« A.U.C. 713 = 41 B.C. »
Dio Cassius 48.33.4 records that an intercalation occurred in A.U.C. 713 = 41, against the rule, nominally in order to avoid the ill-omen of a market day on Kal. Ian. in A.U.C. 714 = 40. Thus, prid. Kal. Ian. A.U.C. 713 = 41 was a market day. Dio says that this intercalation was compensated for "later", so that the calendar would run as Caesar intended it to, though he does not explain exactly how or when.
The year in which this event occurred has been disputed. T. E. Mommsen, Die römische Chronologie bis auf Caesar 283 n. 5, argued that the passage should be dated a year later, since the report of the intercalation is given at the end of a passage that treats the years A.U.C. 713 = 41 and A.U.C. 714 = 40 together. However, allthough the wording is a little confusing, the intent is clear: an intercalary day had been inserted in the "preceding" year (i.e. A.U.C. 713 = 41) so that the first day of the year whose account he is wrapping up (i.e. A.U.C. 714 = 40) would not be a market day.
Dio does not explain how this leap day was compensated. The usual explanation, which assumes that the adjacent triennial leap years were A.U.C. 712 = 42 and A.U.C. 715 = 39, is to suppose that some arbitrary day was omitted from A.U.C. 714 = 40, so that Dio's intercalation was just a minor perturbation. In effect, this model requires that A.U.C. 714 = 40 was a 364-day year in order for the total number of days be unaffected while preserving the phase of the triennial cycle. For analytical purposes one would assume, on this view, that the market day recorded by Dio was Kal. Ian. A.U.C. 714 = 40 not prid. Kal. Ian. A.U.C. 713 = 41.
H. Matzat, Römische Chronologie I 13-18, pointed out that the three-year cycle period = 365+365+366 = 1096 = 8x137 days is a multiple of the nundinal cycle of 8 days. If Dio's intercalation was compensated as suggested, the market day would have recurred on Kal. Ian. every third year after A.U.C. 714 = 40 for as long as the triennial cycle operated, and would also have occurred on Kal. Ian. A.U.C. 711 = 43. Given the clear belief at this time that a market day on Kal. Ian. was ill-omened, this seems rather unlikely.
The only way to avoid this is to suppose that the leap day was "compensated" by omitting a bissextile day from A.U.C. 714 = 40 rather than a regular day. That is, the previous leap year was A.U.C. 710 = 44, so that Kal. Ian. A.U.C. 711 = 43 was not a market day, and the leap day recorded by Dio is actually the first triennial leap day. The analysis of A.U.C. 730 = 24 and A.U.C. 746 = 8 shows that A.U.C. 746 = 8 was also a leap year, which makes A.U.C. 713 = 41 in phase with the triennial cycle.
Dio regards a market day on Kal. Ian. as ill-omened, and no doubt this is how the change in intercalation was officially justified. However, in this year it would also have had immediate and practical political consequences, since under the Lex Hortensia of A.U.C. 467 = 287 such a market day would have prevented comitial business occurring on that day, effectively delaying replacement of the previous year's consul L. Antonius. Since Antonius was at that time the opponent of Lepidus' ally, Octavian, in the Perusian war, it was highly desirable to replace him as soon as and in as normal a fashion as possible.
There was no a priori reason such a localised political exigency should, in itself, have caused a permanent shift in the leap year cycle; the Caesarian cycle would have resumed in A.U.C. 718 = 36. However, in A.U.C. 715 = 39 the pontifex maximus, M. Aemilius Lepidus, took up his triumviral post in Africa. This meant that he was not in a position to prevent the college of pontiffs, taking the official justification at face value, from mechanically using the precedent of A.U.C. 713 = 41 to insert a leap day in A.U.C. 716 = 38 in order to avoid another market day on Kal. Ian. A.U.C. 717 = 37. It is this second triennial leap year that finally institutionalised the incorrect cycle. Lepidus never got the opportunity to correct the error. By A.U.C. 719 = 35 he was under house arrest, where he stayed for the rest of his life.
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