Model for 168-86The analysis of individual years in this period leads to the following results:

- A.U.C. 587 = 167 was a 377 day year.

- A.U.C. 588 = 166 was an intercalary year.

- A.U.C. 590 = 164 was probably an intercalary year.

- A.U.C. 653 = 101 and A.U.C. 659 = 95 were both probably regular years.

- There were 16 intercalations between A.U.C. 586 = 168 and [prid?] Non. Quin. in either A.U.C. 612 = 142, A.U.C. 613 = 141, or A.U.C. 614 = 140, most likely one of the last two.

- There were 10 intercalations between a.d. [lost] Id. Iun. A.U.C. 642 = 112 and Kal. Mart. A.U.C. 668 = 86.
The data for this period is very sparse. Nevertheless, it is possible to establish some of its calendrical characteristics.

The point at which my analysis begins to diverge significantly from Brind'Amour's is Kal. Mart. A.U.C. 696 = 24 February 58. The distance from Kal. Mart. A.U.C. 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

The synchronism of A.U.C. 668 = 86 justifies the assumption of roughly alternating intercalations that underlay the analysis of the

tumultus Lepidianus. Hence we certainly know that there were 12 intercalations of 23 days between Kal. Mart. A.U.C. 676 = 78 and Kal. Mart. A.U.C. 709 = 45, and only 1 of 22 days. The first model, of 50x22 + 4x23 intercalary days, can therefore be absolutely excluded. The strong bias this data shows towards 23-day intercalations demonstrates that the correct model is the last: 4x22 + 48x23 intercalary days.The model is based on applying the proposed reconstruction of the

Lex Aciliato these bounds and the results derived in the discussions of individual years. We first establish what can be inferred from the proposedLex Acilia, beginning with A.U.C. 614 = 140.

As noted, there were 16 intercalations, including 4, 5 or possibly 6 intercalary pairs before the year of the

senatus consultumrecorded in SIG^{3}674. Since there were only 4 22-day intercalations between A.U.C. 586 = 168 and A.U.C. 696 = 58, the inferredLex Aciliaimplies that the first choice is correct, and thesenatus consultummust be dated to this year. This fixes the dates of A.U.C. 614 = 140.Under the proposed

Lex Acilia, it is not possible to squeeze 16 intercalations with 4 intercalary pairs, one of which was A.U.C. 587 = 167/A.U.C. 588 = 166, between A.U.C. 586 = 168 and A.U.C. 614 = 140 unless there were no pairs of consecutive regular years, and unless A.U.C. 614 = 140 itself was intercalary. Therefore A.U.C. 614 = 140 was an intercalary year of 378 days and A.U.C. 615 = 139 was a regular year.Since A.U.C. 587 = 167 was a 377-day year, A.U.C. 586 = 168 was a regular year, A.U.C. 588 = 166 was intercalary (as is already known from the

Fasti triumphales) and 378 days long, and A.U.C. 589 = 165 was a regular year. Since there were no pairs of regular years at this time, A.U.C. 590 = 164 was intercalary, as previously conjectured fromSIG^{3}644.This fixes the Julian conversions from A.U.C. 586 = 168 to A.U.C. 590 = 164. We also now have fixed dates for Kal. Mart. A.U.C. 615 = 26 February 139, Kal. Mart. A.U.C. 642 = 20 March 112 and Kal. Mart. A.U.C. 667 = 22 February 87, and we know that A.U.C. 614 = 140 and A.U.C. 669 = 85 were both intercalary. There must be 10 intercalations between A.U.C. 642 = 112 and A.U.C. 669 = 85, and 13 between A.U.C. 614 = 140 and A.U.C. 642 = 112, and 7 pairs of regular years between A.U.C. 614 = 140 and A.U.C. 669 = 85, exclusive.

5 or 6 of these regular pairs must lie between A.U.C. 642 = 112 and A.U.C. 669 = 85. If the festival-based dates in A.U.C. 660 = 94 and A.U.C. 654 = 100 indicate that these years were candidate intercalary years, we can refine the distribution of the regular pairs: either 1 or 3 must lie between A.U.C. 660 = 94 and A.U.C. 669 = 85, and either 0 or 2 must lie between A.U.C. 654 = 100 and A.U.C. 660 = 94.

The next potentially useful datum is Plutarch's synchronism that a.d. III Kal. Sex. A.U.C. 653 was after the summer solstice, 26 June 101. However, no possible distribution of intercalations violates this condition. The closest match is given if A.U.C. 642 = 112 was followed by 4 consecutive regular pairs each separated by one intercalary year from the next, in which case a.d. III Kal. Sex. A.U.C. 653 = 3 July 101.

The chart given here assumes that festival-based dates do indicate candidate intercalary years, and makes the following essentially arbitrary assumptions:

That A.U.C. 660 = 94 and A.U.C. 654 = 100 were in fact intercalary

- That there was only one regular pair between A.U.C. 660 = 94 and A.U.C. 669 = 85, arbitrarily selected as A.U.C. 667 = 87/A.U.C. 668 = 86.

- That there were no regular pairs between A.U.C. 660 = 94 and A.U.C. 654 = 100, i.e. that the only intervening intercalation was in A.U.C. 657 = 97.

- That there were 5, not 6, regular pairs between A.U.C. 642 = 112 and A.U.C. 669 = 85. One has already been allocated, and the remaining four start at A.U.C. 643 = 111/A.U.C. 644 = 110.

- The remaining two regular pairs between A.U.C. 614 = 140 and A.U.C. 642 = 112 are arbitrarily set at A.U.C. 615 = 139/A.U.C. 616 = 138 and A.U.C. 626 = 128/A.U.C. 627 = 127.

- The four intercalary pairs before A.U.C. 614 = 140 were consecutive.
This reconstruction gives the following estimates for the two literary data points:

27 July 149 = a.d. VII Id. Sex. A.U.C. 605.

- a.d. III Kal. Sex. A.U.C. 653 = 3 July 101.
Both of which are consistent with the sequence of events described.

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