« A.U.C. 730 = 24 B.C. »

The most important data concerning the operation of the Roman calendar between A.U.C. 709 = 45 and A.U.C. 746 = 8 is given by pOxy 61.4175, first published in 1999 (A. Jones, The Astronomical Papyri from Oxyrhynchus (P.Oxy. 4133-4300a), 177). This records the planetary and lunar longitudes on a series of dates in Iulius, Sextilis and September in A.U.C. 730 = 24, giving both Roman and Egyptian dates.

This papyrus shows that the eighth Roman month was called "Sextilis" at this time and that it was 31 days long. This confirms that the month was renamed in A.U.C. 746 = 8 and that the Augustan reform did not change the lengths of the months set by Caesar. Most importantly, the papyrus allows the equivalent Julian dates to be determined precisely. They show that A.U.C. 730 = 24 was precisely aligned to the Julian calendar in these months. According to the standard model there should be a two-day difference. For example, the papyrus gives 8 Mesore year 6 (= 1 August 24 BC) = Kal. Sex., but on the standard model of the early Julian calendar Kal. Sex. AUC 730 = 3 August 24 BC.

A. Jones, ZPE 129 (2000) 159, argued that this showed that the "correct" Julian calendar was followed in Egypt even though it was not followed in Rome. However, this was certainly not the case around A.U.C 749 = 5. In order to explain this discrepancy, Jones proposed that the Roman calendar in Egypt was realigned to the Roman civil calendar between A.U.C. 730 = 24 and A.U.C. 746 = 8. This reconstruction, while certainly possible, is ad hoc and seems implausible on the face of it -- why should the Roman administration in Egypt ever have used a different "Roman" calendar from that used in Rome?

There are 17 proleptic Julian leap days between A.U.C. 730 = 24 and A.U.C. 798 = A.D. 45, the next year for which we have an astronomical synchronism: 21, 17, 13, 9, 5, 1 B.C., A.D. 4, 8 ... 44. Since pOxy 61.4175 shows that the Roman calendar was exactly aligned with the Julian calendar in A.U.C. 730 = 24 and had the same monthly structure, and since the calendars were also provably aligned in A.U.C. 798 = A.D. 45, there must also have been 17 bissextile days between A.U.C. 730 = 24 and A.U.C. 798 = A.D. 45 in the Roman calendar. This is the sum of the number of bissextile days inserted on the triennial cycle before A.U.C. 746 = 8 and the number inserted on the quadrennial cycle after that year.

There are at most 6 triennial intercalations between A.U.C. 730 = 24 and A.U.C. 746 = 8:

The second possibility is ruled out by iPriene 105, which also favours the first solution.

Therefore, after Sextilis A.U.C. 740 = August 24, either (a) the first Julian intercalation was in A.U.C. 757 = A.D. 4, following 6 triennial intercalations ending in A.U.C. 746 = 8 or (b) the first Julian intercalation was in A.U.C. 757 = 1, following 5 triennial intercalations ending in A.U.C. 745 = 9. The second choice is ruled out by the data discussed under A.U.C. 749 = 5. Hence the correct solution is 23, 20, 17, 14, 11, 8 B.C., A.D. 4, 8 ... 44.

In analyzing the lunar and planetary ephemeris data in pOxy 61.4175, Jones assumed a reference local time of 6pm. A. C. Gonzalez-Garcia & J. A. Belmonte, Archaeoastronomy 20 (2006) 97 at 106 n. 7, object that the planets and, for many phases, the moon would not have been observable at this time because it was daylight. They state that "adequate agreement with the given positions [can be obtained] by assuming that the dates for the observations are one day before those given by Jones and that the time of the observation was midnight." It is not entirely clear whether this means that they prefer a reference time which is 18 or 42 hours before the times calculated by Jones; I assume 42.

Since the papyrus is an ephemeris table, it is also not clear why Gonzalez & Belmonte suppose that the position had to be observed rather than calculated -- especially since the moon would certainly have been invisible at some time, no matter what the reference time. More seriously, I am unable to obtain this result with SkyMap Pro, which shows good agreement with Jones' numbers. To take the earliest case, Jones correctly places the moon at 4° Aries on 2 Epeiph year 6 = 26 June 24, but on 25 and 24 June the moon was certainly in Pisces, not Aries.

Accepting their calculations nevertheless, for the sake of argument, the effect of their theory would be to move the Julian dates of the ephemerides one or two days earlier than Jones' calculations, effectively placing the Roman dates one or two days earlier than the same date in the Julian calendar -- i.e. Kal. Sex. AUC = 30 or 31 July 24. In effect, this increases the distance between the Roman dates of the papyrus and reliable Julian dates by one or two days, i.e. we must find room for one or two more Roman leap days than the above analysis assumes between this year and A.U.C. 798 = A.D. 45. But the only possible place for these leap days is between 9 BC and AD 1 or between 8 BC and AD 4. It is not possible to reconcile such a model with the ancient accounts of a 12-year suspension of intercalation, nor with the synchronism discussed under A.U.C. 749 = 5. Hence, no matter whether the astronomical data in isolation allows such variance (and I do not believe it does so), this model may be dismissed on historical grounds.

Another possibility is that the Roman dates in this papyrus represent a day that starts in the evening of the Egyptian day. In that case, the Julian equivalents of the Roman days would be one day later than is assumed here. While the synchronism implied by this interpretation doesn't match the traditional model of the early Julian calendar, or mine, it is possible to create ones that do match it. However, A. Jones, ZPE 129 (2000) 159 at 161 noted that seven similarly double-dated ephemerides are known from the period AD 111-489, at which time the Roman dates are certainly true Julian dates, and in all these cases the lunar data is correct for the evening of the Julian date and the Roman dates are correctly equated to the Egyptian date. There are no grounds to suppose that the epoch of the Roman day was different in this case.

(Gonzalez & Belmonte entirely ignore the Egyptian dates in this papyrus, but presumably they would argue that these are tracking the Roman leap year cycle at this time.)

This analysis proves the phase of the triennial leap year cycle between A.U.C. 709 = 45 and A.U.C. 746 = 8, that the last triennial leap year was A.U.C. 746 = 8, and the first Julian leap year was A.U.C. 757 = A.D. 4. It also shows that the literary accounts stating that intercalation was suspended for 12 years by the Augustan reform are not quite correct. In fact intercalation was suspended until the 12th year of the Augustan reform

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