Abstract
A recently discovered inscription on an ancient Egyptian ointment jar mentions the heliacal rising of Sirius. In the time of the early Pharaohs, this specific astronomical event marked the beginning of the Egyptian New Year and originally the annual return of the Nile flood, making it of great ritual importance. Since the Egyptian civil calendar of 365 days permanently shifted one day in four years in comparison to the stars due to the lack of intercalation, the connection of a date from the Egyptian civil calendar with the heliacal rising of Sothis is vitally important for the reconstruction of chronology. The new Sothis date from the Old Kingdom (3rd–6th Dynasties) in combination with other astronomical data and radiocarbon dating re-calibrates the chronology of ancient Egypt and consequently the dating of the Pyramids. A chronological model for Dynasties 3 to 6 constructed on the basis of calculated astronomical data and contemporaneously documented year dates of Pharaohs is presented.
Introduction
The Egyptian civil calendar consisted of 365 days arranged in the three seasons Akhet, Peret and Shemu, each containing four months with 30 days and at the end, five additional days (Epagomenals) were added. This civil calendar was probably introduced in the first half of the third millennium
The New Sothis Date
Recently a new Sothis date on an ointment jar was discovered.3 The jar mentions the “Forthcoming of Sopdet” and the date of a heliacal rising of Sirius on the beaker. For the stylistic dating of our jar several publications were used.4 Such cylindrical beakers contained perfume oil and were often given to people on special occasions and festivals—a tradition still alive in the Coptic church.5 The jar was stylistically dated into the mid to late 5th Dynasty. Inscription, palaeography and the astronomical date also point to the Old Kingdom. The inscription (Fig. 1) starting from the right column is a nominal sentence with pw:
gsw n s3-rnp.t 3bd 4 pr.t ḫft pr.t spd.t 3bd 4 3ḫt pw ḫft wp.t -rˁ
Ointment made for the protection of the year, month 4, Peret-season, for the forthcoming of Sothis, month 4, Akhet-season it is, made for the first day of the month.
The sign “wp.t -rˁ” is a cow’s horn with sun disc and can be translated as “first day of the month” but also as “beginning of the New Year,” most fitting for this festival.6 It mentions the ointment inside the jar, combined with the production date (4th month, Peret). The reason is the forthcoming of Sothis (Sirius) at the date (4th month, Akhet, 1st day). The Peret date, mentioning the protection of the year may refer to the date of production of the oil: the ointment would have been produced ca. ¾ year in advance of the heliacal rising of Sothis. This is a classic production length for the sacred oils in Egypt.7
Old Kingdom Chronology
Historical dating based on information given in king lists, radiocarbon dating, as well as various astronomical dating attempts resulted in different chronologies of the Egyptian Old Kingdom with varying degrees of disagreement.8 All these dating methods share that they are heavily influenced by the fact that the method of counting years used during Dynasties 3 to 6 is still a matter of debate. The standard theory for many years was that a regular biannual count of regnal years was employed throughout the whole Old Kingdom.9 In the framework of this hypothesis each “year of the xth cattle count” should have been followed by a “year after the xth cattle count.” It has long been noticed that the number of documents containing a “year of the count” and a “year after the count” is not about equal, as one would expect if indeed a biannual year count had been used. Instead—depending on whether graffiti of workmen are included in the statistics or not—the ratio amounts to approximately 2.8:1 and 1.85:1, respectively.10 Disregarding the graffiti results in that a “year after the count” usually occurred approximately every third year, but sometimes already every second year. Based on these numbers John Nolan proposed a connection with the original lunar calendar, namely that a “year after the count” was employed if an intercalary month was inserted into the lunar calendar at the end of the preceding year in order to keep it in line with the sidereal and solar year.11 Nolan’s hypothesis requires a reduction of the number of regnal years usually assigned to Old Kingdom Pharaohs by about 21% and hence a shortening of Old Kingdom chronology.
Drawing of the ointment jar with the Sothis-inscription in the archaeological collection of the University of Zurich, inv. 5821.
Citation: Journal of Egyptian History 10, 2 (2017) ; 10.1163/18741665-12340035
Copyright: Michael Habicht, digitally reworked and coloured by Patrick E. Eppenberger.
Drawing of the ointment jar with the Sothis-inscription in the archaeological collection of the University of Zurich, inv. 5821.
Citation: Journal of Egyptian History 10, 2 (2017) ; 10.1163/18741665-12340035
Copyright: Michael Habicht, digitally reworked and coloured by Patrick E. Eppenberger.Drawing of the ointment jar with the Sothis-inscription in the archaeological collection of the University of Zurich, inv. 5821.
Citation: Journal of Egyptian History 10, 2 (2017) ; 10.1163/18741665-12340035
Copyright: Michael Habicht, digitally reworked and coloured by Patrick E. Eppenberger.The Lunar Calendar and Intercalary Months
Nolan recently proposed that a regular nineteen-year intercalation cycle comparable to the much later well-known Metonic cycle has been used in third millennium ancient Egypt.12 Although the regular Metonic intercalation cycle may well have been known prior to its first unambiguously documented attestation one may doubt that such a cycle was used 2000 years earlier. However, this does no harm to Nolan’s basic hypothesis because the application of a regular intercalation cycle would by no means be a prerequisite for the functioning of the whole system. The so-called original lunar calendar was tied to the heliacal rising of the star Sirius.13 This event refers to the first visibility of the star Sirius in the morning sky shortly before sunrise after a period of invisibility in the night sky. A new lunar month began with the invisibility of the lunar crescent in the morning sky. A normal year consisted of twelve lunar months. Since such a lunar year with twelve months is about ten days shorter than a sidereal year an extra month has to be inserted after three years, and at times already after two years, in order to keep the lunar calendar synchronized with the sidereal year.14 The decisive astronomical phenomenon for the insertion of an additional lunar month was the heliacal rising of the star Sirius. As soon as the beginning of the first lunar month of the next year would have occurred too close to the expected date of the heliacal rising of Sirius, an intercalary month had to be inserted. Otherwise the twelfth lunar month, named after the heliacal rising of Sirius, would have ended before the name-giving event occurred. Such a lunar calendar with a simple but clever intercalation scheme can be operated without knowledge of longer intercalation cycles such as the nineteen-year cycle. Observations of the lunar crescent around new moon as well as a prediction of the date of the heliacal rising of Sirius meet all necessary requirements.
Calculations
All beginnings of lunar months and the dates of the heliacal rising of Sirius for the time span 2700
Contemporary Sources and Astronomical Data
Contemporary documents from Dynasties 4 to 6 mentioning about 150 different years of Pharaohs are known today.19 Some of these dates are well connected to a reign of a king or implemented in a dated architectural context and are generally accepted. Other dates are uncertain in the reading of the year or attributed to several potential reigns. Of special importance are the archives from the mortuary temples of Raneferef and Neferirkare in Abusir.20 Theoretically the majority of the texts from these two archives could date to any king between Shepseskare and Pepy ii. But Paule Posener-Kriéger dated most of the documents from the Neferirkare archive into the reign of Djedkare Isesi and Unas. The same applies for the papyri from the Raneferef archive. The conventional attributions of the documents to kings were accepted (see Table 1) and a minimum High Chronology and a maximum Low Chronology from Khufu down to Pepy ii was established based on contemporary documented data and our calculations summarized in Table 2.
Several attempts have been made in the past to establish absolute dates for Djedkare Isesi and Unas based on different kinds of astronomical data and with varying results.21 On two papyri from the mortuary temple of Raneferef Wagy-feast dates are given: a Wagy date 3rd month […] day 28 in “Document iv” and a second fragmentary date in “Document iii” mentioning 1st month of Akhet day 23–29 or 29.22 The latter probably refers to the immovable Wagy-feast of Osiris fixed on the 1st month of Akhet day 18 in the civil calendar that was celebrated about a fortnight later than the beginning of the New Year on the 1st month of Akhet day 1. The former, however, relates to the moveable Wagy-feast whose feast dates were determined using the lunar calendar. Ulrich Luft derived an assumed heliacal rising of Sothis around the last days of the 2nd month of Akhet during the reign of King Raneferef based on a suggested misreading of the date in “Document iii” and an interpretation to mean 3rd month of Akhet day 23–29 instead of 1st month of Akhet.23 Leo Depuydt in using the same dates calculated an upper threshold for the heliacal rising of Sirius and reconstructed that the Wagy festival took place on 3rd month of [Akhet] day 28. Thus, since the Wagy feast was celebrated on an 18th lunar day the heliacal rising of Sirius might be dated to 3rd month of Akhet day 10 or earlier. Assuming the latest possible date as 3rd month of Akhet day 10, this event would coincide with 2506–2503
Posener-Kriéger identified two further lunar dates in the Neferirkare archive that she tentatively assigned to the reign of Djedkare Isesi.27 The document in her Table 2 (Plate 3–4) allows deducing that in the 2nd month of the Shemu season day 18 was a second lunar day. The verso of this papyrus is dated to year 21 or 22 of an unnamed king. The recto was inscribed earlier, presumably about one year earlier. Due to the mentioned high number of regnal years on the verso the attribution of this date to Djedkare Isesi can be considered rather certain.28 The document in her Table 1 (Plate 5–6–7A) mentions that in the 4th month of the Shemu season days 17 and 18 were lunar days 1 and 2, respectively. The verso of this papyrus dates to the year 4 of an unnamed king, suggesting that the recto was inscribed supposedly one year earlier. This date may belong to either Djedkare Isesi or Unas.29
Recently a new Sothic date from the Old Kingdom has been published by Michael Habicht.30 Unfortunately the name of the king on the jar is missing. The given date, 4th month of Akhet, day 1 allocates the vessel somewhere between 2419–2406
Counting of Regnal Years
After the death of the old Pharaoh the first partial year of his successor was counted as sema ta.wy, as year of unification of the two lands. Afterwards, theoretically a “year of” (rnp.t sp) or a “year after” (rnp.t m-ḫt sp) the cattle count could follow. To our knowledge it is not clear how the Egyptian counting worked if sema ta.wy was followed by a “year after.” Was it designated as “year after sema ta.wy,” as “year 1 after,” in another way, or was it even impossible to have a “year after” following sema ta.wy? The surviving contemporary documents show that no account of a “year after sema ta.wy” exists, but there are two different phrases that may or may not be interchangeable: rnp.t m-ḫt sp 1 and rnp.t m-ḫt sp tpy. So far, they have been treated to mean the same, namely “year 1 after” the cattle count. Years rnp.t m-ḫt sp tpy are documented for Menkaure, Shepseskaf, Djedkare or Unas, Teti and Pepy ii. Years rnp.t m-ḫt sp 1 are preserved from the reign of Userkaf, Djedkare and Merenre. We see that there exists no overlap between the list of kings with documented years rnp.t m-ḫt sp tpy and rnp.t m-ḫt sp 1 with the exception of maybe Djedkare.33 For Menkaure, one has a preserved sequence of years rnp.t m-ḫt sp tpy in the tomb of Meresankh iii, rnp.t m-ḫt sp 2 on a papyrus fragment from Gebelein and rnp.t m-ḫt sp 3 from another papyrus fragment from Gebelein. If one interprets rnp.t m-ḫt sp tpy to be a synonym for rnp.t m-ḫt sp 1 then this sequence can only be explained as a biannual counting system. In connection with a lunar calendar with regular intercalations, it is impossible to have three intercalary months within five years. One would be forced to assume some kind of extra correction for omitted earlier intercalations. If, however, one interprets rnp.t m-ḫt sp tpy to mean “year after the sema ta.wy” one is faced with a common sequence. The evidence from the reign of Menkaure as well as the fact that barely both phrases from the reign of the same king are preserved leads us to the tentative suggestion that rnp.t m-ḫt sp tpy indeed means “year after the sema ta.wy.” However, this interpretation does not significantly alter the results presented in the following section.
Resulting Chronological Models
In the first instance, the beginning of all Egyptian lunar months and the expected dates of the heliacal rising of the star Sirius at Memphis were calculated for all years between 2700 and 2000
Low Chronology
Provided that the Wagy-feast was not celebrated later than in the second month after the heliacal rising of Sirius the earliest possible chronological solution for a Wagy-feast in the 3rd month of Peret on day 28 occurs in 2242
High Chronology
The latest possible chronological solution for a Wagy-feast in the 3rd month of Akhet on day 28 celebrated in the first month after the heliacal rising of Sirius and not occurring earlier than the reign of Raneferef is in 2489
Low Chronology Versus High Chronology
Our Low and High Chronologies are separated by ca. 130 years. The small amount of available astronomical data as well as the documented years of kings do not allow for a justifiable decision to favour one of the two chronological models. One has to state that our Low Chronology with the end of an assumed 54-year reign of Pepy ii in 2150
Comparison with Other Models
The relative chronology of the Old Kingdom together with discussions of the imbalance between documented “years of” and “years after” has been the subject of different studies.45 The two chronological models presented in this paper are based on the results of these studies. With the help of the few available astronomical data two absolute chronologies are established. Concerning the ratio of documented “years of” to “years after” for Dynasties 4, 5, and 6 our numbers slightly deviate from the ones given by Miroslav Verner due to our tentative assumption that rnp.t m-ḫt sp tpy and rnp.t m-ḫt sp 1 do not denote the same year.46 For Dynasty 4 the ratio of documented “years of” to “years after” amounts to 19:9 (68%:32%), for Dynasty 5 to 34:15 (69%:31%), and for Dynasty 6 to 15:13 (54%:46%).47 The calculations show an expected ratio of 64%:36% which is rather close to what the preserved documents from Dynasties 4 and 5 indicate. However, the documented year dates from Dynasty 6 are not easily reconcilable with these numbers, although it is possible to explain all but one mentioned “years after” in both chronological models.
The assumption that a regular biannual counting system was used in Dynasty 6, as presumed by Jürgen von Beckerath, would eliminate our Low Chronology: according to the highest documented years at least 50 years for Pepy i, 12 years for Merenre and 66 years for Pepy ii would have to be counted. This results in an end of reign of Pepy ii in 2128
Table 4 lists the absolute dates of selected Pharaohs from our chronological models, from the handbooks of von Beckerath, Ian Shaw, and Erik Hornung et al., as well as from recent C14 measurements.48 All these chronologies are strongly dependent on the amount of years allocated to each Pharaoh.49 The two chronological models presented in this paper differ from the rest insofar as the number of calendar years counted for each king from Dynasty 4 to 6 is shortened by about 20% due to the assumption that no regular biannual counting of years was employed. However, the basic information about the reign lengths of kings in all these chronologies stems from the same sources: annals, Turin King List, Manethonian tradition and contemporary sources. The different resulting absolute dates in the models of Hornung et al., Shaw, and von Beckerath are due to varying assumptions about the duration of the First Intermediate Period and the absolute dating of the Egyptian Middle Kingdom. On the contrary, in the C14 model of Michael Dee and in our chronological models the length of the First Intermediate Period is a result of the modelling, not a basic parameter. Table 4 shows that the absolute dates of our Low Chronology are close to or up to 25 years lower than the ones given by Hornung et al. Our High Chronology dates resemble very closely the upper boundary defined by the C14 model of Dee and they are about 30 to 60 years higher than the higher dates of von Beckerath. The dates of Shaw and the lower dates of von Beckerath comprise a compromise between high and low chronologies: these are not supported by the lunar dates under our basic assumption that the Wagy-feast was not celebrated later than in the second month after the heliacal rising of Sirius.
Conclusions
Two different chronological models—a minimum High Chronology as well as a maximum Low Chronology—of Dynasties 4 to 6 are presented on the basic assumption that Nolan’s theory about the connection of the occurrence of a “year after the cattle count” with the insertion of an intercalary month in the original lunar calendar is correct. With the help of three lunar data the reigns of Djedkare Isesi and Unas were pinned down. The two chronologies differ in that in the case of the High Chronology the missing month name of the lunar Wagy-feast date was emended to 3rd month of the Akhet season and in the case of the Low Chronology to 3rd month of the Peret season. Afterwards the reigns of the kings up to Khufu and down to Pepy ii have been modelled based on the documented contemporary data and the preserved information from king lists. It was aimed at to stay as close as possible to the minimum attested year number and to account for the documented “year after the cattle count” years. It has to be stressed that the further away in time a Pharaoh is located from Djedkare Isesi the more uncertain are his modelled absolute dates. Both chronologies can explain about 82% of the documented “years after.” The Low Chronology is consistent with a short duration of the First Intermediate Period (30 to 60 years), but disagrees with recent radiocarbon determinations. On the contrary, the High Chronology is in line with the radiocarbon data but it can only be a serious solution if the First Intermediate Period lasted about 150 years.
List of all documented years of pharaohs Khufu to Pepy ii known to us, their source and possible remarks
Abbreviations used:
List for all years between 2636 and 2280 bce with the Egyptian date of the beginning of the lunar month in which the heliacal rising of Sirius presumably occurred, the dates of the heliacal rising of Sirius for an arc of vision of 9° to 10°, the number of lunar months in an Egyptian year, the year count of pharaohs Khufu to Pepy ii according to our High Chronology as well as the documented regnal years, their source, and remarks (uncertain attributions and astronomical data)
Abbreviations used: V—Verner, “System of dating”; G—Gundacker, “Mykerinos”
Absolute dates and number of counted regnal years in our Low Chronology (left) and our High Chronology (right) of the Old Kingdom.
Absolute accession dates of selected pharaohs in different chronological models. From left to right: our Low Chronology; dates given in Hornung, et al., Chronology; Shaw, Oxford History; von Beckerath, “Chronologie”; the modelled 95% probability C14 accession dates of Dee, et al., “Radiocarbon-based Chronology”; and our High Chronology
Footnotes
* This work was supported by grants of the Mäxi Foundation and the Cogito Foundation.
Abbreviations
Annales du Service des Antiquités de l’Égypte | |
Bulletin de l’Institut Français d’Archéologie Orientale | |
Bulletin de la Société française d’Égyptologie | |
Göttinger Miszellen | |
The Journal of Egyptian Archaeology | |
Journal of Near Eastern Studies | |
| RdÉ | Revue d’Égyptologie |
Studien zur Altägyptischen Kultur | |
Zeitschrift für Ägyptische Sprache und Altertumskunde |
Bibliography
Abu Bakr, A.M. and A.Y. Moustafa. “The Funerary Boat of Khufu.” In Aufsätze zum 70. Geburtstag von Herbert Ricke. A.M. Abu Bakr, ed., 1–16. Wiesbaden: Steiner, 1971.
Anthes, R. Die Felsinschriften von Hatnub. Hildesheim: Olms, 1964.
Aston, B. Ancient Egyptian stone vessels: materials and forms. Heidelberg: Heidelberger Orientverlag, 1994.
Baligh, R. “Oil and its importance in Egypt from the oldest times.” [oral presentation] In International Congress of Egyptologists XI (2015).
Bárta, M. “Radiocarbon Dates for the Old Kingdom and their Correspondences.” In Radiocarbon and the Chronologies of Ancient Egypt, A.J. Shortland and C. Bronk Ramsey, eds. 209–217. Oxford: Oxbow Books, 2013.
Baud, M. and V. Dobrev. “De nouvelles annals de l’Ancien Empire égyptien. Une ‘Pierre de Palerme’ pour la vie dynastie.” BIFAO 95 (1995): 23–92.
Beckerath, J. von. “Chronologie des Pharaonischen Ägypten.” Mainz am Rhein: Philipp von Zabern, 1997.
Borchardt, L. “Der zweite Papyrusfund von Kahun und die zeitliche Festlegung des mittleren Reiches der ägyptischen Geschichte.” ZÄS 37 (1899): 89–103.
Borchardt, L. Das Grabdenkmal des Königs Ne-user-re. Leipzig: Hinrichs, 1907.
Borchardt, L. Das Grabdenkmal des Königs Nefer-ir-ke-re. Leipzig: Hinrichs, 1909.
Borchardt, L. Das Grabdenkmal des Königs Sahure, Band 1: Der Bau. Leipzig: Hinrichs, 1910.
Couyat, J. and P. Montet. Les inscriptions hiéroglyphiques et hiératiques du Ouâdi Hammâmât. MIFAO 34. Cairo: IFAO, 1913.
Dee, M.W. “A Radiocarbon-based Chronology for the Old Kingdom.” In Radiocarbon and the Chronologies of Ancient Egypt, A.J. Shortland and C. Bronk Ramsey, eds. 209–217. Oxford: Oxbow Books, 2013.
Depuydt, L. “Sothic Chronology and the Old Kingdom.” JARCE 37 (2000): 167–168.
Dunham, D. and W.K. Simpson. The Mastaba of Queen Mersyankh III G7530–7540. Giza Mastabas I. Boston: Museum of Fine Arts, 1974.
Edel, E. “Die Kalksteintäfelchen.” In Das Sonnenheiligtum des Königs Userkaf. Die Funde. H. Ricke, ed., 2–22. Wiesbaden: Franz Steiner, 1969.
Eichler, E. “Untersuchungen zu den Königsbriefen des Alten Reiches.” SÄK 18 (1991): 141–172.
Eichler, E. Untersuchungen zum Expeditionswesen des ägyptischen Alten Reiches. Wiesbaden: Harrassowitz, 1993.
Gardiner, A.H. “Regnal Years and Civil Calendar in Pharaonic Egypt.” JEA 31 (1945): 11–28.
Gardiner, A.H., T.E. Peet, and J. Černý. The inscriptions of Sinai, Part I. Introduction and Plates. Oxford: Oxford University Press, 1952.
Gauthier, H. “Quatre nouveaux fragments de la pierre de Palerme.” In Le Musée Égyptien. Recueil des Monuments et de Notices sur les Fouilles d’Égypte 3, G. Maspero, ed., 29–53. Cairo: IFAO, 1915.
Gautschy, R. “Der Stern Sirius im Alten Ägypten.” ZÄS 138/1 (2011): 116–131.
Goedicke, H. “The Death of Pepi II.” SÄK 15 (1988): 111–122.
Goedicke, H. “Four Hieratic Ostraca of the Old Kingdom.” JEA 54 (1968): 23–30.
Goedicke, H. Königliche Dokumente aus dem Alten Reich. Wiesbaden: Harassowitz, 1967.
Goedicke, H. Die privaten Rechtsinschriften aus dem Alten Reich. Wien: Notring, 1970.
Gundacker, R. “Materialien zur Länge der Regierung des Mykerinos.” Sokar 21 (2010): 30–43.
Gunn, B. “A Sixth Dynasty letter from Saqqara.” ASAÉ 25 (1925): 242–255.
Günther, P. and R. Wellauer. Ägyptische Steingefässe der Sammlung Rudolph Schmidt (Solothurn). Ägyptologische Hefte des Orientalischen Seminars der Universität Zürich 2. Zürich: Orientalisches Seminar der Universität Zürich, 1988.
Habicht, M.E., R. Gautschy, R. Siegmann, D. Rutica, and R. Hannig. “A New Sothis Rise on a Small Cylindrical Jar from the Old Kingdom.” GM 247 (2015): 41–49.
Haeny, G. “Die Steinbruch- und Baumarken.” In Das Sonnenheiligtum des Königs Userkaf. Die Funde. H. Ricke, ed., 23–47. Wiesbaden: Franz Steiner, 1969.
Hannig, R. Grosses Handwörterbuch Deutsch—Ägyptisch: (2800–950 v. Chr.). Mainz am Rhein: Philipp von Zabern, 2000.
Hassan, S. Excavations at Gîza. 1930–1931. Cairo: Government Press, 1936.
Helck, W. “Gedanken zum Mord an König Teti.” In Essays in Egyptology in honor of Hans Goedicke. B.M. Bryan and D. Lorton, eds., 103–112. San Antonio: Van Siclen Books, 1994.
Hornung, E., R. Krauss, and D.A. Warburton, eds. Ancient Egyptian Chronology. HdO i/83. Leiden: Brill, 2006.
Junker, H. Der Friedhof südlich der Cheopspyramide. Gîza x. Wien: Rohrer, 1951.
Junker, H. Die Mastabas der IV. Dynastie auf dem Westfriedhof. Gîza i. Wien: Hölder-Pichler-Tempsky, 1929.
Junker, H. Der Ostabschnitt des Westfriedhofs. Gîza viii. Wien: Rohrer, 1947.
Kanawati, N. “A new ḥ3t/rnpt-zp for Teti and its implication for Old Kingdom Chronology.” GM 177 (2000): 25–31.
Krauss, R. “Egyptian Sirius/Sothic Dates and the Question of the Sothis-Based Lunar Calendar.” In Ancient Egyptian Chronology, E. Hornung, R. Krauss, and D.A. Warburton, eds., 439–457. HdO i/83. Leiden: Brill, 2006.
Krauss, R. “Lunar Dates.” In Ancient Egyptian Chronology, E. Hornung, R. Krauss, and D.A. Warburton, eds., 395–431. HdO i/83. Leiden: Brill, 2006.
Krauss, R. Sothis- und Monddaten: Studien zur astronomischen und technischen Chronologie Altägyptens. Hildesheim: Gerstenberg Verlag, 1985.
Krauss, R. “Wenn und aber: Das Wag-Fest und die Chronologie des Alten Reiches.” GM 162 (1998): 53–64.
Kuhlmann, K.P. “The ‘Oasis Bypath’ or The Issue of Desert Trade in Pharaonic Times.” In Tides of the Desert—Gezeiten der Wüste. Jennerstrasse 8, eds., 125–170. Köln: Heinrich Barth-Institut, 2002.
Leclant, J. “Fouilles et travaux en Égypte et au Soudan, 1960–1961: I. Fouilles en Égypte.” Orientalia 31 (1962): 197–222.
Leclant, J. “Recherches archéologiques à Tomâs en 1961 et 1964.” BSFÉ 42 (1965): 6–11.
Luft, U. Die chronologische Fixierung des ägyptischen Mittleren Reiches nach dem Tempelarchiv von Illahun. Wien: Verlag der Österreichischen Akademie der Wissenschaften, 1992.
Luft, U. “The Date of the Wagy Feast: Considerations on the Chronology of the Old Kingdom.” In Revolutions in Time: Studies in Ancient Egyptian Calendars, A. Spalinger, ed., 39–43. San Antonio: Van Siclen Books, 1994.
Moussa, A.M. and H. Altenmüller. The Tomb of Nefer and Ka-hay. Mainz am Rhein: Philipp von Zabern, 1971.
Nolan, J.F. “Cattle, Kings and Priests: Phyle Rotations and Old Kingdom Civil Dates.” In Towards a New History for the Egyptian Old Kingdom: Perspectives on the Pyramid Age, P. Der Manuelian and T. Schneider, eds., 337–365. Leiden: Brill, 2015.
Nolan, J.F. “The Original Lunar Calendar and Cattle Counts in Old Kingdom Egypt.” In Basel Egyptology Prize I, S. Bickel and A. Loprieno, eds., 75–98. Aegyptiaca Helvetica 17. Basel: Schwabe & CO AG, 2003.
Parker, R.A. The Calendars of Ancient Egypt. SAOC 26. Chicago: The University of Chicago Press, 1950.
Petrie, W.M.F. A History of Egypt. London: History and Mysteries of Man, 1991.
Posener-Kriéger, P. Les archives du temple funéraire de Néferirkarê-Kakaï. Cairo: IFAO, 1976.
Posener-Kriéger, P. “Les papyrus de Gébélein. Remarques préliminaires.” RdÉ 27 (1975): 211–221.
Posener-Kriéger, P. “Le prix des étoffes.” In Festschrift Elmar Edel 12. März 1979. M. Görg, E. Pusch, A. Wuckelt, and K.-J. Seyfried, eds., 318–331. ÄAT 1. Bamberg: Görg, 1979.
Posener-Kriéger, P. and J.L. de Cenival. The Abu Sir Papyri. Hieratic Papyri in the British Museum. Fifth Series. London: British Museum Press, 1968.
Posener-Kriéger, P., M. Verner, and H. Vymazalová The Pyramid Complex of Raneferef: The Papyrus Archive. Abusir x. Prague: Czech Institute of Egyptology, 2006.
Ricke, H. “Erster Grabungsbericht über das Sonnenheiligtum des Königs Userkaf bei Abusir.” ASAÉ 57 (1956): 75–82.
Ricke, H. “Zweiter Grabungsbericht über das Sonnenheiligtum des Königs Userkaf bei Abusir.” ASAÉ 57 (1956): 305–316.
Saad, Z.Y. Royal Excavations at Saqqara and Helwan (1941–1945). ASAÉ Supplement 3. Cairo: IFAO, 1947.
Schäfer, H. Ein Bruchstück altägyptischer Annalen. Berlin: Reimer, 1902.
Sethe, K. Urkunden des ägyptischen Altertums, Band 1: Urkunden des Alten Reiches. Leipzig: Hinrichs, 1933.
Shaw, I., ed. The Oxford History of Ancient Egypt. Oxford: Oxford University Press, 2000.
Smith, W.S. “Inscriptional Evidence for the History of the Fourth Dynasty.” JNES 11 (1952): 113–128.
Spalinger, A. “Dated Texts of the Old Kingdom.” SÄK 21 (1994): 275–320.
Spence, K. “Ancient Egyptian chronology and the astronomical orientation of pyramids.” Nature 408 (2000): 320–324.
Tallet, P. Les papyrus de la mer rouge I. Le «Journal de Merer». Cairo: IFAO, 2017.
Valloggia, M. “La descenderie de la pyramide de Radjedef à Abu Rawash.” In Études sur l’Ancien Empire et la nécropole de Saqqâra dédiées à Jean-Philippe Lauer. C. Berger and B. Mathieu, eds., 417–428. Montpellier: Université Paul-Valéry, 1997.
Vanderkerckhove, H. and R. Müller-Wollermann. Die Felsinschriften des Wadi Hilâl. 1. Text. Elkab vi. Brepols: Turnhout, 2001.
Verner, M. “Archaeological Remarks on the 4th and 5th Dynasty Chronology.” Archiv Orientální 69 (2001): 363–418.
Verner, M. Baugraffiti der Ptahschepses-Mastaba. Abusir ii. Prague: Universitas Carolina Pragensis, 1992.
Verner, M. The Pyramid Complex of Khentkaus. Abusir iii. Prague: Universitas Carolina Pragensis, 1995.
Verner, M. “The system of dating in the Old Kingdom.” In Chronology and archaeology in ancient Egypt (the third millennium B.C.), H. Vymazalová and M. Bárta, eds., 23–43. Prague: Czech Institute of Egyptology, 2008.
Verner, M. and V.G. Callender. Djedkare’s Family Cemetery. Abusir vi. Prague: Czech Institute of Egyptology, 2002.
Verner, M., M. Bárta, H. Benešovská, V.G. Callender, P. Kočár, and J. Krejčí The Pyramid Complex of Raneferef: The Archaeology. Abusir ix. Prague: Czech Institute of Egyptology, 2006.
Vymazalová, H. and M. Bárta, eds. Chronology and archaeology in ancient Egypt (the third millennium B.C.). Prague: Czech Institute of Egyptology, 2008.
Krauss, Sothis- und Monddaten; Gautschy, “Sirius.”
Krauss, Sothis- und Monddaten; Gautschy, “Sirius”; Luft, Chronologische Fixierung; Borchardt, “Kahun.”
Habicht, et al., “New Sothis Rise.”
Aston, Stone Vessels; Günther and Wellauer, Ägyptische Steingefässe.
Baligh, “Oil and its importance.”
Hannig, Handwörterbuch, 206.
Baligh, “Oil and its importance.”
See, e.g., Shaw, ed., Oxford History; Krauss, “Lunar Dates,” 429–31; Depuydt, “Sothic Chronology,” 183–84; Dee, “Radiocarbon-based Chronology,” 212–13 and 287; Bárta, “Radiocarbon Dates,” 221; Spence “Orientation of Pyramids.”
Gardiner, “Regnal Years.”
Nolan, “Cattle Counts,” 79.
Nolan, “Cattle Counts,” 92.
Nolan, “Phyle Rotations,” 340–44.
Parker, Calendars, 30–50.
A sidereal year is only slightly longer than the tropical solar year, thus a lunar calendar synchronized with a stellar event like the heliacal rising of Sirius is also synchronized with the solar year.
For details about the computations see Gautschy, “Sirius,” 119–20.
These values include refraction.
The clock time error ΔT is due to the fact that Earth’s rotation is not uniform, but slowing down. The slowdown rate is composed of a regular predictable part and of a fluctuating irregular contribution. The time difference between an assumed uniform rotation of the Earth and the actual one is called ΔT. It can only be determined observationally. The earliest securely dated astronomical observations that can be used to derive values of ΔT for antiquity stem from the 7th century
Shaw, ed., Oxford History.
We used the compilations of Spalinger, “Dated Texts”; Verner, “4th and 5th Dynasty Chronology” and “System of Dating”; and of Gundacker, “Mykerinos.”
Posener-Kriéger, et al., Raneferef and Posener-Kriéger, Neferikare.
Krauss, “Lunar Dates,” 429–31; Depuydt, “Sothic Chronology”; and Luft, “Wagy.”
Luft, “Wagy” and Depuydt, “Sothic Chronology,” 172–74 and 183–84.
Luft thus assumes that the moveable Wagy-feast was celebrated in the first month after the heliacal rising of Sirius like the fixed Wagy feast although he discusses the Wagy-feast data from the Middle Kingdom Illahun temple archive where the moveable lunar Wagy-feast was demonstrably celebrated in the second month after the heliacal rising of Sirius (Luft, “Wagy,” 41; Krauss, Sothis- und Monddaten, 86–94).
For a reference point Memphis, Sirius 2° or 3° above horizon and an assumed arc of vision between 9° and 11°.
Krauss, “Wenn und aber,” 56–57 and private communication.
Depuydt, “Sothic Chronology,” 173.
Posener-Kriéger, Neferirkare, 486–88.
Only Pepy i and Pepy ii may be theoretically considered as alternatives.
Posener-Kriéger, Neferirkare, 486–88 and Krauss, “Lunar Dates,” 430–31 both finally argue for an attribution to Djedkare Isesi.
Habicht, et al., “New Sothis Rise.”
Habicht, et al., “New Sothis Rise,” 44–46.
Dee, “Radiocarbon-based Chronology,” 212–13 and 287.
Theoretically nothing speaks against a documented year rnp.t m-ḫt sp tpy and a year rnp.t m-ḫt sp 1 for the same king. Even if not identical years are meant intercalary months after already two years occur from time to time.
In our Low Chronology the documented “year 14 after” of Djedkare Isesi cannot be reproduced by the calculations, in our High Chronology the documented “year 4 after” of Djedkare Isesi cannot be reproduced.
From the archive of Illahun we know that the Wagy-feast was celebrated in the second month after the heliacal rising of Sirius (Luft, Chronologische Fixierung, 217–20). There are several possible solutions later than 2242
Posener-Kriéger, et al., Raneferef, 321–22.
If both lunar dates are ascribed to Djedkare Isesi the year 3 lunar date in 2328/2327
Three out of seven can be explained with an arc of vision of 10° for the heliacal rising of Sirius, the remaining four with an arc of vision of 9°.
The minimum distance we defined to be 30 years for the First Intermediate Period, 106 to 143 years for Dynasty 11 and 103 to 120 years from the start of Dynasty 12 to the beginning of the reign of Senwosret iii. For the Sothic date of the Middle Kingdom see, e.g., Luft, Chronologische Fixierung, 58; Krauss “Sothic Dates,” 448–50 and Gautschy, “Sirius,” 124–25.
In 2489
Six out of twelve can be explained with an arc of vision of 10° for the heliacal rising of Sirius, the remaining six with an arc of vision of 9°.
See, e.g., Dee, “Radiocarbon-based Chronology.”
Spence, “Orientation of Pyramids.”
Habicht, et al., “New Sothis Rise,” 44–46.
See, e.g., Spalinger, “Dated Texts”; Helck, “Teti”; Verner, “4th and 5th Dynasty Chronology” and “System of Dating”; Nolan, “Phyle Rotations.”
Verner, “System of Dating,” 26–38.
Documents for 23 out of 36 years exist for Djedkare Isesi, and for 5 out of 19 years for Unas. Taking only these two comparably well documented kings into account the ratio between “years of” and “years after” amounts to 19:9 (68%:32%).
Beckerath, “Chronologie,” 187–88; Shaw, ed., Oxford History, 480; Hornung, Krauss, and Warburton, eds., Chronology, 490–91; Dee, “Radiocarbon-based Chronology,” 209–17 and 287.
The C14 accession dates are obtained with the help of the wiggle matching method. In the modelling, information about the succession of kings as well as about their reign lengths enters the model.