The Eclipse of Ennius

The eclipse of Ennius is the most tantalising synchronism in Roman chronology.

Cicero, De Re Publica 1.25, notes that Q. Ennius, a poet and annalist who lived and wrote in the early second century, correctly described the nature of an eclipse in saying that the moon and night obscured the shining sun, in connection with an eclipse that occurred on Non. Iun. around the three hundred and fiftieth year after the foundation of Rome. He adds that the date of this eclipse, as recorded by Ennius and by the Annales Maximi, allowed later scholars, with a knowledge of eclipse theory, to fix the dates of earlier eclipses back to an eclipse on Non. Quin. in the reign of Romulus. In this, he is almost certainly referring to research by his contemporary M. Terentius Varro, who we are told in Censorinus 21.5 used eclipse data to determine the exact dates of recorded events.

Historical Accuracy

J. Rüpke, The Roman Calendar from Numa to Constantine 40, suggests that Ennius' date of Non. Iun. is not historical, but a "reverse calculation using dates from the calendar that applied in Ennius’ time". In my view, this suggestion is open to at least three objections:

• Cicero states that the same eclipse was recorded in the Annales Maximi ("quem apud Ennium et in maximis annalibus consignatum videmus"). This is prima facie evidence that Ennius did not invent the date, but Rüpke does not attempt to explain it or to reconcile it with his suggestion.

• Rüpke does not suggest any method by which Ennius might have retrocalculated such a date and I find it hard to imagine one. In theory it could perhaps have been done accurately if the Republican calendar was assumed to have a fixed intercalary scheme of the type described by Macrobius, Saturnalia 1.13.11-13, and if Ennius had a specific historical eclipse in mind, presumably recorded using an Egyptian date. But intercalation was certainly not fixed in Ennius' lifetime, the calculations involved are complex, and the concept anticipates, in reverse and by over a century, precisely the sort of reconstructive techniques that Varro used to reconstruct Roman chronology from eclipse data. Presumably, then, the putative "retrocalculation" was much more arbitrary -- but what could it have been? The obvious basis is to assume a lunar month, in which case the eclipse should have a day or two before the Kalends, as Romans of Ennius' time surely knew.

• Rüpke's suggestion is a result of his adoption of Beloch's argument (K.-J. Beloch, Griechisches Geschichte III¹.2 208ff, Hermes 57 (1922) 119) that the Roman calendar had been lunisolar until the publication of the fasti by the aedile Cn. Flavius in AUC 450 = 304. If Ennius' date is historically accurate this theory cannot be correct, since, whatever the year of the eclipse, it almost certainly predates 304 (see below) and the date Non. Iun. cannot be correct for a solar eclipse in a lunisolar calendar.

  Beloch, who accepted that the eclipse was also recorded in the Annales Maximi, supposed that the year was incorrect and should be emended from c. AUC 350 to c. AUC 450 (see below), thus placing the eclipse after the Flavian reform. Rüpke does not state why he does not accept a similar explanation.

  This argument raises the complex issue of the date of the creation of the republican calendar. It therefore requires a more extended discussion.

  Beloch and Rüpke give the following reasons for believing that the republican calendar was created with the fasti published by Cn. Flavius:

  • For both, the principal argument is that Macrobius, Saturnalia 1.15.9, in explaining the meaning of the term "Kalends", states that the priests used to declare the number of days to the Nones after observing the appearance of a new moon (i.e. first crescent) before Cn. Flavius first published the fasti.

    But as Michels points out (A. K. Michels, The Calendar of the Roman Republic 107ff.) the accounts we possess of Flavius' publication stress that the point was to allow the general public to know on what days legal action was permitted in the praetor's court. It is sufficient to suppose that his fasti were the first to indicate which days were marked as fas by F and which were marked as nefas by N. Such an action does not imply a wholesale calendar reform, but only the fixing of the previously variable dates through the addition of these notations to a preexisting calendar, in much the same way as the nundinal letters and dies comitiales (marked by C, replacing F) were probably added after the passage of the Lex Hortensia in AUC 467 = 287. On this view, Macrobius is describing an earlier instance of variability in the lunisolar calendar, and simply elides the creation of the republican calendar; after all, Macrobius, Saturnalia 1.13.1-7 ascribes this to Numa. Further, Flavius' action, although opposed by the senate, was apparently accepted by the pontifices, who were responsible for managing the calendar. As an aedile, Flavius was low in the government hierarchy. It seems unlikely that the pontifices would have accepted a wholesale calendar reform which had the effect of diminishing their public role.

  • Beloch, Hermes 57 (1922) 119 at 121f., notes that the battle of the Allia was fought on a.d. XV Kal. Sex., i.e. in mid Quintilis, shortly before the sack of Rome by the Gauls in the early fourth century (Livy 6.1.6). He argues that "Die Kelten sind doch ohne Zweifel um die Zeit der Ernte in Italien eingefallen" -- the Celts undoubtedly invaded Italy at harvest time -- and concludes that the calendar must therefore have been roughly aligned with the solar year, i.e. that Quintilis ~ July. But, assuming regular biennial intercalation as described in Macrobius, Saturnalia 1.13.11-12, we would extrapolate that Quinitilis ~ September at this time if the republican calendar was actually instituted by the Decemvirs some 70 years earlier, as is widely believed.

    Rüpke does not repeat this argument. In my view it has no merit. First, Livy's account of the invasion does not relate it to the time of harvest. Indeed, he says that the Senones, the Gauls who sacked Rome, were the last of the tribes to invade Italy and had the furthest distance to travel, and so might very well have reached Rome as late as September. Second, we cannot be sure that the republican calendar religiously practised biennial intercalation in the fifth and fourth century and earlier, and there are some indications that it did not. For example, Macrobius, Saturnalia 1.13.13 states that the Romans realised the system over-intercalated, and modified it so that every third octaeteris inserted 66 days (i.e. 3 intercalations of 22) instead of 90 (4 intercalations of alternating 22 amd 23 days). If Michel's suggestion that triumphs dated by festival dates in Februarius is correct, then biennial intercalation was not in use in the 270s, although the modified cycle described by Macrobius may have been.

    That being said, the underlying methodological point is fair enough: if, as seems likely, the calendar was lunar before the Decemviral reform, we can reasonably expect it to have been fairly close to seasonal alignment at that time, i.e. that Maius c. 450 BC (when the Decemvirs took office) is fairly close to May. Hence we can guesstimate the amount of over-intercalation or under-intercalation since c. 450 for any candidate date of the Ennius eclipse, and compare it to the intercalary schemes described by Macrobius. For example, on the strict biennial scheme described by Macrobius, the accumulated over-intercalation N years after c. 450 should be be about N±10 days.

  • Rüpke notes that the dedication of the temple of Juno Moneta on Kal. Iun. AUC 410 = 344 was accompanied by an eclipse (Livy, 7.28.7 + Ovid, Fasti 6.183-5). Since this is the beginning of the month, this is a date when an eclipse might be expected, consistent with a lunar calendar, and is therefore evidence that the republican calendar had not yet been instituted.

    The equation of AUC years to years BC refects the Varronian scheme, which is probably in error by 4 years at this time, so the identification of the claimed eclipse is no more certain than the eclipse of Ennius. In fact rather less so: Livy does not actually describe an eclipse, but a shower of stones and a darkening of the sky. This could equally well refer to a hailstorm, as suggested by P. Brind'Amour, Le calendrier romain, 189, or -- if Livy's reference to the "old portent on the Alban Mount" applies to a sacrifice held there at the dedication of the temple -- to volcanic activity. Moreover, Macrobius, Saturnalia 1.15.9 clearly describes the Kalends as originally being the day after the first crescent moon. This would only be visible a day or two after an eclipse, which occurs at conjunction, so Kal. Iun. cannot be the date of an eclipse in an true lunar calendar.

  I therefore see no good reason to accept Macrobius, Saturnalia 1.15.9 as evidence that the fixed republican calendar was created as late as AUC 450 = 304.

  The dominant Roman tradition credits the creation of the republican calendar to Numa, the 2nd king of Rome, who traditionally reigned in the 8th century. However, there are at least three contradictory indications in the literary sources which state or directly imply that the calendar was a later creation: Livy, 1.19 credits Numa with the creation of a true lunisolar calendar, complete with 19-year intercalary cycle; Junius Gracchanus (apud Censorinus 20.4), writing in the second century BC, attributed the republican calendar to one of the Tarquins, more probably Tarquinius Priscus, the 5th king, than Tarquinius Superbus, the 7th; and Dionysius of Halicarnassus, Antiquitatum Romanorum 59.1 states that the Roman calendar was still lunar at the start of the second Decemvirate, in the mid 5th century.

  Modern scholars tend to regard the attribution to Numa as a myth. In general, it is seen as a creation of republican times. Some have argued for 509 BC, the traditional date for the foundation of the republic and the dedication of the temple of Jupiter Optimus Maximus (Livy, 7.3). However, since Ideler, the most widely accepted date is the year of the second Decemvirate, c. 450 (see e.g. A. K. Michels, The Calendar of the Roman Republic, 109 with earlier scholars listed at n. 50, also A. K. Michels, TAPA 80 (1949) 320). There is clear evidence that they were responsible for a significant calendar reform:

  • Cicero, Ad. Att. 6.1.8, clearly believed that calendrical fasti had been published in some form by the Decemvirs, well before Flavius' publication.

  • Macrobius, Saturnalia 1.13.21, notes that two second century historians, C. Sempronius Tuditanus and L. Cassius Hemina, attributed a law concerning intercalation to the Decemvirate.

  • Ovid, Fasti 2.47-54 says that the Decemvirs were responsible for making Ianuarius and Februarius consecutive months at the beginning of the year. He claimed that Ianuarius was already the first, and that Februarius was moved from the last place to second, i.e. in effect that Ianuarius and Februarius swapped places. It is unclear how to interpret this, and it is generally held that he was in some way confused, but the relevant point here is the association of a reform with the Decemvirs.

  While the case is not absolutely conclusive, this date seems the most likely to me. In any case, I see no reason to doubt that Ennius' calendar date is authentic, and refers to the standard pre-Julian calendar.

Difficulties of Interpretation

Accepting, then, that Ennius' eclipse is an authentic historical datum, there are nevertheless several difficulties in interpreting Cicero's account of it.

• Cicero's text is only known from a single palimpsest source. In that palimpsest the date is give as "anno quinquagesimo <et> CCC fere post Romam conditam". The "CCC" was added to the original text interlinearly by a different hand, although early, and obviously represents an intended correction to the original text. Thus, there are grounds for doubting the accuracy of the date in the MS.

• The context in which Ennius recorded the eclipse is not given. It is widely assumed to be his Annales, which recorded the history of Rome from its founding until (probably) the triumph of M. Fulvius Nobilior in A.U.C. 567 = 187, and which are largely lost. However, the use of "fere" -- around -- by Cicero, instead of giving an exact date, and the fact that Cicero says that it was recorded by Ennius independently of a record in the Annales Maximi, suggest that Ennius mentioned it in a different context, in which case, it has been suggested, it may well be that it was an eclipse that he had personally observed. Ennius' dates are given as 239-169.

• The magnitude of the eclipse is equally unclear. Cicero's report would appear to imply that Ennius was describing a total or very nearly total eclipse. On the other hand, if Ennius was simply describing the mechanism of an eclipse, as Cicero was, or exercising poetic licence, then his words merely report the occurrence of an eclipse and tell us nothing about its magnitude except that it was observable. B. W. Frier, Libri Annales Pontificum Maximorum, 117 n. 26, noted that the "nox" in Ennius' description of the eclipse ("Nonis Iunis soli luna obstitit et nox") may well imply an eclipse at sunset, though it does not necessarily do so.

• The date for the foundation of Rome that is assumed in Cicero's statement is uncertain. P. Brind'Amour, Le calendrier romain 211, reasonably posits that the choice must be between the chronologies of Ennius and Cicero. In De Re Publica 2.17, Cicero himself follows Polybius 3.22 in dating the foundation of Rome to Ol. 7.2 = 751/0. M. Terentius Varro, De Re Rustica 3.1, quotes some lines of Ennius which refer to Rome as having been founded around 700 years earlier. While we do not know what these lines assume as the base date, they suggest either that Ennius himself dated the foundation of Rome seven centuries before his own adult life at the time he wrote them, i.e. to the period c. 920-870, or that they refer to a date a generation or two after the Trojan War, c. 1100, when Ennius is known to have dated the foundation of Rome in his Annales.

  Brid'Amour argues that the question can be determined by deciding whether Cicero is quoting or summarising Ennius when he gives the date. He shows by metrical analysis that the Latin is not poesy and is therefore probably not a quote. Noting the link that Cicero draws between Ennius and the Annales Maximi, and the likelihood that the Annales Maximi supported a mid-eight century chronology rather than an early ninth century (or late 12th century) one for the foundation of Rome, he opts for the date being Ciceronian rather than Ennian. I suspect he slightly misstates the case: the Annales Maximi probably did not cover the period of the early kings, but ipso facto they would also not have mention an eclipse in c. 520, the latest date possible on the presumed Ennian chronology. Moreover, the fact that Cicero places the statement in an analytical context suggests to me that this conclusion is correct.

Solution Constraints

There are several classes of solution, summarised in N. Prack, Der römische Kalendar (264-168 v. Chr.) 19ff.

1. The first set of solutions take the date and the description of the eclipse literally. Assuming the Varronian chronology, or something close to it, this has resulted in the following proposals of candidate eclipses:

   • Non. Iun. c. A.U.C. 350 = 3 September 404.
     

   • Non. Iun. c. A.U.C. 350 = 18 January 402.
     
   • Non. Iun. c. A.U.C. 350 = 21 June 400.
     
   • Non. Iun. c. A.U.C. 350 = 14 August 394.
     
   • Non. Iun. c. A.U.C. 350 = 12 June 391.
     
   • Non. Iun. c. A.U.C. 350 = 5 November 380.

   Other eclipses visible from Rome in the period 400+25 years that apparently have not been considered as possible solutions are:

   • Non. Iun. c. A.U.C. 350 = 1 June 409
     

   • Non. Iun. c. A.U.C. 350 = 20 March 405
     
   • Non. Iun. c. A.U.C. 350 = 5 November 399
     
   • Non. Iun. c. A.U.C. 350 = 4 September 377.

2. The second set of solutions assume that the MS tradition is corrupt, and have proposed emendations to the year:

   1. K.-J. Beloch, Hermes 57 (1922) 119, proposed that the text should be emended to c. 450 A.U.C. On this basis he proposed the eclipse:

      • Non. Iun. c. A.U.C. 450 = 13 June 288

   2. B. Sepp proposed that the annotation of "CCC" should be ignored, and that "quinquagesimo" (50) should be emended to "quingentesimo" (500). On this basis he proposed the eclipse:

      • Non. Iun. c. A.U.C. 500 = 4 May 249

      R. Knapowski, for reasons apparently given in an unpublished lecture, has proposed the equation:

      • Non. Iun. c. A.U.C. 500(?) = 5 May 230

   3. W. Soltau, Römische Chronologie 186ff, followed by P. S. Derow, Phoenix 30 (1976) 265 at 268 n. 3, suppose that Cicero originally intended c. 550 A.U.C., a date which allows Ennius himself to have seen this eclipse. On this basis they propose the eclipse:

      • Non. Iun. c. A.U.C. 550 = 6 May 203

      The fact that this equation is consistent with the date range for Non. Iun. A.U.C. 551 = 5-7 May 203, arrived at by completely independent arguments, is seen by Derow as verification for this solution.

      Finally, E. Stein proposed two alternate eclipses assuming the same emendation:

      • Non. Iun. c. A.U.C. 550 = 17 July 188
        

      • Non. Iun. c. A.U.C. 550 = 6 August 179

      But at this time Iunius corresponds more closely to February than to July/August.

Derow's argument in support of the eclipse of 203, that the date can be arrived at by a completely different line of analysis, does not consider the possibility that this could be due to chance. Given that the Republican calendar tended to approximate a solar year, one suspects Derow has underestimated the probability of the match being just a coincidence. Moreover, not only does the date not match a literal reading of Cicero's words, but the peak magnitude of the proposed eclipse (c. 40% at Cumae) hardly corresponds to Ennius' description. Nevertheless, it is not hard to persuade oneself that the date could easily be corrupt, and should be corrected to reflect an eclipse that occurred during Ennius' lifetime (though the eclipse of March 190 was surely a much more dramatic candidate); and that Ennius' description was explanatory, not observational, and therefore implies nothing about the magnitude of the eclipse.

That being said, it seems to me to be much harder to explain away the value of an eclipse on such a date to Varro's chronological analysis -- a point Derow completely ignores. Since Varro was evidently trying to reconstruct the chronology of the period around the eclipse, it follows that he perceived there to be a significant discontinuity or uncertainty in the record between that time and his own lifetime. If we can determine the date of that discontinuity then we have a terminus ante quem for the eclipse. This raises the vexed and fascinating question of determining what point the dates in Roman historical narrative become reliable -- or rather, the slightly different question of determining when Varro believed the Roman historical narrative became reliably dated.

The primary records are now all lost. The one about which we have most information was a series of annual tabulae maintained by the pontifex maximus. These were the basis of the document here referred to by Cicero as "the Annales Maximi" (other names are known). As far as we can tell, the tabulae were maintained from the early days of the Republic until c. 130, when they were discontinued by the pontifex maximus P. Mucius Scaevola. They appear to have been transcribed into a set of annals on an ongoing basis while they were maintained -- the "Annales Maximi" of Cicero. At some point, they were published in a redacted form of 80 volumes. This is often supposed to have been by Scaevola, though B. W. Frier, Libri Annales Pontificum Maximorum has plausibly argued against this and suggested that this was done as part of Augustus' religious reforms, at which time the original annals may well have been destroyed.

The tabulae are said to have been headed by listings of the year's magistrates, and to have contained records of events such variations in grain prices, and eclipses and other portents. Thus we can safely say that they were sufficiently complete to provide the basis of fasti consulares and fasti triumphales. However, we have no explicit indication as to whether the tabulae contained intercalary data. At first sight Censorinus' comment that Varro was able to retrieve exact dates using eclipse records suggests that they did. But we are perhaps assuming an unjustified degree of precision if we understand Censorinus to mean that Varro's results were an exact calendrical reconstruction of the sequence of intervening Roman years. It seems rather more likely that Varro only established a Varronian year corresponding to a given eclipse, e.g. that he established that the eclipse of Ennius -- and hence the consular year of the corresponding consuls -- occurred in A.U.C. 351 rather than, say, A.U.C. 352. That is, Varro believed he was able to establish a series of synchronisms between eclipses recorded in years whose position was already approximately known. The eclipse records he used were certainly dated according to a more regular calendar, most likely the Egyptian calendar used at Alexandria. At most, he only needed an approximate model of how intercalation was managed, such as the scheme described in Macrobius, Saturnalia 1.13.11-14, in order to correlate such dates with Roman years; he did not need one that was perfectly accurate.

Thus, we are looking for the latest point where uncertainty about the year of an event, rather than its exact date, may have occurred in the primary records as they existed in Varro's time.

The most obvious such point is the sack of Rome by the Gauls in c. 387. Indeed, though the extent of the loss may be overstated, Livy 6.1 records a tradition that earlier records were lost in this event, and some later historians even considered that pre-Gallic records were wholesale forgeries (see e.g. Plutarch, Numa 1.1). 387 is right at the end of the period in which the eclipse of Ennius must have occurred if the date given by the surviving MS is taken literally. An eclipse that occurred only a few years before the sack would certainly allow Varro to anchor the records for the preceding epoch to a precise date, even if it was not necessarily an accurate one (since Varro may, for example, have chosen the wrong eclipse). Thus, an eclipse in the late 400s or the 390s, rather than one in the late 200s, is very likely to have been of great interest to Varro as a potential chronological anchor.

It is evident that uncertainty extended to later periods. The date of the Gallic sack was synchronised by Greek authors, for reasons that are not now known, with the Peace of Antialcidas in Ol. 98.2 = 387/6, and this synchronism was accepted by Roman authorities. But the fasti consulares are short by 5 years on this basis. These are made up in three different ways by surviving historians, and Varro himself combining two of them -- thereby adding an additional four years. As part of this he made up the fifth year by allocating it to a (historically brief) dictatorship as late as A.U.C. 453 = 301. This shows that fourth century chronology was arguable to the Romans of Varro's time.

However, it seems hard to extend any period of doubt far into the third century. The traceable tradition of Roman historical writing began in the late third century. These writers, all now lost except in fragments, wrote in an annalistic form. The earliest was Q. Fabius Pictor, who wrote in the early years of the Second Punic War, and was able to speak from personal experience of events going back to the First Punic War. Thus, active and accurate Roman historical scholarship was certainly in full swing by the late third century, and it seems impossible to argue that the dating of A.U.C. 551 = 203 could have been a point of uncertainty for Varro. For this reason, the plain meaning of Cicero's words should be accepted for the date of the eclipse: it was around (but not exactly) A.U.C. 350, i.e. c. 400 B.C.

Calendrical Analysis

Censorinus and Macrobius state that intercalations occurred in alternate years and were of alternate length. The data for the period before the Second Punic War could be consistent with this model. Such a rule consistently applied would result in a constant average drift against the Julian year of 1 day per year (2x355+377+378 = 1465 vs 4x365+1 = 1461 days in 4 years). If this rule is correct, then we ought to be able extrapolate backwards from the most likely date for the point at which that model breaks down -- Kal. Ian. A.U.C. 535 = 15 January 218 + 3 days -- and wind up within a few days of one of these eclipses.

This extrapolation gives the following results for the candidates that have been proposed:

• Non. Iun. A.U.C. 350/1 = 24 December 404. Distance to 3 September 404 = +112 days
  

• Non. Iun. A.U.C. 352/3 = 16 December 403. Distance to 18 January 402 = -33 days
  
• Non. Iun. A.U.C. 354/5 = 24 December 400. Distance to 21 June 400 = +186 days
  
• Non. Iun. A.U.C. 360/1 = 4 January 393.      Distance to 14 August 394 = +143 days
  
• Non. Iun. A.U.C. 362/3 = 5 January 391.      Distance to 12 June 391 = -159 days
  
• Non. Iun. A.U.C. 374/5 = 17 January 379.    Distance to 5 November 380 = +73 days

None of these are close enough to claim a match between the eclipse and a simple extrapolation of the Macrobian model. Clearly, the other eclipses in this period that have not been considered -- 1 June 409, 20 March 405, 5 November 399 -- will not give a closer match. The eclipse of 18 January 402 is the closest, and Matzat, Römische Chronologie, fell for that temptation. It is nevertheless necessary to omit two intercalations to reach a distance of +12 days, and then one must still imbalance the ratio of 22:23 day intercalations by moving 12 intercalations (out of 80) from 22 to 23 days. Alternately, one must imbalance the ratio by moving 33 intercalations from 23 to 22. With no actual data to guide us, such manipulations are just cooking the books.

There is one other indication that the sequence of intercalations was more complex than the biennial intercalations that Macrobius implies. If festival-based dates in Februarius indicate candidate intercalary years, then odd years A.U.C. should not have such dates on this model. But triumphs are recorded on [Quiri/Termi]nalia AUC 393 = 361 and Quirinalia AUC 481 = 273. The last was only three years after a triumph on the Quirinalia of AUC 478 = 276.

We must therefore discard the biennial Macrobian model if we want to identify the eclipse.

Having given a circumstantial argument for an early date for the eclipse, and havng shown that the biennial Macrobian model cannot account for its date, it is hard to refrain from trying my hand at coming up with a solution for the synchronism. A spreadsheet (given only in Excel format) available here shows the possible solutions for all solar eclipses visible at Rome in the region 390 B.C. + 25 years. It also shows the number of intercalations, and the possible ratios of 22 to 23 intercalations, required to reach a given eclipse date from the nearest certain Non. Iun., Non. Iun. A.U.C. 564 = 7 February 190.

There are several clues as to which is the right one. First, as noted above, B. W. Frier, Libri Annales Pontificum Maximorum, 117 n. 26, noted that the "nox" in Ennius' description of the eclipse ("Nonis Iunis soli luna obstitit et nox") may well imply an eclipse at sunset, though it does not necessarily do so. The eclipses of 20 March 405 (magnitude 0.693 at sunset), 21 June 400 (magnitude 0.726 at sunset), 5 November 399 (magnitude 0.645 at sunset) and 12 June 391 (magnitude 0.594 at sunset) all meet this condition.

Next, we can assess the impact of the eclipse on the Varronian chronology. As is discussed above, the consular fasti for the fourth century are defective in two respects: the four so-called "dictator years" and the four "years of anarchy". These phenomena both appear in the Varronian chronology. They appear to be devices introduced to reconcile the fasti with dates determined by other means. Since we know that Varro based his chronology at least partly on an eclipse, this suggests that Varro identified the wrong eclipse, choosing an eclipse that was about 4 years earlier than the correct eclipse. In this period, three pairs of eclipses are separated by about this distance: (1 June 409, 20 March 405), (3 September 404, 21 June 400), and (18 January 402, 5 November 399).

Next, Livy 8.20 notes that L. Aemilius Mamercinus & C. Plautius took office as consul on Kal. Quin. A.U.C. 425 = 329 (Varronian), and Livy 5.32 notes that a set of consular tribunes took office on Kal. Quin. A.U.C. 363 = 391 (Varronian), which suggests that this was the normal date at that time (although it had been Id. Dec. as recently as A.U.C. 352 = 402 (Varronian) -- see Livy 5.9). Since in the third century consular terms appear to have begun in early spring, this suggests that in the early fourth century, when the start of the consular year was moved from Id. Dec. to Kal. Quin., Quintilis generally fell in early spring, which in turn suggests that at the time of the eclipse Iunius was approximately aligned with February, March or April. Only one of the candidate eclipses meets this condition, the eclipse of 20 March 405.

Finally, we can examine the number of intercalations, and the ratio of 22 to 23 intercalations, required to reach a given eclipse date from the nearest certain Non. Iun., Non. Iun. A.U.C. 564 = 7 February 190, to assess whether they conform to a known regulatory model. We can also assess the amount of drift required to reach an approximate Julian alignment in c. 450, on the assumption that the calendar was initially well aligned to the seasons when it was created by the Decemvirs.

The following solutions are of interest:

• 20 March 405: 94 intercalations of 23 days.

  It appears that the Lex Acilia of A.U.C. 563 = 191 introduced the use of pairs of intercalary years to correct calendrical drift, and that the 22 day intercalation only appears in the first year of an intercalary pair after that date. This could suggest that all intercalations were of the same length -- either 22 or 23 days -- before that time. The above solution is consistent with this idea, favouring 23 day intercalations both before and after A.U.C. 563 = 191.

  For an even distribution, this solution gives 87 intercalations between the eclipse and the start of the Second Punic War in 218 on the model adopted here, implying intercalations in alternate years with 4 intercalations separated by 3 years from their predecessor.

  The number of intercalations in that war are disputed, but it is universally agreed that there was only one intercalation between A.U.C. 553 = 201 and A.U.C. 563 = 191 (inclusive). For an even distribution over the period between the eclipse of Ennius and 201, this solution gives 18 intercalations separated by 3 years from their predecessor.

  The Roman calendar is about 76 days ahead of the Julian year on this model. This requires significant under-intercalation since the Decemviral reform, with approximately 6 intercalations being omitted since the Decemviral reform out of a nominal c. 22 biennial intercalations.

• 12 June 391: 86 intercalations, 43 each of 22 and 23 days.

  This distribution conforms exactly to the algorithm of Censorinus and Macrobius that intercalations alternated in length, though it does not match the frequency distribution implied by that algorithm.

  For an even distribution, this solution gives 79 intercalations between the eclipse and the start of the Second Punic War in 218 on the model adopted here, implying intercalations in alternate years with 16 intercalations separated by 3 years from their predecessor.

  The number of intercalations in that war are disputed, but it is universally agreed that there was only one intercalation between A.U.C. 553 = 201 and A.U.C. 563 = 191 (inclusive). For an even distribution over the period between the eclipse of Ennius and 201, this solution gives 10 intercalations separated by 3 years from their predecessor.

  The Roman calendar is well aligned to the Julian year on this model. This requires that about 3 intercalations have been omitted since the Decemviral reform out of a nominal c. 30 biennial intercalations.

• 20 March 405: 96 intercalations, 46 of 22 days and 50 of 23 days.

  This distribution is close to the algorithm of Censorinus and Macrobius that intercalations alternated in length, though it does not match the frequency distribution implied by that algorithm.

  For an even distribution, this solution gives 89 intercalations between the eclipse and the start of the Second Punic War in 218 on the model adopted here, implying intercalations in alternate years with 5 intercalations separated by 3 years from their predecessor.

  The number of intercalations in that war are disputed, but it is universally agreed that there was only one intercalation between A.U.C. 553 = 201 and A.U.C. 563 = 191 (inclusive). For an even distribution over the period between the eclipse of Ennius and 201, this solution gives 14 intercalations separated by 3 years from their predecessor.

  As noted above, the Roman calendar is about 76 days ahead of the Julian year on this model. This requires significant under-intercalation since the Decemviral reform, with approximately 6 intercalations being omitted since the Decemviral reform out of a nominal c. 22 biennial intercalations.

• 5 November 399: 99 intercalations, 51 of 22 days and 48 of 23 days.

  This distribution is also close to the algorithm of Censorinus and Macrobius that intercalations alternated in length, though it does not match the frequency distribution implied by that algorithm.

  For an even distribution, this solution gives 92 intercalations between the eclipse and the start of the Second Punic War in 218 on the model adopted here, implying intercalations in alternate years with 2 intercalations that were consecutive with their predecessor.

  The number of intercalations in that war are disputed, but it is universally agreed that there was only one intercalation between A.U.C. 553 = 201 and A.U.C. 563 = 191 (inclusive). For an even distribution over the period between the eclipse of Ennius and 201, this solution gives 3 intercalations separated by 3 years from their predecessor.

  The Roman calendar is about 153 days behind the Julian year on this model. This requires that about three intercalations have been omitted since the Decemviral reform if intercalation was normally biennial.

Conclusions

Combining all these indications together, the most likely solution appears to be the eclipse of 20 March 405. This is a sunset eclipse in spring, occurring shortly before the start of the consular year was moved from Id. Dec. to Kal. Quin. (via a brief stay on Kal. Oct.), which is when Kal. Quin. is most likely to have been in spring. It also occurs about four years after an eclipse with a Julian date that is close to Non. Iun., which suggests that Varro misidentified it as the elipse of 409.

However, there is a strong objection: the Julian date of this eclipse is not close to Non. Iun., and the amount of under-intercalation required to create such a mismatch from a Decemviral calendar aligned to the seasons in c. 450 is significant. The distance between the Decemviral reform and the putative eclipse date -- c. 45 years -- is close to 6 octaeteres. The only regular intercalary schema that I can see which would produce this amount of under-intercalation is a (2, 3, 3) octaeteris in which the intercalary months were inserted in the Roman fashion to add 22 or 23 days to the year, and not in the Greek fashion of adding an extra lunar month.

Although no such scheme appears directly in the literary sources, it is perhaps not as unlikely as it seems. There is a tradition, generally rejected as unhistorical by modern scholars, that the Decemviral reforms were the result of a Roman embassy to Athens (Livy 3.31-3.32), and Macrobius, Saturnalia 1.13.11 describes pre-Julian intercalation as an octaeteris adapted from the Greek model. The scheme of alternating 22 and 23 day intercalations described in Macrobius, Saturnalia 1.13.12 would more accurately be described as a tetraeteris, and the effect of adopting this scheme would certainly be to over-intercalate. If this scheme were adopted shortly after 405, it would take about 80 years to realign the calendar to the correct seasonal position.

Even if this date is correct, it does not help us decide what scheme was used to set the length of intercalary months in the period betwen 405 and 191. It gives a distribution of intercalations that requires that all intercalations were of the same length (23 days) before the Lex Acilia, which could explain the rarity of 22-day intercalations after that period, as well as a distribution which gives nearly equal numbers of 22 and 23 day intercalations, which would fit the scheme of alternating lengths described by Macrobius.

14 Jan 2012: Revise discussion to cover Rüpke's suggestion that Ennius' date was retrocalculated, and to consider drift since a presumably aligned Decemviral reform

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