The Babylonian month and the new moon: Sighting and prediction

Journal for the History of Astronomy

Volumn 39, Issue 1, 2008, Pages 19-42

  Stern, Sacha ^a  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

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EID: 38849131990     PISSN: 00218286     EISSN: None     Source Type: Journal    
DOI: 10.1177/002182860803900102     Document Type: Article

References (113)

1. R. A. Parker and W. H. Dubberstein, Babylonian chronology 626 BC - AD 75 (3rd edn, Providence, RI, 1956), 1-4;
2. P. J. Huber, "Astronomical dating of Babylon I and Ur III", Monographic journals of the Near East, Occasional papers, i/4 (1982), 7 and 24-29;
3. and A. J. Sachs and H. Hunger, Astronomical diaries and related texts from Babylonia (5 vols, Vienna, 1988-2006), i, 13.
4. Parker and Dubberstein (ibid., 3) believe that astronomical calculation and prediction never completely replaced actual sightings of the new moon.
5. P.-A. Beaulieu ("The impact of month-lengths on the Neo-Babylonian cultic calendar", Zeitschrift für Assyriologie und vorderasiatische Archäologie, lxxxiii (1993), 66-87, pp. 86-87) concludes that although both methods were used, "it is probable that observation remained [after the sixth century] the sole authoritative way of fixing the beginning of the month".
6. J. M. Steele ("The length of the month in Mesopotamian calendars of the first millennium BC", in idem (ed.), Calendars and years: Astronomy and time in the ancient Near East (Oxford, 2007), 133-48) argues on the contrary that from the beginning of the Seleucid period, the month was always pre-determined in advance (his argument will be discussed below). I am grateful to John Steele for sending me a copy of his article in advance of publication, as well as for his useful comments on a first draft of this article.
7. See D. Brown, Mesopotamian planetary astronomy-astrology (Cuneiform monographs 18; Groningen, 2000), 113-14, 248.
8. A full moon on the 14th or 15th of the month is compatible with a month beginning at first visibility of the new moon; see for example S. Stern, Calendar and community: A history of the Jewish calendar 2nd century BCE - 10th century CE (Oxford, 2001), 130.
9. J. B. Pritchard, Ancient Near Eastern texts relating to the Old Testament (Princeton, NJ, 1950), 67-68;
10. Brown, op. cit. (ref. 2), 235, 253;
11. and Steele, op. cit. (ref. 1).
12. Huber, op. cit. (ref. 1), 24-25. Astronomical factors determining first visibility of the new moon are so complex that dates of first visibility do not occur in regular cycles or patterns. Huber also points out that although irregular and unpredictable, sequences of 29- and 30-day months based on first visibility are not random, inasmuch as runs (sequences of consecutive months of equal length) are fewer and shorter than they would be in a purely random sequence. Thus according to his calculations, the longest possible runs in a calendar of this kind (at least at the latitude of Babylonia) are 5 months of 30 days, and 3 months of 29 days. Sequences of months in Babylonian sources would appear to conform to these characteristics.
13. The diaries are edited, translated, and astronomically dated by Sachs and Hunger, op. cit. (ref. 1).
14. Some of this material has been preserved only in later (and sometimes much later), Seleucid- or early Parthian-period compilations, but there is no reason to doubt its authenticity. For a general introduction, see H. Hunger, "Non-mathematical astronomical texts and their relationships", in N. M. Swerdlow (ed.), Ancient astronomy and celestial divination (Cambridge, MA, 1999), 77-96.
15. Sachs and Hunger, op. cit. (ref. 1), i, 21-22, refer to "predictions", but it seems to me that "postdictions" are an equal possibility (see further below, ref. 46).
16. How sunset-moonset lag pre/postdictions were made is unknown, but various models have been proposed by L. Brack-Bernsen, Zur Entsehung der babylonischen Mondtheorie (Stuttgart, 1997);
17. eadem, "Goal-year tablets: Lunar data and predictions", in Swerdlow (ed.), op. cit. (ref. 5), 149-78;
18. and Brown, op. cit. (ref. 2), 173-89.
19. One text, TU11, lays down a range of prediction rules: L. Brack-Bernsen and H. Hunger, "TU11: A collection of rules for the prediction of lunar phases and of month lengths", Sciamus, iii (2002), 3-90.
20. See L. J. Fatoohi, F. R. Stephenson and S. S. Al-Dargazelli, "The Babylonian first visibility of the lunar crescent: Data and criterion", Journal for the history of astronomy, xxx (1999), 51-72.
21. For example S. Parpola, Letters from Assyrian scholars to the kings Esarhaddon and Assurbanipal (2 vols, Kevelaer, 1970-83), i, nos. 45 and 70, and ii, p. 54;
22. H. Hunger, Astrological reports to Assyrian kings (State Archives of Assyria 8; Helsinki, 1992), nos. 46-47, 58-60, 83, 257, 267, 516.
23. Parpola, op. cit. (ref. 8), ii, 53;
24. Beaulieu, op. cit. (ref. 1), esp. 67 and 72-76;
25. and Brown, op. cit. (ref. 2), 198-200.
26. The evidence is text E, r., 18-19, in O. Neugebauer and A. Sachs, "Some atypical astronomical cuneiform texts", Journal of cuneiform studies, xxi (1967), 183-218, p. 205 (translation and commentary), which reads: "(18) In 19 years the moon will approach the place of the Normal Stars where it approached before.
27. Where there was a lunar eclipse, it takes place (again). (19) If (the moon) passed by (a Normal Star) high, or if it passed by low, it will repeat this in your year. Determine the full and hollow months." Neugebauer and Sachs correct '19 years' into '18 years' (i.e. the Saros cycle - an interpretation followed by Brown, op. cit. (ref. 2), 199 n. 461),
28. but this correction is rejected as unnecessary by K. P. Moesgaard, "The full moon serpent: A foundation stone of ancient astronomy?", Centaurus, xxiv (1980), 51-96.
29. Neugebauer and Sachs (and Brown, ibid.) interpret the last sentence ("Determine the full and hollow months") as a calculation of the number of full and hollow months in a complete 18-year cycle; however, this is not evident from the text.
30. The interpretation I am suggesting is more cautious: i.e., that a predicted lunar eclipse, repeated after 19 years, can be used to determine the length of its month, and possibly also of some contiguous months - but not that it determines the month lengths of the entire cycle. Note also the suggestion of Brack-Bernsen and Hunger, op. cit. (ref. 6), 59, that in this text, month lengths are predicted not on the basis of lunar eclipses, but perhaps on the basis of lunar latitude.
31. This text is TU11 (Brack-Bemsen and Hunger, op. cit. (ref. 6)), which comes from late third-century B.C. Uruk but is thought to have a pre-Seleucid origin (ibid., 6).
32. It includes a number of rules for predicting month lengths, mostly based on predicted sunset-moonset lags (except for one rule, in obv. 34-35, which seems to be based on the moon's altitude at sunset - or perhaps on lunar latitude: ibid., 55-61).
33. These rules are clearly related to new moon visibility: thus the rule that if the sunset-moonset lag is less than 10°, the 1st of the month will be postponed to the next evening (and the old month will be full: obv. 33, 37, see ibid., pp. 35, 43-45),
34. is clearly based on an assumption that if the lag is less than 10° the new moon will not be visible (another passage, rev. 7, suggests 12° as a visibility criterion: on this apparent contradiction see ibid., pp. 70-71 and n. 62).
35. According to Brack-Bernsen and Hunger, the rule in 'section 14' of TU11 (which uses the 10° criterion) would achieve an accuracy of about 95% (ibid., 45, 48-50 and n. 51), which is good but still means that one prediction in twenty would have been inaccurate.
36. This is presumably because the sunset-moonset lag on its own is an inaccurate new moon visibility criterion, unless used in conjunction with other criteria such as the difference of azimuths between sun and moon: see Y. Loewinger, "Maimonides' new moon visibility criterion", BaDaD - Bekhol derakhekha da'ehu, Journal of Torah and scholarship, iii (1996), 45-85 (Hebrew), esp. p. 61;
37. L. E. Doggett and B. E. Schaefer, "Lunar crescent visibility", Icarus, cvii (1994), 388-403;
38. B. E. Schaefer, "Lunar crescent visibility", Quarterly journal of the Royal Astronomical Society, xxxvii (1996), 759-68;
39. and R. E. Hoffman, "Rational design of lunar-visibility criteria", The observatory, cxxv (2005), 156-68.
40. The Astronomical Diaries suggest that the criterion used for predicting new moon visibility could not have been based on the sunset-moonset lag on its own, and hence did not conform to the rules of TU11. Indeed, some new moon predictions in the Diaries are recorded with predicted sunset-moonset lags as low as 8° or 9° (thus contravening the rules of TU11 - see previous ref.): e.g. for 26 August -261, 9°30′; for 1 November -232, 8°10′; and for 7 September -132, 8°. Conversely, predicted sunset-moonset lags higher than 10° appear elsewhere to have been disregarded as evidence of new moon visibility. Thus in 3 January -253, 1st of month X, the lag is accurately predicted as 27°30′; the previous evening (2 January), assuming that a similarly accurate prediction could have been made, would have had a lag of about 12°, which appears to have been disregarded by the Babylonians as evidence of new moon visibility - and indeed correctly so, since on that evening, according to modern criteria, the new moon would not have been visible. A lag of 10° appears to have been ignored in 5 June - 183, and of 9° in 14 February -86. This apparent inconsistency suggests that the new moon visibility criterion, or the criterion for determining month lengths, was not dependent on the sunset-moonset lag alone. This does not necessarily mean, however, that it was more accurate than the new moon visibility criteria of TU11. As I will show below, the accuracy of new moon predictions in the Astronomical Diaries seems to be less than the 95% accuracy of TU11 (on which see previous ref.).
41. Huber, op. cit. (ref. 1).
42. Actually, Huber considered not only astronomical texts, but also the evidence of administrative and economic documents (ibid., 28-29).
43. The latter yielded very different results, which Huber noted but did not seek to explain. Elsewhere I shall argue that administrative and economic sources are less likely to provide reliable information about the calendar, because of the scribal tendency to assume 30-day months even when they actually had only 29 days (see also M. E. Cohen, The cultic calendars of the ancient Near East (Bethesda, MD, 1993), 4-5). For reasons of scope, this discussion will be omitted from the present study.
44. Huber, op. cit. (ref. 1), 25-27.
45. In one place, Huber (ibid., 7) seems to defend his approach by claiming that the distinction between actual sightings and mere calculation of the new moon is not sufficiently clear in the sources, The Astronomical Diaries, however, normally distinguish very clearly new moons that were "watched" from those that were "not watched". Some cases remain, admittedly, ambiguous, but this does not prevent us from compiling a substantial corpus of actual sightings and pre- or postdictions.
46. Fatoohi et al., op. cit. (ref. 7). Their decision to restrict themselves to actual sightings is governed by their stated objective to assess what might have been the Babylonian astronomical criterion of visibility of the new moon. Their method consists, rather oddly, in cataloguing actual sightings of the new moon in Babylonian sources, formulating a criterion of new moon visibility that would fit these data, and then finally ascribing this criterion, very tentatively, to the astronomers of ancient Babylonia. The speculative nature of this approach is acknowledged, however, by the authors themselves. Far more productive would have been to catalogue new moon predictions in Babylonian sources: if a new moon visibility criterion was assumed and used by the Babylonian astronomers, surely it is from their new moon predictions that such a criterion should be inferred. Against this approach, the authors argue (p. 64) that new moon predictions may have been conditioned by the purely calendrical principle that lunar months can only have 29 or 30 days, and hence, may not be used to infer any astronomical new moon visibility criterion. This argument is somewhat weak (because speculative), and certainly does not justify the decision to ignore new moon predictions altogether.
47. Sachs and Hunger, op. cit. (ref. 1), but I have refrained from using texts that are heavily reconstructed by Sachs and Hunger, or texts of which I consider the astronomical dating uncertain (e.g. ibid., v, no. 40; vi, no. 8).
48. For the correct interpretation of some of the Goal Year lunar texts, in particular ibid., vi, no. 10 (= LBAT 1225), see L. Brack-Bernsen, "Ancient and modern utilization of the lunar data recorded on the Babylonian Goal-Year tablets", in T. Mikocki (ed.), Actes de la Wème conférence annuelle de la SEAC (Warsaw and Gdansk, 1999), 13-39 (on LBAT 1225: pp. 29-31 and 34-37).
49. I have ignored other published sources, e.g. a horoscope reporting a new moon sighting for the second Adaru 53 S.E. (A. J. Sachs, "Babylonian horoscopes", Journal of cuneiform studies, vi (1952),49-75, pp. 58-60), because in the absence of additional astronomical data in this text, it is impossible to confirm with certainty that the date was (as per Sachs, and as might be reasonably expected) 17 March -257.
50. The list of sighted new moons is partially based on the table of Fatoohi et al., op. cit. (ref. 7), 59, but I have checked each entry in their table, and in some cases, I have obtained different results.
51. I have also considerably augmented their table with data from Sachs and Hunger, op. cit. (ref. 1), v-vi (not available to Fatoohi et al.), and with further information not provided by Fatoohi et al. (e.g. whether or not the new moon should have been first visible).
52. New moon sightings have been identified in the sources on the basis of one or more of the criteria of Fatoohi et al. (ibid., 55-56), which are: (1) the sunset-moonset lag is said, in the text, to have been "measured" or "watched"; (2) the appearance of the moon crescent is described, e.g. as faint or bright; and (3) the position of the moon (in relation to the horizon, to the cardinal points, or to various planets and stars) is given. The first two criteria indicate that the moon was actually seen; but the third criterion (which Fatoohi et al. assume without explanation) is not entirely conclusive, as the position of the moon could have been obtained through astronomical calculation rather than through an actual sighting. For good measure, I have noted a question mark along those entries that are based solely on this latter criterion; omission of these entries (which consist of 19 new moons on time, I early, and 3 late) would lead to slightly different results from those that are accounted below, but without affecting my general conclusions. Non-sightings have been identified, quite simply, when the text states that the sunset-moonset lag was not measured or not watched. In two cases (7 November-189 and 31 March-185) the sunset-moonset lag is reported in different sources as having been either watched or not watched; I have therefore listed them in both tables. These cases raise the possibility that the "not watched" report was not based on a pre/postdiction, but rather on the knowledge that the sunset-moonset lag had been watched by someone else (perhaps elsewhere).
53. For this I have followed the method advocated by Fatoohi et al., op. cit. (ref. 7), which is simply to compare the sunset-moonset lag in the Diaries with modern astronomical data. Since this lag increases by as much as 48 minutes per day (approximately, on average), the measurement supplied in the Diaries is a reliable indicator of the date of the first evening of the Babylonian month. Even if this measurement was prone to some imprecision or error, the margin of error does not usually exceed 15 minutes (ibid., 58). Nevertheless, in a few cases the lag of the Diaries did not clearly match the lag of one or the other day according to modem calculations, and thus did not permit a secure dating. In such cases, as well as in sources where the sunset-moonset lag was entirely missing, I have relied on the astronomical datings supplied by Fatoohi et al. (ibid.) and by Sachs and Hunger, op. cit. (ref. 1), which are based on other astronomical data in the text. In some cases, calendrical evidence could also be used: since the length of the outgoing month is normally supplied in the sources (by indicating whether the first of the new month corresponds to the 30th or 31st of the outgoing month), it is often possible to determine the date of a new month provided the date of the previous or the following month is known.
54. There is no agreed criterion for determining first visibility of the new moon. Astronomical models, both ancient and modern, are based on a combination of empirical experience and mathematical inference, and should be treated as guidelines rather than as 'laws' or rules. The various models in existence do not differ substantially from one another; for a range of criteria, see for example Loewinger, op. cit. (ref. 11);
55. Doggett and Schaefer, op. cit. (ref. 11);
56. Schaefer, op. cit. (ref. 11);
57. and Hoffman, op. cit. (ref. 11).
58. To achieve a good balance, however, I have used a Dumber of computer programs and visibility criteria for the calculation of astronomical data and new moon visibility, mainly LunaCal 3.0 Beta 3 (by R. Hoffman, www.geocities.com/royh_il);
59. Planetary, lunar and stellar visibility ver3.0.1 (by N. M. Swerdlow and R. Lange, www.alcyone.de - see N. M. Swerdlow and R. Lange, "Two programs for ephemeris and visibility calculations, useful for historical applications", Journal for the history of astronomy, xxxvi (2005), 335-6);
60. Kiddush 2005 ver.16 (by E. Tzikoni, hazon40νetvision.net.il);
61. and Ephemeris Tool 4.5 (by M. Dings, www.virtualskysoft.de). A small number of borderline and uncertain cases remain. Note that these criteria are purely astronomical and do not take account of other factors, especially atmospheric, that could affect substantially the visibility of the new moon.
62. A total of 209 cases was compiled by Fatoohi et al., op. cit. (ref. 7).
63. For some entries I have entered a comment that another result is "possible" (e.g. 27 October -283: OK, but "possibly late"); this possibility, however, is remote and may be regarded as negligible. Three entries, as indicated in the table, are of uncertain date: October -328 which, if modified, would imply not a late sighting but an early one; February -199 which, if modified, would imply not an early sighting but a late one; and February -145 which, if modified, would imply an additional late sighting. These variations could slightly affect the overall result, but this would not affect my conclusions.
64. On the possibility of false sightings, see Doggett and Schaefer, op. cit. (ref. 11);
65. Stem, op. cit. (ref. 2), 110-11; and www.geocities.com/royh_il. It must be assumed, however, that the ancient Babylonian astronomers were well trained to avoid them.
66. Fatoohi et al., op. cit. (ref. 7), 65. If we omit the cases where it is questionable whether the new moon was actually sighted (see above, ref. 18), we obtain the slightly lower result of 7.46%.
67. A. Jones ("A study of Babylonian observations of planets near normal stars", Archive for history of exact science, lxviii (2004), 475-538, pp. 527-8) finds that the accuracy of Babylonian new moons (without distinguishing between observed and predicted) increases "abruptly" after 201 B.C. My tables suggest no such change: early and late cases in both tables are evenly spread through the entire period.
68. The difference between my results and Jones's presumably arises because Jones relies on the computations of Parker and Dubberstein, op. cit. (ref. 1), themselves dependent on the new moon visibility criterion of Schoch (which is now very outdated, and in some cases inaccurate:
69. see for example my entry for the predicted new moon of September -169), and more importantly, that Jones is using a different sample (based only on Sachs and Hunger, op. cit. (ref. 1), i-iii, but including new moons that cannot be determined as either sightings or predictions, and which I have therefore excluded from my study).
70. Note that in calendrical terms, '30th' and '31st' must be regarded in this context as only notional, since depending on the case, one of these days would have been designated day 1 of the new month.
71. The possibility of the new moon's being sighted on the 29th or 28th of the month is frequently implied in the astrological omen lists, e.g. Hunger, op. cit. (ref. 8), nos. 14 ("if the moon becomes visible on the 28th day as if on die 1st day"), 63 (visible on the 28th), 457 (on the 29th);
72. see also Huber, op. cit. (ref. 1), 7;
73. Beaulieu, op. cit. (ref. 1), 86 n. 39;
74. and Brown, op. cit. (ref. 2), 146-8.
75. An actual sighting on the 29th, some time in the early seventh century, is reported in Hunger, op. cit. (ref. 8), no. 457.
76. In another text, the Assyrian scholar Nabû-ahhe-eriba reports that on the night following the 29th day (i.e. night of the 30th) he did not see the moon because of clouds, and on the following night, the moon looked to be two days old (ibid., no. 79);
77. this suggests that it might have been visible two days earlier, on the night of the 29th. Another report from the same scholar (ibid., no. 63) that "the moon st[ood there] on the 28th day" is most likely referring to the old moon's still being visible (cf. ibid., no. 261). These sources will be discussed further below.
78. One text, Hunger (ibid.), no. 506, reports that in four consecutive months (VI, VII, VIII, and IX) the moon had been sighted on the 1st (i.e. 31st of the outgoing month), which implies a run of four 30-day months. This would likely have caused a subsequent new moon sighting on the 29th or 28th, although this is not mentioned there. By contrast, in the Astronomical Diaries runs of four 30-day months are not attested.
79. This is a conclusion that could have been drawn by Fatoohi et al., op. cit. (ref. 7), had they considered the evidence of pre/postdicted new moons (see my remarks above, ref. 16).
80. In a recent article, Steele, op. cit. (ref. 1), argues that from the beginning of the Seleucid period (i.e. after the fourth century B.C.), the month was determined only by prediction. This is based on the finding that predicted month lengths, as given in Babylonian astronomical texts that contain only predictions (the Almanacs and Normal Star Almanacs), consistently agree with the month lengths that are given in the Diaries and other observational texts. This agreement, he concludes, indicates that month lengths were always determined by advance prediction. Steele's evidence, however, is limited to 50 cases, for a period ranging over two centuries; whilst these cases suggest that agreement between advance predictions and actual calendar months must have been common in this period, they do not prove that disagreement between predicted and actual months never occurred - indeed two of the 50 cases may actually be disagreements (even though Steele attempts to explain them away). The cases of 'late' new moon sightings that I have compiled - and that are not among Steele's 50 cases (as has been confirmed through personal communication) - indicate on the contrary that sometimes the beginning of the month was determined solely by new moon sighting. The clearest 'late' new moon sightings in this period are 26 December -302, 24 August-250, 13 August-249, 14 May-246, 15 October-233, 20 June-225, 4 July-210, 7 October-197, 3 October-194, 19 January-192, 9 May-175, 29 September-161, 8 February -145, 21 September -144, 17 October -141, 7 December -124, 5 August and 4 September -118, and 17 March -86 (19 cases in total). It is most likely that these late new moon sightings conflicted with predictions since, as I have found (above), late predictions are virtually unattested in the Astronomical Diaries; the predictions would have thus been one (or two) day(s) earlier than the new moon sightings, and yet in these cases, it is from the new moon sighting that the month began. This leads to the conclusion that in the Seleucid and later periods, both sighting and prediction were variously used for determining the beginning of the month.
81. For instance, on 4 November -273 the month began with a non-sighting on the 30th (which, as it happens, was an early prediction); the moon was still not sighted on the second evening, which is recorded in the Diary as "very overcast" (Sachs and Hunger, op. cit. (ref. 1), i, 338-9).
82. E.g. on 26 September -264.
83. But a sighting on time (i.e. not false) on the 30th is unlikely to have ever been followed by a prediction for the 31st, since late new moon predictions are generally not attested.
84. That the prediction was early is likely in view of the general tendency in the Diaries for early pre/postdiction of the new moon's visibility, which has been pointed out above.
85. E.g. 26 December -302. It is unlikely that in these cases the predictions were also late and on the 31st, because (as mentioned above) late predictions are generally unattested. See in more detail ref. 30.
86. Thus the months of 2 May -321, 29 January -231, 2 March -196, 15 September -168, 13 September -165, and 29 January -136, began on the 30th without a sighting, followed by a sighting of the moon on the second night (this is apparent at least from the fact that the position of the moon in relation to stars, planets, and/or cardinal points, is recorded in detail on night 2 in the Diaries). Why the month did not begin on that second night is unclear. Another example may be the month of 21 July -266 (Sachs and Hunger, op. cit. (ref. 1), i, 356-7): following the record of a non-sighting on the 30th (with its predicted sunset-moonset lag of 11°50′), the Diary records the sunset-moonset lag for the next evening (18° - according to modern calculations, it should have been 24°). This may indicate that the new moon was sighted on the second night, although the new month began, nevertheless, on the first night (as can be proved from other data provided for that month, e.g. the moonrise-sunrise lag on the day of last visibility dated to the 28th). However, this text is problematic because firstly, the sunset moonset lag is normally not recorded for any night other than the first (and not recorded twice), and secondly, the lag of 18° appears in the text after the heading "1st" (i.e. 1st day of the month), whereas the heading should have been "night of the 2nd". The text may require, therefore, re-examination.
87. Thus in -328, we have a late sighting (and beginning of month) on 14 October (when the new moon should have been predicted the day before - this date is however debatable, as indicated in the table), and yet for the next month we have a prediction on the 30th, on 12 November (when the new moon may well have been sighted the day after). In -302, we have a possibly early prediction on 31 May, and a late sighting on 26 December. Similar inconsistencies occur in -246 (14 May and 8 September), -210 (4 July and 31 August), and -87 (25 May) with -86 (17 March).
88. Note in particular 2 May -321, a non-sighting on the 30th, following a month that had also begun on the 30th. As mentioned above (ref. 36), the new moon was sighted on the next evening, 2nd of the new month (i.e. 3 May -321: see Sachs and Hunger, op. cit. (ref. 1), i, 222-3); the option of beginning this month on that evening (on the 31st) was thus certainly available, as well as calendrically desirable; nevertheless, it began on the 30th.
89. Above, refs 8-9.
90. They may also have been intended for cultic purposes, as well argued by Beaulieu, op. cit. (ref. 1), and Brown, op. cit. (ref. 2), 161-207.
91. The astrological purpose of month length predictions is evident in Hunger, op. cit. (see list of references above, ref. 8).
92. E.g. Hunger, op. cit. (ref. 8), no. 53, reporting that on two consecutive months the moon had "rejected the day". The notion that the moon itself, somewhat anthropomorphically, rejected the day by appearing on day 30, emphasizes that it was the actual appearance of the moon that determined the beginning of the month.
93. Ibid., no. 3.
94. The possibility of early new moon sightings on days 29 or 28 is frequently mentioned in the astrological omen lists (see above, ref. 27). Although it is not clearly stated whether and which days were "rejected" or "completed" in these cases, it seems reasonable to assume that the month would run its course until the end of day 29, since the month could not be shorter than 29 days (months shorter than 29 days are unattested in ancient Mesopotamian sources).
95. This means at the end of the 29th day (Astronomical Diaries and most other sources would have called it the evening of the 30th). For a similar usage see Parpola, op. cit. (ref. 8), i, nos. 91, 96-99, 102,
96. and Parpola's comment ibid., ii, 88 n. 179.
97. Ibid., ii, 102 (with ajudicious interpretation);
98. Hunger, op. cit. (ref. 8), no. 120;
99. and Beaulieu, op. cit. (ref. 1), 66-67 n. 4, whose translation is cited here.
100. In this letter, it is actually a combination of prediction and postdiction. The attempt to sight the moon at the end of the 29th implies that they predicted, to some extent, its visibility; then, after observing the moon's height at the end of the 30th, they postdicted that it should have been visible the evening before.
101. Parpola, op. cit. (ref. 8), i, no. 119 (also ibid., ii, 101-2);
102. idem, Letters from Assyrian and Babylonian scholars (Helsinki, 1993), no. 225;
103. and see Beaulieu, op. cit. (ref. 1), 66-67 n. 4.
104. The remainder of the text is unfortunately lost. This text implies that the king expected scholars to assist him, at the very least, in making his decision. The translation of B. Z. Wacholder and D. B. Weisberg, "Visibility of the new moon in cuneiform and rabbinic sources", Hebrew Union College annual, xlii (1971), 227-42,
105. is incoherent (see also Huber, op. cit. (ref. 1), 7).
106. Brown, op. cit. (ref. 2), 276, rejects any precise dating.
107. In this case it was only a postdiction, based on the height of the moon at its first sighting.
108. Parpola, op. cit. (ref. 8), i, no. 323
109. (see also citation of ABL 895: 5-10 in ibid., ii, 337).
110. Ibid., nos. 91 (Assur), 96, 99 (Arbela). But nos. 119 and 323 (cited above) were presumably sent locally from Nineveh.
111. He informs the king that the moon was seen on the 1st (i.e. 31st of the old month), thus determining the beginning of the month of Du'uzu: ibid., no. 290.
112. This letter suggests the assumption that a single, identical calendar was used throughout Assyria and Babylonia. Whether this assumption was correct, or valid at all times, remains of course to be seen. Parpola, op. cit. (ref. 8), ii, 337, conjectures, with reference at least to the Assyrian period, that separate calendars were reckoned in Babylonia and Assyria because the distance between Assyria and Babylonia caused the new moon to be sighted at different times. However, the difference between the geographical coordinates of Assyria and Babylonia is rarely significant so as to affect new moon visibility and the beginning of the month. If separate calendars were reckoned in Babylonia and Assyria in this period, this is more likely to have been due to the difficulty of communicating new moon reports from Babylonia to Assyria in a sufficiently short period of time. However, positive evidence of discrepancies between the beginning of Assyrian and Babylonian months is yet to be discovered.
113. Sachs and Hunger, op. cit. (ref. 1), i, 130-1, and comment in p. 138.