« A.U.C. 563 = 191 B.C. »
Macrobius, Saturnalia 1.13.21 tells us that the consul M' Acilius Glabro passed a law concerning intercalation in A.U.C 562, just before the start of the Aetolian war. Since Glabro was actually consul in A.U.C. 563, Macrobius has evidently used a system wherein A.U.C. 1 = 752. According to Livy 36.3, Glabro left Rome for the war on a.d. V Non. Mai.
The actual provisions of the Lex Acilia are unknown. Since there had certainly been at most one intercalation in the previous decade, and since it can be shown that intercalations occurred roughly every two years after this time, it seems virtually certain that it mandated the resumption of intercalations. Beyond this, all is conjecture. However, the recoverable statistics allow us to make some reasonable inferences. The key observations are as follows:
First, the distance from a.d. V Id. Quint. AUC. 564 = 14 March 190 to Kal. Mart. AUC 586 = 21 December 169 = 8,083 days of which 8,083-22*355 = 273 days are intercalary. 273 = 3x22 + 9x23, hence there were 3 intercalations of 22 days and 9 of 23 in this interval.
Next, it can be shown that both A.U.C. 568 = 190 and A.U.C. 585 = 169 were regular years. In order to fit 12 intercalations into the period between them without a run of three or more consecutive intercalations, there must be at least three pairs of consecutive intercalary years.
Next, the distance from Kal. Mart. AUC 586 = 21 December 169 to Kal. Mart. A.U.C. 696 = 24 February 58 is 40,242 days. 110x355 = 39,050 days belong to regular months, hence 1,192 are intercalary. Hence the possible divisions of 22 and 23 day intercalations are given by:
1,192 = 50x22 + 4x23 = 27x22 + 26x23 = 4x22 + 48x23
Either 7 out of 8, or all 9, intercalations between Kal. Ian. A.U.C. 677 = 77 and Kal. Mart. A.U.C. 696 = 58 were 23 days long. Hence the first model can be excluded: there are 52 or 53 intercalations in the period of 110 years. In view of the very strong bias shown towards 23-day intercalations in that period, the last solution is almost certainly correct. Hence there were only 4 22-day intercalations between A.U.C. 585 = 169 and A.U.C. 696 = 58.
Finally, the analysis of SIG3 674 shows that there were a minimum of 4, 5 or 6 pairs of consecutive intercalary years between A.U.C. 585 = 169 and the year of that inscription, depending on whether it was written in A.U.C. 614 = 140 or one of the two previous years.
There is a clear match betweeen the number of 22-day intercalations and the minimum number of pairs of consecutive intercalary years. The obvious inference is that 22-day intercalations only occurred in pairs of intercalary years, such as A.U.C. 587 = 167/A.U.C. 588 = 166. Such pairs were clearly intended to compensate for missed intercalations, and the total number of such pairs -- seven -- roughly matches the number of intercalations missed between the start of the Second Punic War and the passage of the Lex Acilia.
The remaining 23-day intercalations therefore must represent unpaired intercalations -- ones which had regular years on either side. If there were more than two consecutive regular years, this would imply a missed intercalation, which would require a compensatory action. Since almost all intercalations in the period were 23-days long, we may presume no such compensation was required until A.U.C. 699 = 55. Hence we may assume that there were no runs of three or more regular years after the passage of the Lex Acilia.
The regulations introduced by the Lex Acilia were therefore as follows:
An intercalary year was normally 378 days long, and was preceded and succeeded by regular years.
Runs of three or more regular years were forbidden, or at least discouraged.
To compensate for the intercalations since the Second Punic War (and possibly for future missed intercalations), pairs or consecutive intercalations would be introduced as convenient.
The intercalary pairs were 377/378 day pairs.
These rules have a loophole: they allow for long runs of pairs of regular years separated by an intercalary year. Although such a run may have occurred in the last decade of the second century, there was certainly one under Caesar's pontificate, apparently because of the desire to avoid a market day on Kal. Ian. This may be the reason why A.U.C. 699 = 55 was a 377 day year, since by that time an intercalary cycle had been slipped. The length of that year probably signalled an intent, which in the event was not realised, to make the following year a 378 day year.
By A.U.C. 708 = 46, three intercalations had been missed. Rather than introduce them as three intercalary pairs stretched over 9 years, Caesar introduced them all at once. The length of the 67-day intercalation of that year = 22+22+23 days represents an extension of the Acilian algorithm, concatenating the compensatory intercalations into a series and collapsing them into a single intercalation.
These may not have been the only provisions of the Lex Acilia. V. M. Warrior, in C. Deroux (ed.) Studies in Latin Literature and Roman History VI 119, has reasonably argued that the Lex Acilia mandated that the decision to intercalate should be made soon enough to communicate the fact to commanders in the field, since intercalations could determine the end of the term of their command. Indeed, since Glabro himself was about to embark on a potentially extended military command, his motive for passing such a law is clear.
Such a provision ipso facto implies that the law did not regulate the determination of which years should be intercalary. Therefore, we cannot automatically infer, per P. S. Derow, Phoenix 30 (1976) 265 at 268 (and many other scholars), that this year was itself intercalary. However, the scarcity of intercalations in the preceding years, the demonstrable frequency of intercalations after A.U.C. 564 = 190, the fact that there was one intercalation between A.U.C. 557 = 197 and A.U.C. 564 = 190, and the apparent passage of an intercalary reform in this year does argue in favour of there having been one in this year. If so, then it was 378 days long under the proposed model, since it occurred after the reform. Nevertheless, the chronological data as such imposes no necessity for an intercalation this year.
Against an intercalation, M. Passehl, in a posting to the Yahoo Romanfederation group on 27 Oct 2007, notes that Livy 36.3 dates the assembly of a Roman army at Brundisium by Id. Mai A.U.C. 563 = 3 January 191 with the proposed intercalation and 27 January 191 without it. The army met Baebius as he and Philip V were campaigning in Thessaly (Livy 36.14), a campaign that had just started as they came out of winter quarters at the beginning of spring (Livy 36.13), i.e. mid-late February, and so evidently it had crossed the Adriatic at the earliest possible moment. Passehl notes that a regular A.U.C. 563 = 191 minimises the delay in Brundisium while an intercalary year adds three weeks of unnecessary delay. While suggestive, however, the argument is not conclusive.
Somewhat arbitrarily, then, I have chosen to follow the general consensus and place the extra intercalation in this year. Should the year turn out to be regular, the next most likely candidate is probably A.U.C. 561 = 193.
Finally, P. Brind'Amour, Le calendrier romain 143, notes that Livy 36.37 ascribes the introduction of the quinquennial festival of jejunium Cereris to this year. In imperial times, this festival was celebrated annually on a.d. IV Non. Oct. Brind'Amour notes that if the festival were seasonal (i.e. Julian) then it would have occurred right at the end of the year, in Februarius (if there was an intercalation), or late Ianuarius (if there was none) in the year of introduction, but the name suggests a date on the eve of the harvest. Assuming the date is calendrical, the Julian equivalents in 191 are 22/23 May (with intercalation) or 14 June (without). Against this, J. Briscoe, JRS 76 (1986) 289 at 290, correctly notes that Livy explicitly places these events at the beginning of this consular year, with the first sacrifice occurring before the consuls left for their provinces. In any case, Brind'Amour's argument does not allow us to detect an intercalation even if he is correct.
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