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9.2.1.4
The Later Lunar Calendar |
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If the conclusions of our calculations and investigations are correct, Egypt introduced a second lunar calendar about 2500 B.C. |
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9.2.1.4.1
A Cyclic Version |
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Of help in considering this calendar is a text published as the Papyrus Carlsberg 9 (Neugebauer and Volten, "Untersuchungen zur antiken Astronomie IV. Ein demotischer astronomischer Papyrus", Quellen und Studien zur Geschichte der Mathematik, Abt. B, Band 4, Berlin 1938, pp. 383406). This papyrus was written in or after A.D. 144. It provides a simple scheme for determining the start of certain lunar months within a cycle of 25 years. This papyrus is the first published Egyptian text to deal with mathematical astronomy. |
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The papyrus represents a rule similar in concept to the Metonic rule. In the Egyptian case, 25 civil years contain 9,125 days, and 309 lunar months contain 9,124.95 days. Years in which a 13th month is intercalated within the cycle are 1, 3, 6, 9, 12, 14, 17, 20, and 23. |
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Although Neugebauer and Volten concluded that the papyrus provides evidence that the basis for the start of the lunar month was the first visibility of the lunar crescent, later work shows that this conclusion is valid only if the cyclic calendar were introduced around A.D. 144. It has been shown that double dates from Ptolemaic times in the papyrus are earlier. Parker (The Calendars of Ancient Egypt, p. 17) finds that invisibility of the crescent would be the rule if the cyclic calendar were introduced
* around 350 B.C. |
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There is no evidence that any method except observation was used prior to the mid-fourth century B.C. The rule governing intercalation can be derived from the Carlsberg Papyrus: If day 1 of lunar month 1 would fall before day 1 of civil month 1, the month is intercalary. This rule could have operated long before the introduction of a cyclic calendar. |
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The later lunar calendar, since it was tied to the civil calendar, therefore also moved through the seasons. |
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9.2.1.4.2
Fifty-Nine Flavors of Divinity |
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In Egypt, two sets of divinities are connected with the year. The first is a set of 36 divinities, which appear as early as the Middle Kingdom, and the second is a group of 59 divinities, which appear later, as early as the 22nd dynasty. The first group is older and simply represents the 36 decans, or constellations. |
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The second group has puzzled historians for some time. It seems to have been derived from the first group. Dividing the first 48 names into units of four, the first, third, and fourth names are those of ordinary decans, and the second is an intrusion. |
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The remaining names are 11 in number, which is the number required to round out the lunar year to match the length of the civil year. The names of the five deities of the |
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