« A.U.C. 585 = 169 B.C. »

Given that Kal. Ian. A.U.C. 702 = 19 November 53 was a market day, and given the known absolute synchronism for A.U.C 586 = 168 we can calculate that the nundinal letter for the market days at the end of A.U.C. 585 was C.

Livy 43.16.12 reports that the censors Ti. Sempronius Gracchus and C. Claudius Pulcher were scheduled to be tried for treason before the comitia centuriata on a.d. IX and VIII Kal. Oct. A.U.C. 585 = 169. These are days with nundinal letters of D and E respectively. Therefore the nundinal letter was not D or E. If there was no intercalation at the end of A.U.C. 585 = 169, then the nundinal letter for Sept. A.U.C. 585 = 169 was F. If there was a 22 day intercalation it was D. If there was a 23 day intercalation it was E. Therefore there was no intercalation at the end of this year.

Since the Julian dates of A.U.C 586 = 168 are known, this fixes the Julian dates of A.U.C. 585 = 169.

We can crosscheck this with the data for A.U.C. 584 = 170. Since this year is known to have ended with an intercalation of 23 days, the result for A.U.C. 585 = 169 gives the nundinal letter for Februarius A.U.C. 584 = 170 as E. Livy 43.11.6 reports that the elections for A.U.C. 585 = 169 were held on a.d. V Kal. Feb. and a.d. III Kal. Feb. of A.U.C. 584 = 170, days with nundinal letters of B and D respectively.

Conversely, if there was a 22 day intercalation at the end of A.U.C. 585 = 169 then the nundinal letter in Februarius A.U.C. 584 = 170 was C, and if there was a 23 day intercalation it was D. Therefore, independently of the data for the trial of the censors, we may conclude that there was not a 23-day intercalation at the end of A.U.C. 585 = 169.

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