Chapter IX
Numbers Cardinal and Ordinal. Divisions of Time: The Calendar, Sothic Period. Chronology.
Numbers.โThe numbers 1 to 9 are expressed by short perpendicular strokes, e.g., ๐บ = 1, ๐ป = 2, ๐ผ = 3, ๐ป๐ฐ๐ป = 4, ๐พ = 5, ๐ฟ = 6, ๐ = 7, ๐ = 8, and ๐ = 9. The number 10 is expressed by ๐, 100 by ๐ข, 1,000 by ๐ผ, 10,000 by ๐ญ, 100,000 by ๐, 1,000,000 by ๐จ, and 10,000,000 by ๐ถ; tens up to 90 are expressed by repeating the sign for ten, ๐, so many times; hundreds up to 900 by repeating the sign for hundred, ๐ข, so many times; thousands up to 9,000 by repeating the sign for thousand, ๐ผ, so many times; and so on. The following extract will illustrate the use of these signs:โ
I.
| Ru geese | ๐พ๐พ๐ฉ๐๐ | = | 6,820 |
| Khet-ฤa geese | ๐ผ๐ฃ๐ฐ๐ฃ๐ | = | 1,410 |
| Turpu geese | ๐ผ๐ข๐ฃ๐ฐ๐ฃ๐๐๐๐ป๐ฐ๐ป | = | 1,534 |
| Tchau geese | ๐ข๐ | = | 150 |
| Mest geese | ๐ฟ๐ | = | 4,060 |
| Water fowl | ๐ฎ๐๐๐ | = | 25,020 |
| Menฤt birds | ๐ญ๐ญ๐ญ๐ญ๐ญ๐ผ๐ผ๐ผ๐ผ๐ผ๐ผ๐ผ๐ฉ๐ | = | 57,810 |
| Paแนญ birds | ๐ฎ๐ผ๐ข๐ง | = | 21,700 |
| Paฤsh birds | ๐ผ๐ฃ๐ | = | 1,240 |
| Birds | ๐พ๐พ๐ข๐ฃ๐ฐ๐ฃ๐ | = | 6,510 |
| Total No. of birds: | ๐๐ฐ๐ค๐ฎ๐พ๐พ๐ฃ๐๐๐ป๐ฐ๐ป | = | 126,254 |
II.
| ๐ ง๐๐ฐ๐๐ฐ๐ฅ๐ป๐ฐ๐ | ๐๐๐๐๐๐๐๐๐๐ฏ๐ฏ๐ฏ๐ฝ๐ง๐ข๐ |
| Large loaves | 992,750. |
Fractions ๐๐ฐ๐ฅ = โ , ๐ = ยฝ, ๐ฆ = โ , ๐๐ฐ๐ = โ โโ, ๐๐ฐ๐ข = โ โโโ, ๐๐ฐ๐ผ = โ โโโโ, ๐๐ฐ๐๐ฑ๐๐ฑ๐๐ฑ๐๐ฐ๐ = โ โโ , etc. Ordinal numbers are indicated by ๐ placed before the figure, or by ๐ placed after it; e.g. ๐๐ฟ = โsixth,โ ๐๐ = โseventh.โ
Divisions of Time.โThe smallest fraction was the ศงnt, ๐ป๐ฐ๐๐๐ฐ๐ณ, one third of a second, or โthe twinkling of an eye.โ Then came the แธฅat ๐๐ฟ๐๐ฐ๐ณ, second; the at ๐๐๐ฐ๐ณ, minute; and the unnut ๐น๐ฐ๐๐๐ฑ๐๐ฐ๐ณ๐ต hour. Twenty-four hours made one day, hru ๐๐ฐ๐๐ ฑ๐ณ๐ฐ๐ค, ten days made one week, and thirty days one calendar month, ๐บ๐ฐ๐ง๐ฐ๐ผ๐ฑ๐ณ. Twelve months plus the five epagomenal days made one vague or calendar year, renpit ๐๐ฐ๐๐ฐ๐ช๐ฑ๐ญ๐๐ณ๐ณ. Longer periods of time were:โ
| Seแนญ period | ๐ด๐ง๐ฐ๐ ๐ณ | = | 30 years. |
| Two-แธคenti period | ๐จ๐จ๐ณ๐ฐ๐ณ | = | 120 โณ |
| แธคeแธฅ | ๐๐ณ๐ | = | An Age. |
| Tchetta | ๐๐ณ๐ท๐๐ฐ๐พ๐ธ | = | Eternity. |
We also have:โ
| ๐ฏ๐ธ | = | Millions of years. |
| ๐ธฅ๐ธฅ๐ธฅ | = | 10,000,000 years. |
| ๐ฑ | = | 1,000,000,000,000 years. |
| = | 10,000,000,000,000 years. | |
| = | 1,000,000,000,000,000,000 years. |
In late times the Sothic Period and the Phoenix Period were used by the Greeks, but there is no evidence that either was known to the Ancient Egyptians.
Chronology, and the ancient Egyptian Year. The Calendars of Lucky and Unlucky Days indicate that in very early times the Egyptian Year consisted of 12 months each of 30 days, i.e., that the primitive year contained 360 days. Whether the Egyptians ever tried to use the lunar year of 354 days there is no evidence to show. Now the progress of the seasons would, in a few years, soon convince those who used the year of 360 days that their year did not agree with the solar year, and that it was too short, and they would be obliged to add to its days in some way. The inscriptions prove that even at so early a period as the reign of Pepi II of the VIth dynasty, the Egyptians were in the habit of adding five days each year to their year of 360 days, and that before B.C. 3000 the year in common use contained 365 days. These โfive daysโ are known as โthe days over the yearโ ๐ณ๐ท๐ฐ๐๐ ฑ๐ณ๐ฐ๐, or ๐ณ๐ฐ๐ฆ๐พ๐ท๐ฐ๐๐ ฑ๐ฏ๐ฐ๐ฅ๐ณ๐๐ฐ๐ค, or โthe five epagomenal days,โ and they were said to be the days on which Osiris, Horus, Set, Isis, and Nephthys respectively were born. The primitive year of 360 days was divided into three seasons. The first season was Shat, or Akhet, ๐ท๐๐ฐ๐ณ; it began about July 19 and ended about November 15, and corresponded practically with the period of the Inundation. The second season was Pert ๐๐ฐ๐๐ฐ๐๐ฑ๐ณ; it began about November 15 and ended about March 15. The third season was Shemu ๐๐ฐ๐; it began about March 15 and ended about July 13. These seasons to the Egyptians represented roughly Winter, Spring, and Summer. Each season contained four months, which were in early times called the first, second, third, and fourth month of that season; in later times a name was given to each month. The following was the early calendar:โ
| Coptic Name.27 | ||||
|---|---|---|---|---|
| ๐บ๐ฐ๐บ๐ท๐๐ฐ๐ณ, | 1st Month of sowing | Thoth. | โซ | Inundation time and Winter. |
| ๐บ๐ฐ๐ป๐ท๐๐ฐ๐ณ, | 2nd โณ โณ | Paophi. | โช | |
| ๐บ๐ฐ๐ผ๐ท๐๐ฐ๐ณ, | 3rd โณ โณ | Athyr. | โช | |
| ๐บ๐ฐ๐ฝ๐ท๐๐ฐ๐ณ, | 4th โณ โณ | Choiak. | โญ | |
| ๐บ๐ฐ๐บ๐๐ฐ๐๐ฐ๐๐ฑ๐ณ, | 1st Month of growing | Tybi. | โซ | Spring. |
| ๐บ๐ฐ๐ป๐๐ฐ๐๐ฐ๐๐ฑ๐ณ, | 2nd โณ โณ | Mechir. | โช | |
| ๐บ๐ฐ๐ผ๐๐ฐ๐๐ฐ๐๐ฑ๐ณ, | 3rd โณ โณ | Phamenoth. | โช | |
| ๐บ๐ฐ๐ฝ๐๐ฐ๐๐ฐ๐๐ฑ๐ณ, | 4th โณ โณ | Pharmuthi. | โญ | |
| ๐บ๐ฐ๐บ๐๐ฐ๐28, | 1st Month of inundation | Pachons. | โซ | Summer. |
| ๐บ๐ฐ๐ป๐๐ฐ๐, | 2nd โณ โณ | Payni. | โช | |
| ๐บ๐ฐ๐ผ๐๐ฐ๐, | 3rd โณ โณ | Epiphi. | โช | |
| ๐บ๐ฐ๐ฝ๐๐ฐ๐, | 4th โณ โณ | Mesore. | โญ |
To these twelve months, as already said, five days were added, and the year thus formed is generally known as the โvague (or wandering) year,โ and the โcalendar year.โ Now it is clear that since this vague year of 365 days was shorter than the true year, or โsolar year,โ of 365ยผ, by nearly a quarter of a day, every fourth vague year would be shorter than the true year by nearly a whole day. Moreover, given a sufficient number of years, the vague year would work backward through all the months of the year, until at length the first day of the vague year would coincide with the first day of the solar year. Thus, supposing the first day of the vague and solar years to have coincided on January 1, B.C. 2000, two hundred years later the first day of the vague year would have worked back about 50 days; and five hundred years later, i.e., about B.C. 1300, the first day of the vague year would fall in the height of the summer instead of in the depth of winter. This defect in their year of 365 days would soon become apparent, and we may be sure that they were not long in discovering some means for correcting it. According to some authorities the Egyptians knew the length of the true, or solar, year with considerable exactitude, and if this be so they were well able to plan their farming operations without any reference to the vague year. According to others the Egyptians were ignorant of the solar year, but were acquainted with a Sothic year, which is so called because it began on the day when the star Sepแนญ (or Sirius, or Sothis, or the Dog Star) rose heliacally, that is to say, with the sun. This happened on July 19 or 20, and as this date was very near the time when the Inundation began, the Egyptians considered it most convenient for their year and the Inundation to begin at the same time. The Sothic year contained practically 365ยผ days, i.e., a few minutes more than the true, or solar, year; and the Sothic Period, i.e., the length of the time which must elapse between two risings of Sothis heliacally, contained 1,460 Sothic years, or 1,461 vague, or calendar, years.
It has now to be considered how the above facts bear upon Egyptian chronology. To make a complete scheme of Egyptian chronology we need a complete list of the kings of Egypt, and to know the order in which each succeeded, and the number of years which each reigned. Now, such a list does not exist, for the lists we have only contain selections of kingsโ names; and of many a king neither the order of his succession nor the length of his reign is known. The facts at present available do not permit the making of a complete detailed scheme of chronology, but one which is approximately correct in many parts of it can be framed. As authorities for the names of the kings there are:โ1. The Royal Papyrus of Turin, which, when complete, contained over 300 royal names. 2. The Tablet of Abydos,29 made for Seti I, containing seventy-six names. 3. The Tablet of แนขaแธณแธณรขrah, containing fifty names. 4. The Egyptian monuments of all periods. 5. The King List of Manetho.30 The Turin Papyrus, which was compiled about B.C. 1500, gave the lengths of the reigns of the kings, but unfortunately most of them are broken. Manetho compiled his King List, it is said for Ptolemy II Philadelphus, in the first half of the third century B.C., but, as the work in which it appeared is lost, we only know it by the copies which have come down to us in the Chronicle of Julius Africanus (third century A.D.), in the Chronicle of Eusebius, Bishop of Caesarea, who died about A.D. 340, and in the Chronography of George the Monk (eighth century A.D.). Eusebius himself also compiled a King List, but his results differ materially from those of Manetho as given by Africanus. Manetho divided the kings of Egypt into thirty dynasties, which he arranged in three groups: Dynasties I-XI, XII-XIX, and XX-XXX. He also gave the lengths of the reigns of the kings, and the cities of their origin, Memphis, Elephantine, Thebes, etc.
Now, although a great many credible facts are to be gathered from the above authorities from which we are justified in making the general deduction that the period of dynastic civilization lasted between four and five thousand years, they none of them help to fix an exact date for the reign of the first dynastic king of Egypt, who, by general consent, is said to have been Menศง or Menes. If Manethoโs List were trustworthy, the difficulty would be settled, but unfortunately one version of it makes 561 kings reign in 5,524 years, whilst another gives the number of the kings as 361, and their total reigns as 4,480 or 4,780 years. Many Egyptologists have accepted Manethoโs statements with modifications, but others have tried to work out more accurate results, astronomically, by the use of the Sothic Period. It has already been said that the Sothic Period of 1,460 years is equal to 1,461 vague, or calendar, years, and it is argued that, if we can find mentions of the risings of Sothis (Sirius, or the Dog-star) expressed in terms of the vague year, and if we can also fix a date for the beginning or end of a Sothic Period, it will be possible to arrive at fixed points in Egyptian chronology. Fortunately some three or four mentions of the rising of Sothis are known in the inscriptions, and thanks to Censorinus, who wrote his work (De Die Natali) A.D. 238, it is known that a Sothic Period came to an end A.D. 139.31 If this be so, it is clear that the Sothic Period to which he refers began in B.C. 1321, the one before that in B.C. 2781, the one previous in B.C. 4241, and so on. The next step is to work out the mentions of the risings of Sothis which are expressed in terms of the vague, or calendar, year, and, provided that the statement of Censorinus be trustworthy and the calculations of modern investigators be correct, it is possible to assign a date in ordinary Julian years to such risings of Sirius.
Want of space renders it impossible to discuss here the various systems of chronology which have been formulated by Egyptologists and others, but the dates proposed by the principal authorities for some of the dynasties may be thus grouped:โ
| Dynasty. | Dates proposed. | |||||
|---|---|---|---|---|---|---|
| 1. | 2. | 3. | 4. | 5. | 6. | |
| I | 5869 | 5702 | 5613 | 5004 | 4400 | 3315 |
| III | 5318 | 5147 | 5058 | 4449 | 3966 | 2895 |
| VI | 4426 | 4402 | 4310 | 3703 | 3300 | 2540 |
| XII | 3703 | 3404 | 3315 | 2851 | 2466 | 2000 |
| XVIII | 1822 | 1655 | 1796 | 1703 | 1700 | 1580 |
| XIX | 1473 | 1326 | 1404 | 1462 | 1400 | 1320 |
| XX | 1279 | 1183 | 1195 | 1288 | 1200 | 1200 |
Of these systems the one proposed by the late Dr. H. Brugsch (No. 5) agrees best with the general evidence of the monuments as to the length of the period of Dynastic civilization; it is therefore used, with some modification of the dates of the XVIIIth dynasty, in this book. It has been declared that the intervals which he placed between the VIth and the XIIth, and the XIIth and the XVIIIth dynasties are too long, but, on the other hand, many objections can be urged against the reductions recently suggested. It is proposed to reduce the date given by Brugsch for Menes, B.C. 4400, to B.C. 3315; but there is no evidence in support of the reduction. The view has been steadily growing for years that some of the dates proposed by Brugsch for the kings of the XVIIIth dynasty must be reduced, and as this view is supported by the evidence derived from the recently published Babylonian Chronicles, and the general testimony of recently excavated monuments, the dates of the reigns of the early kings of that dynasty may well be brought down nearly one hundred years. The other evidence on the point, being of an astronomical character, can only be dealt with by experts. Egyptian chronology is a difficult subject, chiefly because of an insufficiency of facts about the reigns of the kings of the VIIth-XIth, and the XIIIth-XVIIth dynasties. Every year, however, witnesses the removal of a certain number of difficulties, and as long as excavations are made in Egypt a steady increase in the knowledge of the subject may reasonably be hoped for.