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Dating Middle Kingdom, draft, 2022-12-21, Page 1 of 15
The absolute dating of three pharaohs of the Egyptian 12th dynasty
Petra Ossowski Larsson* and Lars-Åke Larsson, Sweden
* Corresponding author: petra@cybis.se
Abstract
In this article we explore the papyrus archive from El Lahun using a strictly schematic
Egyptian civil calendar and a modern astronomical date for the start of the calendar.
This leads to the absolute accession years for three pharaohs of the Egyptian 12th
dynasty. The accession years are compatible with recent radiocarbon dates for
dynastic Egypt and are confirmed by all twenty-six moon dates with explicit regnal
years, as well as by the Sothic date and an additional incomplete moon date included
in the archive. Our investigation also sheds light on periods of co-regency, Egyptian
practices of Sirius and moon observations, and the reliability of the Turin king list.
Introduction
For dynastic Egypt we sometimes have both first hand astronomical information and
relics which can be safely attributed to certain kings; in many cases to their exact
regnal year. Astronomical information may sometimes contain - in addition to the
regnal year - a date in the Egyptian civil calendar. Moreover, the scientific dating of
artefacts or relics which were retrieved through archaeological excavations can
produce absolute or nearly absolute dates without any other prerequisites than
reliable references (which still might be a problem of its own). This should enable us
to reach absolute accession years at least for some long-lived and therefore well-
documented pharaohs.
Now you object that this has been tried by many researchers for more than one
hundred years, with the result that there are more than enough dating proposals.
This situation has led to the collapse of archeo-astronomy as an ancillary science to
Egyptology. Some contemporary scientists even argue that it is impossible to use the
civil calendar for anything that makes sense. But wait a moment, even though it has
been known since its discovery that the Egyptian civil calendar sometimes was used
schematically, nobody has followed through with that idea. It has always been
assumed - without any documented evidence - that the civil calendar was constantly
adjusted according to astronomical observations, which of course would have added
some hardly comprehensible and understandable factors of uncertainty (ref.1). But
what happens if we look at the civil calendar as strictly schematic and with a simple
non-astronomical rule?
Our consequent use of a strictly schematic civil calendar has already led to the
absolute accession years for two New Kingdom pharaohs, year -1497 for
Thutmose III and year -1297 for Rameses II (ref.2). Both are two decades older than
consensus but conform with a recent radiocarbon study. In this article we will try the
same approach for a few pharaohs of the Middle Kingdom's 12th dynasty for whom a
whole wealth of internally coupled first-hand astronomical and chronological
Dating Middle Kingdom, draft, 2022-12-21, Page 2 of 15
information exists. Moreover, the information is written on papyri for which modern
radiocarbon dates are readily available.
Radiocarbon dating
A groundbreaking radiocarbon study by Christopher Bronk Ramsey et al. (ref.3)
utilizes radiocarbon wiggle-matching of short-lived organic material from secure
contexts sequenced according to two historical chronologies (king lists) to produce
nearly absolute dates for the Old, Middle and New Kingdoms of Egypt. The
chronology compiled by Ian Shaw (ref.4) apparently gives the best conformity
towards the radiocarbon study. The chronology compiled by Hornung et al. (ref.5)
appears in many cases too young, and in the case of the Middle Kingdom also too
short.
However, also Shaw's list has a small offset (Shaw's dates being generally a few
years younger than the radiocarbon dates) which opened up for the proposal that
"the New Kingdom might have begun earlier by about a decade than the consensus
date of Shaw" (ref.3). This gets even more marked if you consider our hypothesis
that the dendrochronological time base of the radiocarbon calibration curve might be
eight years too young in the 2nd to 6th millennia BC (ref.6).
How could Shaw's "floating" chronology parts be placed almost correct in time? The
lists of Middle and New Kingdom pharaohs are traditionally anchored in the absolute
astronomical time-line via a few first-hand records of astronomical observations
regarded as trustworthy. These are a couple of so called "heliacal risings of Sothis"
or Sothic dates and moon dates, typically given as the regnal year of a certain
pharaoh plus the day in the Egyptian civil calendar. We will use the same dates to
find an absolutely fitting astronomical solution within a narrow time frame given by a
Sothic date, backed up and secured by radiocarbon dates.
The Egyptian civil calendar
The purpose with our recent study of the Egyptian civil calendar was to see if it could
be useful as a scientific dating tool (ref.7). The civil calendar was a quasi solar
calendar with a year of exactly 365 days distributed to 12 months with 30 days each,
and an additional "intercalary month" of 5 days. The 12 months were grouped into 3
seasons of 4 months each (hence 120 days), initially beginning around midsummer
with the flood season, followed by the growth season starting late in October and
finally the harvest season starting early in spring. New Year was celebrated on
I Thoth 1, the first day of the flood season.
I II III IV V VI VII VIII IX X XI XII Intercalary
month
Thoth Phaophi Athyr Choiak Tybi Mechir Phamenoth Pharmuthi Pachons Payni Epiphi Mesore Hryw Rnpt
(1)
Akhet (2)
Akhet (3)
Akhet (4)
Akhet (1)
Peret (2)
Peret (3)
Peret (4)
Peret (1)
Shemu (2)
Shemu (3)
Shemu (4)
Shemu 5 days
Flood season Growth season, winter Low water or harvest season, summer
Table 1: Months and seasons of the Egyptian civil calendar. A date can be given as a certain day (e.g.
20) either of a month of the year (e.g. IX Pachons 20) or a month of a season (e.g. (1) Shemu 20). To
ease reading, we will if possible translate all civil dates to a short notation with only number of month
and number of day e.g. IX 20.
Dating Middle Kingdom, draft, 2022-12-21, Page 3 of 15
As the astronomical solar year is longer than the civil year, almost ¼ day, the
Egyptian civil calendar lagged about 1 day in 4 years. Therefore the civil year slowly
cycled backwards through the solar year, growing more and more out of phase with
the seasons. One full cycle, when the civil year again was about in phase with the
seasons, took 1460 (4 x 365) years. For this peculiarity the Egyptian civil calendar is
sometimes called the "wandering calendar".
When the Egyptian civil calendar was launched - we propose in -2781 at Memphis -
it was on the day for the heliacal rising of Sirius at this place and only two days after
midsummer. We propose that this Sirius observation was chosen as a straight for-
ward substitute for the more difficult observation of the summer solstice. Hencefor-
ward no further Sirius observations were made or needed to keep the schematic
calendar going. For the first four years the "Sothic date" (day for the heliacal rising of
Sirius) was on I 1. After four years the Sothic date shifted to I 2, and so on. We
believe that this rigorous, non-astronomical rule was the great benefit of the civil
calendar which allowed a long-term count of unique four-years-periods for
administrative purposes. It also makes that we today can firmly synchronize the
Egyptian civil calendar with our calendar if we have some handed-down moon dates
and know the Julian date for the heliacal rising of Sirius in -2781 at Memphis. Modern
astronomical retro-calculations show that this (start or standard) date was July 16
(Julian). Read more about the civil calendar and the heliacal rising of Sirius in ref.7.
Astronomical dates defining the Egyptian Middle Kingdom
A whole papyrus archive from the Egyptian Middle Kingdom was retrieved in the late
19th century from the rubbish heap of a mortuary temple at El Lahun. This temple
complex was commissioned by and dedicated to Senusret II, a pharaoh of the 12th
dynasty. The papyrus archive contains temple diaries and various administrative
documents, many dated in the fashion of the civil calendar. Among the notes are also
one date for the heliacal rising of Sirius (Sothic date), feast dates and a number of
other moon dates, which are marked with the regnal year of the ruling pharaoh who's
name is generally not mentioned. A first description of the archive was made in 1899
by Ludwig Borchardt (ref.8).
The Sothic date
The most important date in the El Lahun archive is the Sothic date contained in
Papyrus Berlin (PB) 10012. The papyrus consists of two fragments. One fragment is
a copy of a letter, in which the date for the approaching heliacal rising of Sirius is
forwarded to a temple priest. The letter is dated VII 25, regnal year 7 of an unnamed
pharaoh, and the heliacal rising is on VIII 16. The second fragment contains
information about the supplies for the Sothis-feast which was held on VIII 17.
To tell when this 7th regnal year appeared in our modern calendar, we use our
schematic conversion table (ref.7, Appendix B. You may also look at the Appendix in
this article.). We see that VIII 16 was the Sothic date in either -421 to -418, or -1881
to -1878. As the pharaohs of the 12th dynasty lived in the 19th century BC (according
to radiocarbon dating, ref.3), we would therefore propose that the 7th regnal year of a
certain pharaoh fell in the range -1881 to -1878 and thus his accession year in the
range -1887 to -1884. According to Bronk Ramsey's radiocarbon data (ref.3), there
Dating Middle Kingdom, draft, 2022-12-21, Page 4 of 15
are two pharaohs with a possible accession year in that range, Senusret II and his
son Senusret III.
That the El Lahun Sothic date was taken from a schematic calendar and not an
observation is evident from the fact that the temple order was forwarded three weeks
in advance. Such a treatment would also ensure that the Sothis-feast was celebrated
on the same day in whole Egypt, and that sufficient supplies were in place.
Interesting is the fact that the actual feast was celebrated one day later than the
schematic Sothic date. We propose that this was done to compensate for the real
observable heliacal rising of Sirius at the latitude of Memphis which happened on the
schematic Sothic date only for the first 500 years or so after the launch of the civil
calendar in -2781. For almost the rest of Egyptian BC-time the star would have
become visible one day later (see ref.7, table 2). Only in late Ptolemaic times it would
have become necessary to compensate two days, which perhaps was the reason
why the Egyptians finally abandoned their outdated civil calendar and halted its
wandering by inserting a leap day each fourth year.
Reign lengths of the late 12th dynasty pharaohs
Before we proceed, this is the right place to discuss reign lengths of some pharaohs
of the 12th dynasty. Senusret II, the founder of the temple, is said to have reigned 19
years according to the Turin king list (ref.9). Borchardt reports the death of one
pharaoh in his 19th year month VIII, while his successor's first year is counted from
the following New Year, I 1, almost five months later (ref.8). Borchardt therefore holds
for sure that this information refers to Senusret II and III.
According to the Turin king list (ref.9) there are two pharaohs after Senusret II who
reigned longer than 30 years: Senusret III 30+ years and his successor Amenemhat
III 40+ years.
However, Shaw gives reign lengths of 7 years for Senusret II, 39 years for Senusret
III and 45 years for Amenemhat III (ref.4). This king list is about conform with Bronk
Ramsey's radiocarbon data (ref.3), though generally a few years too young.
Hornung et al. give 8 years for Senusret II, 19 years for Senusret III (implying that the
pharaoh dying in his 19th year is Senusret III and his successor is Amenemhat III),
and 46 years for Amenemhat III (ref.5). But according to Bronk Ramsey's
radiocarbon data, 19 years for Senusret III seems too short. See also table 9.
As a third alternative, Josef Wegner has proposed that Senusret III had a long co-
regency with Amenemhat III starting around his 20th regnal year (ref.10). There is
evidence for a royal jubilee of Senusret III (usually held in the 30th regnal year), and
building activity at the Senusret III mortuary temple at Abydos in a regnal year 39
which is quite unlikely the 39th year of Amenemhat III. So in this alternative Senusret
III's reign length is 39 years but only 19 years as the sole pharaoh. The remaining 20
years he would have been the senior co-regent with his son Amenemhat III.
El Lahun moon dates
There are a number of papyri containing moon dates in the El Lahun archive which
can be attributed to two groups belonging to the reigns of two different pharaohs,
hereafter called X and XX. We use the 26 entries with specified regnal years listed by
Rita Gautschy in her article about the El Lahun moon data (ref.11, table 1).
The two groups are: twenty moon dates up to pharaoh X’s 36th year (contained in PB
10090, PB 10056, 58065, PB 10052, PB 10103, PB 10006, PB 10206), and six moon
dates up to pharaoh XX’s 18th year (contained PB 10092, PB 10009, PB 10003, PB
Dating Middle Kingdom, draft, 2022-12-21, Page 5 of 15
10248, PB 10011, PB 10016). That the papyri within the two groups are
astronomically correlated via the mentioned regnal years (i.e. are from the same
reign) is consensus and will also be confirmed by us later in this article.
In order to determine which of the groups is from the reign of the pharaoh with the
Sothic date VIII 16 in his 7th year in the range -1881 to -1878 (see page 3), we test
two New Moon dates, one from each group. In PB 10056/1 from group X a New
Moon on IV 26 in the 8th regnal year should appear in the range -1880 to -1877. In
PB 10003 from group XX a New Moon on VII 9 in the 9th regnal year should appear
in the range -1879 to -1876. We simulate the moon ages for those years and dates
using the program Stellarium (ref.12). The result is shown in table 2 below.
A B C D E F
Year
CE
Range for
regnal year 7
in red frame
Sothic date
Group X
PB 10056/1, IV 26,
New Moon, regnal
year 8, calculated
Julian date
Moon age
simulated
Range for regnal
year 8 in red
frame
Group XX
PB 10003, VII 9,
New Moon,
regnal year 9,
calculated
Julian date
Moon age
simulated
Range for regnal
year 9 in red
frame
-1874 VIII 17 Mar 27 day 14 Jun 8 day 27
-1875 day 3 day 17
-1876 day 22 day 7
-1877 day 11 day 24
-1878 VIII 16 Mar 28 day 1 Jun 9 day 15
-1879 day 20 day 4
-1880 day 9 day 24
-1881 day 28 day 11
-1882 VIII 15 Mar 29 day 18 Jun 10 day 2
-1883 day 6 day 21
-1884 day 25 day 11
-1885 day 14 day 28
Table 2: Calculated Julian dates for IV 26 and VII 9 for the years -1885 to -1874, compared with moon
age simulations on these dates for the same years.
Column A includes the years (CE) in the ranges for the 7th to 9th regnal years according to the
El Lahun Sothic date.
Column B gives the schematic Sothic date for each four years period (see ref.7, Appendix B).
For each of the years in column A we calculate the Julian date corresponding to the civil dates
mentioned in PB 10056/1 and PB 10003: the days y between the Sothic date and the civil
date are counted, then the Sothic date is set to (standard) July 16 (Julian) and the searched
for Julian date is found at y days distance (columns C and E).
Example: Convert civil date IV 26 to its corresponding Julian date when the Sothic date is VIII16.
There are 14 + 30 + 30 + 30 + 30 + 5 + 30 + 30 + 30 + 26 = 255 Egyptian days between VIII16 and IV 26.
VIII IX X XI XII I II III IV
With the Sothic date VIII 16 set at July 16 (Julian) we count 255 Julian days from that date:
15 + 31 + 30 + 31 + 30 + 31 + 31 + 28 + 28 = 255
Jul Aug Sep Oct Nov Dec Jan Feb Mar
This means that March 28 is the Julian date corresponding to IV 26.
Finally we simulate the moon age for each year on the calculated Julian date using the
program Stellarium (ref. 12), see columns D and F.
There is only one simulated New Moon (day 1) in the year ranges defined above (red
frames), and that is on March 28 -1878 for a papyrus from group X. That means that
Only group X is compatible with the Sothic date, group XX is not.
-1878 is the 8th regnal year, hence the pharaoh’s accession year is -1885.
Radiocarbon dating supports either Senusret II or III with this accession year.
As group X includes papyri with regnal years up to the 36th, the pharaoh
connected to this group must be Senusret III, as his father had a shorter reign.
Dating Middle Kingdom, draft, 2022-12-21, Page 6 of 15
Analysis of papyrus group X - the moon dates of Papyrus Berlin 10056
As described by Borchardt (ref.8), Papyrus Berlin 10056 contains a list of temple
service periods for priests. The list covers a whole lunar year, i.e. twelve civil dates
with 29 or 30 days spacing. Most probably the service periods were counted from
New Moon day to next New Moon day, but that we shall see. Before the date of the
fourth entry the 31st regnal year of Senusret III (name not mentioned) begins.
The twelve dates (with two entries on each line) are as follows:
X 26 until XI 25
XII 25 until year 31 I 19 (not 20)
II 20 until III 19
IV 19 until V 18
VI 18 until VII 17
VIII 17 until IX 16
As these moon dates are correlated with the Sothic date in the 7th regnal year
in -1879 (thus the accession year would be in -1885, see page 5), we would expect
his 30th and 31st regnal years to be between -1856 and -1855.
There seems indeed to be a series of (observed?) days of first visibility for the
years -1856 to -1855. The whole series of entries in PB 10056 gives the following
results when compared with New Moon (first visibility) simulations for the years -1856
to -1855:
A B C D
PB 10056
entry,
civil date
regnal
year
C
alculated
Julian date
New Moon
(first
visibility)
simulated
X 26
30
Sept 18 -1856 Sept 17
XI 25 Oct 17 -1856 Cct 17
XII 25 Nov 16 -1856 Nov 15
I 19
31
Dec 15 -1856 Dec 15
II 20 Jan 15 -1855 Jan 13
III 19 Febr 13 -1855 Febr 12
IV 19 Mar 15 -1855 Mar 14
V 18 Apr 13 -1855 Apr 12
VI 18 May 13 -1855 May 12
VII 17 Jun 11 -1855 Jun 11
VIII 17 Jul 11 -1855 Jul 10
IX 16 Aug 9 -1855 Aug 9
Table 3: Calculated Julian dates for X 26 up to IX 16 for the years -1856 to -1855, compared with New
Moon simulations around these dates for the same years. The Sothic date for these years (used for
the calculation of the Julian dates) is VIII 22, see the Appendix.
Besides, Borchardt mentioned the accession day of at least one 12th dynasty
pharaoh to be New Year day I 1. This is what we see in table 3 above where the shift
between 30th and 31st regnal year takes place between entry 3 and 4, i.e. XII 25 and
I 19.
Dating Middle Kingdom, draft, 2022-12-21, Page 7 of 15
There are more civil dates in group X, see the following table 4 and note the excellent
agreement of the calculated with the simulated Julian dates:
Papyrus
number
Regnal
year
Civil date
Day of moon
month
Calculated
Julian date
Simulated date
PB 10090 3 (-1883) XI 16/17 *) day 1 Oct 15/16 -1883 Oct 16
PB 10056/1 8 (-1878) IV 26 day 1 Mar 28 -1878 Mar 28
58065 9 (-1877) X 29 day 17 **) Sept 26 -1877 Sept 26
PB 10052 24 (-1862) I 9 day 5 Dec 7 -1863 Dec 7
PB 10103 29 (-1857) IX 15 day 9 Aug 8 -1857 Aug 8
PB 10006/1 32 (-1854) II 9 day 2 Jan 4 -1854 Jan 4
PB 10006/2 32 (-1854) III 7 day 1 Febr 1 -1854 Febr 1
PB 10206 36 (-1850) II 27 day 4 ***) Jan 21 -1850 Jan 21/22
Table 4: Papyri from group X compatible with PB 10056 and the Sothic date in regnal year 7, which
point to an accession year -1885 for Senusret III. Sothic dates used for calculation of the Julian dates
see Appendix.
*) For this civil date, ref. 5 page 425 comments as follows:
The entries mention offerings on III Shemu 15, followed by “sw3 hr III Shemu 16” in turn
followed by “LD 1”. According to Luft “sw3 hr III Shemu 16” means that III Shemu 16 was
skipped. If so, the LD 1 mentioned after III Shemu 16 has to be III Shemu 17.
On -1883 Oct 15 the moon was 1.1 days old but had a too small arc of vision towards the sun to
be observable. Therefore the probably predicted first New Moon date was skipped and the
second date was registered as New Moon on the papyrus instead. See also the discussion.
**) Wagi-festival which was held in the second moon month after Sothis on the second day after full
moon (which fell schematically on moon day 15), ref.5, page 425.
***) Feast “Bekleidung”, certainly held on moon day 4. Simulated moon age 3.5 days on jan.21 and
4.5 days on jan.22.
Analysis of papyrus group XX
Now we turn to the moon dates which are not compatible with the Sothic date and
the moon dates in group X from the reign of Senusret III.
Most significant in group XX are two papyri mentioning Khakaura - the throne name
of Senusret III - as "living eternally", PB 10003 and PB 10248 from a 9th and a 14th
regnal year respectively. Moreover, in PB 10003 Senusret II is designated as "late
lamented". Therefore these papyri have been assumed to be from the reign of
Senusret III (ref.11 and references therein).
But apparently this is not the case as the reign of Senusret III is connected with
papyrus group X. Then how could pharaoh Khakaura Senusret III be alive in
someone else’s reign? This is possible in a co-regency period with his son
Amenemhat III as proposed in ref.10. As Senusret III most probably died in his 39th
regnal year, and Amenemhat III most probably did not access the throne before his
father, both the 9th and the 14th year of Amenemhat III have to be between -1877 and
-1847 (Senusret III's 9th and 39th year resp. if his accession year is -1885).
We make a table similar to table 2 with this year range in column A. Column B gives
the Sothic dates in that range. Columns C and E contain the calculated Julian dates
for the civil years in PB 10003 and PB10248 respectively. And columns D and F list
the simulated moon ages for the Julian dates in each year.
Dating Middle Kingdom, draft, 2022-12-21, Page 8 of 15
A B C D E F
Year
CE
Sothic date
PB 10003, VII 9,
New Moon,
regnal year 9,
calculated Julian
date
Moon age
simulated
PB
10248, II 18,
moon day 2,
regnal year 14,
calculated
Julian date
M
oon age
simulated
-1846 VIII 24 Jun 1 day 0 Jan 1 day 27
-1847 day 20 day 16
-1848 day 10 day 4
-1849 day27 day 24
-1850 VIII 23 Jun 2 day 17 Jan 2 day 14
-1851 day 7 day 3 alt.3
-1852 day 26 day 21
-1853 day 14 day 11
-1854 VIII 22 Jun 3 day 4 Jan 3 day 1 alt.2
-1855 day 24 day 20
-1856 day 13 day 8
-1857 day 1 alt.3 day 27
-1858 VIII 21 Jun 4 day 20 Jan 4 day 18
-1859 day 11 day 7
-1860 day 0 alt.2 day 24
-1861 day 17 day 14
-1862 VIII 20 Jun 5 day 7 Jan 5 day 5
-1863 day 27 day 23
-1864 day 17 day 11
-1865 day 4 day 1 alt.1
-1866 VIII 19 Jun 6 day 24 Jan 6 day 22
-1867 day 14 day 10
-1868 day 4 day 28
-1869 day 21 day 18
-1870 VIII 18 Jun 7 day 11 Jan 7 day 9
-1871 day 1 alt.1 day 27
-1872 day 20 day 15
-1873 day 8 day 5
-1874 VIII 17 Jun 8 day 27 Jan 8 day 25
-1875 day 17 day 14
-1876 day 7 day 2
-1877 day 24 day 21
Table 5: Calculated Julian dates for VII 9 and II 18 for the years -1877 to -1846, compared with moon
age simulations on these dates for the same years. Dating alternatives 1 to 3 see tables 6, 7 and 8.
See also the note below.
As the civil date in PB 10003 is for a New Moon day (psdntjw), we highlight all
simulated moon ages in column D which are day 0, 1 or 2 (to allow for uncertainties
regarding whether psdntjw is the day of invisibility or the day of first visibility
(discussed in ref.2 and below), and to allow for bad observation conditions).
The civil date in PB 10248 is for a second moon day five regnal years later, and if
both civil dates are from the reign of the same pharaoh we should find a one day
later simulated moon age in column F compared with column D.
But note: as it turns out that there is a Julian year end between the calculated Julian
dates in columns C and E, we have to add one year to the five years difference in
regnal years between PB 10003 and PB 10248.
We see that the civil dates in PB 10003 and PB 10248 indeed are correlated, i.e. are
from the reign of the same pharaoh. But there are three alternatives fulfilling the
moon age conditions mentioned in the papyri, see table 5. Which one is the truth?
Together with four more compatible moon dates the alternatives look like this:
Dating Middle Kingdom, draft, 2022-12-21, Page 9 of 15
Papyrus
number
Regnal year
Civil date
Day of moon
month
Calculated
Julian date
Simulated
date
PB 10092 5 (-1875) II 27 day 4 Jan 27 -1875 Jan 28
PB 10009 5 (-1875) VII 1 day 10 May 30 -1875 May 31
PB 10003 9 (-1871) VII 9 day 1 Jun 7 -1871 Jun 7
PB 10248 14 (-1865) II 18 day 2 Jan 5 -1865 Jan 6
PB 10011 16 (-1864) VII 2 day 10 May 29 -1864 May 30
PB 10016 18 (-1862) X 17 day 17 Sept 11 -1862 Sept 10
Table 6: Dating alternative 1 according to table 5. Highlighted Julian dates are astronomically
impossible observations, i.e. the calculated Julian date for an observation is before the simulated date.
Papy
rus
number
Regnal year
Civil date
Day of moon
month
Calculated
Julian date
Simulated
date
PB 10092 5 (-1864) II 27 day 4 Jan 24 -1864 Jan 27
PB 10009 5 (-1864) VII 1 day 10 May 28 -1864 May 30
PB 10003 9 (-1860) VII 9 day 1 Jun 4 -1860 Jun 5
PB 10248 14 (-1854) II 18 day 2 Jan 3 -1854 Jan 4
PB 10011 16 (-1853) VII 2 day 10 May 26 -1853 May 29
PB 10016 18 (-1851) X 17 day 17 Sept 8 -1851 Sept 8
Table 7: Dating alternative 2 according to table 5. Highlighted Julian dates are astronomically
impossible observations.
Papyrus
number
Regnal year
Civil date
Day of moon
month
Calculated
Julian date
Simulated
date
PB 10092 5 (-1861) II 27 day 4 Jan 23 -1861 Jan 23
PB 10009 5 (-1861) VII 1 day 10 May 27 -1861 May 27
PB 10003 9 (-1857) VII 9 day 1 Jun 3 -1857 Jun 3
PB 10248 14 (-1851) II 18 day 2 Jan 2 -1851 Jan 1
PB 10011 16 (-1850) VII 2 day 10 May 26 -1850 May 25
PB 10016 18 (-1848) X 17 day 17 Sept 7 -1848 Sept 6
Table 8: Dating alternative 3 according to table 5. All Julian dates are astronomically possible
observations.
Alternative 1 and 2 are quite bad with four resp. five observations being earlier than
simulated (i.e. astronomically impossible), while alternative 3 is fully possible with
three direct matches and three observations one day later than simulated. Therefore
we choose alternative 3 for the absolute dating of Amenemhat III’s regnal years.
Discussion and Conclusions
Our analysis of the El Lahun papyrus archive using a fully schematic civil calendar
with a modern astronomical start date results in an unequivocal dating alternative
(Julian) for the accession of three 12th dynasty pharaohs: Senusret II -1904, Senusret
III -1885 (more exact -1886 Dec 5) and Amenemhat III -1865, see also the Appendix.
Our dating alternative is broadly compatible with Bronk Ramsey's radiocarbon study
(ref.3), but not with the king lists which were used in that study. Instead it is Josef
Wegner's proposal (ref.10) which we can confirm.
Dating Middle Kingdom, draft, 2022-12-21, Page 10 of 15
Senusret II: we propose that the founder of the mortuary temple at El Lahun to which
the analysed temple archive belonged enjoyed a reign of 19 years. This reign length
arises from both the Turin king list (ref.9) and Ludwig Borchardt's reading of a
papyrus (PB 10055) where a regnal year 19 of one pharaoh changes to regnal year 1
of a second pharaoh within a period of one year (ref.8). The second pharaoh's regnal
years are counted from New Year day, I 1. If the second pharaoh is Senusret III
(accession -1886 Dec 5), his father Senusret II died in -1886 and thus accessed the
throne in -1904.
Senusret III: reign from -1886 Dec 5 to -1847 (39 years). His accession date and
reign length are confirmed by a Sothic date in his 7th year (-1879, PB 10012), twenty
moon dates up to his 36th year (PB 10090, PB 10056, 58065, PB 10052, PB 10103,
PB 10006, PB 10206), a royal jubilee probably held in his 30th year and epigraphic
evidence (control note) from his 39th year (ref.10). However, his sole reign was only
20 years long. In -1865 his son Amenemhat III joined him as a junior co-regent and
took over the affairs of state, therefore Senusret III's official regnal year count
dropped off after his 19th year. Senusret III is still mentioned as "living eternally", that
means alive, in Amenemhat III's 14th year which is Senusret III's 34th year.
Amenemhat III: reign from -1865 and at least 45 years beyond. His reign as a junior
co-regent together with his father is confirmed by six moon dates up to his 18th year
(PB 10092, PB 10009, PB 10003, PB 10248, PB 10011, PB 10016). Two of these
papyri (PB 10003 and PB 10248) mention Senusret III as still alive. Amenemhat III
became sole regent most probably in his 19th year when his father died in his 39th
year.
Accession dates
this study radiocarbon ref.3
(95% highest posterior
density) *)
Shaw ref.4 Hornung et al. ref.5
Senusret II -1904 1895 to 1844 BC 1877 BC 1845 BC
Senusret III -1885 1889 to 1836 BC 1870 BC 1837 BC
Amenemhat III -1865 1851 to 1798 BC 1831 BC 1818 BC
Table 9: Accession dates of three pharaohs of the 12th dynasty according to different chronologies.
*) Probably, dates have to be adjusted older because the dendrochronological time base of the
radiocarbon calibration curve might be eight years too young in the 2nd to 6th millennia BC (ref.6).
Our interpretation of the astronomical data in the El Lahun archive stands in glaring
contrast to recent mainstream interpretations as discussed in e.g. refs.5, 11 and 13.
The two papyri mentioning Senusret III as "living eternally", PB 10003 and PB 10248,
have been assumed to be from the reign of Senusret III, even more because
Senusret II is mentioned as "late lamented" in PB 10003. As the dates in PB 10003
and PB 10248 are not astronomically correlated with the group containing the moon
year of PB 10056 among others, the latter group has consequently been assigned to
the reign of Amenemhat III instead (ref.11 and references therein). This is recent
consensus and has even spilled over to Bronk Ramsey's radiocarbon study (ref.3)
where papyrus samples of PB 10009, PB 10092 and PB 10248 have been measured
as belonging to the reign of Senusret III. However, this does not matter too much as
the relative error is only twenty years.
Dating Middle Kingdom, draft, 2022-12-21, Page 11 of 15
We propose that mainstream scientists long time ago interchanged the pharaohs
assigned to the two groups of internally correlated moon data. This would have made
it simply impossible for them to reach a common solution. Even if they got one group
right, the dating of the other group would inexorably be wrong. No wonder that
contemporary Egyptologists have given up and reject both Sothic dates and moon
dates as meaningless (ref.1).
Our approach of using a fully schematic civil calendar goes all the way back to
Eduard Meyer's first description in 1904 (ref.14). Meyer apprehended that
observations of the heliacal rising of Sirius in connection with the launch of the
Egyptian civil calendar would be the basis for its rigorous non-astronomical rule,
meaning that no further Sirius observations were made or needed to keep the
schematic calendar going. Consequently the El Lahun Sothic date VIII 16 mandates
that the 7th regnal year of Senusret III appears within the four years period -1881
to -1878, neither before nor after. But already in 1899 Borchardt proposed a slightly
younger range, -1875 to -1872, because his astronomical specialists did not apply a
strictly schematic calendar (ref.8). With such a behavior it was inevitable that the
number of dating options became overwhelming.
A bit more tricky is the calculation of the Julian dates for the moon observations.
These dates are needed for comparison with the historical moon phases which can
be retro-calculated or simulated with great accuracy. As the schematic civil calendar
depends on only one single astronomical observation - the date for the heliacal rising
of Sirius when the civil calendar was launched - we have to know this start (standard)
date's Julian day to make the calculations. Most probably the civil calendar was
launched in -2781 at Memphis on July 16 (Julian), a date which was retro-calculated
by Bradley Schaefer in 2000 "with the full power of modern astronomy" (ref.15). Teije
de Jong (ref.5, III.9) reached the same conclusion in 2006. However, since the days
of Eduard Meyer July 19 has been used - and is still used - as the standard date
instead (ref.7). This results in calculated Julian dates which are three days off for the
civil dates mentioned in the papyri, thus concealing the correct match towards the
retro-calculated dates. This is another reason why Egyptologists never even had a
chance to get it right.
Our approach to apply a fully schematic civil calendar with July 16 as the standard
date was immediately successful with the wealth of data in the El Lahun archive. We
take this as a direct proof that our approach is correct. The ancient Egyptians surely
made a lot of astronomical observations all the time but they never changed their civil
calendar accordingly. About five hundred years after the launch of the calendar the
heliacal rising of Sirius no longer happened on the standard date but one day later
(ref.7, table 2). This is what we also can conclude from the 19th century BC letters
reproduced in PB 10012 containing the Sothic date VIII 16: the Sothis feast was held
not on the predicted standard day but one day later on VIII 17, the day on which the
heliacal rising of Sirius could be observed in the standard place Memphis. This
practice was most probably decided on after a long time with yearly observations to
be sure.
The El Lahun papyri have preserved another practice in case astronomical
predictions would not occur. As discussed in ref.2, Egyptian moon day 29 was the
day of last visibility of the old crescent in the morning. Moon day 30 was the day of
invisibility, dedicated to the fertility god Min, the "protector of the moon". On this day
Dating Middle Kingdom, draft, 2022-12-21, Page 12 of 15
the new moon was "conceived". Day 29 and 30 were always determined through
observation, by the priests (or somebody else). If so, day 1 (psdntjw) would be the
day of the new moon's "birth", with first visibility of the waxing crescent in the evening
in about 70% of cases, which could be predicted at least one day ahead (a Karnak
building inscription of Thutmose III quotes the approach of the day of the Feast of the
New Moon). In case the moon did not appear on day 1, it most probably would do so
on day 2.
The moon date entry in PB 10090 is double, XI 16/17. In ref. 5 on page 425 the
following comment appears:
The entries mention offerings on III Shemu 15, followed by “sw3 hr III Shemu
16” in turn followed by “LD 1”. According to Luft “sw3 hr III Shemu 16” means
that III Shemu 16 was skipped. If so, the LD 1 mentioned after III Shemu 16 has
to be III Shemu 17.
According to our interpretation XI 16/17 would be -1883 October 15/16. Simulated
with Stellarium (ref.12) the moon was 1.1 days old on October 15 but had a too small
difference in altitude towards the sun (less than 4 degrees) to be observable. Most
probably the predicted first New Moon date was therefore "skipped" and the following
day was registered as New Moon on the papyrus instead. Interesting is also that
there were offerings made on XI 15 (which was the day of invisibility), most probably
to make sure that the moon would be safely reborn.
Our use of a fully schematic civil calendar restricts our interpretational freedom to just
four years. Therefore we have to accept the moon phases which can be simulated or
retro-calculated within that tight time frame. In the case of the El Lahun archive - and
in the case of the New Kingdom moon data before that (ref.2) - we have seen
consistently that a moon age of about one day is what the ancient Egyptians call New
Moon (psdntjw). This stands in contrast to the consensus among Egyptologists since
Richard Parker's argumentations (ref.16) that the start of the next moon month fell on
the day of invisibility. Parker argued that an indication for this is that the Egyptian day
began in the morning, though the new moon crescent becomes visible first in the
evening. Had the Egyptians reckoned their months from first visibility, their day would
have started at sunset as is the case for example in the Islamic calendar. Therefore
Parker postulated that the Egyptians watched the crescent of the waning moon
instead and that they, on the day when it no longer was visible in the eastern sky at
dawn, started their new month at sunrise. However, his argumentation seems
prompted by the need to reinforce some of his preferred dating options which
generated "impossible" observations, i.e. that the first crescent of the waxing moon
was observed before this was astronomically possible.
We do not have to accept error frequencies of up to 30 percent (ref.13) when
interpreting and retro-calculating the first-hand moon date records, the Egyptians did
better than that. They most probably observed the last appearance of the waning
crescent in the morning, and from that predicted the first appearance of the waxing
crescent in the evening, which they called New Moon (psdntjw) or moon day 1. On
that day they made a second observation to be sure that the moon had returned. All
other moon days were determined schematically, e.g. full moon always on moon day
15. Bad weather could of course advance the last sighting of the waning crescent,
and delay the sighting of the waxing crescent, these are the observation errors we
Dating Middle Kingdom, draft, 2022-12-21, Page 13 of 15
have to accept. But we must not accept observations which are astronomically
impossible, that means that the moon was observed when it was invisible. Frequent
errors of that kind seem rather to be an indication that one’s own proposals are
wrong.
Another outcome of this study is that the number of regnal years for each pharaoh
according to the Turin king list should be taken seriously, however the list seems to
record the total number of a pharaoh’s regnal years regardless of the number of any
co-regency years.
Last of all, let’s make a check with chronological data from El Lahun which we not yet
have used. This is the date for a Wagi-feast in one pharaoh’s 38th year in month XI
(no day given) as reported in PB 10419 (ref.17, 2.63.). Rolf Krauss (ref.13, p.186-87)
could not find a Wagi-feast in month XI for the 38th regnal year which he proposed,
and he made this a reason for a flawed emendation of the El Lahun Sothic date (!),
instead for a revision of his far too low chronological model, see table 9.
The moving Wagi-feast was held in the second moon month after Sothis on the
second day after full moon (which fell schematically on moon day 15), that means on
moon day 17 (ref.5, page 425). This is exactly what we see e.g. in table 4 for papyrus
58065. During the 19th century BC - the time when the El Lahun archive was created
– the Sothis day appeared in civil month VIII (see the Appendix). Therefore most
Wagi-feasts were celebrated in civil month X, with the exception (ca. 25%) if Sothis
appeared early in a moon month. In that case the last half of the second month fell in
civil month XI.
So, was there a Wagi-feast-day in month XI in either Senusret III’s or Amenemhat
III’s 38th year in our model? Certainly, in Amenemhat III’s 38th year (-1828) Sothis
appeared on VIII 29 (moon age six days), and Wagi fell 70 days later on XI 9. Not a
sure-fire proof that we are right, but a fine verification of our approach which in fact is
confirmed by all twenty-six moon dates with explicit regnal years and the Sothic date
included in the El Lahun archive.
References
1. Schneider, T. (2008). Das Ende der kurzen Chronologie: eine kritische Bilanz der Debatte zur
absoluten Datierung des Mittleren Reiches und der zweiten Zwischenzeit. Ägypten Und Levante /
Egypt and the Levant, 18, 275-313. Retrieved August 3, 2021, from
http://www.jstor.org/stable/23788616
2. Ossowski Larsson P. & Larsson L.Å. (2020). Towards an absolute scientific date for the Egyptian
New Kingdom, part 2: the New Moon dates. ResearchGate DOI: 10.13140/RG.2.2.12339.66088
https://www.researchgate.net/publication/341279875_Towards_an_absolute_scientific_date_for_the_
Egyptian_New_Kingdom_part_2_the_New_Moon_dates
3. Bronk-Ramsey, C., Dee, M.W., Rowland, J.M., Higham, T.F.G., Harris, S.A., Brock, F., Quiles, A.,
Wild, E.M., Marcus, E.S. and Shortland, A.J. 2010. Radiocarbon-Based Chronology for Dynastic
Egypt. Science 328: 1554 –1557. https://www.researchgate.net/publication/44683433_Radiocarbon-
Based_Chronology_for_Dynastic_Egypt
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4. Shaw, I. ( Ed.), The Oxford History of Ancient Egypt (Oxford Univ. Press, Oxford, 2000).
5. Ancient Egyptian Chronology. Edited by Hornung E.,Krauss R. and Warburton, D.A. Brill, Leiden,
Boston 2006. https://archive.org/details/AncientEgyptianChronology_201303
6. Ossowski Larsson P. & Larsson L.Å. (2017). Miyake Events from a dendrochronological point of
view. ResearchGate DOI: 10.13140/RG.2.2.15276.26241.
https://www.researchgate.net/publication/316141198_Miyake_Events_from_a_dendrochronological_p
oint_of_view
7. Ossowski Larsson P. & Larsson L.Å. (2020). Towards an absolute scientific date for the Egyptian
New Kingdom, part 1: the Egyptian Civil Calendar revisited. ResearchGate DOI:
10.13140/RG.2.2.33028.07049.
https://www.researchgate.net/publication/338543618_Towards_an_absolute_scientific_date_for_the_
Egyptian_New_Kingdom_part_1_the_Egyptian_Civil_Calendar_revisited
8. Borchardt L. (1899). Der zweite Papyrusfund von Kahun und die zeitliche Festlegung des mittleren
Reiches der ägyptischen Geschichte. Zeitschrift für Ägyptische Sprache und Altertumskunde 37, 89-
103. https://www.semanticscholar.org/paper/Der-zweite-Papyrusfund-von-Kahun-und-die-zeitliche-
Borchardt/bd34421b894a4c62b99aae046faf8bf560ac2ccb
9. Turin king list, https://pharaoh.se/turin-kinglist (accessed 2021-07-15).
10. Wegner, J. (1996). The Nature and Chronology of the Senwosret III-Amenemhat III Regnal
Succession: Some Considerations Based on New Evidence from the Mortuary Temple of Senwosret
III at Abydos. Journal of Near Eastern Studies, 55(4), 249-279. Retrieved July 22, 2021, from
http://www.jstor.org/stable/546190
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Zeitschrift für Ägyptische Sprache und Altertumskunde 138, 1-19.
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unde%5D%20Monddaten%20aus%20dem%20Archiv%20von%20Illahun%20Chronologie%20des%20
Mittleren%20Reiches.pdf
12. Simulation done with Stellarium, http://www.stellarium.org ,with light pollution 1 (minimum) and
extinction coefficient 0.35.
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Egypt”, The Synchronisation of Civilisations in the Eastern Mediterranean in the Second Millennium
B.C. II (editor—Bietak M.) 175–197 (Vienna: Austrian Academy of Sciences).
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Wissenschaften 1904. https://archive.org/details/abhandlungenderk1904kn
15. Schaefer B.E. 2000. The heliacal rise of Sirius and ancient Egyptian chronology. Journal for the
History of Astronomy, Vol. 31, Part 2, 149 - 155. http://adsabs.harvard.edu/full/2000JHA....31..149S
16. Parker R.A., The Calendars of Ancient Egypt. Chicago 1950.
https://oi.uchicago.edu/sites/oi.uchicago.edu/files/uploads/shared/docs/saoc26.pdf
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Tempelarchiv von Illahun. Vienna, Verlag der Österreichischen Akademie der Wissenschaften.
Dating Middle Kingdom, draft, 2022-12-21, Page 15 of 15
Appendix: Regnal years and Sothic dates for all years from -1905 to -1818
Knowing the start- and end-years of the first Sothic cycle, we can write a table which allows the direct
assignation of all possible dates for the heliacal rising of Sirius (i.e. Sothic dates) in the schematic
Egyptian civil calendar to the corresponding four-years period in the Julian calendar (see ref.7,
Appendix B). The table below is an extract of that appendix, covering the reigns of Senusret II and III,
and Amenemhat III according to this study.
Year
CE
Sothic
date Pharaoh and regnal year
-1818
IX Pachons
1
-1819
-1820 Amenemhat III 46
-1821 Amenemhat III
-1822 VIII
Pharmuthi
30
Amenemhat III
-1823 Amenemhat III
-1824 Amenemhat III
-1825 Amenemhat III
-1826 VIII
Pharmuthi
29
Amenemhat III 40
-1827 Amenemhat III
-1828 Amenemhat III
-1829 Amenemhat III
-1830 VIII
Pharmuthi
28
Amenemhat III
-1831 Amenemhat III
-1832 Amenemhat III
-1833 Amenemhat III
-1834 VIII
Pharmuthi
27
Amenemhat III
-1835 Amenemhat III
-1836 Amenemhat III 30
-1837 Amenemhat III
-1838 VIII
Pharmuthi
26
Amenemhat III
-1839 Amenemhat III
-1840 Amenemhat III
-1841 Amenemhat III
-1842 VIII
Pharmuthi
25
Amenemhat III
-1843 Amenemhat III
-1844 Amenemhat III
-1845 Amenemhat III
-1846 VIII
Pharmuthi
24
Amenemhat III 20
-1847 Senusret III 39/ Amenemhat III 19
-1848 Senusret III 38/ Amenemhat III 18
-1849 Senusret III 37/ Amenemhat III 17
-1850 VIII
Pharmuthi
23
Senusret III 36/ Amenemhat III 16
-1851 Senusret III 35/ Amenemhat III 15
-1852 Senusret III 34/ Amenemhat III 14
-1853 Senusret III 33/ Amenemhat III 13
-1854 VIII
Pharmuthi
22
Senusret III 32/ Amenemhat III 12
-1855 Senusret III 31/ Amenemhat III 11
-1856 Senusret III 30/ Amenemhat III 10
-1857 Senusret III 29/ Amenemhat III 9
-1858 VIII
Pharmuthi
21
Senusret III 28/ Amenemhat III 8
-1859 Senusret III 27/ Amenemhat III 7
-1860 Senusret III 26/ Amenemhat III 6
-1861 Senusret III 25/ Amenemhat III 5
-1862 VIII
Pharmuthi
Senusret III 24/ Amenemhat III 4
-1863 Senusret III 23/ Amenemhat III 3
Year
CE
Sothic
date Pharaoh and regnal year
-1864 20 Senusret III 22/ Amenemhat III 2
-1865 Senusret III 21/ Amenemhat III 1
-1866 VIII
Pharmuthi
19
Senusret III 20
-1867 Senusret III 19
-1868 Senusret III 18
-1869 Senusret III 17
-1870 VIII
Pharmuthi
18
Senusret III 16
-1871 Senusret III 15
-1872 Senusret III 14
-1873 Senusret III 13
-1874 VIII
Pharmuthi
17
Senusret III 12
-1875 Senusret III 11
-1876 Senusret III 10
-1877 Senusret III 9
-1878 VIII
Pharmuthi
16
Senusret III 8
-1879 Senusret III 7
-1880 Senusret III 6
-1881 Senusret III 5
-1882 VIII
Pharmuthi
15
Senusret III 4
-1883 Senusret III 3
-1884 Senusret III 2
-1885 Senusret III 1
-1886 VIII
Pharmuthi
14
Senusret II 19
-1887 Senusret II 18
-1888 Senusret II 17
-1889 Senusret II 16
-1890 VIII
Pharmuthi
13
Senusret II 15
-1891 Senusret II 14
-1892 Senusret II 13
-1893 Senusret II 12
-1894 VIII
Pharmuthi
12
Senusret II 11
-1895 Senusret II 10
-1896 Senusret II 9
-1897 Senusret II 8
-1898 VIII
Pharmuthi
11
Senusret II 7
-1899 Senusret II 6
-1900 Senusret II 5
-1901 Senusret II 4
-1902 VIII
Pharmuthi
10
Senusret II 3
-1903 Senusret II 2
-1904 Senusret II 1
-1905
