the sequence of twelve such years would account for the three days which, in the course of thirty-six years, had been introduced by the premature actions of the priests.

So, according to Macrobius,

Some people have had different ideas as to how the leap years went. The above scheme is that of Scaliger (1583) in the table below. He established that the Augustan reform was instituted in 8 BC. The table below shows for each reconstruction the implied proleptic Julian date for the first day of Caesar's reformed calendar and the first Julian date on which the Roman calendar date matches the Julian calendar after the completion of Augustus' reform.

By the systems of Scaliger, Ideler and Bünting, the leap years prior to the suspension happen to be BC years that are divisible by 3, just as, after leap year resumption, they are the AD years divisible by 4.

Pierre Brind'Amour argued that "only one day was intercalated between 1/1/45 and 1/1/40 (disregarding a momentary 'fiddling' in December of 41) to avoid the nundinum falling on Kal. Ian."

Alexander Jones says that the correct Julian calendar was in use in Egypt in 24 BC, implying that the first day of the reform in both Egypt and Rome, 1 January 45 BC, was the Julian date 1 January if 45 BC was a leap year and 2 January if it was not. This necessitates fourteen leap days up to and including AD 8 if 45 BC was a leap year and thirteen if it was not.In 1999, a papyrus was discovered which gives the dates of astronomical phenomena in 24 BC in both the Egyptian and Roman calendars. From 30 August 26 BC (Julian), Egypt had two calendars: the old Egyptian in which every year had 365 days and the new Alexandrian in which every fourth year had 366 days. Up to 28 August 22 BC (Julian) the date in both calendars was the same. The dates in the Alexandrian and Julian calendars are in one-to-one correspondence except for the period from 29 August in the year preceding a Julian leap year to the following 24 February. From a comparison of the astronomical data with the Egyptian and Roman dates, Alexander Jones concluded that the Egyptian astronomers (as opposed to travellers from Rome) used the correct Julian calendar.

Due to the confusion about this period, we cannot be sure exactly what day (e.g. Julian day number) any particular Roman date refers to before March of 8 BC, except for those used in Egypt in 24 BC which are secured by astronomy.

An inscription has been discovered which orders a new calendar to be used in the Province of Asia to replace the previous Greek lunar calendar. According to one translation

Intercalation shall commence on the day after 14 Peritius as it is currently constituted in the third year following promulgation of the decree. Xanthicus shall have 32 days in this intercalary year.

This is historically correct. It was decreed by the proconsul that the first day of the year in the new calendar shall be Augustus' birthday, a.d. IX Kal. Oct. Every month begins on the ninth day before the kalends. The date of introduction, the day after 14 Peritius, was 1 Dystrus, the next month. The month after that was Xanthicus. Thus Xanthicus began on a.d. IX Kal. Mart., and normally contained 31 days. In leap year, however, it contained an extra "Sebaste day", the Roman leap day, and thus had 32 days. From the lunar nature of the old calendar we can fix the starting date of the new one as 24 January, a.d. IX Kal. Feb 5 BC in the Julian calendar, which was a leap year. Thus from inception the dates of the reformed Asian calendar are in one-to-one correspondence with the Julian.

Another translation of this inscription is

Intercalation shall commence on the day after the fourteenth day in the current month of Peritius, occurring every third year. Xanthicus shall have 32 days in this intercalary year.

This would move the starting date back three years to 8 BC, and from the lunar synchronism back to 26 January (Julian). But since the corresponding Roman date in the inscription is 24 January, this must be according to the incorrect calendar which in 8 BC Augustus had ordered to be corrected by the omission of leap days. As the authors of the previous paper point out, with the correct four-year cycle being used in Egypt and the three-year cycle abolished in Rome, it is unlikely that Augustus would have ordered the three-year cycle to be introduced in Asia.