Another fact, which Napoleon, Le Verrier, and Colonel Stoffel appear to have overlooked, alone proves that not 67 days only but 90 days were intercalated in that year. The word nundinae is familiar to many readers of Cicero’s letters. To quote the authors of the article NUNDINAE in Smith’s Dictionary of Greek and Roman Antiquities,[3583] ‘the Romans had a system of eight-day weeks, which, like our seven-day weeks, ran on from one month to another and from one year to another without breaking.’ Every eighth day was a market-day, and was called nundinae. Thus, if the 1st of January was a market-day, the next was the 9th, the next the 17th, and so on. We learn from Dion Cassius[3584] that the Kalends of January, 702, was a market-day; the same writer says that, in order to prevent the Kalends of January, 714, from falling on a market-day—a coincidence which was regarded as ill-omened—a day was intercalated extraordinarily in 713;[3585] and it follows that, if there had been no intercalation in 713, the number of days that elapsed from the Kalends of January, 702, to the last day of December, 713, would have been a multiple of 8. Now, on the theory of Napoleon the Third, Le Verrier, and Colonel Stoffel this number would have been 4,401; on the theory that the year 708 contained 445 days, 4,424. The latter number is divisible by 8; the former is not.
There has never been any question but that the number of days intercalated in 708 was either 67 or 90; and the former number has been proved to be wrong.
IV. In order to obtain an absolutely firm foundation for the chronology of Caesar’s second expedition, one more question remains to be answered. In this country it is generally taken for granted that the Kalends of January, 709, the year in which Caesar’s reform of the calendar came into operation, corresponded with the 1st of January, 45 B.C. Various German scholars have, however, attempted to prove that the Kalends of January, 709, fell on the 2nd of January of the Julian calendar.
Let us first see what there is to be learned from the ancient writers.
Pliny[3586] says that when the error in the execution of Caesar’s reform was discovered, it was corrected by the omission of intercalary days during twelve successive years.
Solinus[3587] tells us that Caesar’s reform was vitiated by the pontiffs; for, whereas it had been enjoined that a day should be intercalated on the completion of the fourth year, they made the intercalation at the beginning of the fourth year, not at the end. Thus, Solinus continues, twelve days were intercalated in thirty-six years, whereas only nine ought to have been intercalated.
Suetonius[3588] says that the calendar, as reformed by Caesar, was thrown into confusion by ‘negligence’, and rectified by Augustus; also that Caesar made the calendar year consist of 365 days, so as to bring it into harmony with the solar year, and, abolishing the intercalary month, ordered that one day should be intercalated every fourth year.[3589]
According to Censorinus,[3590] Caesar directed that, in order to compensate for the quarter of a day by which the solar exceeded the calendar year, one day should be intercalated at the end of every quadriennial cycle, after the Terminalia [that is to say, after the 23rd of February].
According to Macrobius,[3591] Caesar directed that one day should be intercalated every fourth year. Macrobius then makes substantially the same charge against the pontiffs as Solinus, and goes on to say that, after the error for which they were responsible had continued for thirty-six years, Augustus corrected it by ordering that twelve years should pass without any intercalation.
Now it is absolutely certain that of the first five years during which the reformed calendar was in force, namely 709, 710, 711, 712, and 713, not one only but two contained an intercalary day.[3592] For, as we have already seen,[3593] Dion Cassius[3594] states that the Kalends of January, 702, was a market-day, and also that, in order to prevent the Kalends of January, 714, from falling on a market-day, a day was intercalated extraordinarily (παρὰ τὰ καθεστηκότα[3595]) in 713;[3596] and, as I had occasion to remark before, it follows that, if there had been no intercalation in 713, the number of days that elapsed from the Kalends of January, 702, to the last day of December, 713, would have been a multiple of 8. This would have been the case if one of the four years 709, 710, 711, and 712 had contained an intercalary day, but not otherwise.[3597] Which was it?