Calendars Revisited Lynn E. Rose "Calendars" was originally printed in KRONOS VI: 4 (Summer 1981), pp. 28-39. Now that a revised version of that article is appearing, I have taken this opportunity to correct several errors in the original paper, as well as to make other changes. Many of the 84 theses in the original article have been either deleted or modified and the entire set of theses has been renumbered. Indeed, the changes throughout the paper have been so numerous and sweeping that a change of title seemed in order as well! The 84 theses that constitute the main part of this paper are intended as a guide for those who want a better grasp of the interrelationships of various ancient calendars, especially insofar as they have a bearing upon the work of Immanuel Velikovsky.^(1) The Julian calendar contains 12 schematic (that is, non-lunar) months: February has 28 days; April, June, September and November have 30 days each; and January, March, May, July, August, October and December have 31 days each. Every fourth year is a leap year, with an additional day assigned to February. Thus, the Julian year averages exactly 365.2500 days. The original version of the Julian calendar did not have a February 29 in leap years; rather, a second February 24 was observed. Counting backwards and inclusively from March 1, the Romans called February 24 "Calends VI March." Thus it was that a Julian leap year came to be called an annus bissextus, or a year with a second six. Leap years were supposed to occur every four years. But the Romans were accustomed to counting inclusively, and for over 30 years they made every third year intercalary. Matters were not fully straightened out until more than 50 years after the introduction of the Julian Reform. The Gregorian calendar does not recognize quite so many leap years as the Julian calendar. The Gregorian rules are that: Those years not evenly divisible by four are not leap years; years evenly divisible by four but not by 100 are leap years; years evenly divisible by 100 but not by 400 are not leap years; and those years evenly divisible by 400 are leap years. Thus, 1600 and 2000 are leap years but 1700, 1800, and 1900 are not leap years. The Gregorian calendar accommodates the fact that the tropical year is actually somewhat less than 365.2500 days long. (The Gregorian year is 365.2425 days long, as compared to the tropical year of just under 365.2422 days. Even this discrepancy can be greatly reduced, by canceling a scheduled leap year every few thousand years.) The Julian calendar, with its greater simplicity, is often used in preference to the Gregorian calendar, especially where astronomical matters or ancient history are concerned. When Rome conquered Egypt, the Romans had recently adopted the Julian calendar of 365.2500 days. But the Egyptians still used a 365-day calendar, in which each of 12 schematic months had its own Egyptian name and was 30 days long. Five epagomenal days were placed at the end of the year, after the 12 months. These five days were special and did not belong to any of the 12 months. At the end of the Ptolemaic period and at the beginning of the Roman period, the Egyptian year began in late August. This traditional year was divided into three seasons: The first season ( ht) contained the months Thoth, Phaophi, Athyr, and Choiak; the second season (prt) contained the months Tybi, Mechir, Phamenoth, and Pharmuthi; and the third season (smw) contained the months Pachons, Payni, Epeiphi, and Mesore. (In earlier sources, the months within a given season were numbered rather than named.) The Egyptian seasons were somewhat schematic, like the Egyptian months and like the Egyptian year itself. In any case, the seasons were not in phase with the Nile. For example, the rise of the Nile (traditionally around the time of the summer solstice) would have begun some ten weeks or so before the inundation season ( ht). Velikovsky has suggested that the reason for this may be that the Egyptian calendar was geared ultimately to Venus, rather than to the tropical seasons and the Sun ((365 x 8)/5 = 584 days, which is just over Venus' mean synodic period of 583.9140 days).^(2) In earlier centuries, the interval between the rise of the Nile and the beginning of the inundation season would have been even greater. Thus, it is not a matter of gradually slipping out of phase: In earlier centuries, the seasons were actually more out of phase. The Romans wanted the Egyptians to recognize a year of the same length as their own and ordered the Egyptians to use what came to be called the Alexandrian calendar. The Alexandrian calendar was basically the traditional Egyptian calendar, but with a sixth epagomenal day--instead of just five--at the end of every leap year. The Alexandrian and Julian years overlapped, but were of exactly the same length. The two calendars differed not only in the names and lengths and spacings of the months, but also in the location and status of the extra day in leap years. The Julian calendar had no epagomenal days at the end of the year, but allowed an average of more than 30 days per month. (Apparently the Alexandrian calendar was, for a time, subjected to the same error as the Julian; that is, there were Alexandrian leap years every three years, too!) Many of the Egyptians were less than enthusiastic about the Alexandrian calendar imposed upon them and the Egyptian calendar continued to be used--especially for certain religious purposes, which might have included keeping the year in phase with the movements of Venus. The Egyptian calendar and year were also used by various astronomers, such as Claudius Ptolemy. The Egyptian, Julian, Alexandrian, and Gregorian calendars are usually called solar calendars, in that their primary purpose, presumably, is to follow the Sun. In the case of the Egyptian calendar, I have already noted that this presumption may be incorrect, and that the Egyptian calendar of 365 days may have been geared to Venus. The Canopic Reform itself was as much geared to Sirius as it was to the Sun. Thus, not even the Canopic calendar can be said to have been geared exclusively to the Sun. Of those calendars so far mentioned, perhaps only the Gregorian is strictly solar. For to whatever extent the Julian and Alexandrian calendars were in the Canopic tradition, they also might have been both Sothic and solar. The Julian and Alexandrian leap year days were nearly six months apart, but still fell significantly close together, in the sense that both were between the same two heliacal risings of Sirius. Also, between one such pair of Julian and Alexandrian leap year days and the next such pair, all four of the heliacal risings of Sirius that fell on one and the same date of the Egyptian calendar would have occurred. (The subsequent triennial intercalations would have obscured this, of course; nonetheless, it might have been part of the original intent.) By following the tropical year, a solar calendar keeps the same seasons of the year occurring in the same parts of the calendar, year after year. The months are merely schematic and do not correspond to the actual movements or phases of the Moon. The fact that the 30-day months of the Egyptian calendar were schematic--during, say, the last two thirds or so of the 1st millennium--does not of course preclude that these schematic months were inspired by a much earlier state of affairs: Velikovsky has argued that from the 14th century to the 9th or 8th century the lunar months really did average 30 days rather than 29.5000 days.^(3) The Babylonian calendar in the centuries just prior to the beginning of this era was luni-solar: It combined months that were strictly lunar (the first visibility of the new crescent marked the first day of each new lunar month) with a variable year that could average out to the same length as the solar year. The 12 months of the Babylonian calendar were: Nisan, Ayar, Sivan, Tammuz, Ab, Ulul, Tesrit, Arahsamna, Kislev, Tebit, Sabat and Adar. Every two or three years an intercalary lunar month was added (usually a second Ulul or a second Adar). By adding intercalary lunar months at the proper intervals, the Babylonians were able to keep their months lunar and their average years solar. The Jewish calendar that remains in use today is also a luni-solar calendar, whose month names were adapted from the Babylonian calendar. The Macedonian calendar was another example of a luni-solar calendar. From the widespread areas conquered by Alexander the Great, several different varieties of the Macedonian calendar are known to us. The version used in Ptolemaic Egypt, at the time of the Canopus Decree, will be the focus of our attention here. That version of the Macedonian calendar contained 12 lunar months: Dystros, Xandikos, Artemisios, Daisios, Panemos, Loios, Gorpiaios, Hyperberetaios, Dios, Apellaios, Audynaios and Peritios. Certain months (usually Peritios, but sometimes others) were repeated as intercalary. This was usually done biennially. Throughout this paper, the Egyptian and Julian calendars have been freely retrojected into the past, even though many such retrojections may be illegitimate in light of Velikovsky's theories. Similarly, retrocalculations of the heliacal risings of Sirius have been incorporated here, without regard to subsequent Velikovskian near-collisions that would invalidate them. Such retrojections and retrocalculations are included only in order to elucidate the scholarly and popular literature concerning such matters; no endorsement is thereby implied. Heliacal risings are quite fuzzy phenomena and are difficult to pin down to one day. In what follows, however, I generally take for granted that the angular orientation of the Sun to Sirius will produce a heliacal rising of Sirius every summer. During the time of Ptolemy III Euergetes, in whose reign the Canopus Decree was issued, it seems that heliacal risings of Sirius took place sometimes on July 18 Julian and sometimes on July 19 Julian. (This is for the latitude of Memphis.) By the time of Antoninus Pius, in whose reign a Sothic period supposedly came to an end, the heliacal risings of Sirius were sometimes on July 19 Julian and sometimes on July 20 Julian. Many of the dates that are conventionally equated do not coincide exactly, but only overlap. This is because some days are counted from sunset (Jewish, Babylonian, and Macedonian) and others from midnight (Chinese, Julian and Gregorian), or from sunrise (Egyptian and Alexandrian). These differences can usually be neglected, but sometimes they are of major importance.^(4) (A much later example would be the death of Alexander the Great, known to have occurred after sunset and before midnight.) In an equation such as Dios 25 Macedonian = Choiak 8 Egyptian = January 29 Julian, -245, all three dates began at different times; the equation is usually regarded as justified, however, insofar as the same daylight hours were common to all three dates. (These three dates pertain to the ascension of Ptolemy III Euergetes.) In this article, all negative years are astronomical; for example, -237 (astronomical) = 238 BCE (historical). Astronomical dating has an advantage over historical dating in that the arithmetic is simpler with a year 0 than without a year 0. Also, just as all positive years evenly divisible by four are Julian leap years, so all negative years evenly divisible by four are Julian leap years, if one uses astronomical dating. (Velikovsky preferred to use historical dates. Even those he wrote with a minus sign should almost always be taken in the usual historical sense, rather than in the astronomical sense.) The retrocalculation of the superior conjunction of Venus in -608 is based on Schoch's tables in The Venus Tablets of Ammizaduga--as are the lunar dates.^(5) All other retrocalculations of Venus are interpolated from Tuckerman's tables in Planetary, Lunar and Solar Positions 601 B.C. to A.D. 1 at Five-day and Ten-day Intervals,^(6) with the intervals between disappearance and superior conjunction for Venus...derived from Schoch. It should be noted that Tuckerman, guided with regard to his project by Neugebauer and Sachs, stopped his retrocalculations at -600. People like Neugebauer and Sachs claim to believe that little of interest in the way of astronomical observation took place any earlier than that. Thus, Neugebauer dismisses even the Ninsianna observations with: "From the purely astronomical viewpoint these observations are not very remarkable."^(7) 1. By uniformitarian retrocalculation, Sirius would have risen heliacally in July (Julian) for many thousands of years, including not only the 2nd millennium before this era but also the epoch of the Canopus Decree in the 3rd century before this era, as well as the later period that encompassed Claudius Ptolemy, Antoninus Pius, Censorinus, and Theon (the 2nd, 3rd, and 4th centuries of this era). The July 19 Julian date provided by the Canopus Decree for -238 (or -237) and the July 20 Julian date given by Censorinus for +139 serve to enhance the precision of these retrocalculations, in that such dates provide corrective benchmarks, but any retrocalculations of Sirius past the 7th century would of course be invalid in the context of Velikovsky's theories. 2. IV prt 16 Egyptian = July 17 Julian, from -1872 to -1869. (In later times IV prt was called Pharmuthi.) Similarly, IV prt 16 Egyptian = July 16 Julian, from -1868 to -1865. Such a sequence of four years that feature the same situation is often called a quadrennium. The situation regarding Sirius during a given Egyptian-Julian quadrennium can be represented by means of what I shall call a tetrad. Thus, 16-16-17-17 means that Sirius rose heliacally on July 16 Julian of the first two years of that quadrennium and on July 17 Julian of the last two years of that quadrennium. 3. -1871 is Parker's date for the supposed heliacal rising of Sirius in the seventh year of Sesostris III. Unfortunately, Parker's approximations are far too crude for the task at hand. More careful procedures indicate that the retrocalculated heliacal rising of Sirius would have occurred on IV prt 15 Egyptian in -1871. With a tetrad of 16-16-17-17, the heliacal rising of Sirius would have occurred on IV prt 16 Egyptian from -1870 to -1867, which is probably where Parker should have been looking.^(8) 4. Another kind of quadrennium involves this four-year correspondence between the Egyptian calendar and the heliacal rising of Sirius. But since the actual Sothic cycle is a few years shorter than the full 1460 years, there will be several Egyptian-Sothic quadrennia that are compressed into triennia. Such a triennium would cause one tetrad to be replaced by another. For example, if the tetrad was 19-19-19-20 when the Sothic cycle ended in +139, then there were either two or three triennia between say, -240, and +139. If there were two, then the tetrad that began in -240 was 18-19-19-19; if there were three, then the tetrad that began in -240 was 18-18-19-19. (We shall find that there were three.) 5. Thoth 1 Egyptian = July 20 Julian, from -1324 to -1321. Similarly, Thoth 1 Egyptian = July 18 Julian, from -1316 to -1313. 6. According to the conventional chronology, the unusual Nile flood of Tybi 12 Egyptian of the third year of Osorkon II of the Libyan Dynasty^(9) would have fallen in about the second quarter of the 9th century. At that epoch, Tybi 12 Egyptian would correspond to early August Julian = late July Gregorian. Yet late July Gregorian is far too early for the crest of the annual Nile flood, which is usually in September of the Gregorian calendar. Since Velikovsky wrote, several scholars have suggested that the Osorkon of the flood report was Osorkon III, who would have reigned in the early 8th century. At that period, Tybi 12 Egyptian would correspond to mid-July Julian = early July Gregorian, which is even worse. 7. The Mesore 25 Egyptian incident that involved heaven not devouring the Moon is from the 15th year of a Libyan pharaoh--either Takelot II or Sosenk III. According to the conventional chronology, this incident would have fallen in the latter part of the 9th century. At that epoch, Mesore 25 Egyptian would correspond to early March Julian.^(10) There has been much puzzlement about the meaning of this report. Kitchen now assigns the report to Takelot II and translates it "the sky did not swallow the moon, (but) a great(?) convulsion broke out in this land."^(11) 8. Tybi 12 Egyptian = July 14 Julian = July 6 Gregorian, -775. Velikovsky puts the Osorkon flood in -775. July 6 Gregorian--even more than, say, late July Gregorian--is unacceptably early as the crest of the annual Nile flood, but would make sense as an unseasonal flood induced by the near-collision of Earth and Mars in that year. (Such retrojections are illegitimate, of course, but--assuming for now that there were no radical changes in the Egyptian calendar in the meantime--they may at least give some hint as to the time of year. In that case, the summer of -775 would also fit the start of the first year of the first Olympiad, and might even fit the Sivan 11 disappearance of Venus in Year 9 of the Ninsianna observations, which would mean that the observations in Years 1 through 17 would extend from -782 to -766.) The summer solstice would have been on June 29 Julian = June 21 Gregorian, -775. According to tradition, the first Olympiad would have begun in the summer of -775. 9. Phamenoth 6 Egyptian = X 1 Chinese = sin mao (day 28) of the Chinese cycle = September 6 Julian = August 29 Gregorian, -775. (Theses nine, ten, 17, 18 and 19 all concern solar eclipse reports.) 10. June 15 Julian, -762.^(12) 11. Thoth 1 Egyptian = March 1 Julian, from -760 to -757. 12. Thoth 1 Egyptian = February 29 Julian, -756. (If we use a second February 24, then either the year -740 or the year -736 would be the one affected here, depending upon which of the two February 24's is counted as the second one.)^(13) 13. Thoth 1 Egyptian = February 28 Julian, from -755 to -752. (The founding of Rome was in -752.) 14. Thoth 1 Egyptian = February 26 Julian, from -747 to -744. 15. Mesore 25 Egyptian = February 15 Julian, -746. (-746 is Velikovsky's date for the incident of heaven not devouring the Moon.) Had Velikovsky been convinced that the Osorkon flood pertained to Osorkon III, he might have reexamined and even transposed these two events from the Libyan dynasty. The entire matter requires further investigation. 16. The Era of Nabonassar began on Thoth 1 Egyptian = February 26 Julian, -746. (Note the general compatibility of the time of year of the incident of heaven not devouring the Moon and the start of the Era of Nabonassar.) 17. II 1 Chinese = chi szu (day six) of the Chinese cycle = February 22 Julian = February 14 Gregorian, -719. (Legge and Chalmers calculate that it should be month III.) 18. VII 1 Chinese = jen ch'en (day 29) of the Chinese cycle = July 17 Julian = July 9 Gregorian, -708. (Legge and Chalmers, III, i, page 103 and V, i, II, 42, calculate that it should be month VIII. They also say that it was July 8 (Gregorian), as do Muller and Stephenson, page 489, and Stephenson and Clark, page 22. But July 8 Gregorian is wrong. Newton, page 148, gives the date correctly as July 17 Julian--as do Muller and Stephenson themselves on page 509!) 19. X 1 Chinese = October 10 Julian = October 3 Gregorian, -694. (Legge and Chalmers calculate that it should be month XI.) 20. Phaophi 11 Egyptian = IV [4 or 5?] Chinese = sin mao (day 28) of the Chinese cycle = March 23 Julian = March 16 Gregorian, -686.^(14) 21. Venus was in superior conjunction with the Sun on Epeiphi 22 Egyptian = December 9 Julian, -608. If the disappearance in the east was on November 16 Julian and if the heliacal rising of Sirius was on Mechir 28 Egyptian = July 18 Julian, -608, then Venus and Sirius would both have been visible in the pre-dawn sky for just over four months and those four months would have included the highest levels of the Nile inundation. This sort of situation would have occurred every eight years. As we shall see, over the next centuries Venus would have tended to disappear earlier and earlier with respect to the heliacal rising of Sirius and the Nile flood, until finally, a few years after the Canopus Decree, Venus would have disappeared even before the heliacal rising of Sirius. Each century, however, the disappearances of Venus would have moved on the average only about 5.3750 days earlier in the Egyptian calendar; this would have been due to the fact that five synodic periods of Venus amount to slightly less than eight Egyptian years (8 x 365 = 2920 and 5 x 583.9140 = 2919.5700). The -608, -512, -416 and -320 referred to in this paper have been selected only for purposes of illustration, in that they seem to feature disappearances of Venus just over four months, three months, two months and one month, respectively, after the heliacal rising of Sirius. (In this paper, disappearance refers to first invisibility, rather than to last visibility.) 22. From -523 to -520, January 1 Julian fell on Thoth 1 Egyptian. 23. -520 was a Julian leap year, with an extra day in February. 24. In -520, both January 1 Julian and December 31 Julian fell on Thoth 1 Egyptian. 25. From -520 to -517, December 31 Julian fell on Thoth 1 Egyptian. 26. Thoth 1 Egyptian = December 30 Julian, from -516 to -513. 27. Venus was in superior conjunction on Epeiphi 15 Egyptian = November 8 Julian, -512. If the disappearance was on October 17 Julian, then both Venus and Sirius would have been visible in the pre-dawn sky for just over three months. 28. Venus was in superior conjunction on Epeiphi 8 Egyptian = October 8 Julian, -416. If the disappearance was on September 17 Julian, then both Venus and Sirius would have been visible in the pre-dawn sky for just over two months. 29. Daisios 29 Macedonian = Pharmuthi 2 Egyptian = June 11 Julian, -322. Yet Alexander the Great died after sunset and before midnight on Daisios 29 Macedonian, which would still have been on Pharmuthi 1 Egyptian = June 10 Julian. This illustrates the type of situation in which it is not entirely appropriate to equate dates on the basis of the daylight hours that they have in common. 30. Venus was in superior conjunction on Epeiphi 3 Egyptian = September 9 Julian, -320. If the disappearance was on August 18 Julian, then both Venus and Sirius would have been visible in the pre-dawn sky for just over one month. 31. On Thoth 1 Egyptian = October 27 Julian, -260, the western elongation of Venus from the Sun would have been just over 46.5°, and would have remained above 46.5° for about 2.5 weeks, with Venus as the Morning Star riding high in the pre-dawn eastern sky. (Sirius itself, more than three months past heliacal rising, would have been conspicuous in the southern sky.) This situation would have been repeated in -252, -244 and -236, and may well have been the benchmark in terms of which the Egyptian calendar was at that time regarded as linked to the motions of Venus. In any case, I have found no other such benchmark. Neither the appearances nor the disappearances nor the conjunctions are closely correlated with Thoth 1 Egyptian. The closest apparent correlation is that the disappearances in the west in such years as -249, -241, -233 and so on, were in early Thoth. (In earlier times, they would have been later in Thoth.) 32. Venus was in superior conjunction on Payni 30 Egyptian = August 21 Julian, -256. If the disappearance was on July 29 Julian, then there were only 11 days between the heliacal rising of Sirius on Pachons 26 Egyptian = July 18 Julian, -256, and the disappearance of Venus. 33. On Thoth 1 Egyptian = October 25 Julian, -252, the elongation of Venus would have been just over 46.5°, and would have remained above 46.5° for about 2.5 weeks. 34. Venus was in superior conjunction on Payni 30 Egyptian = August 19 Julian, -248. If the disappearance was on July 27 Julian, then there were only nine days between the heliacal rising of Sirius on Pachons 28 Egyptian = July 18 Julian, -248, and the disappearance of Venus. 35. The ascension of Ptolemy III Euergetes to the throne of Egypt was on Dios 25 Macedonian = Choiak 8 Egyptian = January 29 Julian, -245. 36. Year 2 of the reign began on Dystros 24 Macedonian, which was in May or June of -245, depending upon the intercalations. 37. On Thoth 1 Egyptian = October 23 Julian, -244, the elongation of Venus would have been just over 46.5° and would have remained above 46.5° for about 2.5 weeks. 38. Venus was in superior conjunction on Payni 30 Egyptian = August 17 Julian, -240. If the disappearance was on July 24 Julian, then there were only six days between the heliacal rising of Sirius on Pachons 30 Egyptian = July 18 Julian, -240, and the disappearance of Venus. This dramatic transition-in-progress may have initiated the agonizing reappraisal that led to the Canopus Decree and may thereby provide a partial explanation of the timing of the Canopus Decree, especially if Velikovsky is correct in saying that the Canopus Decree involved a change from a Venus year to a Sirius year. This eighth-year pattern provided a dramatic heavenly display that Venus and the Egyptian calendar were simply not keeping pace with the seasons--as registered in the Nile flood--and that Sirius was keeping pace. Venus and the Venus-based calendar were slipping backwards through the seasons, yet Sirius was not slipping. (Actually, the heliacal rising of Sirius would have been moving slightly forward with respect to the seasons, but this movement would have been so slow--less than one-thirtieth the rate at which Venus was moving backwards--as to have remained unnoticed at the time and the heliacal rising of Sirius would have continued to occur at about the same phase of the rise of the Nile. Ancient writers took the Sothic period to be 1460 years; they did not recognize that it was somewhat less than this.) 39. Thoth 1 Egyptian = October 22 Julian, from -240 to -237. 40. Pachons 30 Egyptian = July 18 Julian, from -240 to -237. Similarly, Payni 1 Egyptian = July 19 Julian, from -240 to -237. By uniformitarian retrocalculation from +139, the tetrad would have been either 18-18-19-19 or 18-19-19-19. (It depends upon the locations and numbers of the triennia, points to be addressed in a moment.) Thus Sirius would have risen heliacally on Pachons 30 Egyptian in -240; on either Pachons 30 Egyptian or Payni 1 Egyptian in -239; and on Payni 1 Egyptian in -238 and in -237. It will turn out that the only plausible explanation of the Canopus Decree's emphasis on Year 9 is that the tetrad was 18-18-19-19, that the first heliacal rising of Sirius on Payni 1 Egyptian was in -238 and that that event occurred early in Year 9. 41. Year 9 of the reign of Ptolemy III Euergetes began on Dystros 24 Macedonian, which was in the spring or summer of -238. 42. The Canopus Decree carries both the date of Tybi 17 Egyptian and the date of Apellaios 7 Macedonian. But these two dates cannot be equivalent. Tybi 17 Egyptian = March 7 Julian, -237, which would have fallen on the 30th day of a lunar month, not the seventh day. On the other hand, the seventh day of a lunar month could only have fallen on Choiak 24 Egyptian = February 12 Julian, -237, or on Tybi 24 Egyptian = March 14 Julian, -237. 43. The heliacal rising of Sirius in -238 probably did fall early in Year 9, but using the past tense regarding what had been been remembered in Year 9 does not in itself establish that the heliacal rising of Sirius in Year 9 had already occurred at the time of the Canopus Decree.^(15) 44. The Canopus Decree never mentions Venus; both Sopdet and Isis mean Sirius here. 45. July 19 Julian of -237 fell on the 16th day of a lunar month. If that lunar month was Dystros (which it would be, if there was an intercalary Peritios in Year 9), then Dystros 24 Macedonian was later than Payni 1 Egyptian = July 19 Julian, -237. 46. Depending upon the intercalations, Year 9 might have ended either before or after the heliacal rising of July 19 Julian, -237. Indeed, an intercalary Peritios in Year 9 could have caused Year 9 to encompass both the -238 rising and the -237 rising. 47. Thoth 1 Egyptian = October 22 Julian, -237, which would have been the sixth epagomenal day prescribed by the Canopic reform, if that reform had pertained to Year 10. Thoth 1 Canopic would have been Thoth 2 Egyptian = October 23 Julian, -237. 48. Payni 1 Egyptian = July 18 Julian, from -236 to -233. 49. It is highly likely that the Canopus Decree was sabotaged, either by omitting the date of application and then reading it as applying to Year 10 when it was supposed to be applied to a later year of the reign, or simply by issuing it too early, so that it would automatically be misapplied. 50. The Canopus Decree was issued in Year 9, but pertained either to Year 11 (ending in -235) or to Year 12 (ending in -234). By considering the tetrads, we shall find that we can decide between Year 11 and Year 12. 51. With an 18-19-19-19 tetrad, the heliacal rising of Sirius would have been on Pachons 30 Egyptian in -243, -242, -241 and -240; on Payni 1 Egyptian in -239, -238, -237 and -236; and on Payni 2 Egyptian in -235, -234, -233 and -232. The sixth Canopic epagomene would have been Thoth 1 Egyptian = October 21 Julian, -236, in Year 11. This would have worked. But if the Canopus Decree had been read as applying to Year 10, the reform would have been judged a failure in that the very next heliacal rising of Sirius would have been on Pachons 30 Canopic = Payni 1 Egyptian = July 18 Julian, -236. The main problem with 18-19-19-19 is that, according to it, the first heliacal rising of Sirius on Payni 1 Egyptian would have been in -239 and would, therefore, have been at the beginning of Year 8. Yet the Canopus Decree makes it clear that the first heliacal rising of Sirius on Payni 1 Egyptian happened in Year 9. 52. With an 18-18-19-19 tetrad, the heliacal rising of Sirius would have been on Pachons 30 Egyptian in -242, -241, -240 and -239; on Payni 1 Egyptian in -238, -237, -236 and -235; and on Payni 2 Egyptian in -234, -233, -232 and -231. The sixth Canopic epagomene would have been Thoth 1 Egyptian = October 21 Julian, -235, in Year 12. This, too, would have worked (barring any sudden triennium). But if the Canopus Decree had been read as applying to Year 10, the reform would have been judged a failure in that the very next heliacal rising of Sirius would have been on Pachons 30 Canopic = Payni 1 Egyptian = July 18 Julian, -236. Even if the Canopus Decree had been applied to Year 11, the next heliacal rising after that would have been on Pachons 30 Canopic = Payni 1 Egyptian = July 18 Julian, -235, and the reform would likewise have been judged a failure. The Canopus Decree's emphasis on Year 9 is precisely because that was the first year of the reign in which the heliacal rising of Sirius was on Payni 1 Egyptian. This settles both the question of what the tetrad was (it was 18-18-1919) and that of whether the -238 heliacal rising of Sirius fell within Year 9 (it did). The reformers' concern was about what would happen after four years since they wanted to ensure that the heliacal rising on July 18 Julian, -234, would remain on Payni 1 Canopic if an extra day was intercalated in the previous October--that is, in Year 12. Do we also solve the triennia problem? (See thesis five above.) Yes, there were three triennia between -240 and +139. The first of these may even have come relatively soon. By -235, -231, -227, -223, or some such year in that sequence, the heliacal rising of Sirius would have moved to Payni 2 Canopic anyway. Thus the Canopus Decree was doomed to failure even if it had been applied in Year 12 as the sponsors of the reform intended. There was no need to sabotage it! 53. On Thoth 1 Egyptian = October 21 Julian, -236, the elongation of Venus would have been just over 46.5° and would have remained above 46.5° for about 2.5 weeks. 54. Venus was in superior conjunction on Payni 29 Egyptian = August 14 Julian, -232. If the disappearance was on July 21 Julian, then Venus would have remained visible for two more days after the heliacal rising of Sirius on July 18 Julian. (This was the last time in an eighth-year cycle that Venus would have remained visible even after the heliacal rising of Sirius.) 55. Venus was in superior conjunction on Payni 29 Egyptian = August 12 Julian, -224. If the disappearance was on July 18 Julian, as Schoch's tables indicate, then Venus would have been seen for the last time on July 17 Julian and Sirius would have been seen for the first time on July 18 Julian! 56. The Julian reform was introduced in Rome in -45, when 23 days were intercalated in February and another 67 days were intercalated between November and December, for a total of 90. The first Julian leap year was -44, with further leap years scheduled to occur every fourth year thereafter. But Julius Caesar was assassinated on March 15 Julian, -43, and his Julian Reform was badly mishandled. Until and including the year -8, leap years were mistakenly triennial, instead of quadrennial. To correct this error, leap years were skipped in -4, 0 and +4, and only resumed in +8. Thereafter, intercalation was quadrennial. 57. The ascension of Octavian (later called Augustus) to the Egyptian throne took place on Thoth 1 Egyptian in -29. Because of the triennial leap years (there had been two extra Julian leap years by then), Thoth 1 Egyptian in fact fell on the day that was at that time called August 29 Julian. In other words, Thoth 1 Egyptian = August 29 Julian (actual) = August 31 Julian (retrojected), -29. Those later writers who used the Alexandrian calendar may have counted the first year of Augustus--and the Era of Augustus in Egypt--from Thoth 1 Alexandrian (retrojected) = August 30 Julian (retrojected), -29. At the time, however, Thoth 1 Alexandrian (actual) = Thoth I Egyptian = August 31 Julian (retrojected), -29. (The Era of Augustus in Egypt that began in -29 should not be confused with the Roman Era of Augustus that began on January 16 of -26, the day that Octavian received the title of Augustus. January 16 is presumably the date obtained at the time, in which case the idealized and retrojected date would be January 17 Julian, since there had been one intercalation too many at that point.) 58. Thoth 1 Egyptian = August 30 Julian (retrojected), from -28 to -25. 59. Thoth 1 Egyptian = August 29 Julian (retrojected), from -24 to -21. 60. Thoth 1 Alexandrian (retrojected) = Thoth 1 Egyptian, from -25 to -22. 61. The first quadrennium of the Egyptian calendar and the retrojected Alexandrian calendar (this is still another variety of quadrennium) began on Thoth 1 Egyptian = Thoth 1 Alexandrian (retrojected) . August 30 Julian (retrojected), -25. This would have been the beginning of the fifth year--whether Egyptian or Alexandrian--of Augustus on the Egyptian throne. But what in fact happened was that Thoth 2 Egyptian = August 29 Julian (actual) = Thoth 1 Alexandrian (actual), -25. This would have been on August 31 Julian (retrojected). 62. The Alexandrian years overlapped the Julian years; as far as we know, the sixth epagomenal day of the Alexandrian leap year always fell on August 29 Julian of the Julian year immediately preceding each Julian leap year. (Using the bissextus style, we can say that February 25 Julian to August 28 Julian always had the same Alexandrian equivalents.) 63. Thoth 1 Egyptian = July 20 Julian (Calends XIII August), from +136 to =139. 64. Thoth 1 Egyptian = July 19 Julian, from +140 to +143. Epeiphi 26 Alexandrian = July 20 Julian (in any year). 65. Sirius rose heliacally on Thoth 1 Egyptian, from +139 to +143; the tetrad was 19-19-19-20. 66. Antoninus Pius became emperor on July 10 Julian, +138. In Egypt, his Year 1 was counted from Thoth 1 Alexandrian = August 29 Julian, +137; his Year 2 from Thoth 1 Alexandrian = August 29 Julian, +138. 67. Thoth 1 Alexandrian = August 30 Julian in +139. 68. Thoth 1 Egyptian = June 25 Julian (Calends VII July), from +236 to +239. 69. Censorinus wrote on or after Thoth 1 Egyptian = June 25 Julian and before Thoth 1 Alexandrian = August 29 Julian, +238. This follows from his report that he is in the 100th (Egyptian) year of the new cycle, and that he is in the 267th (Alexandrian) year of the Era of Augustus in Egypt. 70. Censorinus is correct in thinking that Sirius rose heliacally on Thoth 1 Egyptian = July 20 Julian (Calends XIII August), +139. (The standard emendation of the XII in the text to XIII is entirely justified on the basis of Censorinus' other remarks, which show that he did indeed mean XIII.) 71. Percy Davis is mistaken in denying that this heliacal rising occurred in +139. 72. Censorinus relates the heliacal rising of Sirius to the Egyptian calendar, a relationship he thought would repeat itself every 1460 years; he is not concerned with the Alexandrian calendar when he talks about +139. 73. Censorinus should perhaps have had his Sothic period extend 1452 years, from -1313 to +139, in order to reflect the retrocalculated facts, but he assumes, along with other ancient writers, that the Sirius year and the Julian year are equal. 74. The Julian and Gregorian calendars coincide exactly from March 1, +200, to February 28, +300. (This is with a February 29 in leap years rather than with a second February 24.) Before and after that century they are out of phase. 75. Theon relates the Alexandrian calendar and the Egyptian calendar, another relationship that repeats itself every 1460 years; he is not concerned with the heliacal rising of Sirius, however, and the 1460 year period he discusses is not a Sothic period. He is speaking only of the fact that, retrospectively, Thoth 1 Alexandrian (retrojected) would first have fallen on Thoth 1 Egyptian in the fifth year of Augustus. 76. The Theon annotator said that "from Menophreus" to the end of the Era of Augustus there were 1605 years. This is our only source about Menophreus, and is the only known allusion to any Era of Menophreus. 77. The Era of Augustus in Egypt ended with the fifth epagomene Alexandrian = August 28 Julian, +284. (Diocletian actually became emperor on September 17 Julian, +284, but the first year of his reign was counted in Egypt from the Thoth 1 Alexandrian immediately preceding his ascension. The later Era of Diocletian in Egypt, like Year 1 itself, came to be counted from Thoth 1 Alexandrian = August 29 Julian, +284.) 78. The calendar years employed by the Theon annotator in arriving at 1605 years were Alexandrian, not Egyptian. Taking 1605 years from +284 puts Menophreus in -1321, the same year found by taking 1460 years from +139. 79. It is possible that Menophreus is the Hyksos king named Mennofirre or Merneferre. Placing a Hyksos king in the late 14th century is permitted in the revised, but not in the conventional, chronology. 80. The Theon annotator computes that there was a heliacal rising of Sirius--latitude unspecified--on Epeiphi 29 Alexandrian = July 23 Julian, +384. This seems to be an arithmetical error for Epeiphi 30 Alexandrian = July 24 Julian, +384. But details of the overall computation remain obscure and have been diversely interpreted. At one point, he adds five days, without explaining why. It has been suggested that, since the heliacal rising of Sirius at Memphis was still on July 19 Julian in +384, these five days must be accounted for in terms of a difference of latitude. But the Theon annotator remains characteristically obscure about what he is doing here. 81. Aside from this obscurity of detail, the remarks of the Theon annotator, of Theon and of Censorinus are entirely consistent with one another. 82. The Gregorian calendar was introduced in +1582. October 4 Julian = October 14 Gregorian, +1582, was observed as Julian and October 5 Julian = October 15 Gregorian, +1582, was observed as Gregorian. Many people were upset because they had "lost" ten days. When the English finally adopted the Gregorian calendar, in +1752, it was necessary to skip 11 days; this even led to riots, with cries of "Give us back our 11 days!" 83. May 29 Julian = June 10 Gregorian, +1895. 84. November 4 Julian = November 17 Gregorian, +1979. 1. For further discussion of the issues raised in this article, see my forthcoming book, Sun, Moon, and Sothis. 2. Immanuel Velikovsky (A), "Astronomy and Chronology," Peoples of the Sea supplement, pp. 235-243. 3. Immanuel Velikovsky (B), Worlds in Collision (New York, 1950), pp. 330-359. 4. Velikovsky (B), op. cit., pp. 65-66. 5. Stephen H. Langdon, John K. Fotheringham and Carl Schoch, The Venus Tablets of Ammizaduga (London, 1928). 6. Bryant Tuckerman, Planetary, Lunar, and Solar Positions 601 B.C. to A.D. 1 at Five-day and Ten-day Intervals, p. 1. 7. Otto Neugebauer, The Exact Sciences in Antiquity, (New York, 1969), p. 100. 8. KRONOS VI: 1 (Fall 1980): 58-60. 9. Velikovsky (B), op. cit., p. 209. 10. Velikovsky (B), op. cit., p. 355; Velikovsky (A), Peoples of the Sea (New York, 1977), p. 215. 11. Kitchen, The Third Intermediate Period in Egypt (1100-650 B.C.), Second edition with supplement, p. 546. 12. Velikovsky (C), Harper's (June, 1951): 64; Newton, The Moon's Acceleration and Its Physical Origins (1970), I, pp. 49-53. 13. Samuel, Greek and Roman Chronology, p. 156. 14. Velikovsky (B), op. cit., p. 234. 15. KRONOS VI: 4 (Summer 1981): 88 and VIII: 2 (Winter 1983): 68. _________________________________________________________________ \cdrom\pubs\journals\velikov\vol0101\calendar.htm