mirrored file at http://SaturnianCosmology.Org/ For complete access to all the files of this collection see http://SaturnianCosmology.org/search.php ========================================================== *Egyptian Dates* This page gives access to a set of conversion tables for determining the Julian equivalent of Egyptian civil and lunar dates in the Ptolemaic era. Two tables are provided: a table converting civil dates to Julian dates, and a table notionally converting lunar dates to civil dates according to the lunar cycle of /pCarlsberg/ 9. In this section, several topics are discussed: * *The regnal eras * * *The **Carlsberg ** cycle * * *The financial year * * *The Alexandrian reform * * *The Soter era * *The Wandering Year* Egyptian dates from the Ptolemaic period are dated according to the wandering civil year. Knowledge of the structure of the wandering year has never been lost. The astronomical works of Claudius Ptolemy, the most famous of which today is the /Almagest/, which were based on this calendar and required knowledge of its structure, continued to be used by scientists, first Arab and Byzantine, and then Western, throughout the Middle Ages. The alignment between the wandering Egyptian calendar and the Julian calendar in the Ptolemaic period -- a constant drift of 1 day every four years -- is generally assumed without proof. If there is discussion of proof, a pointer is usually made to the Canopic Decree (OGIS 56) of year 9 of Ptolemy III = 238. This decree was an attempt to reform the Egyptian calendar which, according to the decree itself, was wandering by a day every four years against the heliacal rising of Sothis, which occurred at that time on 1 Payni. Equating Sothis to Sirius, a second rising of Sothis is reported on 1 Thoth = 20 July AD 138 in/ /Censorinus 21.10 . Since the drift from 1 Payni to 1 Thoth is what would be expected if the calendar continued to wander at the same rate, the two observations are held to confirm that there was no change in alignment. QED. There are some difficulties with the fine detail of this account, discussed in P. F. O'Mara, /JNES/ 62 (2003) 17. The MS tradition dates the event to a.d. XII Kal. Aug. -- 21 July -- not 20 July (a.d. XIII Kal. Aug.). This is universally corrected to a.d. XIII Kal. Aug. since Censorinus also says in the same section that in the year he is writing, 100 years later (A.D. 238), 1 Thoth corresponds to a.d. VII Kal. Jul. (25 June) and in 100 years the drift of 1 Thoth against the Julian calendar is 25 days not 26. A second issue is that 1 Payni in 238 corresponds to 19 July 238, not 20 July (let alone 21 July) on a constant drift. Several explanations of this discrepancy are possible. The two most plausible are as follows: * M. F. Ingham, /JEA/ 55 (1969) 36, noted that the astronomical Sothic cycle is actually slightly different from the cycle of 1460 Julian years assumed by ancient authors, and the cycle ending c. AD 138 was slightly shorter, at c. 1456 years. This means that the heliacal rising gains 4 days against the Julian calendar over the course of the cycle, so that a 1 day discrepancy can be explained by a gain of a day between 238 B.C. and A.D. 138, a distance of slightly over a quarter of the cycle. * P. F. O'Mara, /JNES/ 62 (2003) 17 argued that Censorinus' prime purpose was to exalt the birthday of his patron. He noted that ancient authorities apart from Censorinus gave a number of dates for the heliacal rising, ranging from 19 July to 22 July. He supposed that Censorinus selected the one most appropriate to his purpose, as occurring exactly a century before the birthday in question. These issues are important for calibrating the Sothic cycle as a chronological yardstick for deeper Egyptian chronology. However, since the distance in years between the Canopus Decree and Censorinus is firmly established, the discrepancies involved are too small to invalidate the argument that the Canopus Decree shows a constant drift over this period. Nevertheless, while the explicit statement of the Canopic Decree is clearly sufficient evidence for constant drift before 238, the validity of the argument for the years immediately after the decree has been challenged by radical chronological revisionists of various stripes. The Velikovskian school, for example, claims that the Sothis of the Canopus Decree is not Sirius but the planet Venus. Such assumptions require that the Canopic reform was effective for some considerable time, despite, for example, the absence of any wandering / fixed double dates comparable to those found between the wandering and Alexandrian calendars in Roman times. These arguments are generally not taken seriously by the academic community, but they have at times attracted great attention in the media and in circles of interested and intelligent laymen. As a pedagogical exercise and as an exercise in intellectual method, therefore, there seems to be value in constructing additional analyses that confirm (or, in principle, refute) that the drift of the Egyptian year against the Julian year was constant throughout the Ptolemaic Period. Moreover, such an analysis will provide additional evidence of the identity of the Sothis of the Canopus Decree. One class of evidence that confirms the correctness of the standard model which is not discussed here is a set of double dates in the Aramaic Elephantine papyri from the 5th century BC, as was noted by L. Depuydt, /JARCE/ 32 (1995) 43. This analysis is surely correct, but to prove it requires a study of the chronology of the Achaemenid period. In the following discussion, I seek to address this issue using data provided by contemporary, classical and Hellenistic sources. _Alignment of the Wandering Year in the First Century A.D._ To begin at the beginning, I am aware of one direct synchronism between the wandering year and the Julian calendar from a contemporary document that certainly predates both Censorinus and the /Almagest/: * /pLond/. 130: Year 3 Titus, 6 Pharmouthi = 1-2 Pachon ("old") = Kal. Apr. [= 1 April A.D. 81] /pLond/. 130 is a horoscope recorded at the third night hour, and also gives the current civil date as 6 Pharmouthi. O. Neugebauer & H. B. van Hoesen (/Greek Horoscopes/ 23, 25) point out that the double wandering date represents a night between two successive Egyptian days, and therefore that the civil and Roman dates are starting at sunset. The proleptic wandering date corresponding to 1 April 81 is 2 Pachon, matching the daylight portion of Kal. Apr. year 3 of Titus. I would be interested to learn of any other early synchronism of this type. The same papyrus also provides the earliest synchronisation between the Julian calendar (i.e. after the completion of the Augustan reform) and the Alexandrian calendar, the fixed Egyptian civil year. The earliest unambiguous synchronism between an Alexandrian date and the wandering year I have found is /pRyl/ 2.381: Year 4 Caligula, 4 Mesore = 20 Mesore ("Egyptian") [= 28 July A.D. 40]. These synchronisms clearly establish the alignment of the wandering year in the first century AD, which is then the starting point for studying the projection of that alignment into Ptolemaic times. _Bounds on the Canopus Decree __s__et by Egyptian Lunar Double Dates_ The first set of evidence outside the Canopic Decree is provided by the Egyptian lunar / civil double dates. These allow us to bound the maximum drift between the historical civil calendar and the proleptic civil calendar that is under test. Supposing the Canopic reform to have been effective up to some year X, so that the historical civil calendar matches the proleptic calendar _after_ date X, this drift should increase by one day for every four years before X until we reach 238. The effect is that a lunar conversion based on the proleptic calendar should be increasingly later in the lunar cycle. For example, if the reform were effective for 120 years, a lunar conversion should be essentially correct in c. 120, 15 days out of phase in c. 180 and in phase again by c. 240, having slipped by an entire lunar cycle. The following table shows the alignment of the five explicit civil/lunar Ptolemaic double dates, on the assumption that the proleptic civil calendar was historically accurate. For comparison the expected drift for a fixed calendar based on the Canopic reform is also given: [..] The lunar calendar should have shown substantial phase differences for all but the first civil date if the Canopic calendar had been in effect. Evidently, however, it maintained a fixed phase relationship to the proleptic wandering civil calendar from at least 237 onwards. We may conclude that the lunar double dates prove that there was _at most_ one or two leap days under the Canopic reform. This result severely limits the range of possible Julian dates for 1 Payni year 9 of Ptolemy III, to 17-19 July 238. This in turn is sufficient to prove that the Sothis of the Canopic Decree must be Sirius since no other stellar or planetary event of similar magnitude occurred within the period 17-19 July 238. Conversely, for each additional leap day supposed to have occurred after the Canopic reform, the date of the heliacal rising of Sirius, 19 July 238, must be pushed one day later in the _pre-reform_ calendar. That is, if there was 1 leap day after 238, then 19 July 238 should correspond to 2 Payni year 9 of Ptolemy III, not 1 Payni, in the calendar of OGIS 56; if 2 then 3 Payni etc. Censorinus dates the rising of Sothis to 20 July, not 19 July. On the ideal Sothic cycle normally posited by Egyptologists, in which Sothis moves through the Egyptian calendar in 1461 Egyptian years = 1460 Julian years, the Julian date in 238 should still be 20 July in 238. But, as noted above, the astronomical Sothic cycle is slightly shorter than the ideal cycle of 1460 years, so a date of 19 July is quite in order. However, this argument does not allow an earlier date. Moreover, there is classical astronomical testimony for the date of the heliacal rising from Dositheos, a third century Alexandrian astronomer who was a contemporary of the Canopus Decree (P. F. O'Mara, /JNES/ 62 (2003) 17 at 18 n. 5 suggests he might even have been the designer of the reform.) Geminus, /Elementa Astronomiae/, preserves a collected parapegma, or a list of dates of the annual risings and settings of stars combined with weather predictions as cited by various authors. Geminus cites Dositheos as dating the heliacal rising of Sirius to day 23 of a count starting with the summer solstice. In the mid third century, the summer solstice occurred on 26/7 June, so the heliacal rising, for Dositheos, occurred on 18/9 July. Furher support comes from /pdem/ Berlin 13146+13147, a table of lunar eclipse possibilities (discussed further below <#pdem Berlin 13146+7>) with an accompanying statement of algorithms for calculating the civil dates of solstices and equinoctes. O. Neugebauer et al., /Proc. Am. Phil. Soc. /125 (1981) 312 showed by analysis of the eclipse data that it covers the period 84 to 74. By the above discussion, this is well after any attempt to effect the Canopic Decree had failed, and the Egyptian dates given for the eclipses are correct on the modern understanding of the civil calendar. The algorithm given in /pdem/ Berlin 13146+13147 for calculating the date of the summer solstice starts by subtracting 22 days from 10 Epeiph. R. A. Parker & K.-T. Zauzich in D. W. Young, /Fs. Polotsky/ 472, showed that this gives the correct Egyptian dates for the solstices and equinoctes in the early first century if 10 Epeiph is dated to 84, the year of the first eclipse, in which year 10 Epeiph = 19 July. Hence the date should be interpreted as the canonical date of the rising of Sothis. _Non-Canopic Astronomical Dates__._ The next set of evidence is the Ptolemaic-era astronomical observations recorded in the /Almagest/ and /pdem/ Berlin 13146+13147. These observations cover most of the first two centuries of the Ptolemaic period. They are dated according to the Egyptian wandering year, with years usually assigned to the Era of Nabonassar (or, less often, the Era of the Death of Alexander ). The wandering year used by Claudius Ptolemy is exactly aligned with the wandering year reflected in Roman-era records, and the observations he dates by it are mostly confirmed by modern calculations. The following is the list of explicitly and precisely dated observations, grouped by apparent source, in chronological order per source (from the translation by G. J. Toomer, /Ptolemy's Almagest/ -- section highlighted in green), of the observations gives from before his own time: [..] Menelaus at Rome It is evident that many of Ptolemy's dates have been redacted from the original source dates into the Egyptian calendar. In other words, what Ptolemy uses is an _astronomical_ wandering year. The chronological question is whether a date in that specialised, technical calendar was also the date of the same day in the _historical_ civil year of Ptolemaic times, or whether it is simply a proleptic projection of the astronomical wandering year used in Ptolemy's own time, the second century A.D., rather as we use the Julian calendar to date events before 1 B.C. In order to address this question it is necessary to trace the history of the astronomical wandering year itself, to determine, if we can, at what point it came into existence in the form that Ptolemy uses it. This is primarily an exercise in source criticism of Ptolemy's text. Fortunately, Ptolemy identifies the ultimate source for many of his observations, and frequently gives double dates for the observations he uses. Where he does not do so, the evidence of the dates themselves suggests that it is either because the source dates were not available to him (e.g. for the pre-Hellenistic Babylonian observations, only one of which is independently known from the Babylonian astronomical diaries), or because the source dates were already in a usable and canonical form (e.g. the observations of Hipparchus and Menelaus.) It is not precisely known what earlier sources were available to Ptolemy. The latest named source for pre-Roman observations is Hipparchus, active in the middle of the second century B.C. However, A. Jones, /AHES/ 54 (1999) 255, has drawn attention to /pOxy/ 61.4133, a fragment of a treatise similar to the /Almagest/ that described an observation of Jupiter's position in A.D. 104/105, and which referred to an earlier observation made on 30/1 December 241 B.C., the details of which are unfortunately lost. This date is a little under three months after an observation of Jupiter reported by Ptolemy for 10 Parthenon year 45 Dionysian Era = 3/4 September 241. Jones suggests the author of this treatise was possibly Menelaus of Alexandria, cited by Ptolemy for an observation in A.D. 98, and that he was the proximate source of at least some of Ptolemy's observational data. The first point to note about the observational dates is that Ptolemy does use a wandering year, not only for the Nabonassar era dates that the earlier observations have been translated into but also for his own observations (not listed here). Although he lived in the Antonine period, he never uses, or even mentions, the fixed civil year which by then had been stable for well over a century, although he does use it in the /Phaseis /. This fact alone suggests that Ptolemy's wandering year was already in use for astronomical purposes in Ptolemaic times. Direct evidence of this is supplied by /pdem/ Berlin 13146+13147, a table of 23 (surviving) lunar eclipse possibilities with an accompanying statement of algorithms for calculating the civil dates of solstices and equinoctes. Although the papyrus has significant lacunae, O. Neugebauer et al., /Proc. Am. Phil. Soc. /125 (1981) 312 was able to show by analysis of the eclipse data that it covers the period 84 to 74. The eclipse years are dated, and A. Jones, /ZPE / 129 (2000) 141 , showed that the dates refer to years in the 4th Callippic cycle , used in the /Almagest/ for dates provided by Timocharis and Hipparchus. J. M. Steele, /Observations and Predictions of Eclipse Times by Early //A//stronomers/ 89, noted that an eclipse cycle of 23 eclipses in 135 synodic months was known in Babylon, and suggests that this papyrus may have been intended to cover one complete cycle of this type, though he also allows the possibility that it is part of a Saros cycle of 223 synodic months. While the table is mostly written in the future tense, it occasionally includes detail in the past tense which must have been observed. Thus, the papyrus transcribes a compilation made in the late 70s, well before the Roman conquest, and clearly shows that the astronomical wandering year was in use at that time. The fact that it was not necessary to translate dates for observations made or reported by Hipparchus shows that the Hipparchan dates represent the dates that Hipparchus himself used. Hence we may safely say that the astronomical wandering year was unchanged at least from Hipparchus' time onwards. Further, it appears that Hipparchus also included the source dates of his own sources where possible, notably the three eclipses of 383/2 correlated with Athenian months. The three lunar eclipse observations reported by Hipparchus in 201 and 200 are specifically noted as having been made in Alexandria. Since neither Hipparchus nor Ptolemy translate the dates, we can accept these as also being the dates in the report Hipparchus used. Hence the Hipparchan observations bring the demonstrable use of the astronomical wandering year back to 201. The two observations dated by the regnal years of Egyptian kings were certainly made in Alexandria. The first is said to have been reported by Timocharis, who was based in Alexandria, and the second is the report of an eclipse that Ptolemy explicitly states was made in Alexandria. Both observations are given using the double-day convention for night-time observations that was used by Ptolemy and Hipparchus themselves, and only the regnal year is translated into the Nabonassar era. The second observation may well be in the original form, but since it was made 25 years after the three Hipparchan eclipse observations it does not advance our /terminus ante quem/ for the astronomical wandering year. There are three indications, however, that the first of these observations has been manipulated between the time of Timocharis and the source used by Ptolemy. * First, the regnal year 13 is dated according to the coregency epoch of Ptolemy II. This epoch is not otherwise provably recorded for contemporary (as opposed to retrospective) Egyptian dates before year 19. Against this, however, it is not unreasonable to suppose that the coregency epoch may have been used for the Egyptian calendar in court circles since this era was used for Macedonian dates starting in year 4. * Second, all other surviving observations associated with Timocharis have the form = , but this one has no associated Athenian date. * Third, the Egyptian date associated with other Timocharan observations gives a single day number even for nighttime observations, but this observation is given with two dates, which is the later convention for nighttime observations. For these reasons, we cannot be confident in concluding that the date we have is in the form that Timocharis reported it, and therefore cannot estimate when it took this form. The three observations dated according to the "Chaldean" calendar (i.e. the Seleucid era) also do not allow us to determine when they were translated into the astronomical wandering year. This calendar was still current in Ptolemy's time, so transmission and translation could have occurred at any intermediate point. The case of the observations recorded according to the Dionysian era (which is unknown outside the /Almagest/) is more complex. This era was certainly an Alexandrian era, since it coincides with the accession of Ptolemy II as a coregent; A. Jones, /Centaurus/ 45 (2003) 69 has recently published scholia on the Almagest confirming that Dionysios was an Alexandrian astronomer. B. L. van der Waerden, /AHES/ 32 (1985) 95, has also suggested that the Dionysian calendar governed the astrometeorological parapegmata that are described as being "of the Egyptians". Since it is not known after the reign of Ptolemy III, one might reasonably suppose that the Egyptian equivalent of the Dionysian dates was established early, implying that these conversions were done at the latest in the late third century. However, Ptolemy mentions a conclusion that Hipparchus had drawn from the evidence of the observation of 28 Leonton year 24, which is evidence that he knew of this data through Hipparchus. But Hipparchus himself did not use the Era of Nabonassar, which is the form in which we know the conversions. Hence we may infer that Ptolemy, or some intermediate source, was responsible for the conversion into the form given in the /Almagest/, and that the original translations, if they existed, were discarded in the process. Further, A. Jones, /Centaurus/ 45 (2003) 69 at 73, further points out that "several of the observations do not best fit the Egyptian dates to which Ptolemy assigns them", suggesting that the conversions were based on an incorrect understanding of the Dionysian calendar. If correct, this would imply that the conversions were done much later than the third century. Unfortunately, he does not discuss better fits that might reveal the correct structure of the calendar, which would confirm this conjecture. I think Jones is unlikely to be right, because the calendrical structure implied by the conversions is quite different from any other known zodiacal calendar. Nevertheless, these considerations show that the Dionysian conversions are not safe evidence for the alignment of the astronomical Egyptian calendar in the third century. The oldest set of Hellenistic observations, and the most important for our purpose, are those of Timocharis. All but one of them are triple-dated, first according to an astronomical Athenian calendar equated to an Egyptian date in the First Callippic Cycle, and secondly with a refinement of the Egyptian date into the convention that Ptolemy generally uses. The purpose of the second conversion is clearly to show that the observations were made in the night following the daytime date given in the first conversion; the dates in the first conversion follow the standard Egyptian day running from dawn to dawn. Since Ptolemy and Hipparchus followed the same double-dating convention for night-time events, and since Ptolemy does not convert Hipparchan dates, we must conclude that the original double-dating was performed before Hipparchus. Since the first conversion does not use the double-dating convention, we may safely conclude that it arose after Timocharis' time. However, it is not immediately obvious that the first conversion was done by Timocharis himself. The key question is in what direction the first conversion took place: Athenian to Egyptian or /vice versa/? The scholars who have studied these dates in recent years suppose that Timocharis originally recorded the observation in the Egyptian calendar and that he or a later scholar subsequently converted this to an Athenian date in some fashion. If so, then these dates are direct evidence that the astronomical wandering year was already in use under Ptolemy I. However, the arguments that have directly addressed the issue of which calendar Timocharis used as his primary calendar are not as strong as one might hope. B. R. Goldstein & A. C. Bowen, /Centaurus/ 32, 272, sought to determine when the need for a lunar / civil conversion would have arisen. They first noted that Timocharis could not have used actual Athenian or Babylonian months, since there was no way for him to know precisely what days they would actually start in those remote cities. Therefore, they concluded that the "Athenian" months must represent a retrocalculated astronomical month. They then noted that the four Timocharan dates implied a lunar month that in each case started one day before first crescent visibility in Alexandria according to modern calculations, and pointed out that these days are precisely the days that would be marked as the start of a lunar month if the /pCarlsberg/ 9 calendar were in use at that time (assuming the reconstruction of R. A. Parker, /The Calendars of Egypt/, 24ff.). They noted that the average month length on the Carlsberg cycle (29.53074 days) is virtually identical to that of a Callippic cycle (29.53085 days), and argued that the Carlsberg cycle was therefore simply derived from the Callippic cycle. They concluded that if Timocharis had performed the first conversion then it follows that the Carlsberg cycle must have already existed in his time. They next argued that the Macedonian calendar was stable until Ptolemy II's reform of his regnal years, which they dated, following A. E. Samuel, /Ptolemaic Chronology/ 26ff., to year 16 = 268/7. For this reason they held that Timocharis would have used the Macedonian calendar to record dates in a lunar form rather than an Athenian one if he had included lunar dates in his original observations. Now, the earliest known double date from the Carlsberg cycle is from 237, and (outside the Timocharis observations) there is no explicit evidence of lunar/civil double dating in the Macedonian calendar before year 22 (Mac.) = year 21 (Eg.) of Ptolemy II = 264. The only earlier Ptolemaic lunar dates known, the Timocharis observation of year 13, and (by inference) year 6 on the Pithom Stele (A. E. Samuel, /Ptolemaic Chronology/ 69ff.), use regnal dates that are coregency-based, which proves that they were reworked after the reform of year 16. Hence they concluded that both the lunisolar "Athenian" Callipic calendar of the Timocharis observations and the Carlsberg cycle were not derived before the mid-third century, probably in response to Ptolemy II's reform. It follows that Timocharis' original dates were the Egyptian dates, and that the "Athenian" dates were retrocalculated at some later time. This analysis is open to some serious objections, of which the ones relevant here are: * It is unversally agreed that the "Athenian" calendar must be schematic, due to the factors Goldstein and Bowen identify. However, it does not follow that the dates were retrocalculated -- they could, for example, have been precalculated into a table similar to /pCarlsberg/ 9. * A. Jones, /ZPE / 119 (1997) 157 showed in detail that the four Timocharan dates are simply not sufficient to determine what algorithm was used to determine the start dates of the "Athenian" months. Both the Geminus and Carlsberg / Parker algorithms are good approximations to the astronomical lunar cycle. It is therefore completely unsurprising that they result in very similar estimates for the length of a synodic month, and the probability that both algorithms will provide the same estimates for the start dates of three months selected at random (the fourth providing the baseline for alignment) is high; Jones estimates 8/27. Therefore there is no basis to assume any connection between the Callippic calendar of Timocharis and the dates of the Carlsberg cycle. * It is simply not true that the Macedonian calendar was stable before year 16 of Ptolemy II. While we have very little positive data from the reign of Ptolemy I, it is absolutely clear that a simple forward projection of a lunar calendar with intercalations every other year, starting with the established date for the death of Alexander the Great, does not align with the calendar as we know it under Ptolemy II -- there are six apparently missing intercalations. Hence there is no basis whatsoever for arguing that the stability of the Macedonian calendar before year 16 of Ptolemy II precludes use of the "Athenian" calendar. * R. A. Hazzard, /Phoenix/ 41 (1987) 140 showed that the reform of Ptolemy II's Macedonian years happened in his Macedonian year 4. Hence the gap between the reform and the earliest clearly documented double date is 17 years. Moreover, the reform only concerned the numbering of regnal years, not the lunar nature of the Macedonian month, nor the alignment of Macedonian to Egyptian years. Hence there is no structural basis for arguing that the "Athenian" calendar was a response to this reform. To my mind, a stronger argument that reaches the same conclusion, based on pragmatic grounds, is implied by B. L. van der Waerden, /AHES/ 29 (1984) 115 at 122. In this paper, he presented an interpretation of the algorithm of Geminus for calculating lunar dates in the Callippic cycle from Egyptian civil dates which satisfactorily explained the Timocharan equations. The key point is that it is much easier to calculate the exact number of days between two events (say, the start of the Callippic cycle and the date of an observation) with the Egyptian calendar than it is to go in the reverse direction, starting with a lunar calendar, even the schematic one assumed by van der Waerden. Whether van der Waerden's particular algorithm represents what was actually done is a moot point -- for example, as noted above, the Callippic rule used by Timocharis may not have been as represented by Geminus. However, _any_ algorithm for calculating a Callippic date must take account of the number of days from the starting point of the Callippic cycle, even if it is only performed once in order to generate handy conversion tables like /pCarlsberg/ 9. For this reason, it is far more likely that the conversions were made from the Egyptian dates to the "Athenian" one than in the other direction. Let us suppose for the sake of argument, however, that Timocharis did originally use the "Athenian" rather than the Egyptian calendar. There are some clear indications that the Athenian calendar was not ordinarily used in Alexandrian astronomy after his time. The Babylonian eclipse observations that are the ultimate source of the ones reported by Ptolemy were translated into Greek by order of Callisthenes in the early 320s. There is no indication that the original Babylonian dates, other than the regnal years, were preserved. If Ptolemy is to be believed, at least the Bablyonian dates of three of the instances reported to him by Hipparchus had been fully converted into Athenian equivalents, which suggests that the Athenian calendar was the basis of Callisthenes' translation. The solstice observation attributed to the school of Meton and Euctemon was also originally recorded as an Athenian date (13 Skirophorion -- Milesian parapegma fragment 84 (e.g. D. R. Lehoux, /ZPE/ 152 (2005) 125 ). Yet almost all of these dates were dropped well before they reached Ptolemy, although the Miletus parapegma shows that the original date of Euctemon's solstice observation was preserved. (It can be shown that this date, 13 Skirophorion in the archonship of Apseudes, is either wrong or, more likely, not from an astronomically based calendar, and was converted to a retrocalculated Egyptian date determined by astronomical theory, probably by Hipparchus -- see A. C. Bowen & B. R. Goldstein, /Fs Sachs/ 39.) Only the Timocharan observations have preserved Athenian day numbers. The three Babylonian eclipses for which Athenian dates survive are only dated by month, and the solstice of Euctemon, do not even have that. The history of the three eclipse records with Athenian dates is controversial -- see J. P. Britton, /Models and Precision: The Quality of Ptolemy's Observations and Parameters/ 61ff. The first, being only a small eclipse starting only a few minutes before sunrise, was almost certainly unobservable in Babylon. Oppolzer in 1881 suggested that they were actually observed in Athens (see also here , at end) and combined with the Babylonian data; against this, B. H. van der Waerden, /MH/ 15 (1958) 106 argued for a reinterpretation of the text that allowed them to have been observed in Babylon. Britton himself supposes that at least the first of these eclipses was actually a calculated eclipse that was misunderstood or mistranslated (by Callisthenes?) as an observed eclipse. If these observations were actually Athenian, this would open up the possibility that even the original conversion of the Babylonian dates was directly into the Egyptian calendar. Against this, however, is that the Egyptian dates in the /Almagest/ use the dual-dated nighttime form, which was certainly unknown to Timocharis, a generation after Callisthenes. Therefore, even if the original conversion to Egyptian dates was done by Callisthenes, the form in which we have the dates suggests that there was a second conversion between Callisthenes and Hipparchus. Finally, the four Timocharan observations date from the reign of Ptolemy I, while the observations from the reign of Ptolemy II (with the one exception of an Egyptian date attributed to Timocharis) are dated by the Dionysian calendar. It is clear that the astronomical Athenian calendar fell into disuse in the reign of Ptolemy II. Since the Timocharan dates were preserved, and since they could not be translated into the Dionysian Era, which they predated, it is most likely that the first conversion into the Egyptian calendar was performed _no later_ than the reign of Ptolemy II -- assuming that they were originally made in the Athenian calendar. Thus, regardless of whether Timocharis used the Athenian or the Egyptian calendar, the formats of his double dates show that the astronomical Egyptian calendar was used throughout the Ptolemaic era, probably from the reign of Ptolemy I, but certainly from well before the Canopic reform. If so, then we must conclude that the astronomical Egyptian calendar was exactly aligned with the historical wandering year throughout the Ptolemaic era. That is, the standard Julian synchronisation with the Egyptian civil year is in fact correct. Website © Chris Bennett , 2001-2005 -- All rights reserved