HORUS VOL I. Issue 1
Ancient Astronomical Values Revealed
in The Book of the Secrets of Enoch
by Alban Wall
The modern editor of the English translation of The Book of the Secrets of Enoch provided the following information concerning that ancient document:
"This new fragment of early literature came to light through certain manuscripts which were recently found in Russia and Servia and so far as is known has been preserved only in Slavonic. Little is
known of its origin except that in its present form it was written somewhere about the beginning of the Christian era. Its final editor was a Greek and the place of its composition, Egypt."
An introduction at the head of Chapter I supplies a brief description of some of the book's contents:
"An account of the mechanism of the world showing the machinery of the Sun and Moon in operation. Astronomy and an interesting ancient calendar."
A thoughtful perusal of the entire book leads one to the inescapable conclusion that the author of "Secrets" was not himself an astronomer but merely a religious writer, and that, therefore, the astronomical data
presented by him was drawn second-hand from reference sources available in that era. This fact will prove useful in helping to date the time of the book's composition.
The astronomical information with which this paper deals is found in Chapters XV and XVI of "Secrets" and I quote the relevant passages:
Chapter XV. verse 3.
"And the gates which it enters, these are the great gates of the computation of the hours of the year: for this reason the Sun is a great creation, whose circuit lasts twenty-eight years and begins again from
Chapter XVI. verses 3. 4. & 8
'And it [the Moon] goes through the western gates in the order and number of the eastern, and accomplishes the three hundred and sixty-five and a quarter days of the solar year....'
"Thus, too, the great circle contains five hundred and thirty-two years.
"It [the Moon] has a sevenfold course in nineteen years."
I have carefully analyzed these statements for their individual and interrelated mathematical and astronomical implications and have culled the following information from them:
- The length of the solar year was calculated at exactly 365.25 days.
- Twenty eight years was considered to be an exact Sun cycle.
- Nineteen years was considered to constitute an exact Sun-Moon cycle rather than just a close one.
- Five hundred and thirty-two years was considered to constitute an additional exact Sun-Moon cycle.
Point number 2 (Chapter XV, verse 3), is a statement of the fact that in corresponding years of recurrent 28-year cycles, the days of the week will recur on the same days of the month, provided that the length
of the solar year is in actuality exactly 365.25 days.
365.25 + 7 = 52.1785714 weeks in a solar year
52.1785714 wks. X 28 yrs. = 1461 weeks.
We can see from this that in exactly 28 years the fraction of a week left over in each year will accumulate to a full week with no fractions left over. However, by using the correct value for the solar year of
365.242199 days we have
365.242199 + 7 = 52.177457 weeks in a solar year
52.177457 wks X 28 yrs. =1460.9668796 wks.
or 1460 wks., 6d 18h 46m
It can be seen that the 28-year cycle is not the exact cycle that Enoch believed it to be, but falls out of synchronization after 112 years, a fly in the ointment of his celestial chronometry.
Point number 3 (Chapter XVI, verse 8) is, of course, a reference to the Metonic 19-year cycle, with its 7 intercalations, wherein the Moon's phases repeat on the same days of the year every 19 years within a
little over 2 hours. As with the 28-year period, Enoch erroneously assumed this to be an exact cycle wherein a whole number of lunar months are equal to a whole number of solar years with no fractional
leftovers. That he did in fact assume such exactitude for the 19-year span will be proved clearly.
From the "Secrets of Enoch" I have thus extracted 3 cycles of the Sun and Moon that were considered in the document to be exact:
- 19-year (Moon's phases repeat on same days of year.)
- 28-year (days of week repeat on same days of month.)
- 532-year cycle.
It is obvious that if 19 years constituted a precise cycle, then so would all years that are multiples of that number 39, 57, etc. The same would, of course, be true of the 28-year cycle- 56, 84, and so on. We can
then ask, what is significant about a 532-year span that it should have been considered to constitute a "great" cycle? (I suspect that the astute reader is already ahead of me on this.)
Mathematically, 532 is the product of 19 times 28. Astronomically, the 532-year cycle combines the phenomena of the two lesser cycles so that, in corresponding years of successive 532-year cycles, the moon's
phases would repeat, to within the exact second,
- on the same day of the week
- on the same day of the month, and
- on the same day of the year.
What a neat chronological package. What amazing astronomical order. What fodder for practitioners of numerology. Whoever the astronomer, I'm sure he believed he had
stumbled upon some great mystical secret of the universe.
Unfortunately, it is the very slight difference in the true length of the solar year and that assumed by Enoch that brings this mathematical house of cards tumbling down.
Correct length of year
Enoch's length of year
| = 365.242199 days |
= 365.250000 days
= 0.007801 days
= 0.187224 hrs.
= 11. 233440 min.
This difference amounts to less than 1/500th of I percent, but in 532 years it accumulates to over 4 full days. Only an assumption on the part of Enoch that the 19 and 28-year cycles were exact would have led
him, by extrapolation, to the belief that the 532-year cycle was also exact.
Not stated in the book but readily deducible from the few facts given, is the value of the lunar month and the value of the sidereal month assumed in the astronomical computations. We can accept with certainty
that the ancients knew how many lunar months there are in 19 solar years, even allowing for slight errors in the calculations. To obtain the value of the lunar month as calculated by them, we merely have to
divide the number of months, which happens to be 235, into the number of days in 19 years. This works out as follows:
19 X 365.25 = 6,939.75 days.
6939.75 + 235 = 29-530851 days in a lunar month
This value of 29.530851 days for the length of the lunar month deduced from the astronomical data
in the "Secrets of Enoch" enables us to date the document with some degree of accuracy. In KRONOS [vol.1,
Livio Stecchini cites certain Greek estimates of the length of the lunar month as calculated by them during specific eras:
|Meton, ca. 430 B.C.
Callippus, ca. 330 B.C.
Hipparchus, ca. 150 B.C.
[difference -0.000007 day or 0.6048 sec.]
As all the listed astronomers were Greek, and there is good indication that the author of "Secrets" was a
Greek living in Egypt, the probability is distinct that the astronomical data in that book was drawn from
sources current sometime after Callippus but preceding Hipparchus, that is to say, somewhere between 330
and 150 B.C., since the estimate of the lunar month given by Callippus is identical to that which I
have deduced from the "Secrets of Enoch".
By the same process of quantitative deduction, I have been able to determine the value calculated by
the ancient astronomers of that period for the sidereal month, which relates not to the moon's phases, but to
the return of that body to the same position against the starry back-ground. In 532 years this will occur
very nearly 7,112 times, which is to say that in 532 years there are almost exactly 7,112 sidereal months.
In 532 years of 365.25 days there is a total of exactly 194,313 days. Dividing this by 7,112 sidereal months we get:
194313 + 7112 - 27-321851 days in the sidereal month.
When we compare the correct values for the lengths of the lunar and sidereal months with those deducible from the "Secrets of Enoch", we find that the differences are astonishingly small:
||27.32185 10 d|
||0.000 1897 d|
|or 22.723 sec.
||or 16.39008 sec.|
||less than 1/1000th|
The remarkable precision of the ancient astronomical calculations that I have deduced from The Book of the Secrets of Enoch may be hard for some readers to accept. Yet it is only one example of
observational excellence and numerical precision in pre-Christian centuries. In the paper by Livio Stecchini mentioned above, it is indicated that Hipparchus, around 150 B.C., had correctly calculated the length
of the mean lunar month to within less that I second of absolute accuracy. It is not by chance that the ancients came so close to values obtained by modern techniques. It seems clear that whatever religious or
mystical significance a given cycle may have had, the precise measurement of the cycle and its integration with other cycles was essential in the ancient astronomer's art.
The "GREAT CIRCLE" of ENOCH