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Calendars

LYNN E. ROSE

Copyright (C) 1981 by Lynn E. Rose

The 84 theses that constitute the main part of this paper are intended as a guide for those who wish to obtain a better grasp of the interrelationships of various ancient calendars, especially insofar as they have a bearing upon the work of Immanuel Velikovsky.

These theses are generally consistent with what Velikovsky wrote in the Supplement, "Astronomy and Chronology", to Peoples of the Sea, although most of them are not explicitly stated either there or anywhere else in Velikovsky's writings.

* * *

The Julian calendar in the form that has become familiar contains twelve 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 1/4 days. (The original version of the Julian calendar seems to have assigned somewhat different lengths to the various months, but from the beginning the length of the Julian year has been 365 1/4 days.)

The Gregorian calendar that we use today does not recognize quite so many leap years as the Julian calendar. The Gregorian rules are: that those years not evenly divisible by 4 are not leap years; that those years evenly divisible by 4 but not by 100 are leap years; that those years evenly divisible by 100 but not by 400 are not leap years; and that 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 a little less than 365 1/4 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 reduced, by skipping a scheduled leap year several thousand years from now.) 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 a Julian year of 365 1/4 days. But the Egyptians still used a 365-day calendar, in which each of twelve schematic months had its own Egyptian name, and was 30 days long. (In earlier sources, the months within a given season were usually numbered rather than named.) Five epagomenal days were placed at the end of the year, after the twelve months. These five days were special, and did not belong to any of the twelve months.

At the end of the Ptolemaic period and at the beginning of the Roman period, the Egyptian year began in late August. The year was traditionally divided into three seasons, governed by the Nile. The first or "inundation" season contained the months Thoth, Phaophi, Athyr, and Choiak; the second or "growing" season contained the months Tybi, Mechir, Phamenoth, and Pharmuthi; and the third or "harvest" season (called by some the "deficiency" season) contained the months Pachons, Payni, Epiphi, and Mesore. Notice that these "seasons" are not quite in phase with the Nile, since the rise of the Nile would have begun some ten weeks or so before the "inundation" season. Velikovsky has suggested that the reason for this may be that the Egyptian calendar was geared ultimately to Venus, rather than to the seasons and the Sun (365 x 8 5 = 584 days, which, to the nearest day, is the mean synodic period of Venus).

The Romans wanted the Egyptians to join with them in recognizing a strictly solar year of 365 1/4 days, and they ordered the Egyptians to use what is called the Alexandrian calendar. The Alexandrian calendar is basically the traditional Egyptian calendar, but with a sixth epagomenal day instead of just five at the end of every fourth 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.

The Egyptians were less than enthusiastic about the Alexandrian calendar that had been 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, including Claudius Ptolemy. (The Canopic reform under the Macedonians seems to have met with even stronger resistance than the essentially identical Alexandrian reform under the Romans.)

The Egyptian, Julian, Alexandrian, and Gregorian calendars are usually called solar calendars, in that their primary purpose, it is presumed, is to follow the Sun, rather than, say, the Moon. (In the case of the Egyptian calendar, we have already noted that this presumption may be incorrect, and that the Egyptian calendar of 365 days may have been geared to Venus.) 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 at all to lunar movements. No effort is made to have calendar dates reflect the actual movements or phases of the Moon.

(The fact that 30-day months were schematic during, say, the periods of Tanitic, Persian, Macedonian, and Roman domination of Egypt does not of course preclude that these schematic months were inspired by a much earlier state of affairs: Velikovsky has argued that from the fourteenth century to the ninth or eighth century the lunar months really did average 30 days rather than 29 l/2 days.)

The Babylonian calendar in the centuries just prior to the beginning of this era was of the type called luni-solar: it combined months that were strictly lunar (the first visibility of the crescent Moon marked the first day of each new lunar month) with a variable year that averaged out to the same length as the tropical year. The twelve months of the Babylonian calendar were: Nisan, Ayar, Sivan, Tammuz, Ab, Ulul, Tesrit, Arahsamna, Kislev, Tebit, Sabat, and Adar. Twelve such lunar months of 29 or 30 days produced a year of about 354 days. Every two or three years an intercalary lunar month usually a second Ulul or Adar was added, to produce a year of about 384 days. 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, and was in part derived from the ancient Babylonian calendar.

The Macedonian calendar was still another instance of a luni-solar calendar. From the widespread areas conquered by Alexander the Great, there are several different varieties of the Macedonian calendar that are known to us. The version used in Ptolemaic Egypt, especially at the time of the Canopus Decree, will be the focus of our attention here. That version of the Macedonian calendar contained these twelve lunar months: Dios, Apellaios, Audynaios, Peritios, Dystros, Xandikos, Artemisios, Daisios, Panemos, Loios, Gorpiaios, and Hyperberetaios. Various of these months (usually Peritios, but sometimes others) were from time to time repeated as intercalary months.

In what follows, the Egyptian and Julian calendars have been freely retrojected into the past, even though such retrojections are illegitimate in the light of Velikovsky's theories. (For example, Velikovsky argues that the five epagomenal days of the Egyptian calendar were not used in the period between the fourteenth century and the ninth or eighth century, when the year was of 360 days, but were added in the seventh century.) 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, this is ignored, and it is taken for granted that the angular orientation of the Sun to Sirius will produce a heliacal rising of Sirius every summer. For the latitude of Memphis, retrocalculation indicates that this would have occurred on July 19 Julian for many centuries down to and including the Canopus Decree, but on July 20 Julian throughout the period that encompassed Claudius Ptolemy, Censorinus, Theon, and the Theon annotator.

Some of the dates equated here do not coincide exactly, but only overlap. This is because some "days" are counted from sunset (Jewish, Babylonian, and Macedonian), and others from midnight (Julian and Gregorian), or from sunrise (Egyptian and Alexandrian). These differences have been ignored in what follows, but they can be of major importance: see Worlds in Collision, pages 65-66. 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 justified, however, insofar as the daylight hours of January 29 Julian were common to all three dates.

In this paper, all negative years are astronomical: for example, -237 (astronomical) = 238 B.C.E. (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 4 are Julian leap years, so all negative years evenly divisible by 4 are Julian leap years, if one uses astronomical dating. (Velikovsky nearly always used historical dates; even when he wrote them with a minus sign, they are to 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 the tables of Schoch in Langdon-Fotheringham-Schoch, The Venus Tablets of Ammizaduga as are the lunar dates. All other retrocalculations of Venus are interpolated from the tables of Tuckerman in Planetary, Lunar, and Solar Positions 601 B.C. to A.D. 1 at Five-day and Ten-day Intervals, except that the intervals between disappearance and superior conjunction for Venus are derived from Schoch. It might be noted that Tucker man, who was guided with regard to his project by Neugebauer and Sachs, stopped his retrocalculations at -600. Such people like 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" (The Exact Sciences in Antiquity, second edition, page 100).

* * *

1. The fifth epagomenal day of the Egyptian calendar fell on July 19 Julian from -1324 to -1321. (Remember, such claims involve the retrojection of both calendars well beyond any historical justification.)

2. Thoth I Egyptian = July 20 Julian, from -1324 to -1321. (Such a sequence of four years that feature the same situation is often called a "quadrennium".)

3. -1321 was the last year before +136 in which a Thoth I Egyptian would have fallen on a July 20 Julian.

4. Thoth I Egyptian = July 19 Julian, from -1320 to -1317.

5. By uniformitarian retrocalculation, Sirius would have risen heliacally on July 19 Julian for several millennia, including not only the fourteenth century before this era but also the time of the Canopus Decree in the third century. The July 19 Julian date provided by the Canopus Decree for -238 and the July 20 Julian date given by Censorinus for +139 serve to enhance the precision of this retrocalculation, in that they provide corrective benchmarks, but any retrocalculations past the seventh century would be invalid in the context of Velikovsky's theories.

6. According to the conventional chronology, the unusual Nile flood of Tybi 12 Egyptian of the third year of Osorkon II (see Worlds in Collision, page 209) would have fallen in about the second quarter of the ninth century. At that epoch, Tybi 12 Egyptian would correspond to early August Julian and late July Gregorian. Yet late July Gregorian is far too early for the crest of the annual Nile flood, which is usually in early autumn of the Gregorian calendar.

7. According to the conventional chronology, the Mesore 25 Egyptian incident in the fifteenth year of a Libyan pharaoh either Takelot II or Sosenk III that involved heaven devouring the Moon would have fallen in about the last third of the ninth century. At that epoch, Mesore 25 Egyptian would correspond to early March Julian. (See Worlds in Collision, page 355, and Peoples of the Sea, page 215.)

8. Tybi 12 Egyptian = July 14 Julian = July 6 Gregorian, -775. Velikovsky puts the Osorkon II flood in -775. July 6 Gregorian, even more than 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 they may at least provide a hint as to the time of year. In that case, the summer of 1775 would also fit the start of the first year of the first Olympiad, and might even fit a 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.)

9. Thoth 1 Egyptian = March 1 Julian, from -760 to -757.

10. Thoth 1 Egyptian = February 29 Julian, -756.

11. Thoth 1 Egyptian = February 28 Julian, from -755 to -752.

12. Thoth 1 Egyptian = February 26 Julian, from -747 to -744.

13. Mesore 25 Egyptian = February 15 Julian, -746. (-746 is Velikovsky's date for the incident of heaven devouring the Moon.)

14. The Era of Nabonassar began on Thoth I Egyptian = February 26 Julian, -746, which was neither the beginning nor the end of a quadrennium. (Note the general compatibility of the time of year of the incident of heaven devouring the Moon and the start of the Era of Nabonassar.)

15. Thoth I Egyptian = February 11 Julian, from -687 to -684.

16. Phaophi 11 Egyptian = sin mao of the Chinese cycle = March 23 Julian = March 16 Gregorian, -686. (See Worlds in Collision, page 234.)

17. Phaophi 6 Egyptian = sin mao of the Chinese cycle = March 18 Julian = March 11 Gregorian, -685. (Legge wrongly uses this -685 date, instead of -686.)

18. Venus was in superior conjunction with the Sun on Epiphi 22 Egyptian = December 9 Julian = December 2 Gregorian, -608, if we allow retrocalculation of orbits that far back in time. If the disappearance in the east was on about November 16 Julian, and if the heliacal rising of Sirius was on Mechir 29 Egyptian = July 19 Julian = July 12 Gregorian, -608, then Venus and Sirius would both have been visible in the pre-dawn sky for some 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, the disappearances of Venus would have moved on the average only about five and three-eighths 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 583.914 = 2919.57). The -608, -512, -416, and -320 have been selected only for purposes of illustration, in that they seem to feature disappearances of Venus about 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.)

19. From -523 to -520, January 1 Julian fell on Thoth 1 Egyptian.

20. -520 was a Julian leap year, with a February 29.

21. In -520, both January I Julian and December 31 Julian fell on Thoth I Egyptian.

22. From -520 to -517, December 31 Julian fell on Thoth 1 Egyptian.

23. Thoth I Egyptian = December 30 Julian, from -516 to -513.

24. Venus was in superior conjunction on Epiphi 15 Egyptian = November 8 Julian = November 2 Gregorian, -512. If the disappearance was on about October 17 Julian, then both Venus and Sirius would have been visible in the pre-dawn sky for about three months.

25. Venus was in superior conjunction on Epiphi 8 Egyptian = October 8 Julian = October 3 Gregorian, -416. If the disappearance was on about September 17 Julian, then both Venus and Sirius would have been visible in the pre-dawn sky for about two months.

26. Venus was in superior conjunction on Epiphi 3 Egyptian = September 9 Julian = September 4 Gregorian, -320. If the disappearance was on about August 18 Julian, then both Venus and Sirius would have been visible in the pre-dawn sky for about one month.

27. On Thoth I Egyptian = October 27 Julian, -260, the western elongation of Venus from the Sun would have been just over 46 1/2 degrees, and would have remained at least that high for about two and one-half weeks, with Venus as the Morning Star riding high in the pre-dawn eastern 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.

28. Venus was in superior conjunction on Payni 30 Egyptian = August 21 Julian = August 17 Gregorian, -256. If the disappearance was on about July 29 Julian, then there were only about ten days between the heliacal rising of Sirius on Pachons 27 Egyptian = July 19 Julian, -256, and the disappearance of Venus.

29. On Thoth I Egyptian = October 25 Julian, -252, the elongation of Venus would have been just over 46 1/2 degrees, and would have remained at least that high for about two and one-half weeks.

30. Venus was in superior conjunction on Payni 30 Egyptian = August 19 Julian = August 15 Gregorian, -248. If the disappearance was on about July 27 Julian, then there were only about eight days between the heliacal rising of Sirius on Pachons 29 Egyptian = July 19 Julian, -248, and the disappearance of Venus.

31. Thoth I Egyptian = October 24 Julian, from -248 to -245.

32. The accession of Ptolemy III Euergetes I to the throne of Egypt was on Dios 25 Macedonian = Choiak 8 Egyptian = January 29 Julian, -245. The Choiak 7 in Samuel and in Parker is an error (see KRONOS VI:1, page 64).

33. Year 2 of the reign began on Dystros 24 Macedonian, which was probably in May or June of -245. I have not been able to discover any adequate basis for Parker's flat equation of Dystros 24 Macedonian with Pachons 4 Egyptian = June 24 Julian, -245. Parker does refer to Samuel, who gives the same equation, but Samuel describes what he is doing as "hypothetical", and does not offer any proof for the equation. It depends mainly upon the intercalations, and the intercalations are not known.

34. On Thoth I Egyptian = October 23 Julian, -244, the elongation of Venus would have been just over 46 1/2 degrees, and would have remained at least that high for about two and one-half weeks.

35. Venus was in superior conjunction on Payni 30 Egyptian = August 17 Julian = August 13 Gregorian, -240. If the disappearance was on about July 24 Julian, then there were only about five days between the heliacal rising of Sirius on Payni I Egyptian = July 19 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 eight-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, and 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.)

36. Thoth I Egyptian = October 22 Julian, from -240 to -237.

37. Payni I Egyptian = July 19 Julian, from -240 to -237.

38. Year 9 of the reign of Ptolemy III Euergetes I began on Dystros 24 Macedonian, which was probably in the late spring or early summer of -238.

39. Sirius rose heliacally on Payni 1 Egyptian = July 19 Julian, -238.

40. July 19 Julian of -238 fell on about the sixth day of a lunar month. If that month was earlier than Dystros or was Dystros itself (neither of which can be absolutely excluded), then Dystros 24 Macedonian was definitely later than Payni 1 Egyptian = July 19 Julian, -238.

41. The Canopus Decree carries both the date of Tybi 17 Egyptian and the date of Apellaios 6 Macedonian. But these two dates do not seem to be equivalent. Tybi 17 Egyptian = March 7 Julian, -237, which would have fallen on about the first day of a lunar month, not the sixth day. On the other hand, the sixth day of a lunar month could only have fallen on about Choiak 23 Egyptian = February 11 Julian, -237, or on about Tybi 22 Egyptian = March 12 Julian, -237. Whichever of the reported dates we follow, the Canopus Decree seems to belong to the second half of Year 9 and to the first half of -237 (Julian).

42. Year 10 of the reign began on Dystros 24 Macedonian, which was probably in the spring or summer of -237.

43. Sirius rose heliacally on Payni I Egyptian = July 19 Julian, -237.

44. July 19 Julian of -237 fell on about the sixteenth day of a lunar month. If that lunar month was earlier than Dystros or was Dystros itself (neither of which can be absolutely excluded), then Dystros 24 Macedonian was definitely later than Payni I Egyptian = July 19 Julian, -237.

45. Depending upon the intercalations, Year 9 could have begun either before or after the heliacal rising of July 19 Julian, -238, and could have ended either before or after the heliacal rising of July 19 Julian, -237. Just in terms of probabilities, however, it does seem much more likely that Year 9 would have included the -238 rising but not the -237 rising. I have not been able to discover any adequate basis for Parker's flat statement that "calculation would show" that Dystros 24 Macedonian was "certainly before" Payni I Egyptian = July 19 Julian, -238; it depends upon the intercalations, and the intercalations are unknown. (Parker is referring to "calculation" here, not to the testimony of the Canopus Decree itself.) The "calculation" cannot be based on the two dates of the Canopus Decree in any case, since those two dates are mutually incompatible and are no longer accepted as a pair by anyone.

46. Thoth I Egyptian = October 22 Julian, -237, which would have been the sixth epagomenal day prescribed by the Canopic reform. Thoth I "Canopic" would have been Thoth 2 Egyptian = October 23 Julian, -237.

47. The Canopus Decree was issued in Year 9, but pertained to Year 10.

48. On Thoth I Egyptian = October 21 Julian, -236, the elongation of Venus would have been just over 46 1/2 degrees, and would have remained at least that high for about two and one-half weeks.

49. Venus was in superior conjunction on Payni 29 Egyptian = August 14 Julian = August 10 Gregorian, -232. If the disappearance was on July 21 Julian, as Schoch's tables indicate, then Venus could have still been seen one day after the heliacal rising of Sirius on July 19 Julian. (This was the last time in the eight-year cycle that Venus could have still been seen after the heliacal rising of Sirius.)

50. The Julian reform was introduced in Rome in -45, when 67 days were intercalated between November and December; the first Julian leap year was -44.

51. The accession of Augustus to the Egyptian throne took place on Thoth I Egyptian = August 31 Julian, -29. Those later writers who in retrospect used the Alexandrian calendar may have counted the first year of Augustus from Thoth I Alexandrian = August 30 Julian, -29.

52. Thoth I Egyptian = August 30 Julian, from -28 to -25.

53. Thoth I Egyptian = August 29 Julian, from -24 to -21.

54. Thoth I Alexandrian = Thoth I Egyptian, from -25 to -22.

55. The first quadrennium of the Alexandrian calendar began on Thoth I Egyptian = Thoth I Alexandrian = August 30 Julian, -25. This marked the beginning of the fifth year whether Egyptian or Alexandrian of Augustus on the Egyptian throne. (When we refer to the fifth year of Augustus, it does not matter whether we use the Egyptian year or the Alexandrian year, for the Egyptian year and the Alexandrian year were exactly the same for his fifth, sixth, and seventh years.)

56. The Alexandrian years overlapped the Julian years; 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.

57. The fifth epagomenal day of the Egyptian calendar fell on July 20 Julian (Calends XIII August) from +132 to +135.

58. Thoth I Egyptian = July 20 Julian, from +136 to +139.

59. Sirius rose heliacally on Thoth I Egyptian = July 20 Julian, from +136 to +139.

60. Thoth I Alexandrian = August 30 Julian in +139.

61. Thoth I Egyptian = June 25 Julian (Calends VII July), from +236 to +239.

62. Censorinus wrote in +238 and referred to +139.

63. Censorinus is correct in saying that Sirius rose heliacally on Thoth I 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 meant "XIII".)

64. Davis and others who deny this heliacal rising probably used Thoth I Alexandrian instead of Thoth I Egyptian (see Peoples of the Sea, page 231).

65. Censorinus thought that he was in the one hundredth year of the new cycle, but he should have said the one hundred third year, counting from Thoth I Egyptian = July 20 Julian, +136.

66. Censorinus knew that Thoth I Egyptian = June 25 Julian, +238, which implies that Thoth 1 Egyptian = July 20 Julian, +138. This in turn implies that the quadrennium was not from +139 to +142.

67. Even if we give Censorinus the benefit of any doubt, and say that he knew that the quadrennium was from +136 to +139, he is still wrong: Thoth I is a beginning, not an end. Instead of focusing on the last year of the initial quadrennium of the new cycle, he should have focused either on the first year of that quadrennium or else on the last year of the terminal quadrennium of the old cycle.

68. Censorinus relates the heliacal rising of Sirius to the Egyptian calendar, a relationship that he thought would repeat itself every 1460 years; he is not concerned with the Alexandrian calendar when he talks about +139.

69. Censorinus should have had his Sothic period extend 1456 years from -1320 to +136, in order to reflect the retrocalculated "facts", but he assumes that the Sirius year and the Julian year are equal.

70. The Julian and Gregorian calendars coincide exactly from March 1, +200, to February 28, +300. Before and after that century they are out of phase.

71. Theon knew that Thoth I Alexandrian first fell on Thoth I Egyptian in the fifth year of Augustus.

72. 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, and the period of 1460 years that he discusses is not a Sothic period.

73. The Theon annotator said that "from Menophres" to the end of the Era of Augustus was 1605 years. (This is our only source about "Menophres", and is the only known allusion to any "Era of Menophres".)

74. The Era of Augustus ended on the fifth epagomene Alexandrian = August 28 Julian, +284.

75. The Era of Diocletian began on Thoth I Alexandrian = August 29 Julian, +284.

76. The years employed by the Theon annotator in arriving at "1605 years" were Alexandrian years, not Egyptian years. Taking 1605 years from +284 puts "Menophres" in -1321, the same year that is found by taking 1460 years from +139.

77. It is possible that "Menophres" is the Hyksos king named Mennofirre or Merneferre Placing a Hyksos king in the late fourteenth century is permitted in the revised chronology, but not in the conventional chronology.

78. The Theon annotator places the heliacal rising of Sirius latitude unspecified on Epiphi 29 Alexandrian = July 23 Julian, +384. This seems to be an arithmetical error for Epiphi 30 Alexandrian = July 24 Julian, +384. But the details of the computation remain obscure, and have been variously interpreted. At one point, he in effect adds five days, without explaining why. Perhaps one of these days is for the shift from July 19 Julian to July 20 Julian, and perhaps the other four days are for a difference of latitude. But none of this is stated; the Theon annotator remains quite obscure about what he is doing.

79. Aside from this obscurity of detail, the remarks of the Theon annotator, of Theon, and of Censorinus are entirely consistent with one another.

80. Censorinus and the Theon annotator make the same error, of focusing on the last year of an initial quadrennium, rather than either on the last year of a terminal quadrennium or else on the first year of an initial quadrennium.

81. The error of the Theon annotator could have been based upon the error of Censorinus, or both errors could have been derived from a common source. It is possible, but unlikely, that such an error could have been repeated independently.

82. The Gregorian calendar was introduced in +1582.

83. May 29 Julian = June 10 Gregorian, +1895.

84. November 4 Julian = November 17 Gregorian, +1979.

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