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Egyptian Dates

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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 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 139 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; see further under the discussion of the Canopic reform. These issues are important for determining the intercalary phase of the Canopic calendar, and 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 calendrical 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 throughout Egyptian society.

These arguments are generally not taken seriously by the academic community. It is usually held that the Canopic reform had no permanent effect on the ordinary Egyptian calendar: either it was never implemented, or (the position held here) it was abandoned after a period of time in which Canopic dates existed alongside wandering dates, as occurred with the later Alexandrian reform. However, 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 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 SB 1.684: Year 17 Tiberius, 18 Tybi ("Greek") = 1 Mecheir ("Egyptian") [= 13 January AD 30].

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 set 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:

Civil Date

Lunar Date

Julian Date
(constant drift)

Lunar Day 1

Nearest Conjunction

Difference

Canopic Difference

III Shomu 13
6 Cleopatra VII

[III Shomu] 5

13 July 46

9 July 46

8 July 46

+1 days

48 days

II Shomu 8
30 Ptolemy VIII

II Shomu 6

2 July 140

28 June 140

28 June 140

0 days

24 days

IV Shomu 18
28 Ptolemy VIII

III Shomu 23

10 Sept. 142

19 Aug. 142

18 Aug. 142

+1 day

24 days

III Shomu 7
10 Ptolemy IV

[III Shomu] 6

17 Aug. 212

12 Aug. 212

12 Aug. 212

0 days

6 days

III Shomu 7
10 Ptolemy III

[III Shomu] 6

23 Aug. 237

18 Aug. 237

18 Aug. 237

0 days

1 day

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 -- independently of Censorinus. 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, since the astronomical Sothic cycle is slightly shorter than the ideal cycle of 1460 years, 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) 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:

Source Date

Nabonassar Era Date

Julian Date (BC)

Observer Notes

Babylonian (Egyptian Calendar)

4.6: 29/30 Thoth year 1 Mardokempad

[None]

19/20 Mar. 721

[None]

4.6: 18/9 Thoth year 2 Mardokempad

[None]

8/9 Mar. 720

[None]

4.6: 15/6 Phamenoth year 2 Mardokempad

[None]

1/2 Sep. 720

[None]

5.14: 27/8 Hathyr year 5 Nabopolassar

[Same] 127

21/2 Apr. 621

[None]

5.14: 17/8 Phamenoth year 7 Cambyses

[Same] 225

16/7 July 523

[= 14 Duzu year 7]

4.9: 28/9 Epeiph year 20 Darius I

[None]

19/20 Nov. 502

Used by Hipparchus

4.9: 3/4 Tybi year 31 Darius I

[None]

25/6 Apr. 491

[None]

School of Meton and Euktemon (Athenian)

3.1: 21 Phamenoth, archon Apseudes

[None]

27 June 432

[= 13 Skirophorion]

Babylonian (Athenian Calendar)

4.11: Poiseidion, archon Phanostratos

26/7 Thoth 366

22/3 Dec. 383

Used by Hipparchus

4.11: Skirophorion, archon Phanostratos

24/5 Phamenoth 366

18/9 June 382

Used by Hipparchus

4.11: Poiseidion I, archon Evandros

16/7 Thoth 367

12/3 Dec. 382

Used by Hipparchus

Timocharis (Callippic Era, Athenian/Egyptian)

 

 

7.3: 25 Poiseidion = 16 Phaophi year 1.36

16/7 Phaophi 454

20/1 Dec. 295

Timocharis

7.3: 15 Elaphebolion = 5 Tybi year 1.36

5/6 Tybi 454

9/10 Mar. 294

Timocharis

7.3: 8 Anthesterion = 29 Hathyr year 1.47

29/30 Hathyr 465

29/30 Jan. 283

Timocharis

7.3: a.d. 6 Pyanepsion = 7 Thoth year 1.48

7/8 Thoth 466

8/9 Nov. 283

Timocharis

Timocharis (Egyptian Calendar)

10.4: 17/8 Mesore year 13 Ptolemy II

[Same] 476

11/2 Oct. 272

Report only

"An ancient source" (Dionysian Calendar)

10.9: 25 Aigon year 13

20/1 Hathyr 476 = 52 Alex.

17/8 Jan 272

[None]

9.10: 22 Scorpion year 21

18/9 Thoth 484

14/5 Nov. 265

[None]

9.7: 21 Hydron year 23

17/8 Choiak 486

11/2 Feb. 262

[None]

9.7: 4 Tauron year 23

0/1 Phamenoth 486

25/6 Apr. 262

[None]

9.7: 28 Leonton year 24

30 Payni 486

23 Aug. 262

[None]

9.7: 7 Didymon year 28

5/6 Pharmouthi 491

28/9 May 257

[None]

11.3: 10 Parthenon year 45

17/8 Epeiph 83 Alex.

3/4 Sep. 241

[None]

Babylonian (Seleucid Calendar (Babylon))

9.7: 5 Apellaios year 67

27/8 Thoth 504

18/9 Nov. 245

[None]

9.7: 14 Dios year 75

9/10 Thoth 512

29/30 Oct. 237

[None]

11.7: 5 Xandikos year 82

14 Tybi 519

1 Mar. 229

[None]

Anon. Alexandrian Source (Egyptian Calendar)

6.5: 27/8 Phamenoth year 7 Ptolemy VI

[Same] 574

0/1 May 174

[None]

Hipparchus (Callippic Era, Egyptian)

4.11: 16 Mesore year 2.54

[None]

22 Sep. 201

Anon. Alexandrian

4.11: 9 Mecheir year 2.55

[None]

19 Mar. 200

Anon. Alexandrian

4.11: 5 Mesore year 2.55

[None]

11 Sep. 200

Anon. Alexandrian

3.1: 30 Mesore year 3.17

[None]

27 Sep. 162

Anon.

3.1: 1 Epagomene year 3.20

[None]

27 Sep. 159

Anon.

3.1: 3/4 Epagomene year 3.32 = 178 Alex.

[None]

26/7 Sep. 147

Hipparchus (?)

3.1: 27 Mecheir year 3.32 = 178 Alex.

[None]

24 Mar. 146

Hipparchus (?)

3.1: 4 Epagomene year 3.33

[None]

27 Sep. 146

Hipparchus (?)

3.1: 4 Epagomene year 3.36

[None]

26 Sep. 143

Hipparchus (?)

6.5: 2/3 Tybi year 3.37

[None]

27/8 Jan. 141

Hipparchus

3.1: 29/30 Mecheir year 3.43

[None]

23/4 Mar. 135

Hipparchus (?)

3.1: 1 Phamenoth year 3.50

[None]

23 Mar. 128

Hipparchus (?)

5.3: 16 Epeiph year 3.50

[None]

5 Aug. 128

Hipparchus

5.5: 11 Pharmouthi year 197 Alex.

[None]

2 May 127

Hipparchus

5.5: 17 Payni year 197 Alex.

[None]

7 July 127

Hipparchus

Agrippa (Bithynian Calendar)

7.3: 7 Metroös year 12 Domitian

2/3 Tybi 840

29/30 Nov. AD 92

Agrippa

Menelaus (Egyptian Calendar)

7.3: 15/6 Mecheir year 1 Trajan

15/6 Mecheir 845

10/1 Jan. AD 98

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 Astronomers 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.

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. A. Jones, Ann. Sci. 63 (2006) 255 discusses these observation in detail, and shows that three of the seven Dionysian observations were off by one or two days, both early and late. Jones suggests that the actual Dionysian calendar was not based on 30-day months, which is what the date equations imply and a later scholion explicitly states. Whetever the explanation of tis discrepancy, 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:

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. Whether or not this algorithm was actually used, 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. These are the latest, and almost the only, uses of the "Athenian" calendar in the Almagest, although Egyptian-style Callipic dates are reported by Hipparchus 150 years later. This suggests that the Athenian calendar was not ordinarily used in Alexandrian astronomy after Timocharis' time (although it was apparently not abandoned: A. Jones, ZPE 129 (2000) 141 at 145 does show its use in pOxy 61.4137, in the mid first century AD). Other data appears to support this. The Babylonian eclipse observations that are the ultimate source of the "Athenian" 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 Babylonian 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 at 69ff.) 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.

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.

19 Nov. 2006: Note that "Athenian" eclipse of Dec. 383 is now proven to have been observed in Babylon
23 Dec. 2007: Note Jones' detailed analysis of Dionysian observations

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