44. These data are of significance and value in two respects. In the first place, they demonstrate the very early advance of the Egyptians in the discernment and calculation of astronomical and calendrical phenomena. For we know from the use of the Egyptian year by classic astronomers and mathematicians that the calendar coincided with the Sothic year, and that a new Sothic cycle began, some time in the period 140/41 to 143/44 A. D.a It must therefore also have coincided with the Sothic year 1,460 years earlier; that is, in 1320 B. C.; and still earlier, in 2780 B. C. Now, it is impossible that this calendar was first introduced so late as the twenty-eighth century, in the midst of the highest culture of the Old Kingdom. Moreover, the five intercalary days at the end of the year, proving the use of the shifting year of 365 days, are mentioned in the pyramid texts, which are far older than the Old Kingdom.

45. The calendar, therefore, existed before the Old Kingdom; but if this be true, we must seek its invention at a time when its three seasons coincided roughly with those of nature, as they must have done at its introduction. This carries us 1,460 years back of their coincidence in the Old Kingdom; that is, the calendar was introduced in the middle of the forty-third century B. C. (4241 B. C.). This is the oldest fixed date in history. This fact demonstrates not only a remarkable degree of scientific knowledge in that remote age, but also stable political conditions, and a wide recognition of central authority, which could gradually introduce such an innovation. The date employed was that for the rising of Sothis in the latitude of Memphis or the southern Delta, and this fact is a significant indication of the high culture prevailing in the north at this time."

aCensorinus, 21, 10, and Meyer, op. cit., 28.

bFor convenience, ignoring the uncertainty of four years.
cSee Meyer, op. cit., 38 ff.

46. In a second respect the calendar is of inestimable value to us in establishing the chronology of Egyptian history. Where the heliacal rising of Sothis is recorded in terms of the calendar, it is a matter of the simplest arithmetica to determine, within a margin of four years, in what year B. C. the rising occurred. As we have seen, three such dates are preserved to us, two of which each give the year of the king's reign, and from these the entire Twelfth Dynasty, and the reign of Amenhotep I in the Eighteenth Dynasty, are established within four years in terms B. C. They show that the Twelfth Dynasty began in 2000 B. C., and the reign of Amenhotep I in 1557 B. C., thus determining the accession of the Eighteenth Dynasty as 1580 B. C. The third Sothic rising, in the reign of Thutmose III, is not dated in a particular year of the reign, so that it furnishes only a rough approximation of the date of his reign, proving that the year 1470 B. C. fell within his reign. This approximation may be rendered precise by a computation based upon the feasts of the New Moon, which Thutmose III is recorded to have celebrated in his twenty-third and twentyfourth years (II, 430). These new-moon dates establish the date of Thutmose III's reign as May 3, 1501, to March 17, 1447 B. C. The two other early dates are chiefly of

aThus: The rising of Sothis at the beginning occurs on the first day of the calendar year. From a given calendar date of its rising the amount of the shift of the calendar can be computed in an instant. In the 120th year of the Twelfth Dynasty Sothis arose 225 days after New Year's Day. As the shift occurred at the rate of one day in four years, the 225 days' shift had taken place in 900 years since the calendar coincided with nature; that is, since 2780 B. C. The 120th year of the Twelfth Dynasty was thus 1880 B. C., and the dynasty began in 2000 B. C. (or between 2000 and 1996 B. C.).

bMeyer, op. cit., 46 ff.

The phases of the moon occupy the same position in the calendar every nineteen years. The date of Thutmose III's reign being roughly determined by the Sothic rising, the new-moon dates can then be employed to place this reign more precisely. Without the Sothic date the new-moon dates would be of no use, as they merely present conditions recurring every nineteen years.

dMeyer, loc. cit.

significance in demonstrating the fact of the shift of the calendar in the Old and Middle Kingdoms, but are not precise enough to determine with exactness the date B. C.

47. Besides the above astronomical method, minimum dates as far back as the beginning of the Eighteenth Dynasty can be determined by dead reckoning back from a fixed starting-point. The result thus obtained, without reference to the astronomically determined dates, can then be compared with these, for the sake of testing both. The dates by dead reckoning are obtained by simply adding together the totals of reigns and dynasties, and with these reckoning back from the accession of the Persians in 525 B. C. In this process I have employed only the testimony of the contemporary monuments.a

48. Our first task is to determine the length of the dynasties preceding the invasion of the Persians; that is, the Eighteenth to the Twenty-sixth Dynasty. The method is first to seek the highest known date in each reign of a dynasty, and thus to determine the minimum length of the dynasty. In the use of royal dates given in years of the reign only, there is danger both of over- and of under-reckoning. Thus Ramses III reigned thirty-one years and forty days; but a date from his thirty-second year might lead one to think he had reigned thirty-two years, which is nearly a year in excess of the truth. As the newly crowned successor to the throne began to number his years from the death of his predecessor, it will be seen that the remainder of what would have been Ramses III's complete thirty-second year is included in the reign of his successor. If counted in both reigns, it is therefore counted twice. It has therefore

b

aWherever he can be controlled, Manetho is generally wrong in his figures, and any chronology based on his data is hopelessly astray.

bThis is supposing that, as in the Eighteenth Dynasty, the years of a king began with the day of his accession, and not on the New Year's Day preceding his accession, as in the Middle Kingdom and the Twenty-sixth Dynasty.

been thought necessary to deduct one year for every transfer of the crown.a This method, however, is extreme, as we shall show. In the first place, it applies only when the maximum date preserved is actually the respective king's last year. Again, it does not always apply even then. Thutmose III reigned fifty-four years lacking thirty-four days. The reign of his successor, therefore, included only the last thirty-four days of what would have been Thutmose III's complete fifty-fourth year. To deduct a year at this transfer of the crown is as extreme as to count the thirty-second year of Ramses III's reign. It is evident that the last year of a king's reign is as likely to be nearly complete as it is to be scarcely begun; hence the only fair method of reduction for double counting at the transfers of the crown is to count the number of transfers in an entire dynasty, and for each transfer to deduct a half-year; that is, a mean between the two extremes of deducting a whole year for each transfer, or of deducting nothing. In the course of a whole dynasty the errors both ways will probably compensate each other.b

49. In the following table I have made no deduction for transfer of the crown either to or from a king from whose reign we have no dates, but in all such reigns (marked x) such deduction has been included in the estimate of the reign. It is needless to add that in cases of coregency such deduction is unnecessary. In estimating the x, or unknown years in a given reign, the historical facts of the reign, if any, have been duly considered, though there has not always

a Mahler, Zeitschrift für ägyptische Sprache, 32, 104 f.; Lehmann, Zwei Hauptprobleme, 56.

bThis method can apply with certainty only in the Eighteenth Dynasty, in which the king's year begins with his accession. I have supposed, however, that this system of numbering continued until the end of the Ethiopian period. In the Twelfth and Twenty-sixth Dynasties such allowance must be differently computed.

been space to note the said facts. That this is absolutely necessary will be evident. Thus Sheshonk I took out the stone from the Silsileh quarry for his Karnak building in his twenty-first year. The vast forecourt of the Karnak temple of Amon, or the enormous front pylon, was then built by him. Yet his highest date is that of the said quarry operations in the twenty-first year. It is clear, therefore, that he must have ruled several years more, and no fair chronological reckoning can disregard these years.

50. Observing the above precautions, we obtain as a minimum for the Empire and following dynasties, down to the accession of the Persians, the following figures: a

As the accession of the Persians occurred in 525 B. C., the beginning of the Eighteenth Dynasty will have been 1,052 years earlier, or about 1577 B. C.b

51. Our second task is now to compare with this result the dates in the Eighteenth Dynasty obtained by astronomi

A detailed table by reigns will be found §§ 58-75; and for the Twenty-first, Twenty-second, and Twenty-sixth Dynasties still further details will be found in IV, 604-7, 693-98, 959, 974, 984, 1026, 1027.

bThis result of a dead reckoning from minimum dates cannot be brought down any later. Mr. Cecil Torr's attempt (Memphis and Mycena) to establish a much later date for the beginning of the Eighteenth Dynasty by the same process was extreme in method, and rested upon incomplete material.