Model for 218-190The analysis of individual years in this period leads to the following results:

Seven intercalations between A.U.C. 537 = 217 and A.U.C. 564 = 190.

- Five intercalations between A.U.C. 539 = 215 and A.U.C. 564 = 190.

- Five intercalations between A.U.C. 542 = 212 and A.U.C. 564 = 190.

- Four intercalations between A.U.C. 544 = 210 and A.U.C. 564 = 190.

- Four intercalations between A.U.C. 547 = 207 and A.U.C. 564 = 190.

- Three or four intercalations, more likely three, between A.U.C. 548 = 206 and A.U.C. 564 = 190.

- Two intercalations between A.U.C. 550 = 204 and A.U.C. 564 = 190.

- Two intercalations between A.U.C. 551 = 203 and A.U.C. 564 = 190.

- Probably two intercalations between A.U.C. 552 = 202 and A.U.C. 564 = 190.

- Probably one intercalation between A.U.C. 557 = 197 and A.U.C. 564 = 190.
In addition, there are circumstantial indications that A.U.C. 536 = 218 and A.U.C. 546 = 208 were regular years, and weak indications that A.U.C. 552 = 202 was an intercalary year.

Hence we may assign the intercalations between A.U.C. 536 = 218 and A.U.C. 564 = 190 as follows:

Intercalary: A.U.C. 537 = 217, A.U.C. 538 = 216, and probably A.U.C. 547 = 207

- Regular: A.U.C. 536 = 218, A.U.C. 539 = 215, A.U.C. 540 = 214, A.U.C. 541 = 213, A.U.C. 544 = 210, A.U.C. 545 = 209, A.U.C. 546 = 208, A.U.C. 550 = 204 and A.U.C. 552 = 202
We are left with three uncertain intercalations, one in A.U.C. 542 = 212 or A.U.C. 543 = 211, another in A.U.C. 548 = 206 or A.U.C. 549 = 205 and one more between A.U.C. 557 = 197 and A.U.C. 564 = 190.

Since A.U.C. 547 = 207 was probably intercalary, it is assumed here that A.U.C. 549 = 205 was intercalary rather than A.U.C. 548 = 206.

- Having no basis to choose between A.U.C. 542 = 212 and A.U.C. 543 = 211, A.U.C. 543 = 211 is arbitrarily selected as intercalary.

- The
Lex Aciliawas introduced in A.U.C. 563 = 191. The general opinion is that this year was intercalary for this reason. While I don't find the argument compelling, its perfectly plausible, so the year is modelled here as intercalary, and 378 days long under the inferred provisions of that law.The lengths of all intercalations are unknown, but are modelled 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.

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