Model for 168-86

The analysis of individual years in this period leads to the following results:

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

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:

This reconstruction gives the following estimates for the two literary data points:

Both of which are consistent with the sequence of events described.

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