Babylonian and Seleucid Dates
Intro page | How to Read the Tables | The Babylonian Calendar | Sources | Analysis
This page gives access to two conversion tables in Excel format (905 kB), with a copy in HTML format (2.57 MB), useful for determining the Julian equivalent of Babylonian and Seleucid civil dates in the Ptolemaic era. The dates of some important events early in the Ptolemaic era, such as the death of Alexander, and of a number of Seleucid events involving Ptolemaic princesses, can be determined from these tables.
Three tables are provided:
1) The standard conversion table generated by Parker & Dubberstein in 1956 (PD)
2) A corrected conversion table, consisting of PD overlaid by data from contemporary astronomical diaries, lunar tables, eclipse reports, eclipse predictions, goal year texts and horoscopes.
3) A difference table, showing the differences between the first two tables.
The second of these tables is also provided in a CSV text format.
Analysis of the Tables
The following notes give additional information on the processes used to generate these tables.
The standard conversion table of PD was based on the calculated new moon tables for Babylon developed by Schoch, combined with tables for 1 Nisanu determined by Sidersky. Where there were discrepancies, Parker and Dubberstein started with Sidersky's number and calculated lunar months backwards and forwards till they reached agreement with Schoch's tables. The tables do not indicate which dates are taken directly from Schoch, or which are derived from Sidersky or by this interpolation process, nor have I tried to determine this. These tables replace and silently correct a previous version published in 1942. They should be understood to be accurate only to within a day. Parker and Dubberstein themselves estimated that their numbers were 70% accurate. Schoch's calculations have been superseded by other tables.
Moreover, the dates are for Babylon. Even if they are completely accurate for Babylon, and even if the start of the month outside Babylon was also determined by the same techniques, dates at points further west (e.g. Judea, Egypt) may occasionally be one day earlier, owing to the rotation of the earth, causing moonrise to be observed at a slightly later point in its cycle. In most cases these uncertainties do not matter, since Babylonian or Seleucid dates of Egyptian-related events are usually known only to the year, or occasionally to the month.
In recent years a considerable volume of contemporary Babylonian data has been published which allows large sections of the PD table to be confirmed or corrected. The corrected conversion table provided here is based on this data. In no case does the discrepancy between the PD calculations and the Babylonian data demonstrably exceed 1 day, as Parker and Dubberstein themselves expected.
I have no doubt that there are errors in these tables. They should only be regarded as a draft edition of a corrected table. The years 324-300 have been carefully crosschecked against the corrected table prepared by Tom Boiy in "Aspects chronologiques". Remaining discrepancies in this period represent points that I believe are in error in his table. Additionally, all years have been checked against the observed lunar first visibility dates given in Table 1 of L. J. Fatoohi et al., JHA 30 (1999) 51 and Table 1 of S. Stern, JHA 39 (2008) 1, and thre predicted dates given in Table 2 of Stern's article. As an indicator of reliability, I found about 50% more errors in my original version than I found in Boiy's table, and 8 out of 184 dates (2 of which were consequential to an initial error) were in error compared to Fatoohi et al. (4.3%); I found only one error in their table; Stern disagrees with them on four dates. For comparison, the error rate for the lunar first visibility dates predicted by PLSV compared to the Babylonian observations as given by Fatoohi et al. is 7.2%. Fatoohi et al., using their own software derived from the lunar ephemeris ELP2000-85, found that about 3.8% of the observations were early (they don't give an analysis of late observations). Stern, who used programs he considers more accurate than PLSV, found that about 8.15% of observed crescents were late or early and about 6.36% of predicted screscents wre early (none were certainly late).
The Babylonian data is incorporated in the corrected tables as follows.
The corrected tables have been primarily based on eclipse data in the diaries, and by optimising the match of monthly run lengths against the calculations of PD, as discussed below. Since I am not an astronomer, let alone familar with Babylonian astronomical terminology, I have not attempted to determine Julian dates through retrocalculation of lunar, planetary, sidereal or other data. However, many of the lunar visibility dates calculated by Fatoohi et al. and by Stern were based on the time given between sunset and moonrise on day 1 of the month in the Babylonian sources, or from other such data, which allows the equivalent Julian dates to be precisely determined in most cases. Where these dates are not determinable by the procedures given above, I have taken advantage of their results without calculating them independently. Lunar visibility dates that are not also eclipse dates are underlined on unbolded entries, usually in red.
The Julian date for the start of a Babylonian month can be determined with certainty for virtually any month in which an eclipse occurred, or was predicted on a Babylonian date that is either given directly or is unambiguously recoverable from surrounding dates. These months form the absolute anchors for the correlation. Observed eclipses are bolded and marked in red without underlining; predicted eclipses that were not observed, or whose observation status is uncertain, are bolded, underlined and marked in red.
Eclipses are taken from the astronomical diaries (AD) in volumes 1-III of Sachs & Hunger, the eclipse reports (ER) of volume V, the horoscopes (BH) reported by Rochberg, the eclipse observations (EO) of Huber & de Meis, and the eclipses reported in Stephenson (HER). If both lunar and solar eclipses occurred in the same month, observed eclipses are used rather than predicted eclipses.
The Babylonian dates in these reports are frequently not given explicitly in the surviving portion of the texts, or only survive in part. In the great majority of cases, however, the precise Julian dates can be recovered from the detailed eclipse description or from other astronomical data within the texts. There is, so far as I know, no reason to doubt the accuracy of these assignments. F. R. Stephenson & J. M. Steele, JHA 37 (2006) 55, is a detailed analysis of the astronomical data for a solar eclipse explicitly dated to 29 Addaru II SE 175 in BM 34034 and to 29 [lost] [x]75 SE in BM 45745, showing that the only matching eclipse in the years 750 BC to AD 100 is that of 15 April 136 BC, which is sufficient to establish an anchor point.
Since the algorithm for equating Babylonian months to lunations is fixed and well known in this period, the Julian date of an eclipse is sufficient to determine the equivalent Babylonian month and year. For this reason, I have not distinguished here between years and months which are explicitly given Babylonian dates and years or months which are only recovered by retrocalculation from the astronomical data. However, since the first day of the Babylonian month was usually determined by observation, the precise Babylonian date of an eclipse can only be estimated to a precision of +1 day unless the day number survives, or can be inferred from other data. For this reason, eclipse reports which cannot be associated with a specific day in the Babylonian month have not be used for the conversion tables.
Modern dates as given in Sachs & Hunger are also sometimes ambiguous, especially for lunar eclipses and predicted eclipses; e.g. it is not always immediately obvious whether a lunar eclipse on a certain date occurred between midnight and dawn or between sunset and midnight. Accordingly, the times have all been checked against Fred Espenak's historical eclipse tables. Any remaining ambiguities have been resolved in favour of the date that matches PD; there are very few such cases.
In order to justify the use of predicted eclipses it is necessary to determine the accuracy of the ability of the Babylonians to predict eclipses that were not actually observed. This problem is studied in J. M. Steele, Observations and Predictions of Eclipse Times by Early Astronomers (Dordrecht 2000) 68-75. Summary lists of timed predicted and observed eclipses recorded in Babylonian sources known to Steele are given by astronomical date in tables 2.4-2.8. Several eclipses are mentioned in more than one table.
Steele divided both lunar and solar eclipses into two categories, and determined the mean accuracy of the ability of the Babylonians to predict eclipses to be as follows:
Solar: (A) Observable at the latitude of Babylon: 2.01 hr (B) Not observable at the latitude of Babylon: 3.55 hr
Lunar: (A) Umbral eclipses, observable somewhere on Earth: 1.31 hr (B) Penumbral eclipses: 2.86 hours
In addition, Steele found two predicted lunar eclipses that simply did not occur; only one of these (-278 Nov 15) is in the Hellenistic period. A third (-225 July 17) is discussed below.
In short, the Babylonian eclipse algorithms are very reliable, though not perfect, and quite precise. The use of predicted eclipses as a reliable chronological anchor is based on these results.
As a measure of the completeness of coverage of my own research, Steele's tables were cross-checked against the eclipses found in the Astronomical Diaries (AD) or Eclipse Reports (ER) of Sachs & Hunger, in Rochberg's Babylonian Horoscopes (BH), in Stephenson's Historical Eclipse Records (HER) and in Huber & de Meis' Babylonian Eclipse Observations (EO). For all observed eclipses listed by Steele, and for most predicted eclipses, the source report was found, although quite a few of the eclipses, both predicted and observed, cannot be used for calendrical conversion because the Babylonian day number is not recoverable from the source text, as discussed above.
The following eclipse predictions given by Steele were not found in any of these sources, and represent additional potential synchronisms:
Lunar: -214 Jan 5, -191 Apr 19, -185 Jun 11, -139 Jun 12, -122 Feb 7, -122 Dec 29, -110 May 24, -110 Nov 16
- Solar: -255 Mar 24, -229 May 5, -206 Jan 22, -206 Jul 17, -205 Jan 11, -204 Jun 25, -199 Mar 4, -185 Nov 20, -183 May 6, -168 Jan 22, -154 Oct 10, -139 Jun 27, -132 Aug 7, -127 Apr 16, -122 Jul 19, -121 Jan 12, -119 Nov 11, -116 Mar 16, -77 Mar 6
If you know where the reports of these predictions are published, please email me.
A very small number of Steele's dates appear to be in error, since Espenak indicates that no eclipses actually occurred on the date in question. In most cases the error is easily identifiable as an editorial blunder or a minor discrepancy; in one case (-122 Feb 7) a lunar eclipse prediction has been misfiled as a solar eclipse prediction. I am unable to account for the solar eclipse prediction listed by Steele for -182 Jun 7.
Three eclipses, two of them recorded in the same tablet, call for particular discussion.
The predicted solar eclipse given in Steele's Table 2.8 as -225 July 17 [= 28 Simanu SE 86 (AD225)] does not appear in Espenak's tables, nor in the standard catalogue H. Mucke & J. Meuss, Canon of Solar Eclipses -2003 to +2526. Steele marks this eclipse as having occurred on -225 July 17 but not being visible at the latitude of Babylon. The closest eclipse in the standard solar catalogues is that of -225 August 17. This date is covered by AD225, assuming the diary is correctly dated, but no solar eclipse prediction appears there for it. The year date for AD225 does not survive, but the diary gives a highly detailed report of a lunar eclipse on the night of 14 Duzu, including an approach to a star identified as a Cygni, which is the basis for dating the eclipse as that of -225 1 August. There is good reason, therefore, to suppose the assigned year is correct.
Steele (pers. comm. 7 July 2003) informs me that the dates of the eclipse predictions only represent the operation of the Babylonian eclipse algorithm, and that in essence the algorithm failed in this instance, by predicting an eclipse on -225 July 17 and failing to predict the eclipse of -225 August 17. J. M. Steele, AHES 54 (2000) 421 at 428, suggests that the exact day of the eclipse was predicted by observing the precise positions of the sun and the moon on the previous few days. Since we apparently have a failure of the algorithm, the proposed synchronism -225 July 17 = 28 Simanu SE 86 must be dismissed for lack of evidence.
Goal Year text LBAT 1304 was originally dated to -40, and was believed to give the latest lunar eclipse observation in the corpus on -40 Mar 2 = 15 Addaru SE 270. This date is reflected in Steele's table. However, EO (p66) notes that a new reading has recovered additional data that invalidates this date, and concluded that the best match is to -199 Mar 19 = 15 Addaru SE 111. Accordingly, the solar eclipse prediction in the same text must be redated from -40 Feb 15 = 29 Shabatu SE 270 (as in Steele) to -199 Mar 4 = 29 Shabatu SE 111. These revised dates are incorporated here.
The First Day of the Month
The tables reflect the general assumption that the start of the month was actually determined in this period by observation of the new crescent moon wherever possible. Recently, however, J. M. Steele in idem (ed.), Calendars and Years 133, has argued that this is not the case, but that the first day of the month was always based on the predicted date of the first crescent moon. Steele's argument is based on a comparison of observed and predicted dates for first crescents, which showed only two possible conflicts, both of which were, in Steele's view, arguably due to misreadings of characters that have only partially survived in the source text. Against this, S. Stern, JHA 39 (2008) 1 at 22 n. 30 notes that Steele relies on only about 50 examples, and that we should expect a very high correlation between observed and predicted dates if a prediction algorithm is any good.
More importantly, Stern observes that some 21 out of 331 observed new crescent moons were certainly late, while none of 110 predicted new crescent moons were late, and conversely that only 3 observed new crescent moons were certainly early, while at least 7 predicted new crescent moons were actually or most probably early. Stern holds, in my view correctly, that this difference shows that the conventional view is correct: that the start of the months were determined by a mixture of observation and prediction.
At the opposite extreme from Steele, L. Depuydt, in J. M. Steele (ed.), Calendars and Years 35 at 76 n. 43 and elsewhere has stated the view that "not even in Babylonian astronomy did first crescent visibility play a role as the beacon of computation [of the beginning of the lunar month], in spite of all kinds of indications to the contrary". His reasoning and evidence for this remarkable suggestion is as yet unpublished; based on Fatoohi's and Stern's results it seems highly unlikely to me. However, there are two weaker forms of this assertion that are more plausible and seem worth addressing. First, the calendar of the Babylonian astronomers may not have been the ordinary calendar in daily use in Babylon, and, second, months of the Babylonian calendar may not have been determined by first crescent visibility outside Babylon.
These questions can be answered, even though J. M. Steele in idem (ed.), Calendars and Years 133 at 139f. notes that the amount of non-astronomical calendrical data is very small. He cites sixth century cultic sacrifice records from Uruk as showing that 29-day months occurred in approximately the right ratio, and also letters asking for rapid notification from nearby cultic centers as to whether the month was 29 or 30 days. This establishes that the calendar months of the general populace were established by the local priests. In Babylon, these were certainly the priests of E-Sagila, which was the center of astronomical observation. The Diaries contain references to observations made at other sites, e.g. Borsippa, so in all likelihood Babylonian astronomical practice was standard at least throughout southern Mesopotamia.
To my knowledge, there is practically no evidence allowing us to decide whether the same answer applied to more distant regions in the Hellenistic period. For example, we have no data allowing us to decide whether the start of Antiochene lunar months were determined astronomically or more loosely in the usual Greek fashion. For the Achaemenid period, we have the Egyptian/Aramaic double dates of the Elephantine papyri, listed most recently by L. Depuydt, in J. M. Steele (ed.), Calendars and Years 35 at 55. Depuydt compares these to lunar conjunction; comparing the 12 unproblematic double dates to first visibility using PLSV, we get an accuracy of slightly less than 50%, comparable to the accuracy seen in Egyptian lunar dates and much less than the 90%+ accuracy of Babylonian dates. This suggests that months were determined using ad hoc techniques at sites that were too distant from an astronomical center to use ther results of astronomical techniques.
The length of a Babylonian month is usually determined from their convenient habit of recording whether a named month began after the 29th or the 30th day of the preceding month. Sachs and Hunger frequently provide summaries of each diary of the type "VI 0 = V 30", i.e. that the day before the start of month VI (Ululu) was day 30 of month V (Abu). These summaries must be used with care, since they are sometimes provided even though the surviving portion of the corresponding diary entry does not explicitly give this data. Once I realised this problem, I relied only on the diary translations.
Month lengths are not always recorded when naming a month, but they are standard in the astronomical diaries (if not always recoverable) and are common in the horoscopes and the lunar tables, and in the "lunarrr six" portion of the goal year texts. The diaries, goal year texts and horoscopes are regarded as primary sources, either directly reflecting source observations (horoscopes) or being the official redaction of the source observations (diaries and goal year texts). Sequences based on these month lengths are shown in red. Lunar tables are assumed to be derived from diaries, and hence are considered secondary sources. Sequences based on these month lengths, that are not also covered in part by diaries or horoscopes, are shown in green.
Clearly, an entry for day 29 in the diaries without a day 30 is not sufficient to assure a restoration of a 29-day month. Less obviously, a standalone entry for day 30 in the diaries is not sufficient to assure a restoration of a 30-day month, since the last day of the month could be called day 30 retrospectively, regardless of its length. In theory, however, it is possible to recover the lengths of 30 day months from the diaries if they record entries for days 29 and 30. I have not checked the diaries for this phenomenon. Note that this concern does not apply to contemporary documents such as letters or contracts; for example, the 30-day length of Aiaru 219 SE = 93 BC was recovered this way.
Month lengths show the difference between the start date of two consecutive months. Thus, the month preceding the first named month of a sequence must also be considered part of the sequence. The first month of a sequence, unnamed, is shown in brown (unless it contains an eclipse).
Month lengths can be correlated against the corresponding month lengths in PD. However this does not by itself allow us to fix the absolute dates of the months, even though the longer the sequence the likelier it is that the highest correlations do in fact represent absolute dates. The highest reliability is obtained if a sequence of months includes one or more months in which eclipses are observed.
A basic assumption of the corrected table is that the standard correlations are not significantly in error, i.e. that the true start dates of Babylonian months do not differ from PD by more than a day, early or late, and that any such divergencies are corrected by a compensating divergence, usually in the next month but in any case within a very few months. Many of the sequences available in the source data show divergencies that are self-corrected in precisely this fashion.
Where a sequence of month lengths ends with a date that diverges from PD I have usually chosen the next available month in PD after the end of the sequence that would allow the appropriate compensation (29->30 or 30->29 days as appropriate). This is frequently an arbitrary choice, though, since first-cresent sightings could easily be missed it is likely that a 29 day month that became a 30 day month due to a missed sighting will be followed by a compensating 29 day month. Occasionally, eclipse data, or a long run of month lengths matching PD with a single early divergence, shows that a compensation is required before the start of the contemporary data. These adjustments have not been checked against modern lunar tables for plausibility. In essence, they were chosen to give the minimum possible divergence from PD. For these reasons, the merging of recorded month sequences with PD should be regarded as preliminary only.
There are three cases where this strategy was not possible. All involve exceptionally long runs in the source data surviving from Lunar table BM32327 = LT39. When complete, this table covered 32 years, from SE 62 to 93.
Aiaru SE 71 (241 BC) - Tashritu SE 73 (239 BC): An unbroken sequence of month lengths for over 2 years is given in Lunar tables BM32327 = LT39 and BM40091 = LT40, with absolute anchors of observed lunar eclipses on 14 Arahsamnu SE 72 = 3 November 240 BC (BM 32236 = HER 155 (11)) and the night of 13 Nisanu SE 73 = 28 April 239 BC (Diary BM55511 = AD238). The total distance between these events is one day too short in both lunar tables. LT39 and LT 40 conflict on the lengths of Tebetu and Shabatu SE 72, but both give 59 days for the total. PD gives 60. PD is (with some reluctance) preferred here.
- Simanu SE 75 (237 BC) - Kislimu SE 77 (235 BC): An unbroken sequence of month lengths for over 2 years is given in Lunar table BM32327 = LT39, with both partial confirmation and a self-compensating contradiction from BM41641+41930+41963+41997 = AD234. There is no absolute anchor in the sequence. If correlation with PD is assumed at the start, then there is a consistent one day lead over PD starting in Addaru SE 75. Sachs & Hunger indicate that the 30 day length of Ululu SE 75 given in LT39 is questionable; the reason is not clear (the three previous months are also in conflict with PD). Correcting this to 29, matching PD, solves the problem.
- Nisanu SE 86 (226 BC) - Addaru SE 90 (221 BC): An unbroken sequence of month lengths for 5 years is given in Lunar table BM32327 = LT39, with an absolute anchor of an observed lunar eclipse on night of 14 Duzu SE 86 = 1 August 226 BC (Diary BM33655 = AD225). Correlation with PD is essentially perfect until Abu and Ululu SE 89 (222 BC); thereafter the sequence is usually two days early. The month lengths for these two months are marked as questionable by Sachs & Hunger; if both are corrected from 29 to 30 days per PD the discrepancy disappears. (I do not know why they are marked as questionable; it may be for precisely this reason).
The following source conflicts, indicated in magenta, were detected in preparing the corrected table.
Tebetu year 1 Philip (323 BC): The translation of diary BM2240+32430+32489 = AD322D gives X 0 = IX 30; Lunar table BM 34075 = LT36 gives X 0 = IX 29. LT36 is preferred; the translation of AD322D is in error by comparison to the transliterated source.
- Nisanu year 2 Philip (322 BC): Diary BM2240+32430+32489 = AD322D gives I 0 = XII 30; Diary BM 34093+35758 = AD321 gives I 0 = XII 29. AD322D is preferred since it is wrapping up year 1, hence is more likely to be concerned with the length of month XII; Fatoohi et al. also accept the date of AD322D. This conflicts with PD, but also compensates for a 1 day conflict with PD in Shabatu year 1 given by AD322D, which would otherwise lead to a 2-day discrepancy in Aiaru year 2 because of a discrepancy with PD for that month in AD321.
- Arahsamnu, Shabatu, Addaru SE 27 (285/4 BC): Lunar table BM40493 = LT37 gives VIII 0 = VII 30, XI 0 = X 30, XII 0 = XI 29. BM45927 = AD284 gives VIII 0 = VII 29, XI 0 = X 29, XII 0 = XI 30. AD284 is preferred as being closer to the source observations; Fatoohi et al. also accept the date of AD284. Coincidentally it also matches PD.
- Addaru SE 69 (242 BC): Lunar table BM32327 = LT39 gives XII 0 = XI 29; Diary BM34920 = AD242 gives XII 0 = XI 30. AD242 is preferred as being closer to the source observations; coincidentally it also matches PD.
- Tebetu, Shabatu SE 72 (239 BC): Lunar table BM32327 = LT39 gives X 0 = IX 30, XI 0 = X 29; Lunar table BM40091 = LT40 gives X 0 = IX 29, XI 0 = X 30; PD predicts X 0 = IX 30, XI 0 = X 30. There is no obvious reason to prefer one LT over the other. Both LT39 and LT40 create a problem in reconciling the lunar data with both PD and the observed lunar eclipses of Arahsamnu SE 72 and Nisanu SE 73. Since PD gives the correct distance between the eclipses, PD is (with some reluctance) preferred here.
- Tashritu, Arahsamnu SE 77 (235 BC): Lunar table BM32327 = LT39 gives VII 0 = VI 30, VIII = VII 29; BM41641+41930+41963+41997 = AD234 gives VII 0 = VI 29, VIII = VII 30. AD234 is preferred as being closer to the source observations; Fatoohi et al. also accept the date of AD234. Coincidentally it also matches PD.
- Tashritu SE 92 (220 BC): Lunar table BM32327 = LT39 gives VII 0 = VI 30; Horoscope BM36620 = BH14 gives VII 0 = VI 29. Selecting LT39 would terminate a run of discrepancies with PD at runlength 1 instead of 4+. However, BH14 is preferred as being closer to the source observations; coincidentally it also matches PD.
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