#
The Sothic Cycle, Corrected

**by Brendan Bombaci**

**Copyright 2015**

**All Rights Reserved**

**ISBN 978-1-329-51731-8**

#### Abstract

**“**Sothic Cycle” is the name given to the astrophysical discrepancy between the 365-day ancient Egyptian solar year and the heliacal rising of Sirius. An estimated duration of the cycle (1,461 years) has been used to more accurately date events in ancient Egyptian historical records, but fails to account for (1) the 400-year leap

*cycles*which subtract

*extra leap days that accumulate as an artifact of leap years being useful only for a solar year of 365.25 days rather than the actual 365.2422 days, as well as (2) the precession of equinoxes, a cycle so-called because it desynchronizes any given constellation on the ecliptic from the spring equinox sunrise by one degree every 72 years (coming full circle in nearly 26,000 years). In this brief article I describe these complications and the mathematics that must be used to correct for the multi-decade error in the Sothic Cycle caused thereby.*

**Keywords:**Sothic Cycle, Sirius, calendar, Egypt, Precession, relative dating, calibration, intercalation, leap year

#### Introduction

The Sothic Cycle is a name given to the no longer observable
but once confusing desynchronization and resetting of the heliacal rising of the
star Sirius (“Sothis” in Greek) with sunrise on the first day of the ancient Egyptian
solar year. This was caused by a lack of leap year intercalation. It has been rightly
asserted by historians and archaeologists that this cycle caused the numerous
discrepancies seen in ancient Egyptian history regarding the start of the solar
year, but it is causal only in part. It has been and still is an incomplete application
of the cycle to simply multiply the 4 years it takes to acquire a Leap Year day
by 365.25 days in order to derive its duration. As such, the cycle has been imprecisely
determined to be 1,461 years. There are
two mechanisms that are unaccounted for, one unavoidably astrophysical and the
other merely mathematical.

#### Background

The current school
of thought on the Sothic Cycle originated in historian Eduard Meyer’s original
1904 realization about it when researching Egyptian historical records. His
idea was soon professionally perpetuated, starting with its uncritically
promotional inclusion in an annex of the influential Egyptian history textbook
from 1924, “A History of Ancient Egypt, 2

^{nd}Ed.,” written by the Rockefeller-funded professor J.H. Breasted of the University of Chicago (Mackey 2003). This annex was titled “Chronological Table of Kings,” and in it Breasted boldly altered known ancient Egyptian historical dates via Meyer’s Sothic Cycle calculation, calling them “*astronomically fixed*.” His Sothic Cycle calibration method became granted, but criticism of it existed prior to my own.
Perhaps the
earliest criticism, published by Luby (1941), was of the incorrect application
of leap year mechanics in this cycle. As such, he calculated the Sothic Cycle
duration by dividing 365.2422 days per year by 0.2422 (to obviate both leap
years and leap cycles), and was satisfied with the resulting solution of 1,508
years. Rose (1994) later called for a wider acceptance of the idea that
Egyptians used a 3-year “triennium” from time to time when the 4-year
quadrennium (after which one degree of sky would precess) desynchronized from
the actual rising of Sirius. She offers an elaborate but oddly estimated
accounting for the discrepancy between the Egyptian 365-day and actual solar
year lengths, resulting in a declaration that the Sothic Cycle is actually 1452
years in duration. More recently, it has been suggested that the value used for
the current cycle “is not totally exact: the Sothic cycle is not fixed because
of the proper motion of the star and the length of [the] Sothic year evolves
over time” (Quiles et al. 2013:424, emphasis added). The authors provide no
explanation for this statement, however.

#### Methods

*The Sothic Cycle Mechanism*

The first of the two missing factors in the current value of
the Sothic Cycle is the

*leap cycle*(Seidelmann 2005) that Luby corrected for. With his simple math in mind, we don’t need to retroactively remove 3 leap years per every 400 years of the current value (a process that can easily lead to error). In as much, to reveal the actual duration of the cycle, we can begin by resetting it to a value of 1,508 years. Starting there, we must account for the much more slowly slipped degrees of celestial/solar alignment, caused by the Precession of Equinoxes or “Platonic Great Year” cycle. That cycle, in total, was estimated by the Hebrews to resolve in 25,920 years (Hebra 2003) when it realigns the rise of the sun at the spring equinox with a particular sub-degree of the ecliptic. This number was either (1) approximated to the actual precession duration to be well-rounded for the Babylonian sexagesimal or “base 60” divisional system that our modern timekeeping and navigation systems are based on, or (2) actually quite representative of the precessional duration as it existed then, when the Earth’s axial tilt (the cause for precession) was at a different degree of obliquity. In as much that 1,508 years divided by the 72 years in one degree of said precession is an extra 20.244 shifted degrees during that time, we must deduce that the cycle actually completes sooner than 1,508 years: 20.244 times the 4.058 years in one degree of properly intercalated Sothic Cycle shift equals 82.15 years. Subtracting this from 1,508 gives a corrected ancient Sothic Cycle duration of 1425.85 years. Recently, however, we have come to recognize with advanced technology that precession takes 25,772 years to complete, so each degree takes 71.6 years rather than 72, meaning that 21.06 extra degrees or 85.467 years would have to be subtracted from the 1,508 year basis, giving a Sothic Cycle duration of 1422.533 years. Until it is proven that axial tilt changes affect the duration of precession, it may be best to use this latter calculation. For purposes of dating events within dynasties, the variance is somewhat negligible.*Additional Factors*

There has been another
critique of the Sothic Cycle which calls into question the original historical
dates offered by Censorinus (which the cycle became cross-referenced with),
pointing out a lack of historical specificity in astronomical viewing
locations, as well as differences in calendrical system nuances between
geographically and temporally distanced population groups whose accounts we
reference, and even differences in star-shrouding atmospheric haze over the millennia
and periodically during extreme weather regimes (O’Mara 2003). It appears that there
is a multitude of factors we must consider, outside of celestial mechanics, to
derive a veritable astronomical referencing system. An example of some very
recent and impressively thorough research, that can easily hit that mark with a
future revision including the Sothic Cycle correction, is the Bayesian modeled
period-matching of solar, lunar, and Sothic calendars, cross-referenced with
radiocarbon dating, performed by Quiles et al. (2013) for the purposes of
providing an absolute chronology for the 18

^{th}Dynasty.#### Conclusions

Much research
continues to use or attempt usage of the currently valued Sothic cycle
referencing system as either a result of it being presumed totally verified by the
peer review process, and/or a result of there being no better tool for the task.
By the data I provide, it becomes obvious that this following leads (1) researchers
to depend upon and publish work based on officially granted but actually confounded
data, and (2) therefore a vast readership of journals, textbooks, and magazines
to a misguided trust in the results. It is now apparent that we must not only
realign the historical dates that we do surely know of with this proposed Sothic
Cycle correction, but also reevaluate a large number of dates by way of deeper
textual research and correlation of it with absolute dating methods used on germane
artifacts and features. There is hope yet for justifiably method-skeptical
Egyptologists (and for all who aren’t but should be), and for those
archaeologists and historians working with other cultures who derive their relative
dating from Egyptological work.

### References

Hebra, Alex,

*Measure for Measure: The Story of Imperial, Metric, and Other Units*, The John Hopkins University Press (2003), 53.
Mackey, Damien
F., ‘Fall of the Sothic Theory: Egyptian Chronology Revisited,’

*Journal of Creation*17, issue 3 (2003), 70-73.
O’Mara, Patrick, ‘Censorinus,
The Sothic Cycle, and Calendar Year One in Ancient Egypt: The Epistemological
Problem,’

*JNES*62, no. 1 (2003), 17-26.
Quiles, A., E.
Aubourg, B. Berthier, E. Delque-Količ, G. Pierrat-Bennefois, M.W. Dee, G.
Andreu-Lanoë, C. Bronk Ramsey, and C. Moreau, ‘Bayesian Modeling of an Absolute
Chronology for Egypt’s 18

^{th}Dynasty by Astrophysical and Radiocarbon Methods,’*JoAS*40 (2003), 423-432.
Rose, Lynn E., ‘The
Astronomical Evidence for Dating the End of the Middle Kingdom of Ancient Egypt
to the Early Second Milennium: A Reassessment,’

*JNES*53, no. 4 (1994), 237-261.
Seidelmann, P.
Kenneth, ed.,

*Explanatory Supplement to the Astronomical Almanac*, University Science Books (U.S. Naval Observatory: Washington, D.C., 2005), 580-581.