Model for 262-218
The analysis of individual years in this period leads to the following results:
The consular year started on Kal. Mai. before A.U.C. 532 = 222
- There were at most 14 intercalations between A.U.C. 526 = 228 and A.U.C. 564 = 190, probably c. 12-14.
- There were probably at least 10 intercalations between A.U.C. 522 = 232 and A.U.C. 564 = 190
- A.U.C. 518 = 236 was an intercalary year
- There were 19 intercalations between A.U.C. 512 = 242 and A.U.C. 564 = 190
- A.U.C. 512 = 242 was very probably an intercalary year
- There were 22 intercalations between A.U.C. 505 = 249 and A.U.C. 564 = 190, or 23 if A.U.C. 505 = 249 was intercalary
- There were 22 or 23 intercalations between A.U.C. 504 = 250 and A.U.C. 564 = 190; hence A.U.C. 505 = 249 and A.U.C. 504 = 250 were not both intercalary
- There were 24-26 intercalations between A.U.C. 501 = 253 and A.U.C. 564 = 190, most likely 24
- There were 24-25 intercalations between A.U.C. 499 = 255 and A.U.C. 564 = 190, most likely 25
- There were 27-28 intercalations between A.U.C. 496 = 258 and A.U.C. 564 = 190, most likely 27
- There were 28-29 intercalations between A.U.C. 494 = 260 and A.U.C. 564 = 190, one of which was certainly in A.U.C. 494 = 260
- There were 29-31 intercalations between A.U.C. 492 = 262 and A.U.C. 564 = 190.
All these constraints are met by a very simple model: intercalation every other year from A.U.C. 492 = 262 to A.U.C. 534 = 220. This model was also arrived at by N. Prack, Der römische Kalender (264 - 168 v. Chr.) 70, though for some reason he starts the series in A.U.C. 490 = 264, a year for which we have no evidence, and stops it at A.U.C. 518 = 236. He doesn't otherwise consider the period between the Punic Wars.
The lengths of all intercalations are unknown. Evidence for earlier periods, notably the data for A.U.C. 494 = 260 and A.U.C. 496 = 258, suggests a bias in favour of 23 day intercalations. However, in view of the literary descriptions of intercalation, they are modelled here as alternating between 22 and 23 days. Hence its implications for the distribution of intercalations, cannot be regarded as settled, the possible range is indicated in the table by text of the form "D = +N/-M", where N is the maximum number of days by which the true conversion could be early and M is the maximum number of days by which the true conversion could be late.
While some variation is possible, the only indication I see that it might be required is in A.U.C. 504 = 250. This model requires the battle of Panormus to have been fought right at the very beginning of June, with Metellus and his elephants leaving almost immediately in order to get to Rome in time for his triumph; especially if there was a strong tendency towards 23 day intercalations. This is certainly possible, but is perhaps a little tight. A bias towards 23-day intercalations could also allow one fewer intercalation between A.U.C. 499 = 255 and A.U.C. 564 = 190.
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