The Calendar

We discussed some of the instruments used in Egypt and their use in calendrical operations in §3.3. Aside from shadow clocks and sundials (cf. Figure 4.4a), and from the vague suggestions of funerary texts, however, we do not understand fully what was observed or how it was done. What we do know is that observations must have been made to determine the time and the seasons. According to van der Waerden (1974, pp. 8-10) and other usually reliable sources, astronomical references from the Old Kingdom of Egypt are rare, but one possible reference to the star Sirius (Sopdet or, in Hellenistic form, Sothis) is mentioned in an ivory tablet from a tomb at Abydos. The reference is said to associate Sirius with the Nile flooding and the new year. Clagett (1995, pp. 9-11) shows that it is unlikely that there is any mention of Sirius, of Nile flooding, or of the new year in this text. They were, however, certainly associated through most of Egyptian history.

The civil year of ancient Egypt was a 365-day year, later called the "Egyptian Year," or the "Astronomer's Year." The Egyptian year was divided into three seasons of four months

Table 8.4. The Egyptian month names.

akh-t

per-t

shemu

Inundation or

Cultivation or

Harvest or

winter

spring

summer

1 Thoth

5 Tybi

9 Pachon

2 Phaophi

6 Mechir

10 Payni

3 Hathyr

7 Phamenoth

11 Epiphi

4 Choiakh

8 Pharmuthi

12 Mesore

each. Each month was a fixed length of 30 days, summing to 360 days for the year. Within each month, the days were organized into decades. Already in the Old Kingdom, these 10-day periods were marked by asterisms, which have been called decans (see §3.3 and §4.1). A period of five days, called epagomenal days, was added to the calendar at the end of the calendar year. The months are shown in Table 8.4. Parker (1950) suggests that this calendar had its basis in an unattested, older 12-month luni-solar calendar, in which the month began the day after the last visible waning crescent. The same set of names was used both for lunations and for the 30-day period throughout the time when both were in use. This results in statements of the form "1 Tybi [lunation] fell on 10 Mechir [civil]," which can be confusing even to those who understand the basic principle.

A 25-year lunar/solar cycle is given in a document written in or after 144 a.d. This was being used in spite of the fact that the internal details were no longer correct. According to Parker, they had been correct for a cycle starting in 357 b.c. Neugebauer thought that the cycle may have been recognized as early as the 5th century b.c. The fact that it uses lunar invisibility as the first day of a lunation, contrary to the Greek practice of beginning with first visibility, is strong support for a purely Egyptian origin. The document is given by Clagett (1995, pp. 295-306) with much of Parker's commentary.

The intercalation was based on the equation: 25 Egyptian years «309 lunations (25 x 365 = 9125 « 309 x 29.530 589 = 9124.95 days). The text indicates that the 309 months are composed of 16 "small years" of 6 "double-months" of 59 days each and 9 "great years" of 6 "double-months" of 59 days and an extra month of 30 days. After every five years, the Egyptians added a half-day to each of the last two months to give them a length of 30 days instead of 29.5 days.

Although Parker did not think that the formal lunar cycle antedated the 4th century b.c., he thought that the repetition of lunations in a 25-year interval was recognized prior to the invention of the civil calendar, and that it was regulated by the heliacal rising of Sirius. Once the civil calendar had been adopted, and the discrepancy between the 30-day civil "months" and the lunations of the same name had been recognized, a simple rule would have created the structure later formalized as the 25-year lunar cycle. The rule would have been "whenever the first day of lunar Thoth would fall before the first day of civil Thoth, the month is intercalary" (Parker 1950, p. 26). Contrary to Clagett (1995, pp. 8-13), DHK thinks that the associations of the lunar cycle with the heliacal rising of Sirius, postulated by Parker, is plausible a priori, although Clagett demonstrates that some of the evidence used by Parker to support that position is invalid or may be differently interpreted. Thus, we think that Clagett (1995, p. 37ff.) is entirely justified in rejecting Parker's use of the Ebers calendar as evidence for his position.

The names of the three divisions, "Inundation," "Cultivation," and "Harvest" were presumably appropriate to the seasons at some instant in the past, prior to the adoption of the 365-day year. A good approximation to the beginning of the season of Inundation was given by the heliacal rising of Sirius. This association continued after the adoption of the civil year. During the historic period, however, the months slipped regularly through the seasons. The rate of slippage is obtained by comparing the "Egyptian Year" to the tropical year. It can be seen that 365 x (1/0.2422) = 1507.0 tropical years = 1508 civil years. There was a comparable slippage of the heliacal rise of Sirius through the civil year. Because of factors involving both precession and proper motion, the heliacal rising of Sirius occurred through much of Egyptian history at intervals closely approximating the Julian year. The cycle of the slippage was calculated by Censorinus3 as 1460 Julian years. Such a calculation must be based on a close approximation to the mean length of the sidereal year (365.2564 days).4 The last previous cycle, ending in 139 a.d., was called by Censorinus the "Era of Menophres," and presumably began in 1322 b.c. The Egyptians probably thought that the tropical year and sidereal year slippages were identical. During the Ptolemaic period, an attempt was made to modify the civil year to remain in step with Sirius and the seasons. Ptolemy III (Euergetes 1,246-222 b.c.) issued what is known today as the Canopus Decree, from the location of an inscription. The decree, issued in 238 b.c., stated

3 Censorinus (writing in 238 a.d.) reported that the 1st day of the month Thoth occurred on JDN 1772028 or July 20, 139 (a.d.) in the Julian Calendar and coincided with a heliacal rising of Sirius.

4 365 x 1460 = 532, 900d and 365.2564 x 1460 « 533, 274d, differing by 1y9d.

that a 6th epagomenal day was to be added to the calendar every four years. In 238 b.c., it is stated that the heliacal rising of Sirius corresponded with 1 Payni, in full agreement with the testimony of Censorinus. However, no reform was carried out until a similar decree was issued during the reign of Octavian as Caesar Augustus. Relative to the previous civil year, this reform would have created a 1460-year cycle.

Clagett (1995, pp. 331-333) translates an inscription of Ptolemy IV that he dates to 218 b.c. and shows that it is direct evidence of the recognition of a Sothic cycle (sometimes called the Sothic period; see §4.2) of 1460 years at that time. His translation (omitting his textual comments) is

Hail to you, Isis-Sothis, Lady of 14 and mistress of 16 who has followed her dwelling place for 730 years, 3 months, 3 days, and 3 hours.

His interpretation is that the 730 years is a reference to the time needed to move through half of the civil year, that the three months refer to an additional shift of a quarter year (implicitly taking 360 years) then a shift of three days (taking 12 years) and finally three hours, referring to a half year. The base would be 1320 b.c., which corresponds to the same 4-year period as the "era of Menophres" of Cen-sorinus, although slightly off. This important discovery by Clagett shows clearly that the concept of the Sothic cycle was not something developed in the Roman period as some scholars have claimed.

Between 4236 and 2776 b.c., the one-day shift of the heliacal rising of Sirius occurred after five years instead of four in one case; between 2776 b.c. and 1318 b.c., there was one case in which it occurred after three years instead of four; in the period 1318 b.c. to 139 a.d., there were three times when the heliacal rising shifted one day in the civil calendar after three years instead of four (Clagett 1995, p. 313). This undoubtedly meant that observers at a particular location would expect recurrence to shift every four years. They would certainly have known that observers at different locations would have seen the rising at different dates. A small number of heliacal risings of Sirius are given in terms of the civil calendar (including one prediction), and these have been used to create an astronomical framework for Egyptian chronology. Lunar dates in the civil calendar have been used to give greater precision to such a framework.

Parker (1950, pp. 33-39, 63-69) discussed all inscriptions then postulated to refer to heliacal risings of Sirius. There are three that have been particularly important: one in the 7th year of a 12th Dynasty monarch, unfortunately unnamed, but apparently either Sesostris (Senusert) III or Amenemhet III; the Ebers calendar, dated to year 9 of Amenhotep I; and a date in an unspecified year of Thutmose III. More recently, all have been considered by Clagett (1995, especially pp. 37-48).

Parker, by examining reign lengths in conjunction with a schematized lunar cycle of 25 years and a range of dates for heliacal rising of Sirius, concluded that the document came from year 7 of Sesostris III and referred to July 17,1872 b.c., thus, fixing the chronology of the XII Dynasty and the final part of the XI Dynasty. This was widely accepted until Krauss (1987) challenged the place of observation, the appropriateness of the arcus visionis values used, and the

Lunar Dynasty

schematized pattern of lunations used by Parker. Krauss considered lunar data that became available after Parker's work, and, assuming Elephantine as the place of observation, argued for a date of 1536 b.c. [Clagett 1995, p. 141, f.n. 49]. More recently, Rohl (1995, pp. 390-391) cites the work of Rose on lunar observations, maintaining that the month lengths attested in XII Dynasty documents do not fit any of the placements that have been suggested. Rohl also challenges the interpretation of peret as "heliacal rise," pointing out that the same term is used to mean the bringing forth of the statue of a deity for a ceremonial procession. It is, however, used for the heliacal rising of Sirius in the Canopus decree, and Clagett (1995, pp. 357, 377, 380, 391, f.n. 36) shows that the Book of Nut describes the heliacal rising of Sirius on the very day that appears in the XII Dynasty "year 7" text. The description and the context seem to DHK to make it certain that this was, indeed, a heliacal rising of Sirius. It is said that the rising followed 70 days after the setting. Rohl (1995, pp. 134-135) also argues that the ditto marks under peret Sopdet in each successive month in the Ebers calendar mean that the phrase cannot refer to a heliacal rising of Sirius. Many Egyptologists now reject the conventional interpretation of this document, although it is still defended by Clagett (who rejected Parker's view of the correlation of the civil year with a lunar calendar). If it is accepted as a date in the Sirius cycle, the limits would be 1544-1537 b.c. for observation at Memphis or Heliopolis; 1525-1517 b.c. if the observations were made at Thebes. Krauss, arguing for observation at Aswan and stipulating a lunar interpretation as well, opted for 1506 b.c. (Clagett 1995, pp. 41-42). The limits could be slightly broadened for exceptionally good viewing conditions and a particularly sharp-eyed observer (see §3.1.4).

It has been calculated (assuming observations from Heliopolis) that the rising mentioned under Thutmose III occurred between 1465 and 1462 b.c. but could be placed anywhere in his reign of more than 50 years.

An interesting text (which has been studied with reference to Egyptian cosmology, but not astronomically) refers to the 75 manifestations of Re, depictions of which sometimes show only 74 figures (see Figure 8.1).

The number is a close approach to 1/5 of a year (5 x 73 = 365) and may suggest that the sequence implies some sort of division of the sun's path into segments of about 5. The

74th figure might have been added to represent the portion of the year beyond 365 days. There is an absolute correspondence between the sequence of representations in the tombs of Thutmose III and Seti I. So far, no one seems to have recognized sequential correspondences with other lists, although many individual depictions have parallels.

The Egyptian Year was used throughout the Hellenistic world because of the ease of calculation it afforded in obtaining the interval of days between two dates (see §4.1.2).

Sirius was one of the 36 asterisms known as decans. From the time of the Middle Kingdom, these were used in tables known as diagonal calendars or star clocks. A single column shows the progression of the stars rising through the night, and the different columns chronicle the changing list of such stars in the course of the year. We briefly discussed the historical importance of the decans in §4.1 for both the 24-hour day and calendrics. Neugebauer and Parker (1969, Vol. III) published a collection of diagonal calendars drawn on the interior surfaces of coffin lids. One of these, reproduced in Figure 8.2, is a coffin lid from the time of the IXth and Xth dynasties (about 2100 to 2150 b.c.) from Tomb 7, sepulchral chambers, pit 3, at Asyût.

Other coffin lid interiors portray Nut, the goddess of the sky5 covering the deceased as the night enfolds the Sun, awaiting the morning's resurrection. The locations of the zodiac suggest that it was intended to provide temporal orientation for the resurrected soul, but the information about the date of birth and the incantations suggests a different purpose, an introduction of the deceased to the gods of the underworld and supplications for his passage through it. Neugebauer (1964a) discusses the star clocks in these tombs and suggests that the 24-hour day had its origins in the decans. The tombs of the Ramesside kings (Romer 1981, p. 66) were known as "the corridor of the Sun's path," and they have abundant astronomical depictions. Constellations from a temple at Dendera (or Denderah) dating from the Ptolemaic period, 2nd century b.c., shows the Greek zodiac amidst traditional Egyptian constellations, such as

5 R.A. Wells (1996/1997) has proposed that the goddess Nut originated as a perception of the Milky Way as it was seen in the skies of ancient Egypt at about 3500 b.c.

Round Zodiac Dendera Louvre Images Middle Kingdom Star Clock Coffins

Figure 8.2. A coffin lid interior from ~2100 b.c., which illustrates the diagonal calendar. (a) Entire coffin lid in miniature, and detail of right half. (b) Detail of left half. From Neugebauer and Parker (1969, Vol. I, Plates 5 and 6, "Coffin 3"). Oriental

Figure 8.2. A coffin lid interior from ~2100 b.c., which illustrates the diagonal calendar. (a) Entire coffin lid in miniature, and detail of right half. (b) Detail of left half. From Neugebauer and Parker (1969, Vol. I, Plates 5 and 6, "Coffin 3"). Oriental

Institute of the University of Chicago photographs 27047-51, the Coffin Texts Project Documentary Photographs, reproduced here with permission.

Figure 8.3. (a) and (b) Details from Dendera: Note the combination of Greek with traditional Egyptian constellations. Photos courtesy of Jon Polansky. (c) The coffin lid of Heter, who died in Egypt in 125 a.d.: The planets among the zodiacal constellations confirm a date of birth of October 1, 93 a.d. From Neugebauer and Parker (1969, Vol. III (Plates), Plate 50, "HETER (71).")

Figure 8.3. (a) and (b) Details from Dendera: Note the combination of Greek with traditional Egyptian constellations. Photos courtesy of Jon Polansky. (c) The coffin lid of Heter, who died in Egypt in 125 a.d.: The planets among the zodiacal constellations confirm a date of birth of October 1, 93 a.d. From Neugebauer and Parker (1969, Vol. III (Plates), Plate 50, "HETER (71).")

the foreleg of the bull. A figure holding a grain of wheat is Virgo, near Libra and Leo in Figure 8.3a. We take up the identifications of the traditional Egyptian asterisms in §8.1.6.

Personal astrology was introduced with Hellenistic culture. An example of how astrology can be useful is provided by the details on the lid of the coffin of an Egyptian named Htr (Heter), who lived in Hellenistic times (Figure 8.3c). He died at age 31y 5m 25d, according to a demotic inscription on his coffin. The dominating female figure is that of the sky goddess, Nut. The zodiacal constellations flank her. Heter's birthdate is given by the location of the planets among the zodiacal constellations. Over Leo is the inscription, "Jupiter and Saturn in Leo." Over Virgo, it reads, "end of Virgo," and "Mars." To the left of and above Scorpius:

"Mercury in Scorpius" and "ascendant," respectively. Finally, between Scorpius and Sagittarius, the inscription reads, "Venus." From these locations, Neugebauer and Parker (1969, Vol. III, Texts, pp. 93-95) were able to show that a date in the first half of October, 93 a.d., satisfies the planetary positions for the birth of Heter, who, therefore, died in 125 a.d.

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