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KRONOS Vol VI, No. 1

Weighing The Anchor


The popular fiction of a "Sothic dating system" that was supposedly used in Egypt as far back as the Middle Kingdom or even the Old Kingdom has been severely criticised by Velikovsky in his "Supplement" to Peoples of the Sea . Sothic theory is a speculative retrojection loosely based on the ideas of various classical - and relatively late - writers, including Geminus, Censorinus, and Theon.

My brief remarks here will be focused on some conceptual and computational aspects of Parker's recent defence of Sothic dating, and on one of those late classical sources, namely, Censorinus. I will leave it to others to comment on Parker's use of Middle Kingdom documents.

Parker says:

"Now from Censorinus and coins of Antonius Pius it is safe to conclude that in the years AD 139 to 142 Sirius rose heliacally on I 'ht I Egyptian, corresponding to July 20 for AD 139 and July 19 for AD 140 to 142. From this anchor in time. . . ",

and then he goes on to describe the efforts of Oppolzer, Meyer, and Ingham to extrapolate backwards from "this anchor in time".

Such extrapolations must be conducted with great care, precision, and accuracy. Even then, the results of different investigators may vary considerably. If the project is to have any chance at all, great rigour is required, both conceptually and computationally. In these respects, Parker's remarks leave much to be desired.

Even Parker's arithmetic is less than auspicious. He puts the length of the tropical year at "365.24220 days (365 days, 5 hours, 48 minutes, 45.5 seconds)". But these two quantities are not well matched. 365.24220 days converts to exactly 365 days, 5 hours, 48 minutes, 46.08 seconds; and 365 days, 5 hours, 48 minutes, 45.5 seconds converts to a little over 365.242193 days. These discrepancies are small, but figures that purport to be accurate to the nearest one hundred thousandth of a day should not be put forward unless they are.

Parker gives a mistaken definition of arcus visionis : he puts the Sun on the horizon, instead of the star. Yet the whole point of the concept of arcus visionis is that the Sun must be a certain number of degrees below the horizon, in order for a star on the horizon to be visible.

Parker attributes the variation in the length of the "Sothic year" to the motion of Sirius. This is usually understood as a motion in declination, as well as a change in the orientation of Sirius with respect to the equinoxes and solstices, which are the four cardinal points on the ecliptic. Both of these variations are reflections of Earth's own precessional motion. In his explanation, however, Parker makes the puzzling remark that "Sirius is not a fixed star but one with a motion of its own". If this is taken as a "proper motion", then any "fixed star" might have a motion of its own, whether detectable or not. Sirius is indeed rather close to us about 8.7 light years and does have a relatively large proper motion for a "fixed star", over a second of arc per year. But that proper motion was not even measured until well into the age of the telescope, and is for our purposes negligible. In astronomical parlance, Sirius is indeed a "fixed star", as opposed to, say, a planet. Parker does not seem to recognise just why it is that the alleged "Sothic cycle" would vary in length. It must be stressed that this variation would not be traceable to the proper motion of Sirius, which is a very minor factor in all of this, but to Earth's precessional motion, which produces both a change in the declination of Sirius and a change in the orientation of Sirius with respect to the equinoxes and solstices. (Another of Parker's remarks suggests that by a "fixed star" he may mean "one whose position did not vary for long periods of time and so could be measured by the sidereal year". Aside from the misuse of the expression "fixed star", there are no stars at all that have regular appearances and disappearances that "could be measured by the sidereal year", and only a star lying on the pole of the ecliptic would have a fairly stable declination though even that would be susceptible to the gradual variations in obliquity.)

Some of Parker's conclusions are not as "safe" as he seems to imagine. Thoth 1 Egyptian (or I 'ht I Egyptian) did indeed fall on July 20 Julian in +139 and on July 19 Julian in +140, +141, and +142, as Parker says. But the (calculated) heliacal rising of Sirius seems to have fallen on July 20 Julian both for many years before and also for many years after +139. Thoth I Egyptian fell on July 20 Julian in +136,+137,+138, and +139, so that +139 would have been the last, not the first, of the four years during which Thoth I Egyptian marked the heliacal rising of Sirius. Thus the heliacal rising of Sirius did not fall on "July 19 for AD 140 to 142". Censorinus, writing in the latter part of +238, thought that he was in the one hundredth year of the new Sothic cycle, but he should have said the one hundred third year, counting from Thoth I Egyptian = July 20 Julian, +136.

(Of course, even if we agree with Censorinus that the heliacal rising of Sirius fell on Thoth I Egyptian in +139 as indeed it did that in itself does not mean that Censorinus or anyone else would be justified in concluding that that same situation had occurred, and had been noted, more than fourteen centuries earlier.)

Parker's "anchor in time" seems not to have been very securely placed. The "Sothic theories" to which that anchor is fastened seem as a result to have been left somewhat adrift.

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