BACKGROUND

The ancient Egyptians used a 365-day “civil” calendar of 30 days × 12 months plus five epagomenal days (Hornung et al. Reference Hornung, Krauss and Warburton2006). In theory, the first day of the civil year was intended to coincide with the rising at dawn of Sothis for 4 days after a 70-day disappearance, as it is recorded as doing in 139 CE (Ward Reference Ward1992). As the Egyptian calendar had no correction for being 0.24 days short of a solar year, a single day was lost every 4 yr. The result was an incremental shift of 1 day every 4 yr, with approximately 1460 yr (4 × 365) passing before it returned to its original position, creating what is known as the Sothic cycle. Retrojecting from 139 CE, this event would also have taken place around 1317 and 2773 BCE. Thus, any document including both a civil date and a Sothic observation can be assigned an absolute date. The earliest such observation is Papyrus 10012A, which records the anticipated heliacal rising of Sothis in the fourth month of prt, day 16 (Luft Reference Luft1992). Papyrus 10012B notes the offerings given for Sothis on day 17 (Luft Reference Luft1992). Despite apparently precise Egyptian record-keeping, numerous unknowns remain, including the geographical location of the observation, the observer’s altitude, and meteorological conditions and to which of the 4 days of helical rising the observation referred. These, together with the need to refine this datum with lunar observations, has resulted in various computed year dates: 1872 (Parker Reference Parker1950), 1866 (Luft Reference Luft1992), and 1831–1830 (Hornung et al. Reference Hornung, Krauss and Warburton2006; Krauss Reference Krauss2006).

SAMPLES

Both pieces of Papyrus 10012 (labeled A and B) are housed in the Egyptian Museum, Berlin. A 20-mg section of Papyrus 10012B was obtained for analysis at the Oxford Radiocarbon Accelerator Unit (ORAU). The piece was split first in two in order to obtain duplicate dates. No glues or preservatives were observed on the fragments, but for robustness they were subjected to a triplicate solvent wash to eliminate such contamination. The duplicate samples were treated using sequential acetone (45°C, 45 min), methanol (45°C, 45 min), and chloroform (RT, 45 min) rinses interspersed with three washes in distilled water. After air-drying overnight, the samples were subjected to ORAU’s standard aqueous pretreatment process (see Brock et al. Reference Brock, Higham, Ditchfield and Bronk Ramsey2010). This treatment is designed to isolate the holocellulosic fraction. This comprised washing in acid (1M HCl, 80°C, 20 min), base (0.2M NaOH, 80°C, 20 min), and acid (1M HCl, 80°C, 20 min), with a final oxidation step (acidified NaClO₂, 0–5%, 20–80°C, 20 min). The strength of the oxidant employed in the final step was based on the fragility of the sample. Again, washing in ultrapure water was applied between each pretreatment step. The resultant holocellulose fractions were freeze-dried overnight. Approximately 4-mg samples were then combusted in an elemental analyzer coupled to a mass spectrometer, which measured the δ¹³C value. The CO₂ produced was collected cryogenically, graphitized, and dated at ORAU’s AMS facility (see Bronk Ramsey et al. Reference Bronk Ramsey, Higham and Leach2004).

RESULTS AND INTERPRETATION

Duplicate ¹⁴C measurements made on a fragment from Papyrus 10012B were combined into one ¹⁴C determination (see Table 1). In order to correctly calibrate this result, we employed the additional “growing season offset” proposed by Dee et al. (Reference Dee, Brock, Harris, Bronk Ramsey, Shortland, Higham and Rowland2010) The calibrated date range produced was 1886–1750 BCE (95.4% probability, Figure 1). Owing to the plateau on the calibration curve, this calendrical range easily encompasses all suggested single-year estimates for this Sothic date, with no preference for any one particular solution. These results compare extremely well with results from other previously published samples of inscribed and dated papyri from Illahun, including from proximal regnal years (Bronk Ramsey et al. Reference Bronk Ramsey, Dee, Rowland, Higham, Harris, Brock, Quiles, Wild, Marcus and Shortland2010). They also demonstrate that the absolute position of the Egyptian chronology during the first half of the 2nd millennium BCE is correct. Clearly, any radical shifts in Egyptian chronology, as have been seemingly noted in the past (Bietak and Höflmayer Reference Bietak and Höflmayer2007: 14, Figure 1) find no support in the ¹⁴C data presented here or previously (Bronk Ramsey et al. Reference Bronk Ramsey, Dee, Rowland, Higham, Harris, Brock, Quiles, Wild, Marcus and Shortland2010). In addition, the upper bound of the probability distribution (1886 BCE) shows that the true date cannot be much higher than that posited by the highest estimate.

Table 1

The isotopic measurements obtained on the papyrus sample. Note that a correlated error of ±8 BP was also included in the averaging process to allow for intra-annual ¹⁴C variation.

Figure 1

Calibrated age ranges for Papyrus 10012B

Further insight may be gained into the consistency of this result with the three leading historical estimates of the document’s age by comparing the measurement directly with values taken from the calibration curve for these specific years. In order to do this, we interpolated IntCal13 (Reimer et al. Reference Reimer, Bard, Bayliss, Beck, Blackwell, Bronk Ramsey, Buck, Cheng, Edwards, Friedrich, Grootes, Guilderson, Haflidason, Hajdas, Hatté, Heaton, Hoffmann, Hogg, Hughen, Kaiser, Kromer, Manning, Niu, Reimer, Richards, Scott, Southon, Staff, Turney and van der Plicht2013) to annual resolution using the software OxCal (Bronk Ramsey Reference Bronk Ramsey1995). The values obtained and their uncertainties are given in Table 2. As both the annual calibration values and the Sothic papyrus measurement are realizations of normally distributed random variables, they may be readily compared using classical statistical techniques. The right-hand column of Table 2 shows the t statistics obtained by applying the test described in Ward and Wilson (Reference Ward and Wilson1978). Such data follow a χ² distribution, whereby two results are considered statistically indistinguishable if t < 3.8 (at 95% probability, df=1). The t statistics obtained for each candidate year all easily meet this criterion. The same comparison was made without including the seasonal effect, in order to evaluate its contribution. Once more, the t statistics showed the result was still compatible with all three candidate years, although the values were slightly higher overall. This approach also revealed an interesting dichotomy. If the seasonal effect is included, our measurement is slightly more compatible with the atmospheric ¹⁴C concentration corresponding to the date of Parker but, if it is ignored, the lower date of Krauss and Hornung is more favored. This pattern is clearly illustrated in Figure 2.

Figure 2

Calibration with and without the seasonal effect for the Sothic papyrus

Table 2

Comparison of the ¹⁴C determination on the Sothic papyrus with IntCa13 interpolated to annual resolution. The test statistics are given in the right-hand column. If t <3.8 (n=2, df =1), the IntCal and Sothic measurements may be considered statistically indistinguishable at 95% probability (see Ward and Wilson Reference Ward and Wilson1978). The t statistics are given for each year, with and without the proposed seasonal effect for Egypt (Dee et al. Reference Dee, Brock, Harris, Bronk Ramsey, Shortland, Higham and Rowland2010). Note that 1831 BCE was used for the date of Krauss and Warburton.