HOOFDARTIKEL EGYPTIAN LUNAR DATES and TEMPLE SERVICE MONTHS Chris BENNETT 1. Introduction Richard Parker's Analysis of The

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HOOFDARTIKEL This conclusion was based on Parker’s analysis of syn- chronisms between civil and lunar dates. He used two classes of data for this analysis. The first was a set of direct syn- EGYPTIAN LUNAR DATES AND TEMPLE chronisms between civil and lunar dates. The second was a SERVICE MONTHS set of civil dates of temple service months. A temple service month was a period of time in which a group of priests was Chris BENNETT1) required to perform various temple duties. For this purpose, priests were organized into groups known as “phyles”. Each 1. Introduction phyle was identified by a phyle number. For most of pharaonic history there were four phyles. The Canopic reform Richard Parker’s analysis of the regulation of Egyptian of 238 B.C. added a fifth. lunar months in Ptolemaic and Roman times has influenced While a direct synchronism allows the date of the start of all subsequent discussions of many important calendrical and a lunar month to be determined by simple subtraction, a tem- chronological topics, including the schematic lunar cycle of ple service date requires knowledge of the lunar date on pdem Carlsberg 9, the Macedonian calendar under Ptolemy which a service month began before it can be used to deter- II-VI, and the precise chronology of the 12th dynasty.2) mine the date of the start of the lunar month. Parker assumed The problem of regulating the lengths of lunar months that the first day of temple service fell on the first day of the arises because a calendar month is only an approximation to lunar month, ps∂ntyw.5) Since we have no explicit statement the length of an astronomical lunation, the time it takes for to this effect, the only way to verify it is to compare known the moon to cycle around the earth to the same position rel- civil dates for the start of temple service to the moon and to ative to the sun. A calendar lunar month is a count of the the Carlsberg cycle. number of days it takes for a chosen reference phase of the Although Parker used nine temple service dates from moon to repeat itself. In many cultures, such as Babylonia, Ptolemaic and Roman times, seven of these came from a the reference phase is the first visibility of the lunar crescent papyrus which did not give a year: pdem Cairo 30801 recto. around sunset. In Egypt, it was the day in which the lunar These dates clearly show that the first day of temple service crescent ceases to be visible at dawn. The name of the first was based on a lunar month, but, without a year, they do not day of the Egyptian lunar month, ps∂ntyw, reflected this con- allow us to determine which day in the lunar month was the cept.3) Similarly, the second day of the month, bd, was first day of the month of service. Parker dated them to year regarded as the day of first crescent visibility.4) 26 of Ptolemy VIII = 145/4 B.C. by assuming a priori that Since the moon does not cycle around the earth in an exact they represented the most recent ps∂ntyw to fall on the named number of days, and the time taken can vary slightly from civil dates, according to the Carlsberg cycle, before the date cycle to cycle, the length of a lunar month varies between 29 of the verso, year 41 of Ptolemy VIII = 130/29 B.C. and 30 days from month to month. There are several possi- Only two of the Julian dates of Parker’s temple service ble methods for determining the first day of a lunar month. documents were certain.6) These came from two documents In Babylonia, the start of the lunar month was determined by from the reigns of Nero (iMoscow 145) and Commodus observation of the first crescent, although in poor weather (oThebes D31). Both directly equate a day of temple service conditions it would be necessary to estimate the occurrence to a civil date in an unambiguously named year.7) However, of this event. Another approach is to use an algorithm that only one of the dates that Parker derived for the first days of predicts the behaviour of the moon. Such algorithms may not the two lunar months actually corresponded to the day of be perfectly accurate, but can be sufficiently accurate on aver- lunar invisibility according to the astronomical tables he used. age that they allow the start of a lunar month to be predicted The other fell on the following day. Parker reconciled this independently of the moon, with an error margin of one day, conflict by noting that both dates fell on the first day of the for a long period of time. Parker concluded that one such schematic lunar months of the Carlsberg cycle, which he algorithm, the schematic lunar cycle of pdem Carlsberg 9, assumed was ps∂ntyw. He concluded that temple service was used to regulate the Egyptian lunar calendar in Ptolemaic months were regulated by the Carlsberg cycle in both Ptole- and Roman times. maic and Roman times, even though a data set of only two samples is clearly too small to draw such a conclusion with any certainty. 1) My thanks to Mark Depauw and Sandra Lippert for helpful comments Thissen noted several additional temple service dates in on earlier drafts of this paper, particularly for their guidance on demotic the Medinet Habu graffiti from the later Ptolemaic period, issues. Preliminary versions of parts of this paper were presented to the annual meeting of the American Research Center in Egypt (ARCE) in 2006 some of which appeared to be aligned with bd, not ps∂ntyw, and placed on the web in 2005 at http://www.tyndale.cam.ac.uk/ Egypt/ptolemies/chron/egyptian/chron_eg_anl_lun.htm. 2) R. A. Parker, The Calendars of Egypt (Chicago, 1950), 9-29, 63-69. 5) Parker (n. 2), 17 §67, with reference to the temple service month Parker’s theories of the Carlsberg cycle were first applied to the Macedonian given by oThebes D31: “we may take IIII prt 28 to be ps∂ntyw.” Depuydt calendar by A. E. Samuel, Ptolemaic Chronology (Munich, 1962), 54-61. (n.4), 177, describes the assumption as “reasonable”. 3) Cf. L. Depuydt, “The Hieroglyphic Representation of the Moon’s 6) Cf. Depuydt (n. 4), 184-185. Absence (Ps∂ntyw)”, in L. H. Lesko (ed.), Ancient Egyptian and Mediter- 7) iMoscow 145: W. Spiegelberg, “Eine neue Bauinschrift des Parthe- ranean Studies in Memory of William A. Ward (Providence, 1998), 71-89. nios”, ZÄS 66 (1930), 42-43; S. Hodjash & O. D. Berlev, The Egyptian 4) For bd as notional first crescent visibility, Parker (n. 2), 12 §38-39; Reliefs and Stelae in the Pushkin Museum of Fine Arts Moscow (Leningrad, as the day after ps∂ntyw, L. Depuydt, Civil Calendar and Lunar Calendar 1982), no. 145. oThebes D31: A. H. Gardiner et al., Theban Ostraca: ed. in Ancient Egypt (Leuven, 1997), 149. Astronomical invisibility can last for from the originals, now mainly in the Royal Ontario museum of archaeol- two or even three days (B. E. Schaefer, “The Length of the Lunar Month”, ogy, Toronto, and the Bodleian library, Oxford (Toronto, 1913), 51-52. Archaeoastronomy 17 (1992), 32-42 at 33), so the moon must often, in prac- oThebes D31 actually gives both a start and end date for a service month, tice, have been invisible on bd. Parker (n. 2), 13 §44, suggests that the but Parker only considered the start date usable; this question is discussed name of day 3 (mspr — arrival) covers this case. further below. He did not use the service start date given in oThebes D235. 1710_BIOR_2008/5-6_01_Tekst 30-01-2009 10:44 Pagina 526

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on the Carlsberg cycle.8) Parker suggested to him that this received some attention for their chronological value,13) nei- phenomenon reflected the lunar alignment of the Macedon- ther they nor the dates given by the service contracts have ian calendar, whose months, according to Samuel, were been studied for the information they provide about the lunar intended to start on the evening of the second day of Carls- date of the start of temple service. berg cycle months, i.e. on the evening of bd, which notion- The problem is of interest for several reasons. First, the ally represented first crescent visibility. Parker supposed that data allows us to assess Parker’s proposal that lunar months this arrangement had been imposed on the Theban priest- were governed by a schematic cycle in Graeco-Roman times. hood after the suppression of the Theban revolt by Ptolemy Parker’s specific proposal of the Carlsberg cycle has domi- IX in 88 B.C. Neither scholar explained why the Alexan- nated discussions of both Egyptian and Macedonian Ptole- drian government should have taken such a step some 60 maic lunar cycles for several decades, but it has recently been years after it had itself ceased to use the lunar Macedonian questioned for several reasons. Spalinger and Jones both calendar.9) noted that the data Parker used was insufficient to validate In addition to the Medinet Habu graffiti, Kaplony-Heckel the theory.14) Depuydt’s reanalysis of the papyrus led to a has recently collected and republished a set of ostraca con- reconstruction of the cycle that differs from Parker’s.15) taining contracts leasing or exchanging months of temple While only one of the points at which they differ is reflected service at various Theban temples,10) and a papyrus from the in the data Parker used — the entry for III prt in pdem Cairo Fayyum has been published containing a temple service date 30801 — this is sufficient to show that the Carlsberg cycle from Socnopiau Nesos.11) Further, Lippert has recently was not used in Gebelein if Depuydt is correct, since the inferred a set of temple service dates from grain receipts match should be perfect. Lippert’s results clearly show the from Dime for offerings to the god at Socnopiau Nesos, Carlsberg cycle was not used in Socnopiau Nesos. However, based on the observation that wheat was allocated to a phyle she correctly noted that another schematic cycle may have at the fixed rate of 1 artaba a day. She showed that the ser- been used. The data considered here allows us to evaluate vice dates she inferred did not always match the dates pre- that proposition. dicted by the Carlsberg cycle, and did not closely correspond The possible methods are not restricted to schematic cycles to astronomical crescent invisibility. She suggested that they or astronomical observation. For example, the Babylonian may have been governed by a different, unknown, schematic lunar theory known as Lunar System B was very probably cycle.12) known in Egypt at this time. This possibility cannot be tested In this paper I consider the dates provided by those sources directly since the precise method used to predict first and last of temple service dates which give direct synchronisms crescent visibility in System B is not yet known.16) However, between civil dates and specific days of temple service, usu- we may suppose that the theory gave results which were ally the first. To my knowledge, we currently have 15 pub- acceptable to Babylonian observers, which suggests that it lished Ptolemaic and Roman documents over the interval 131 was quite accurate. B.C. to A.D. 199 giving 25 civil dates of specific days in tem- The question has wider ramifications. Luft concluded that ple service months. Although the Medinet Habu dates have the first day of temple service fell on bd in the Middle King- dom, based on analysis of the distances between the temple service dates of pBerlin 10056 and, ultimately, a ps∂ntyw date 8) gr. Med. Habu: H. J. Thissen, Die demotischen Graffiti von Medinet given in pBerlin 10090.17) This proposal evidently conflicts Habu: Zeugnisse zu Tempel und Kult in ptolemäischen Ägypten (Sommer- with Parker’s assumption. If both scholars were correct it hausen, 1989), with epigraphic comments in a review by M. Chauveau, RdE 46 (1995), 250-255. The original graffiti are published in W. F. Edgerton, would imply that there was a change in the lunar date of the Medinet Habu Graffiti: Facsimiles (Chicago, 1937). 9) Thissen (n. 8), 181. The last known double date showing an inde- pendent Macedonian calendar is 1 (or 30 or 4) Xandikos = 25 Thoth year 13) M. Chauveau, “Ères nouvelles et corégences en Égypte ptolé- 26 (of Ptolemy VI) (UPZ I 113). While direct evidence is lacking, it seems maïque”, in B. Kramer et al. (eds), Akten des 21. Internationalen Papy- likely that the Macedonian calendar was finally subordinated to the Egypt- rologenkongresses (Stuttgart,1997), I 163-171. Cf. C. J. Bennett & M. ian one by Ptolemy VIII on or soon after his accession. The process was Depauw, “The Reign of Berenike IV (Summer 58 — Spring 55 BC)”, ZPE certainly complete by the late 120s B.C., when the alignment was changed 160 (2007), 211-214. from Thoth = Dystros to Thoth = Dios. See Samuel (n. 2), 132-135. On the 14) A. J. Spalinger, “Calendrical Comments”, BiOr 51 (1994), 5-20 at Macedonian calendar in Egypt see now C. J. Bennett, “Alexandria and the 13-16; A. Jones, “On the Reconstructed Macedonian and Egyptian Lunar Ptolemaic Macedonian Calendar”, a[forthcoming]. Calendars”, ZPE 119 (1997), 157-166. 10) odem Zauzich: U. Kaplony-Heckel, “Rund um die thebanischen 15) L. Depuydt, “The Demotic Mathematical Astronomical Papyrus Tempel (Demotische Ostraka zur Pfründen-Wirtschaft)” in F. Hoffmann & Carlsberg 9 Reconsidered”, in W. Clarysse et al. (eds), Egyptian Religion H. J. Thissen (eds.), Res Severa Verum Gaudiam: Festschrift für Karl- — The Last Thousand Years: Studies Dedicated to the Memory of Jan Theodor Zauzich zum 65. Geburtstag am 8. Juni 2004 (Leuven, 2004) [Fs. Quaegebeur (Louvain, 1998), II 1277-1297. Zauzich], 283-337. Although documents published in Fs. Zauzich are 16) Visibility criteria in Lunar System B: O. Neugebauer, A History of referred to as “pZauzich” in the Demotic Berichtigungsliste, all such doc- Ancient Mathematical Astronomy (New York, 1975), I 533-540; L. J. uments used in this article are ostraca and are identified accordingly. Fatoohi et al., “The Babylonian First Visibility of the Lunar Crescent: Data 11) pdem Ox. Griffith 41: E. Bresciani, L'Archivio demotico del tempio and Criterion”, JHA 30 (1999), 51-72 at 60-63. System B in Egypt: A. di Soknopiau Nesos nel Griffith Institute di Oxford (Milan, 1975), 52-53, Jones, “A Greek Papyrus Containing Babylonian Lunar Theory”, ZPE 119 126-127. My thanks to Prof. Zauzich (pers. comm., 3 May 2005) for bring- (1997), 167-172; idem, “Babylonian Lunar Theory in Roman Egypt: Two ing this example to my attention and to him and Sandra Lippert for dis- New Texts”, in J. M. Steele & A. Imhausen (eds.), Under One Sky: Astron- cussing its interpretation with me. omy and Mathematics in the Ancient Near East (Münster, 2002), 168-174. 12) DDD II: S. L. Lippert & M. Schentuleit, Demotische Dokumente aus These documents are Greek, but results of Babylonian theory were known Dime II: Quittungen (Wiesbaden, 2006), 145-183; S. L. Lippert, “Au clair to the Egyptian community: O. Neugebauer, R. A. Parker & K-T. Zauzich, de la lune: The organisation of cultic service by moon calendar in Soc- “A Demotic Lunar Eclipse Text of the First Century B.C.”, Proc. Am. Phil. nopaiou Nesos”, in M. Chauveau et al. (eds.), Actes du IXe Congrès Inter- Soc. 125 (1981), 312-327. national des Études démotiques, Paris 2005 (Cairo, [forthcoming]). My 17) U. Luft, Die chronologische Fixierung des ägyptischen Mittleren thanks to Leo Depuydt for drawing my attention to this work, and to San- Reiches nach dem Tempelarchiv von Illahun (Vienna, 1992), 189-195, 205- dra Lippert for sharing a draft copy of her paper and for discussing her 208. Cf. R. Krauss, “Lunar Dates”, in E. Hornung et. al. (eds.), Ancient results with me. The Dime data is summarily analysed in Table 3. Egyptian Chronology (Leiden, 2006), 395-431, at 426. 1710_BIOR_2008/5-6_01_Tekst 30-01-2009 10:44 Pagina 527

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start of temple service months between the Middle Kingdom service month is referred to as an bd. The two items used and the Ptolemaic period. Krauss has, in effect, proposed this by Parker, iMoscow 145 and oThebes D31, were respectively resolution in connection with his analysis of the date of a wrs- a wrs date and a service agreement. Both types of document feast in year 5 of Shoshenq I.18) often, though not invariably, associate the service month with Finally, Wells has raised the question of whether it is even a phyle number. Nineteen of the dates, from nine documents, possible to deduce the correspondence of civil dates to the are wrs dates; six are from temple service agreements. Julian calendar from lunar data of the type exemplified by The data is of variable quality. Several of the documents the Illahun papyri. He argued that matches of the month do not specify a reign, and could be assigned to more than lengths of the Illahun data to sequences of month lengths cal- one possible king. Others give dates which are not perfectly culated from the moon are of low statistical significance since preserved, or are of uncertain reading or interpretation. For there are many sources of possible error, and an error in the this reason, it is necessary to proceed as Parker did, by first length of one month affects the lengths of neighbouring analyzing the unambiguous dates and then applying the months, making the procedure very susceptible to false results to the others to determine whether reasonable, and matches.19) However, this argument takes no account of the preferably unique, solutions can be derived for them consis- constraints set by non-lunar data, notably the Sothic date of tent with the lunar structure of temple service months. pBerlin 10012. This limits the number of possible solutions. Even when the source dates are completely unambiguous, Krauss has stressed that analysis of last crescents associated they are of variable reliability. Wrs dates are inherently more with individual lunar dates in the various possible solutions likely to be reliable, since at least the start date of the tem- allows us to determine which last crescents are likely to be ple service is certainly retrospective in all documents.22) The subject to observer error, and has shown that astronomical reliability of dates in the service agreements depends on the solutions exist in which the majority of last crescents can be date of the agreement and the actual significance of the dates. accepted.20) Unless the agreement was reached on the first day of service, Both arguments assume that the start of the Egyptian lunar as in odem Zauzich 20, the dates given in the agreement are month was determined by observation of lunar invisibility in anticipatory. We do not know whether such dates were pre- the Middle Kingdom. The point of contention is whether we determined or merely estimates. can safely assume that modern calculations of such dates are If they were predetermined, they will still be reliable ser- sufficiently reliable that a precise chronology can be derived vice dates, but if they are only estimates, e.g. because start by matching these lunar dates to calculated astronomical of service was actually determined by observation, the dates invisibility. Krauss assumes an accuracy of 85-95%, based in service agreements may sometimes fall a day before the on analyses of first crescent observations in the Babylonian actual start of temple service. Therefore, the only certain astronomical diaries.21 This validates our ability to calculate statement we can make about such a date, unless it is known dates of lunar invisibility, but it does not demonstrate that the that agreement was reached on the first day of service, is that start of an Egyptian lunar month was actually determined by it represents the earliest date that the grantee could expect to observing invisibility. start temple service. As a result, an uncertainty of one day is For chronological purposes, it does not really matter pre- assumed when analyzing this data: the service month may cisely how the start of the lunar month was determined. The have started on the named date or on the following day. For important question is whether the method, whatever it was, this reason even the date given for the first day of service in was astronomically accurate. This can only be assessed by oThebes D31, accepted by Parker as fully reliable, is here analyzing lunar dates from a chronologically secure period, regarded as uncertain. such as the Ptolemaic and Roman periods. Unless it can be This assumption may well be unduly conservative, since shown that the method used to determine the start of the lunar there is at least one case (odem Zauzich 28) of a named ser- month in Ptolemaic and Roman times was not used in earlier vice start date that fell more than a month after the date of times, we may reasonably expect lunar dates from other peri- agreement, suggesting that the date was predetermined.23) ods, notably the Middle Kingdom, to exhibit the same level Nevertheless, the date named on a service agreement is of accuracy. assumed here to be only an expectation made at the time of

2. Characteristics of the Source Data 22) Depuydt (n. 4), 183, has suggested that pdem Cairo 30801 is a list As noted above, the sources considered in this paper fall of future temple service month dates. This seems unlikely, in view of the into two classes: graffiti and other documents mentioning the fractional and arbitrary amounts of wheat that would have to have been ordered months in advance (e.g. 9.25 artabas for the month I prt 19 to II dates of an executed temple service month, called a wrs, and prt 18, and 11.25 artabas for I smw 17 to II smw 16). It is assumed here agreements to lease or exchange temple service, in which the that the dates in this document are also retrospective. He has made the same suggestion (loc. cit., 180) with respect to pBerlin 10056. In this case the internal evidence does not appear to me to allow it to be tested one way or the other. 18) R. Krauss, “Das wrs-Datum aus Jahr 5 von Shoshenq [I]”, DE 62 23) DDD II 45 = pVienna D6819ro may point in the opposite direction. (2005), 43-48, at 46; see discussion at the end of this paper. This is a receipt for 1 artaba of offering wheat (1 day’s rations) given to 19) R. A. Wells, “The Role of Astronomical Techniques in Ancient phyle 2 dated I Ìt 22 year 3 of Claudius = 3 September A.D. 42 on the wan- Egyptian Chronology: The Use of Lunar Months in Absolute Dating”, in dering calendar. This date is not considered as a service month synchronism Steele & Imhausen (n. 16), 459-472. in Lippert (n. 12). However, it was a day of lunar invisibility following a 20) Krauss (n. 17), 399-404. last crescent on 2 September. According to the theory advanced here, this 21) Krauss (n. 17), 399-400, based on the 209 dates of observed first would most probably be the last day of temple service; the less likely pos- crescents studied in Fatoohi et al. (n. 16); now superseded by S. Stern, “The sibility being that it is the first day of the following service month, based on Babylonian Month and the New Moon: Sighting and Prediction”, JHA 39 a missed last crescent. While many of these receipts are only for a few days (2008), 19-42, giving 441 observed and predicted first crescent dates, but at a time, this receipt could represent the unexpected extension of a 29 day with nearly identical levels of accuracy. service month into a 30 day month, if the first choice is correct. 1710_BIOR_2008/5-6_01_Tekst 30-01-2009 10:44 Pagina 528

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the agreement, though it is regarded as the more likely date the start of the first service month. In this case, the uncer- for the start of service for this reason. tainties are even greater, since not only is the end date not While most of the dates considered are directly related to given explicitly but the start date may be a day early. Nei- the date of start of a service month, five documents give dates ther end date is usable, unless we assume that service month for the end of a service month without also giving the date dates were predetermined. of the start of the next month. Three are wrs dates and two Finally, Roman-era dates may be given according to either are from service agreements. One of the latter is from oTh- the Alexandrian calendar or the wandering calendar. Since ebes D31. Parker rejected this date on the grounds it was we know from pdem Cairo 30801 that temple service months impossible to tell whether the date represented the last day were lunar, the calendar that gives the better lunar match is of a service month or the first day of the next service month. assumed to be correct. Parker showed that this assumption This ambiguity has also been central to interpreting the end required that the two items known to him were dated on the dates of temple service months in the Illahun data.24) Alexandrian calendar, and Lippert showed that the receipts It is clear from the data considered here that there was no she considered were dated by the wandering calendar for the agreed convention for the date of an end of service. Exam- same reason. However, it cannot be assumed a priori that all ples exist for both the possibilities considered by Parker. Roman-era dates at a given temple were according to one cal- Pdem Cairo 30801 reports the last day of each temple ser- endar or the other. It will be seen that three of the service vice month (wrs) as the day before the first day of the ser- agreements from Medinet Habu are dated on the wandering vice month of the next phyle. However, two of the Medinet calendar. Roman-era service dates must be tested against both Habu graffiti — gr. Med. Habu 51 and gr. Med. Habu 228 calendars to determine which one is in use.26) — date the last day of a temple service month (wrs) to the st 31 day of service, which must also be the first day of the 3. Method of Analysis next service month. Also, odem Zauzich 21 = oThebes D175 is a 31-day temple service lease, from IV Ìt 9 to I prt 9, in With these qualifications, five of the dates for the start of an unknown year. The solution to gr. Med. Habu 48 proposed temple service, from four documents, are complete and cer- below suggests that both conventions were followed at tain. All are retrospective and all are wrs dates. The remain- Medinet Habu at different times.25) The explanation perhaps ing twenty dates, from eleven documents, are uncertain, lies in the possibility that a phyle could report for duty on the either for inherent reasons discussed above, or because they day before its first day of service. require some degree of reconstruction in order to determine Hence, care must be taken in using the end date of a tem- their civil and Julian date. Thirteen of these are wrs dates; ple service month to determine the start of the following ser- the rest are from service lease or exchange agreements. vice month. If an end date is 29 days after the start date of The five certain dates are listed in Table 1; the other the same service month, then it is certainly the day before the twenty are listed in Table 2. The tables compare the date for first day of the next month. If it is 31 days later, then it is day 1 of a service month to the date for day 1 of the nearest certainly also the first day of the next month. If it is 30 days month of the Carlsberg cycle and to the nearest date of astro- later, or if only an end date is available, then either case is nomical last crescent visibility, which is used to estimate possible. Thus, only end dates of service months known to ps∂ntyw as the following day.27) The dates of last crescent be 29 or 31 days long can be used. visibility were calculated using the program PLSV 3.0,28) Two of the documents considered, odem Zauzich 20 and which provides direct estimates of first and last crescent vis- odem Zauzich 28, are leases for two months. The first is a ibility using an empirical formula derived by Caldwell and lease ending 59 days after the start date (i.e. on day 60, count- Laney.29) ing the start date as day 1). In this case, the start date given The default parameter settings of the Caldwell-Laney for- by the lease is certain, since the agreement was reached on mula appear to make it a good estimator, correctly predict- the same day. However, there are still three possible ing 193 of the 209 Babylonian first crescent observations sequences which affect the significance of the end date. If studied by Fatoohi et al. — a success rate of 92.3%.30) How- there were actually two 29 day months, the lease ended on ever, it does occasionally miss observable crescents, or pre- the second day of the third service month. If the leased dict unobservable ones. More significantly, the default set- months were a 29 day month and a 30 day month, the lease tings are optimistic in two respects. First, they assume that ended on the first day of the third month. If the leased months the observer is experienced, trained, and has good vision. were two 30 day months, the lease ended on the last day of the second month. Odem Zauzich 28 is a lease-and-exchange agreement covering 60 days which was agreed 10 days before 26) For the Alexandrian calendar, the standard model of intercalations every four years starting in 22 B.C. is assumed here. See now C. J. Ben- nett, “The Two Egyptian Birth Days of Augustus”, ZPE 161 (2007), 195- 24) G. H. Wheeler, “The Chronology of the Twelfth Dynasty”, JEA 9 198. (1923), 196-200 at 199; Parker (n. 2), 64-66 §§321-329. 27) The date of first visibility is not included because it certainly falls 25) This may also be true at Dime. Most receipts clearly show one ser- after ps∂ntyw had already been determined — see n. 4. vice month ending on the day before the next, but DDD II 47 = pVienna 28) R. Lange & N. M. Swerdlow, “Two Programs, for Ephemeris and D6134ro B+C includes a receipt dated I prt 10+[x] for 29 artaba for phyle Visibility Calculations, Useful for Historical Applications”, JHA 36 (2005), 2 from IV Ìt 12 to I prt 11, and the period covered by the receipt for phyle 334-335; freely available at http://www.alcyone.de/PVis/english/ 3 starts on I prt 11. Lippert & Schentuleit (n. 12), 161 B 5+8, regard the 29) J. A. R. Caldwell & C. D. Laney, “First Visibility of the Lunar Cres- first mention of I prt 11 as a scribal error for I prt 10, noting that the sur- cent”, African Skies 5 (2001), 15-23, at 18 (Fig. 3) and 21 (Table 1). This viving traces of the second numeral of the date of the receipt preclude I prt study incorporates and extends earlier surveys by Schaefer and others. 1[1], meaning that the record was made after the start of the following ser- 30) Similar accuracy is seen with Stern’s data (n. 21). Fatoohi’s study is vice month. While there most probably is an error here, a transition on the retained here as the basis for comparison because the statistical differences first day of the next service month cannot be excluded, in light of the are very small and because this is the study Krauss used (n. 17) as the basis Medinet Habu examples. for his analysis of the Illahun lunar dates, discussed below. 1710_BIOR_2008/5-6_01_Tekst 30-01-2009 10:44 Pagina 529

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While these are reasonable assumptions for the observers at Gr Med. Habu 45, dated I Ìt 14 year 5 of Ptolemy XIII the E-Sagila temple in Babylon, we do not know a priori and Cleopatra VII = 48/7 B.C.,36) notes that the day was day whether they are valid for observers in contemporary Egypt. 20 of a wrs of phyle 1. Second, the formula was developed for observations of first Gr Med. Habu 47, dated II prt 21 year 15 of Cleopatra VII crescent visibility. Wells noted that last crescent visibility = 38/7 B.C., notes that the day was day 17 of a wrs of phyle presents greater psychophysical challenges to the 1. observer.31) IMoscow 145, a stele from Koptos dated to year 12 of Nero In order to detect whether a PLSV result may be sensitive = 65/6 A.D., notes that IV prt 23 was day 6 of a wrs. This to the visibility threshold, the program was run with baseline document was analyzed by Parker, who showed that the date lunar altitude settings of 10.8° and 12.3° in addition to the is on the Alexandrian calendar.37) Caldwell-Laney setting of 11.3°.32) If an alternate solution Only one of these dates match the first day of Carlsberg was found for the lower or higher threshold, both possibili- cycle months. The other four are one day later. Table 1 con- ties are included in the tables. This only indicates that the firms Lippert’s conclusion that the Carlsberg cycle was not solution given by the default threshold may be sensitive to used to regulate temple service.38) reasonable variations in visibility threshold assumptions. The All five dates in Table 1 fall two days after last crescent solution given by the default threshold setting is to be pre- visibility on PLSV default settings, although one could be ferred. The PLSV results were also compared to those affected by a lower visibility threshold. Thus, the start of tem- obtained from LunaCal 3.0 and AccurateTimes 5.1.33) Both ple service appears to be correlated with the second day after programs gave slightly more conservative results than the last crescent visibility. We may conclude that temple service PLSV default settings in a few of the cases which had already most probably did not begin on ps∂ntyw. The data appears been found to be sensitive to visibility assumptions, but nei- most consistent with the theory that a Ptolemaic or Roman ther program gave results more conservative than the “worst- temple service was intended to begin on bd, day 2 of the case” altitude setting of 12.3°. lunar month, as Luft had concluded for the Middle Kingdom. The margin of error for the difference between universal This conclusion explains a feature of a demotic papyrus in time and terrestrial ephemeris time due to tidal deceleration Vienna giving a set of eclipse omina which are double dated of the rotation of the earth over time (DT), which is signifi- in the Egyptian and Babylonian (Aramaic) calendars. Parker cant for analyzing eclipses and the Illahun lunar data, is not showed that these double dates imply that the text was prob- important for crescent visibility calculations in this period. ably composed in the late sixth or early fifth centuries B.C. The model used for DT by PLSV is based on an older and The Babylonian months of this document are described as less accurate analysis than that developed by Morrison and wrs, a term usually denoting temple service months; only on Stephenson,34) but the difference is less than 2 minutes in the one occasion is the more normal bd used (here indicating a period in question. This is less than the estimates given by month rather than lunar day 2). Parker noted the point but did the Morrison-Stephenson formula for the error margin for not elucidate it. The term is clearly explicable as referring to DT, which range from about ±5 minutes in 131 B.C. to about a month starting on bd, lunar day 2, in the Babylonian style, ±3:30 minutes in A.D. 199. In theory, such variations could rather than ps∂ntyw.39) cause a last crescent visibility to be predicted a day early or late for a given visibility threshold. However, the change in 5. Determination of the Remaining Service Dates the relative position of the sun and the moon in 5 minutes is much smaller than the sensitivity range used for the thresh- We can test the proposed alignment to bd by assessing old of vision. whether it allows us to determine reasonable solutions for other temple service dates which are incomplete or ambigu- 4. Analysis of Complete and Certain Service Dates ous. The documents considered in Table 2 fall into this cat- egory. They are considered in most likely chronological The background to the dates included in Table 1 may be order. They were subjected to the same sensitivity analysis briefly described, in chronological order. One of these dates as those of Table 1. was used by Parker; the remaining four are given by the Medinet Habu graffiti. Pdem Ox. Griffith 41 Gr Med. Habu 43, dated to year 26=3 of Ptolemy XII and This papyrus, from Socnopiau Nesos in the Fayyum, Berenice IV = 56/5 B.C.,35) gives two service dates. It notes includes mention of phyle 4 assembling on II Ìt 19 year that I prt 1 was day 12 of a wrs of phyle 2, and that the wrs 40.40) The king can only be Ptolemy VIII, giving the Julian of phyle 3 started on I prt 19. date 12 November 131. Taken literally, the papyrus says “Before II Ìt 19, the wrs, we came to the temple in order to give libation in our month of libation”, which appears to 31) Wells (n. 19), 465. 32) For a Babylonian eclipse observation most likely made possible by exceptional visibility conditions, see J. M. Steele, “Ptolemy, Babylon and 36) For Ptolemy and Cleopatra “Philopatores” as Ptolemy XIII and the Rotation of the Earth”, Astronomy & Geophysics 46 (2005), 5.11-5.15. Cleopatra VII, rather than Ptolemy XII and Cleopatra V, as proposed by 33) AccurateTimes 5.1 is freely available from the Islamic Crescents Thissen, see Chauveau (n. 13), 168. Observation Project (ICOP) online at http://www.icoproject.org/accut.html; 37) Parker (n. 2), 18 §70. LunaCal 3.0 is freely available from the Israeli New Moon Society online 38) The Carlsberg cycle is still useful to locate candidate years for a lunar at http://www.geocities.com/royh_il/software.htm. match. 34) L. V. Morrison & F. R. Stephenson, “Historical Values of the Earth’s 39) R. A. Parker, A Vienna Demotic Papyrus on Eclipse — and Lunar- Clock Error DT and the Calculation of Eclipses”, JHA 35 (2004), 327-336. Omina (Providence, 1959), 8 n. 18. 35) For 26=3 rather than 26=4, as read by Thissen, see Chauveau (n. 13), 40) Ll. 4-6, correcting Bresciani’s reading of line 4 to Ì.t 2 Ì.t sw 19 167. Berenice IV is named as “Cleopatra”. p wrs tw-n (K.-T. Zauzich, pers. comm., 4 May 2005). 1710_BIOR_2008/5-6_01_Tekst 30-01-2009 10:44 Pagina 530

535 BIBLIOTHECA ORIENTALIS LXV N° 5-6, september-december 2008 536

indicate that the service month began on II Ìt 19. However, He concluded that the recto dates to the last cycle year 13 Zauzich notes that the syntax is irregular and suggests that before year 130/29 B.C., i.e. to 145/4 B.C., 15 years before the intended sense may be that the phyle came to the tem- the date of the verso. ple on the day before the start of phyle service, i.e. that the Steps (1) to (4) of Parker’s argument are unexceptionable. correct date for the start of service is II Ìt 20.41) Alterna- However, the dates listed in Table 1 suggest that the list tively, Lippert notes that the term wrs in this context could should instead be dated to the last year before year 41 in refer to the wrs feast rather than the month of phyle ser- which the start of the temple service corresponds most closely vice.42) Quack interprets the Demotic Chronicle as stating to the second day after last crescent visibility, i.e. to a lunar that the wrs feast was held on the last day of the month.43) date of bd, not ps∂ntyw. On this basis, the best match for If both scholars are correct, it again follows that a phyle ser- pdem Cairo 30801 is year 40 of Ptolemy VIII = 131/0 B.C. vice began on II Ìt 20. This dating implies that the recto and verso were used in con- Hence, while II Ìt 19 year 40 of Ptolemy VIII is taken secutive years, which seems more likely than the separation here as the date of the start of phyle service given by the of 15 years required by Parker’s solution. papyus, there are grounds for supposing that the correct date is in fact II Ìt 20. II Ìt 19 year 40 is a day early against the Gr. Med. Habu 48 Carlsberg cycle and 12 November 131 is a day early against This graffito gives start and end wrs dates for phyle 1. the moon, while II Ìt 20 matches both criteria. These are very incomplete, and are the most problematic in the series.46 Thissen read them as II Ìt (?) 1[5] to III [Ìt] Pdem Cairo 30801 recto 14, but the traces of the month name permit reading either of This papyrus, from Gebelein, is the most important of the other two seasons. The only certain day number is 14, the these documents. It is an account of grain deliveries, which day number of the end of service, but we do not know a pri- includes the following list of wrs dates: ori whether the temple service month lasted for 29 or 30 IV Ìt 20 days, nor do we know whether the graffito marked the end I prt 19 to II prt 18 (Phyle 1) of the service month as the day before the start of the fol- II prt 19 to III prt 18 (Phyle 2) lowing service month, or as the first day of the following ser- III prt 19 to IV prt 17 (Phyle 3?) vice month. Thus, the two dates could be 29, 30 or 31 days IV prt 18 to I smw 16 (Phyle 4) apart, implying a start date of 14, 15 or 16. [I smw 1]7 to II smw 16 (Phyle 5) The document is double dated to the reign of a Ptolemy [II smw 17] to III smw 16 (Phyle 1) and a Cleopatra. Only the second year number is legible. All except the first are explicitly given as wrs dates for the Thissen read it “year 10” and restored the double date as: named phyles. The first is given in a summary of the grain Year [21?] Ptolemy (VI?) and Cleopatra (II?) = Year 10 deliveries and is presumably also a wrs date. Parker studied (Ptolemy VIII?) this document in depth.44) As he recognized, the dates clearly Year 21 of Ptolemy VI = 161/0 B.C. is a Carlsberg cycle show that temple service dates were controlled by a lunar year 22, which includes a cycle month from II 14 to III structure. They also show that a temple service month was Ìt 13. On Parker’s theory of the Carlsberg cycle, these dates normally assigned in order of phyle number. This question Ìt correspond to a temple service month beginning on day 2 of will be considered in more detail below. a Carlsberg cycle month. Parker dated the papyrus to 145/4 B.C. on the following However, the joint reign of Ptolemy VI, Cleopatra II and grounds: Ptolemy VIII had ended in year 7 = 164/3 B.C., and there 1. The mention of a fifth phyle shows that the papyrus post- is no known reason for years 8-25 of Ptolemy VIII to appear dates the creation of that phyle by the Canopus Decree of on Egyptian documents, since he ruled in Cyrene in these 238 B.C. years. While at least four other documents have been 2. The paleography is of late Ptolemaic date. assigned to Ptolemy VIII in this period, all are at best doubt- 3. The verso contains an account of grain deliveries in a dif- ful. The stele iCairo JdE 55941, which was originally read ferent hand dated to year 41, which must therefore be of as year 20=9, and therefore assigned to Ptolemy VI and Ptolemy VIII, i.e. 130/29 B.C. Ptolemy VIII, was reread as year 20=5 by Chauveau and 4. The recto was usually written before the verso. reassigned to Cleopatra VII.47) Kaplony-Heckel proposed 5. The (even)45) month dates match the Carlsberg cycle dates that an archive of ostraca from Oxyrhynchus should be for cycle year 13, which at the time of Ptolemy VIII were assigned to Ptolemy VIII, including odem Pisa 925, dated a good match to lunar invisibility (i.e. ps∂ntyw). year 9, and odem Pisa 936, dated year 24. Depauw has sug- gested instead that odem Pisa 925 should be read as “year 29”, and that the date of odem Pisa 936 is grounds for redat- ing it to Ptolemy VI. He has also suggested that the year 41) Zauzich (n. 40), interpreting the intended sense as: (Ìpr) 2 Ì.t sw [22?] = 11 proposed by Spiegelberg for pdem Cairo 31211 19 Ì.t p wrs — (it was) 19 Phaophi (the day) before the wrs. 42) S. L. Lippert, pers. comm., 23 June 2008. should instead be restored as year [8] = 11 of Ptolemy X and 43) H. Felber, “Die demotische Chronik”, in A. Blasius & B. U. Schip- per (eds.), Apokalyptik und Ägypten (Leuven, 2002), 65-111 at 76-77, cit- ing the opinion of J. F. Quack. 46) My thanks to Michel Chauveau, John Gee, Heinz Thissen, Steve Vin- 44) Parker (n. 2), 19-21 §§86-101. son and Karl-Theodor Zauzich for discussing this graffito with me at vari- 45) Parker followed Neugebauer in supposing that pdem Carlsberg 9 ous times. My earlier comments on it in C. J. Bennett, “The Early Augus- only gave dates for every second cycle month. Depuydt’s reanalysis (n. 15), tan Calendars in Rome and Egypt: Addenda et Corrigenda”, ZPE 147 argued that the papyrus assigned the same day number to every pair of cycle (2004), 165-168 at 166 (5), were jejune and should be ignored. months. The start date in III prt in pdem Cairo 30801 conflicts with the 47) M. Chauveau, “Un stratège indigène contemporain de la dernière Carlsberg cycle on Depuydt’s interpretation. Cléopâtre”, RdE 50 (1999), 272-274. 1710_BIOR_2008/5-6_01_Tekst 30-01-2009 10:44 Pagina 531

537 EGYPTIAN LUNAR DATES AND TEMPLE SERVICE MONTHS 538

Cleopatra III.48) Thissen’s proposal thus lacks both histori- Year 9 = 12 of Ptolemy X and Cleopatra III, II smw 16 to III cal context and reliable precedent. smw 14. In addition, the reading “year 10” should be corrected to 49 If this restoration is correct, we are dealing with a 29-day “year 11”. ) But, while a putative year [22] Ptolemy VI and temple service month. Thus the following service month Cleopatra II = year 11 (Ptolemy VIII) = 160/59 B.C. does not began on III smw 15. provide a lunar match, neither do the known double dates involving a year 11: year 14 Cleopatra III = year 11 Ptolemy Gr. Med. Habu 51 X = 104/3 B.C., and year 8 Ptolemy X = year 11 Cleopatra This graffito gives dates for a service month (wrs) of III = 107/6 B.C. phyle 4 in year 11 of Cleopatra VII = 42/1 B.C. Thissen The only year 11 involving a Cleopatra that does provide read the two dates as IV Ìt 19 and I prt 19. Chauveau cor- a lunar match is year 11 of Cleopatra VII. A perfect match rected the reading of the end date to I smw 15(?), though is possible, with last visibilities on 11 June and 11 July 41 he also considers readings of 12 or 13 to be paleographi- B.C., giving II smw 15 = bd and III smw 14 = ps∂ntyw (13 cally possible. He corrected the starting month to IV prt.52) June to 12 July 41 B.C.). This solution most likely implies a Accepting Thissen’s theory that the temple service cycle restoration of year 1? Ptolemy XV? = year 11 Cleopatra VII. was regulated according to Samuel’s application of Parker’s However, it is highly unlikely on circumstantial grounds. No reconstruction of the Carlsberg cycle to the Macedonian cal- double dated era is known at this time, nor is it likely that endar, Chauveau proposed IV prt 17 for the start date, but Ptolemy XV would appear before his mother in a dating for- considered the restoration paleographically doubtful: the mula. Further, gr. Med. Habu 51 (considered next) is at most two day numbers appear to both Thissen and Chauveau to a few months earlier, and shows no sign of a double date. be identical. Nevertheless there is one datum which might support this Comparing these solutions to the moon, the most likely solution. Iseum stele 1970/52 is a stele for the mother of Apis dates for the temple service month are: T-nt-ípy(?) dated to year 11 of Ptolemy “p Wynn” (Ptolemy “the Greek”), a king who is otherwise unknown by Year 11 of Cleopatra VII, IV prt 15 to I smw 15. this epithet. T-nt-ípy(?) is also named on stele H.5-4887, Since we are dealing with a 31-day phyle service month, dated IV smw 18 year 11 of Cleopatra VII = 15 August 41 I smw 15 also marks the first day of the following service B.C. The two stelae name the same workman and both record month. the opening of the catacomb “in one night”, hence they have the same date, which is only a month after the putative date Odem Zauzich 20 of gr. Med. Habu 48. Conceivably, therefore, the double date This document is a 2-month lease of temple service for of gr. Med. Habu 48 could reflect a short-lived era, official 50 phyle 1 from IV Ìt 1 to II prt 30 in year 35 of an unnamed or anticipated, of Ptolemy “the Greek”. ) pharaoh, agreed on IV Ìt 1. Kaplony-Heckel assigned it to A more likely possibility is that “year 11” is actually a year 35 of Ptolemy IX, on the grounds that the paleography partially-erased “year 1<2>”, even though Edgerton failed to 51 is first century and the names on the contract are typically notice any erasure in his facsimile. ) This suggests a solu- Ptolemaic rather than Roman, though she noted Augustus was tion of year 15 Cleopatra III = year 12 Ptolemy X = 103/2 also possible. However, there is no lunar match for Ptolemy B.C. or year 9 Ptolemy X = year 12 Cleopatra III = 106/5 IX (nor for Ptolemies II, VI or VIII). Year 35 Augustus = B.C. The surviving traces of the first year number could be A.D. 5/6 is the only possible solution, with the temple ser- compatible with a 9, though not a 15, although it would be vice dates being given according to the wandering year: an unusual form of the numeral. However, the double date year 9 = 12 is compatible with Ptolemy X being named first. Year 35 of Augustus, IV Ìt 1 to II prt 30 More importantly, on this reading there is a reasonable lunar Since the lease was agreed on the first day of service, IV solution: Ìt 1 is a certain date. However, since it is for two months, we cannot tell whether II prt 30 marks the first day or the last 48) U. Kaplony-Heckel, “Wasser für den Aussenposten (Das demotis- day of a service month. cher Archiv der Oxyrhynchos-Ostraka)”, in B. Menu (ed.), Les problèmes institutionnels de l’eau en Égypte ancienne et dans l’Antiquité méditer- Odem Zauzich 23 ranéenne (Cairo, 1994), 239-238 at 230-231 and 231 n. 8; M. Depauw (ed.), This document is a lease agreement for 15 days dated IV A Chronological Survey of Precisely Dated Abnormal Hieratic and Demotic 8 year 39 of Augustus = A.D. 9/10. The date of start of Sources (Köln/Leuven, 2008, Version 1.0 (2007), online at http://www.tris- prt megistos.org/top.php), xi-xii. My thanks to Mark Depauw for discussions service does not survive, but the lessee agreed to pay the on this point. lessor by IV prt 15. Kaplony-Heckel dated this to 10 April 49) M. Chauveau, pers. comm. (13 April 2005). This correction has the A.D. 10, which corresponds to IV prt 15 on the Alexandrian consensus of all other demoticists I have consulted on the point. calendar, but this date is not near to either the new moon or 50) H. S. Smith, “Dates of the Obsequies of the Mothers of Apis”, RdE 24 (1972), 176-187 at 186 n. 20. To my knowledge, these stelae are not yet the full moon. On the wandering calendar, IV prt 15 was 2 published. Assuming the reading p Wynn is confirmed, it is most likely April A.D. 10, one day after last crescent visibility. Thus, the that he is Caesarion, as Smith suggested, though this date is about the time lease was for the first half of a service month. Since IV prt Cleopatra met Antony in Tarsus. 51) This solution was independently suggested to me by Michel Chau- 15 was also the last day of payments, it may be accepted as veau (n. 49) and John Gee (pers. comm., 16 May 2006); my thanks to them, the start date of the lease: and to Karl-Theodor Zauzich and Steve Vinson for discussing it with me. Year 39 of Augustus, IV prt 15 As of late 2005, the graffito was covered by a thick layer of mud which had washed in from the roof of the small temple; my thanks to Christina di Cerbo for examining it in situ, and to Richard Jasnow for asking her to do so on my behalf and for conveying this information (pers. comm., 21 52) Chauveau (n. 8), 253 no. 51, with additional comments in idem (n. November 2005). 49). 1710_BIOR_2008/5-6_01_Tekst 30-01-2009 10:44 Pagina 532

539 BIBLIOTHECA ORIENTALIS LXV N° 5-6, september-december 2008 540

However, since the document is a lease agreed in advance, A.D. 147/8. While the exact dates are not mentioned in the the service month may have started on IV prt 16. initial contract formula, the body of the text notes that one portion of the 60 days starts on II Ìt 17, which is three days OThebes D235 = odem Zauzich 25 after last crescent visibility on 11 October A.D. 147 on the This document is a multi-month lease for service in the wandering calendar. Hence we have a temple service date of: temples of Medinet Habu, Karnak and the temple of Monthu Year 11 of Antoninus, II Ìt 17 in Luxor ending in Thoth of year 3 of Vespasian. Although the year number of the lease is lost, the pharaoh was Ves- However, since the document is a lease agreed in advance, pasian, so year 2 = A.D. 69/70 is the only possible restora- the service month may have started on II Ìt 18. Morever, tion. Thompson read the date of the start of the lease as 4 since the lease is for two months, we cannot tell whether the Tybi (I prt 4), and concluded that the lease was for 8 months end date of the lease, IV Ìt 16, marks the first day or the of service. I prt 4 in year 2 of Vespasian is 30 December A.D. last day of a service month. 69 on the Alexandrian calendar and 7 December A.D. 69 on the wandering calendar. The nearest date of last crescent vis- OThebes D31 = odem Zauzich 31 ibility is 31 December A.D. 69, or 30 December if visibility This document, used by Parker, is a lease agreement for was poor, placing the nominal start of service three or two phyle 1 from IV prt 28 to I smw 27. Thompson had read the days early. Nevertheless, there appears to be no doubt about date as year 12 of Commodus, but Parker showed that the the reading.53) Hence the temple service date, given accord- correct reading was year 30 = A.D. 189/90. He also showed ing to the Alexandrian calendar, is: that the dates were Alexandrian.54) Hence we have a temple Year 2 of Vespasian, I prt 4. service month of: Year 30 of Commodus, IV prt 28 to I smw 27. Since the document is a lease agreed in advance, the ser- vice month may have started on I prt 5. However, although Parker regarded the date of the service month given by this lease as certain, it may have started on Gr. Med. Habu 228 IV prt 29, since the document is a lease agreed in advance. This document is a long graffito by several hands located Morever, since the lease is for 30 days, we cannot tell in room S of the small temple at Medinet Habu. It includes whether the end date of the lease marks the first day or the mention of temple service (wrs), for a phyle whose number last day of a service month. is lost, starting on I smw 16 and ending on [II smw] 16 in year 10. The ruler is unnamed, and I could find no direct or Odem Zauzich 32 prosopographical indication of Ptolemaic or Roman date, This document is a lease dated to year 8 of the Sebastoi although other graffiti from the same location (including gr. for a month of temple service starting on I Ìt 8. The Sebas- Med. Habu 48) are clearly of Ptolemaic date. Text preceding toi are Severus and Caracalla rather than Aurelius and Verus the mention of this service month includes dates from years because the lessee, the god’s father Chapochonses son of Hor, 19 and 9, in that order. is also named on oThebes D221 = odem Zauzich 33, dated There is no lunar match for a year 10 following a year 19 to year 11 of the Sebastoi, who can only be the Severi.55) The in the Ptolemaic era. Possible Roman matches exist for years exact date on which the lease was agreed is not given, so it 10 of Claudius (11 May A.D. 50), Trajan (11 May A.D. 107) is at first sight unclear whether the service month started in and Hadrian (11 May A.D. 126), all interpreting the start date I Ìt in year 8 or year 9; nor is it clear whether the calendar on the Alexandrian calendar. Of these, Trajan can be elimi- in use is the Alexandrian or the wandering calendar. How- nated, since the most recent preceding year 19 was Tiberius, ever, the only lunar match is for I Ìt 8 = 12 July A.D. 199, over seven decades earlier. The solution for Claudius requires with last crescent visibility on 10 July. Hence the only pos- a late start to the service month, since lunar invisibility was sible solution, with the temple service date being given on 9 May A.D. 50, but there are other examples of this. The according to the wandering year, is: best match is to Hadrian, with lunar invisibility on 10 May Year 8 of Severus and Caracalla, I Ìt 8. A.D. 126. We therefore have two possible solutions: However, since the document is a lease agreed in advance, Year 10 of Claudius, I smw 16 to II smw 16, or Year 10 of Hadrian, I smw 16 to II smw 16. the service month may have started on I Ìt 9. This document also provides insight into the transition of In either case, we are dealing with a 31-day temple service regnal years under the wandering calendar in Roman Egypt. month, so II smw 16 marks the first day of the following ser- In principle, there are two ways this could have been done. vice month. Both solutions for this date fall three days after First, wandering and Alexandrian years could be accounted last crescent visibility, so this second month does not help to separately, so that a regnal year in the wandering calendar distinguish which solution is correct. began (and ended) before the Alexandrian year of the same year number.56) Second, the regnal year could have been Odem Zauzich 28 strictly regulated according to the Alexandrian calendar, so This document is a lease and exchange agreement for II that the start of the regnal year was gradually retarded in the Ìt and III Ìt agreed on I Ìt 8 in year 11 of Antoninus =

54) Parker (n. 2), 18 §67. 53 M. Depauw, pers. comm. 15 May 2007. Presumably Parker excluded 55) Cf. H. Thompson in Gardiner et al. (n. 7), 55 n. 2. oThebes D235 from his lunar dates because of this mismatch. A date of I 56) Except perhaps in the case of an accession between 1 Thoth (wan- smw 4 (Alex.) = 29 April A.D. 70, initiating a 4 month lease, would fit well dering) and 5 or 6 Epagomene (Alexandrian), in which case an Alexandrian with last crescent visibility on 28 April. year 2 would theoretically begin shortly after the start of wandering year 1. 1710_BIOR_2008/5-6_01_Tekst 30-01-2009 10:44 Pagina 533

541 EGYPTIAN LUNAR DATES AND TEMPLE SERVICE MONTHS 542

wandering calendar. Only two of the double dates listed by meeting this criterion. Three of them match: items (1) and Hagedorn and Worp give evidence on this issue.57) pFayum (7) on IV Ìt 20 of (Carlsberg)62) cycle year 2; items (2) and 139 is a Greek horoscope dated to year 1 of Aurelius and (8) on I prt 19 of cycle year 2; and items (16) and (19) on Verus, 5 Mesore = 16 Thoth, which conforms to the second (most likely) IV prt 15 of cycle year 16. However, items (13) model.58) pAberd. 13 is another Greek document apparently and (14) both probably start in II smw of cycle year 2, but on dated to year 27 (Commodus) Mesore 7 = year 28 Thoth 23, II smw 17 and II smw 16 respectively. While both dates are which conforms to the first model, but the first year number restored, and the second is rather more doubtful than the first, is uncertain and requires emendation. it is not possible to restore the first as II smw 16, nor the sec- Since odem Zauzich 32 is a lease agreed in year 8 for a ond as II smw 17. If the month and year of item (14) has been service month which began before the start of Alexandrian correctly identified, this discrepancy makes it unlikely that year 8, the year 8 of the agreement must be a wandering reg- the two service dates were controlled by the same schematic nal year number. Hence, the lease proves conclusively that cycle. The possibility cannot be completely excluded with- the Roman regnal year could begin on 1 Thoth in the wan- out more data, or more information about possible cycles, and dering calendar in demotic documents, ahead of the Alexan- one might also suppose that different temples used different drian new year. schematic cycles, or that some used ad hoc techniques while others used a schematic cycle. Nevertheless, the evidence cur- 6. Use of a Schematic Cycle to Regulate the Lunar Month rently available gives us no reason to believe that ps∂ntyw was determined by a schematic cycle in Ptolemaic or Roman The items in Table 2 show greater variability than those of times. Table 1. Again there is no discernable correlation with the Finally, we may consider the age of the Carlsberg cycle. Carlsberg cycle. However, in only one case is the most likely The evidence considered here demonstrates that temple ser- date more than one day removed from the second day fol- vice was almost certainly not regulated by it, and also that lowing last crescent visibility. In four cases, there is a possi- temple service most likely began on bd. Parker dated the bility that service began four days after last crescent visibil- cycle to the fourth century B.C. because the first day of cycle ity, but three of these require that the default visibility months gave their best match to lunar invisibility at this threshold is significantly in error and one of them is for a time.63) This argument presupposes that cycle months were case (item 22) where a second solution exists. Combining intended to predict ps∂ntyw, and that there was no lunar cycle Table 1 and Table 2, and ignoring items 21 and 22, for which of interest to contemporary Egyptians beginning on bd. But two solutions exist, 10 out of 23 items most likely fall two it now appears that the temple service month was just such a days after last crescent visibility; 7 fall on the day after, and cycle, one that was recognized as a second month type (wrs) 5 fall three days after. If we further add the 7 likely service beginning on a different day from an ordinary lunar month dates inferred by Lippert, given in Table 3, 15 out of 30 items (bd). This suggests that the Carlsberg cycle could in fact most likely fall two days after last crescent visibility; 7 fall have been intended to estimate bd and not ps∂ntyw, even if on the day after, and 7 fall three days after. This distribution it was not actually used to regulate service months. If so, it is clearly consistent with the conjecture that temple service is almost certainly of Roman date, since it gives a good match was based on bd, as the day following ps∂ntyw. to the second day after last crescent visibility in this period. How ps∂ntyw was determined remains unclear. While it The earliest cycle mentioned in the Carlsberg papyrus itself seems certain that the Carlsberg cycle was not used, Lippert started under Tiberius,64) and the only lunar cycle definitely has suggested use of a different, unknown, schematic cycle.59) known from Ptolemaic times, the Rylands cycle, is clearly One other cycle, the cycle of pRylands IV 589 from the reign different from the Carlsberg cycle. of Ptolemy VI, is known, but only in enough detail to show 60 that it was different from the Carlsberg cycle. ) Neverthe- 7. Long-term Stability of Phyle Rotation less, one document (item 1) gives a start date for a service month (II Ìt 20) which is covered by the surviving portion The data considered here allows us to analyse an aspect of of year 1 of the Rylands cycle, and it does not match the the temple service cycle that was not open to Parker: the sta- cycle date (II Ìt 19). While the two dates could still be rec- bility of the sequence of phyles in successive service months onciled if the Rylands cycle was intended to predict ps∂ntyw, over the long term. Pdem Cairo 30801 records seven suc- Turner and Neugebauer concluded that it was intended to cessive phyle service dates and the associated phyle numbers, match first crescent visibility, and was probably used to reg- which are in order from one to five, cyclically repeated. This ulate the dates of festivals of Greek gods; Hermes, Demeter suggests that the temple service was normally assigned to and Hephaistos are mentioned.61) phyles in order of phyle number at Gebelein. Gr. Med. Habu Without a candidate cycle to test, the only way to disprove 43 shows a transition from phyle 2 to phyle 3, which sug- the use of a different schematic cycle is to compare the start gests that the same rule applied at Medinet Habu. The Dime dates of service months that are an exact multiple of 25 years data considered by Lippert shows the same rotational behav- (309 months) apart. There are four pairs of service months iour in the short term. Before the Canopic reform of 238 B.C., there were four phyles; the reform created a fifth. Since 309 lunations is very 57) D. Hagedorn & K. A. Worp, “Das Wandeljahr im römischen Ägypten”, ZPE 104 (1994), 243-255. 58) The scenario described in n. 56 is excluded since Antoninus died on 7 March A.D. 161 (Dio 72.33-4). 62) Carlsberg cycle year numbers are used for convenience, but the 59) Lippert (n. 12). Carlsberg month started on IV Ìt 19. 60) E. G. Turner & O. Neugebauer, “Gymnasium Debts and New 63) Parker, (n. 2), 17 §61, 24-29 esp. 29 §140. Moons”, BJRL 32 (1949/50), 80-96. 64) For “Tiberius” as Tiberius rather than (Ti.) Claudius, see now Lip- 61) Turner & Neugebauer (n. 60), 86-87. pert (n. 12). 1710_BIOR_2008/5-6_01_Tekst 30-01-2009 10:44 Pagina 534

543 BIBLIOTHECA ORIENTALIS LXV N° 5-6, september-december 2008 544

close to 25 Egyptian civil years, to within about an hour, and on an expected crescent, even though it was not actually pre- since 4 and 5 are both relatively prime to 309, the combina- sent. tion of phyle number and temple service date would create a Adding the 8 known direct synchronisms of lunar dates combined cycle that, in principle, does not repeat for several listed in Table 465) to the items listed in Table 1 — Table 3, 25-year lunar cycles, if temple service months were always we have 38 items (omitting items 21 and 22) that allow us to assigned rotationally by phyle number. With four phyles, the estimate the accuracy of Egyptian lunar dates.66) Assuming resultant cycle gives combinations that do not repeat for 100 that all items are correctly dated, that wrs service began on Egyptian years. With five phyles, the resultant cycle gives bd, that lease dates mark the actual start of service, and that combinations that do not repeat for 125 Egyptian years. the default visibility threshold is correct, only 20 out of 38 Hence, if we could confirm that the assignment of phyles in observations are correct: an accuracy of 53%. In the best rotation was stable over long periods, we would potentially case, if we deliberately bias all assumptions in favour of two be able to provide exact Julian dates for documents based on days after last crescent visibility, the number rises to 24: 63% phyle number and service date alone, once the date could be accuracy. In the worst case, if we deliberately bias all localized within a century and one phyle synchronism was assumptions against two days after last crescent visibility, the fixed for the same temple. number falls to 16: 42% accuracy. The range is illustrated in Against this hypothesis, odem Zauzich 18 is a temple ser- Figure 1. vice lease for 4 months, odem Zauzich 20 is a temple service lease for 2 months for phyle 1, and oThebes D235 = odem Zauzich 25 is a temple service lease apparently for 8 months. However, there may be other interpretations of this data. Odem Zauzich 18 leases service “for the five phyles”, and odem Zauzich 25 leases service over several temples. Only odem Zauzich 20 appears to be a lease of two consecutive months of service for a specific phyle in a specific temple. A stronger test is to match expected phyle numbers against documented phyle numbers. The data from Medinet Habu can be reliably matched to specific lunations from 56/5 B.C. to A.D. 202/3, an interval of over 250 years. The data from Dime covers the interval from 25/4 B.C. to A.D. 90/1. Thus, we now have phyle numbers for service at two temples over very long intervals. This provides an opportunity to test the stability of rotational phyle assignment. By adding the num- ber of lunations between two temple service months to the phyle number of the first service month, modulo 5, we obtain a prediction for the phyle number that should be in service Fig. 1. Astronomical Accuracy of Ptolemaic and Roman Lunar for the second service month. This can then be compared to Dates the known phyle number of the second service month. The results are given in Table 5 for Medinet Habu and in Both extremes are unrealistic, but clearly this suggests that Table 6 for Dime. Unfortunately, it is clear from these tables true accuracy is unlikely to be much better than 60%. An that temple service was not always assigned in rotational accuracy of 60% or worse is much lower than the 85-95% order of phyle number from month to month. However, rota- which Krauss assumes. While the data set considered here is tion appears to have been much more stable at Dime than at significantly larger than the Illahun data set, it is still only Medinet Habu, with only one detected interruption, between about 19% of the size of the Babylonian data set considered 25/4 and 13/2 B.C. by Fatoohi (and 8.6% of the size of the Babylonian data set considered by Stern), and the quality of the data is far more uneven. More data points are needed to confirm the result. 8. Astronomical Accuracy of Egyptian Lunar Dates Nevertheless, it suggests either, that Egyptian observers were The data considered here allows us to estimate how well considerably less accurate than Babylonian observers, or, that the Egyptian procedure for determining the start of the lunar observation was not the only or the primary factor determin- month, whatever it was, matched astronomical observation. ing the start of a lunar month. It seems very likely that the Assuming that ps∂ntyw was intended to fall on the day after date was not primarily determined by observation, but also last crescent visibility, the data includes examples of ps∂ntyw that the prediction algorithm was poor, and not based on a which are both earlier and later than expected by one day. good estimating theory such as Lunar System B. It may well Ps∂ntyw falling on the day of last crescent visibility is most have been determined by a simple rule, only loosely coupled simply explained by supposing that the last crescent was to the moon by ad hoc adjustments, as Spalinger and Depuydt missed. Dates falling two days after last crescent visibility may be due to several causes. In two cases, it is possible that visibility conditions were better than the defaults assumed by 65) These synchronisms may not all be equally reliable. Depuydt (n. 4), 157, suggests that item (28) may have been artificially adjusted to fall on PLSV. When associated with service leases, such dates may the exact 25th anniversary of item (27), although the lunar match seems be due to the fact that the service date named in the lease is good. Cf. Spalinger (n. 67), 397-398 and n. 114. a prediction. In some cases last visibility may have been pre- 66) Compare with the 21 Illahun dates accepted by Krauss, consisting dicted based on the lunar phase of the previous day. Other- of temple service dates and lunar festival dates, many of which are subject to similar uncertainties to those discussed here. I have not tried to survey wise, one may suppose that the start of the month was based possible Late Period, Ptolemaic or Roman lunar festival dates. 1710_BIOR_2008/5-6_01_Tekst 30-01-2009 10:44 Pagina 535

545 EGYPTIAN LUNAR DATES AND TEMPLE SERVICE MONTHS 546

have suggested.67) If so, the procedure seems to have been within a few decades, there are several possible solutions, all reasonably effective, since only one ps∂ntyw date is separated of which lie within the limits of precision set by the lunar from true invisibility by more than a day. dates of the Graeco-Roman period. The distribution of errors in astronomical accuracy sug- The same problem also exists with the Illahun dates, unless gests that observation was one factor involved in deciding the uncertainties on the Sothic date of pBerlin 10012 can be the start of the lunar month. When the start of a lunar month considerably reduced, even if all the relative lunar dates is determined observationally, the observer must decide which have been deduced by Luft and Krauss are correct. It whether to announce the start of the month if conditions do is certainly possible to make correct calendrical inferences not permit the moon to be observed on day 29 or 30 of the from this data. The Graeco-Roman data confirms Luft’s argu- previous month. Two types of error are possible: a “nega- ment that temple service started on bd, not ps∂ntyw. How- tive” error, which incorrectly assumes the absence of a cres- ever, this does not automatically imply that such results are cent that is in fact present, and a “positive” error, which chronologically useful: Luft’s argument does not require that incorrectly assumes the presence of a crescent that is in fact the ps∂ntyw of pBerlin 10090 actually fell on a day after last absent. Krauss assumes that these errors are equiprobable crescent visibility, only that the average length of a lunation on both days, with the eventual result that his model of the is a good estimate of the average length of a service month accuracy of the Egyptian lunar calendar, based on Baby- in the Middle Kingdom. lonian figures, predicts that 15% of lunar dates in the Fayyum should be negative errors while 2.6% should be positive errors.68) While this is a reasonable assumption for day 30, for missed observations on day 29, one would expect to see an observer bias in favour of making the deci- sion which is less likely to be invalidated on the following day. For months based on observation of the first crescent, such as Babylonian months, such a bias favours negative errors, since this minimizes the probability that a decision announcing the start of the month will be invalidated by the absence of the crescent on the next day. However, for Egyptian lunar months, the same bias favours positive errors, since the Egyptian lunar month is based on lunar invisibility: it is safer to assume that a last crescent was pre- sent on day 29 if observation is not possible. The data on positive and negative errors considered here matches this prediction: 24% of the dates are positive errors of one day, while 18% are negative errors of one day. Fig. 2. Matching Illahun Astronomical Dates to Expected Whatever the method used to determine the start of the Observer Accuracy70) Egyptian lunar month, the results presented here clearly sup- port Wells’ concerns regarding the utility of astronomical The chronological difficulty is that a match of the astro- calculations for matching lunar dates from earlier times. nomical first crescents to the level of accuracy seen in the Since the lunar date of the start of temple service seems to Ptolemaic and Roman data gives multiple solutions. The have been fixed at bd in both the Middle Kingdom and problem is illustrated in Figure 2, which shows the calculated Graeco-Roman times, and since we are unable to demon- astronomical accuracy for the Illahun lunar dates, for 37 can- strate that the data matches any specifically Graeco-Roman didate values of year 1 Amenemhat III at 25 year intervals mechanism, such as schematic cycles or Lunar System B, over an interval of 900 years. On Krauss’ assumption that we have no reason to believe that the procedure used in Egyptian lunar dates are essentially astronomically accurate Graeco-Roman times was any different from that used in to Babylonian levels, the most probable solution is year 1 earlier times. Hence, we have no reason to suppose that ear- Amenemhat III = 1818/7, with a probability of 0.114. How- lier lunar dates were any more accurate. ever, with the levels of accuracy shown by the data consid- A considerable number of agreed or candidate pre-Saite ered in this paper, the probability that this solution is correct lunar dates have been identified.69) The analysis of these falls to 3.6x10-5. It is apparent from Figure 2 that many solu- lunar dates must take into account a much larger probability tions exist which give better matches to an expected accu- of error than has previously been assumed. For example, racy level of 53%. Figure 3 shows the probabilities of each attempts to distinguish candidate years for isolated ps∂ntyw solution for observer accuracy levels of 82% and 53%. synchronisms of year 23 of Thutmose III and year 52 of Clearly, at 53% accuracy, the right solution can only be deter- Ramses II on purely astronomical grounds are clearly futile. mined by considering extraneous data, such as constraints set Because the dates of these kings are otherwise only firm to by the Illahun Sothic date.71)

67) Depuydt (n. 4), 180; A. J. Spalinger, “Egyptian Festival Dating on 70) After Krauss (n. 17), 406 Fig. III.8.4, with mean levels of observer the Moon”, in Steele & Imhausen (n. 16), 379-403, at 397-398. accuracy overlaid. The level of Babylonian-based accuracy shown is that 68) Krauss (n. 17), 401-402. used by Krauss. 69) Summarised by Krauss (n. 17), 408-431; 424-427 for the Illahun 71) For additional remarks on Krauss’ use of lunar dates to derive an dates accepted by Krauss. While these lunar dates may not all be valid (cf. absolute chronology, see C. J. Bennett, review of Hornung et al. (n. 17), n. 22), it is assumed for the purposes of this discussion that they are, since BiOr 65 (2008), 114-122. The Egyptian accuracy figures given here cor- the point at issue is methodological. rect those given in that review. 1710_BIOR_2008/5-6_01_Tekst 30-01-2009 10:44 Pagina 536

547 BIBLIOTHECA ORIENTALIS LXV N° 5-6, september-december 2008 548

example is the wrs feast celebrated on IV prt 25 in year 5 of Shoshenq I and recorded on a stele from Dakhla. Krauss has argued that a lower bound can be set for year 5 of Shoshenq I by dead-reckoning backwards using the highest known reg- nal years from 841 B.C. as the accession year of Shoshenq III (itself determined by analysis of dates for the lunar tpj smw feast), and an upper bound based on the famous syn- chronism with Rehoboam, giving an uncertainty of about decade. If these bounds are accepted, then it is indeed possi- ble to fix the date of the wrs feast precisely, once we know its lunar phase, despite the apparent limits of observational uncertainty. Krauss’ solution, IV prt 25 year 5 = 5 December 939 B.C., is one day after last crescent visibility, thus an expected ps∂ntyw. A difficulty with his argument is that he supposed that the wrs feast was held on the first day of the temple service, while Quack has argued that the Demotic Fig. 3. Probabilities of Candidate Matches to Illahun Dates Chronicle shows that the wrs feast was held on the last day of the month in the Late Period. Krauss proposed that this This is not to say that lunar dates are useless for fixing represented a change in the start of the month due to later absolute chronology, only that their limits are not yet suffi- Persian influence, and so could be ignored.73) However, if ciently well understood. We have seen above that lunar temple service began on bd in both Middle Kingdom and dates can be used successfully to fix the dates of documents Ptolemaic times, it is all but certain that it also began on which are known a priori to belong within a firm chrono- bd in the Libyan period, not ps∂ntyw. It may be that the logical framework. In practice, given an imprecision of one last crescent, which had a calculated phase of 1.9%, was day in a lunar date, we can often use an isolated lunar date missed on IV prt 24 in Dakhla, but it seems more likely that to fix the absolute date of a document which is dated within the Demotic Chronicle was referring to the month of the a framework that is already firm to within a decade on other wrs. If so, the wrs feast was indeed held on ps∂ntyw, yet grounds. not because it was the first day of temple service, but One example of this is the lunar double date of year 12 of because it was the last. Amasis given in pLouvre 7848, which allowed Parker to precisely date the Saite dynasty because the preexisting San Diego, July 2008 uncertainty in its chronology was only a year.72) Another

Table 1: Analysis of Complete Direct Civil/Temple Service Synchronisms

No Source (Regnal Year) Synchronism74) Service day Carlsberg day Difference Julian date77) Last visibility78) Difference 175) 176) (cycle year) (days) (Service day 1) (per cent) (days) 1 gr Med. Habu 43 I prt 1 = 2, 12 IV Ìt 20 IV Ìt 19 (2) +1 24 Dec. -55 22 Dec. (1.5%) +2 (26=3 Pt. XII & Ber. IV) 2 gr Med. Habu 43 I prt 19 = 3, 1 I prt 19 I prt 18 (2) +1 22 Jan. -54 20 Jan. (3.8%) / +2/+1 (26=3 Pt. XII & Ber. IV) 21 Jan. (0.9%) 3 gr Med. Habu 44 I Ìt 14 = 1, 20 IV smw 30 IV smw 29 (9) +1 29 Aug. -47 27 Aug. (1.0%) +2 (5 Pt. XIII & Cleo. VII) 4 gr Med. Habu 47 II prt 21 = 1, 17 II prt 5 II prt 4 (20) +1 3 Feb. -36 1 Feb. (1.6%) +2 (15 Cleo. VII) 5 iMoscow 145 IV prt 23 = [X], 6 I smw 10 I smw 10 (22) 0 13 Apr. 66 11 Apr. (4.8%) +2 (12 Nero) (= I smw 15)

72) R. A. Parker, “The Length of Reign of Amasis and the Beginning of the Twenty-sixth Dynasty”, MDAIK 15 (1957), 208-212. This is item (33) in Table 4. 75) All dates are on the wandering calendar. 73) Quack (n. 43); Krauss (n. 18), 46. Cf. also Lippert’s suggestion 76) Based on Depuydt’s reconstruction (n. 15). The differences from (above) that the wrs of pdem Ox. Griffith 41 is a wrs feast rather than a Parker’s reconstruction only affects item 10 in Table 2. phyle service month. 77) Julian years are numbered according to the astronomical convention: 74) Given in the format = ,. If the date is an Alexandrian date, the equivalent date on the wan- 78) Item 5 is calculated for Koptos (26°0’N; 32°49’E). All other items dering calendar is given in parentheses. calculated for Thebes (25°42’N; 32°38’E). 1710_BIOR_2008/5-6_01_Tekst 30-01-2009 10:44 Pagina 537

549 EGYPTIAN LUNAR DATES AND TEMPLE SERVICE MONTHS 550

Table 2: Analysis of Incomplete Direct Civil/Temple Service Synchronisms

No Source (Year) Synchronism Service day Carlsberg day Difference Julian date Last visibility81) Difference 179) 1 (cycle year) (Days)80) (Service day (per cent) (days)80) 1)80) 6 pdem Ox. Griffith 41 II Ìt 19 = 4, 1 or II Ìt 19 or II Ìt 20 (2) -1/0 12 Nov. -130 / 11 Nov. (4.1%) +1/+2 (40 [Pt. VIII]) II Ìt 20 = 4 (5?), 1 II Ìt 20 13 Nov. -130 7 pdem Cairo 30801 IV Ìt 20 = [5?, 1?] IV Ìt 20 IV Ìt 19 (2) +1 12 Jan. -129 9 Jan. (3.3%) +3 ([40 Pt. VIII]) 8 pdem Cairo 30801 I prt 19 = 1, 1 I prt 19 I prt 18 (2) +1 10 Feb. -129 8 Feb. (1.7%) +2 ([40 Pt. VIII]) 9 pdem Cairo 30801 II prt 19 = 2, 1 II prt 19 II prt 18 (2) +1 12 Mar. -129 9 Mar. (3.5%) / +3/+2 ([40 Pt. VIII]) 10 Mar. (0.9%) 10 pdem Cairo 30801 III prt 19 = [3], 1 III prt 19 III prt 17 (2) +1 11 Apr. -129 8 Apr. (2.2%) +3 ([40 Pt. VIII]) 11 pdem Cairo 30801 IV prt 18 = 4, 1 IV prt 18 IV prt 17 (2) +1 10 May -129 8 May (1.2%) +2 ([40 Pt. VIII]) 12 pdem Cairo 30801 [I smw 1]7 = 5, 1 I smw 17 I smw 16 (2) +1 8 June -129 6 June (2.8%) +2 ([40 Pt. VIII]) 13 pdem Cairo 30801 [II smw 17] = 1, 1 II smw 17 II smw 16 (2) +1 8 July -129 6 July (1.8%) +2 ([40 Pt. VIII]) 14 gr Med Habu 48 II smw(?) 1[6] = 1, 1 II smw 16 II smw 16 (2) 0 30 June -104 29 June (2.5%) +1 ([9] = 1<2> Pt. (X) & Cleo. (III)) 15 gr Med Habu 48 III [smw] 14 = 1, (29) III smw 15 III smw 15 (2) 0 29 July -104 28 July (4.1%) +1 ([9] = 1<2> Pt. (X) & Cleo. (III)) 16 gr Med Habu 51 IV prt 15? = 4, 1 IV prt 15 IV prt 16 (16) -1 14 Apr. -40 13 Apr. (2.4%) +1 (11 Cleo. VII) 17 gr Med Habu 51 I smw 15? = 4, 31 I smw 15 I smw 15 (16) 0 14 May -40 13 May (1.4%) +1 (11 Cleo. VII) 18 odem Zauzich 20 IV Ìt 1 = 1, 1 IV Ìt 1 IV Ìt 1 (12) 0 20 Nov. 5 19 Nov. (2.1%) +1 (35 [Augustus]) 19 odem Zauzich 23 IV prt 15 = [X], 0 IV prt 15/16 IV prt 16 (16) -1/0 2/3 Apr. 10 1 Apr. (4.9%) +1/+2 (39 Augustus) 20 oThebes D235 = I prt 4 = [X], 1 I prt 27/28 I prt 29 (1) -2/-1 30/31 Dec. 69 31 Dec. (1.6%) / -1/0 odem Zauzich 25 (= I prt 27) 30 Dec. (4.8%) ([2] Vespasian) 21 gr Med Habu 228 I smw 16 = [X], 1 II smw 4 or II smw 3 (6) or +1 or 11 May 50 or 8 May (2.5%) or +3 or (10 [Claudius]) or (= II smw 4 or 9 May (1.1%) / (10 [Hadrian]) II smw 23) II smw 23 II smw 22 (7) +1 11 May 126 8 May (4.1%) +2/+3 22 gr Med Habu 228 II smw 16 = [X], 31 III smw 4 or III smw 2 (6) or +2 or 10 June 50 or 7 June (1.0%) / +3/+4 or (10 [Claudius]) or (= III smw 4 or 6 June (4.1%) or (10 [Hadrian]) III smw 23) III smw 23 III smw 21 (7) +2 10 June 126 7 June (1.2%) +3 23 odem Zauzich 28 II Ìt 17 = [X],1 III Ìt 29/30 III Ìt 27 (4) +2/+3 14/15 Oct. 147 11 Oct. (2.0%) +3/+4 (11 Antoninus) (= III Ìt 29) 24 oThebes D31 = odem IV prt 28 = 1, 1 II smw 21/22 II smw 21 (21) 0/+1 23/24 Apr. 190 20 Apr. (4.3%) / +2/+3/+4 Zauzich 31 (= II smw 21) 21 Apr. (1.2%) (30 Commodus) 25 odem Zauzich 32 I Ìt 8 = 1, 1 I Ìt 8/9 I Ìt 7 (6) +1/+2 12/13 July 199 10 July (0.8%) / +2/+3/+4 (8 Severus & 9 July (3.2%) Caracalla)

79) Where multiple solutions are possible, because the document is a service contract agreed in advance, the preferred solution (bolded) is the date given on the document. 80) Where multiple solutions are possible, the preferred solution (bolded) is that associated with the preferred service day. 81) Item 6 calculated for the Fayyum (29°10’N; 30°50’E); items 7-13 for Gebelein (25°29’N, 32°29’ E); all others for Thebes. Where multiple solutions are possible, because the sighting may be sensitive to the visibility threshold, the preferred solution (bolded) is the date given by the default settings in PLSV 3.0. 1710_BIOR_2008/5-6_01_Tekst 30-01-2009 10:44 Pagina 538

551 BIBLIOTHECA ORIENTALIS LXV N° 5-6, september-december 2008 552

Table 3: Analysis of Inferred Civil/Temple Service Synchronisms from Dime82)

No Source (Regnal Year) Synchronism Service day Carlsberg day 1 Difference Julian date Last visibility Difference 1 (cycle year) (days) (Service day 1) (per cent) (days) 26 pVienna D6044 D = II prt 13 = 5, 1 II prt 13 II prt 13 (8) 0 7 Feb. -23 5 Feb. (3.7%) +2 DDD II 43 (6 Augustus) 27 pVienna D6044 D = III prt 11 = 5, 29 III prt 12 III prt 12 (8) 0 8 Mar. -23 6 Mar. (6.0%) +2 DDD II 43 (6 Augustus) 28 pVienna D6134ro B = IV Ìt 12 = 2, 1 IV Ìt 12 IV Ìt 11 (25) +1 15 Nov. 68 12 Nov. (2.6%) +3 DDD II 47 (2 Galba) 29 pVienna D6134ro C = I prt [11] = 3, 1 I prt 11 I prt 10 (25) +1 14 Dec. 68 12 Dec. (1.8%) +2 DDD II 47 ([2] Galba) 30 pVienna D6835 D = IV prt 22 = 1, 1 IV prt 22 IV prt 22 (21) 0 20 Mar. 90 18 Mar. (3.1%) +2 DDD II 48 (9 Domitian) 31 pVienna D6835 E = I smw 22 = 2, 1 I smw 22 I smw 21 (21) +1 19 Apr. 90 17 Apr. (2.2%) +2 DDD II 48 (9 Domitian) 32 pVienna D6817 B = [I smw] 12 = 2, 1 I smw 12 I smw 10 (22) +2 9 Apr. 91 6 Apr. (2.3%) +3 DDD II 49 (10 Domitian)

Table 4: Other Fixed Egyptian Lunar Synchronisms

No Source (Year) Synchronism Lunar day 1 Julian date Last visibility Difference (civil = lunar) (ps∂ntyw)(ps∂ntyw) (per cent)83) (days) 33 pLouvre 7848 II smw 13 = I smw 15 I smw 29 5 October -558 4 October (3.7%) / +1/0 (12 Amasis) 5 October (0.9%) 34 Edfu VII.5 III smw 7 = [III smw] 6 III smw 2 18 August -236 17 August (1.0%) / +1/+2 (10 Pt. III) 16 August (4.4%) 35 Edfu VII.6 III smw 7 = [III smw] 6 III smw 2 12 August -211 10 August (3.5%) +2 (10 Pt. IV) 36 Edfu VII.7+IV.2 IV smw 18 = III smw 23 III smw 26 19 August -141 16 August (4.5%) / +3/+2 (28 Pt. VIII) 17 August (0.8%) 37 Edfu VII.8 II smw 9 = II smw 6 II smw 4 27 June -139 26 June (3.2%) +1 (30 Pt. VIII) 38 LdR IV 411 III smw 13 = [III smw] 5 III smw 9 9 July -45 7 July (1.5%) +2 (6 Cleo. VII) 39 iBucheum 13 IV prt 21 = [IV prt ] 16 IV prt 6 2 April -28 1 April (3.1%) +1 (1 Augustus) 40 pdem Rhind 1 III smw 10 (=III smw 14) = [II smw] 16 II smw 29 19 June -8 18 June (1.6%) +1 (21 Augustus)

82) Six of the service month dates inferred by Lippert are not included here (nos 3, 4, 7-9 and 13 in her Table 2), since I regard them as insufficiently cer- tain for the purposes of this paper. However, four of these six months are still usable for the phyle phase calculations of Table 6. Her nos 8 and 9 (both from pVienna D6835 B = DDD II 48) are omitted from Table 6 because the positions of both months within prt are reconstructed on the assumption under test, that phyle rotation was sequential. On Lippert’s analysis, one service date (no 3) is two days late against the moon, at most one (no 9) may be accurate to the moon, and the remaining four or five are one day late. The net effect of including all of Lippert’s reconstructions of these dates would be to depress the estimated astronomical accuracy to 57% (best case), 45% (most likely) and 36% (worst case). 83) Items 33 and 40 calculated for Thebes; items 34-37 for Edfu (24°58’N, 32°52’E); item 38 for Memphis (29°51’N, 31°15’E); item 39 for Armant (25°37’N, 32°32’E). 1710_BIOR_2008/5-6_01_Tekst 30-01-2009 10:44 Pagina 539

553 EGYPTIAN LUNAR DATES AND TEMPLE SERVICE MONTHS 554

Table 5: Analysis of Phyle Number Assignments vs Lunations at Medinet Habu (Djeme)

Source Month of Service84) Lunations since last Predicted Phyle Actual Phyle Difference recorded service gr Med. Habu 43 IV (2) -55 - - 2 - gr Med. Habu 43 V (2) -55 1 3 3 0 gr Med. Habu 44 XIII (9) -48 94 2 1 -1 gr Med. Habu 47 VI (20) -37 129 5 1 +1 oThebes D31 X (21) 189 2,798 4 1 +2 odem Zauzich 32 I (6) 199 114 5 1 +1 odem Zauzich 3385) XIII (9) 202 or II (10) 203 49 or 51 5 or 2 3 -2 or +1

Table 6: Analysis of Phyle Number Assignments vs Lunations at Socnopiau Nesos (Dime)

Source Month of Service Lunations since last Predicted Phyle Actual Phyle Difference recorded service pVienna D6044 A = DDD II 43 XII (7) -25 - - 4 - pVienna D6044 D = DDD II 43 VI (8) -24 6 5 5 0 pBerlin P 15594 = DDD II 44 VIII (20) -12 150 5 2 +2 pVienna D6819ro = DDD II 4586) XIII (23) 41 660 2 2 0 pVienna D6826 A = DDD II 46 XI (13) 56 184 1 1 0 pVienna D6134ro A = DDD II 47 III (25) 68 140 1 1 0 pVienna D6134ro B = DDD II 47 IV (25) 68 1 2 2 0 pVienna D6134ro C = DDD II 47 V (25) 68 1 3 3 0 pVienna D6835 D = DDD II 48 VIII (21) 89 263 1 1 0 pVienna D6835 E = DDD II 48 IX (21) 89 1 2 2 0 pVienna D6817 B = DDD II 49 IX (22) 90 12 4 4 0 pVienna D6817 C = DDD II 49 X (22) 90 1 5 5 0 pVienna D6817 D = DDD II 49 XI (22) 90 1 1 1 0

84) For ease of calculation, service months are represented according to the Carlsberg cycle year and month that most closely approximates the actual ser- vice month, and are assigned a nominal astronomical year which represents the Julian year in which the corresponding Egyptian civil year began. Thus, IV (2) -55 represents Carlsberg month 4 in cycle year 2, starting in 56 B.C. and ending in 55 B.C. Since the expected phyle is determined by adding the count of lunations to the first phyle number modulo 5, its value is independent of the structure of the Carlsberg cycle. 85) Lease for service starting in IV smw dated IV smw 1 year 11 of the Sebastoi (Severi). Since the day number for the start of the leased service is not given, it is not possible to determine whether the date is according to the wandering or the Alexandrian calendar. Both possibilities are considered. 86) The date of the receipt is most probably for the last day of a service month, as shown, but could also be for the first day of the following month. See n. 23.