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KRONOS Vol XI, No. 10

AN EVALUATION OF THE PRACTICAL OPERATION OF THE STONEHENGE CALENDAR

BENJAMIN A. BOSHER

I found Alban Wall's paper, "A Calendric View of Stonehenge" (KRONOS VIII:2, Winter 1983, pp. 35-46), to be a well thought-out solution that the functional use of Stonehenge was that of an accurate solar and lunar calendar. His explanation of the use of the horseshoe of 19 Bluestones to keep track of the 19-year cycle adds significantly to the search for the full solution to the riddle of Stonehenge, as does his explanation of the five Trilithons to divide the lunar month into six equal parts and thereby track the Moon's phases.

However, in presenting his theory of the calendric capability of this ancient stone edifice, he, quite naturally, emphasizes the sophisticated line-ups of the three marker stones at each quarter period of the 19-year cycle, while glossing over the meticulous intercalation of 7 lunations and extra days necessary to keep the Stonehenge calendar chronologically aligned with the orbiting relationships of the Sun and the Moon throughout the entire 19-year cycle. This detailed operation of the calendar attracted my attention, and I offer the following as a workable method of keeping the calendar on track.

Let us study first the Aubrey Sun Circle, which, as Wall has shown, tracks the solar year by counting off 28-day solar "months", 13 times for 1 year.

On page 37 of the referenced paper, Wall says: "The Sun marker will move around the circle exactly 247 times during the 19-year cycle, ticking off 6,940 days in the process. These twenty-eight day divisions - 13 per year - can be considered as solar months which will interrelate with the lunar months." The first sentence quoted is not exactly true, since 28 days x 247 = 6916 days, not 6940 days. Thus 6940 - 6916 or 24 days must be added during the 19-year cycle to keep the calendar on target with the actual completion time of the Earth's orbit around the Sun. This amounts to 24/19 or 1.263 days per year.

(More precisely: 6939.602 - 6916 = 23.602
23.602/19 = 1.2422 days per year)

This addition of 1.2422 days can best be introduced by delaying the movement of the Sun marker stone from hole No. 56 to hole No. 2 by one day at the end of the first, second, and third years and by delaying it two days on the fourth year. This correction would be repeated on the following three 4-year periods. For the last three years of the cycle, the delay would be one day at the end of the 17th and 18th years and two days at the end of the 19th year. With these corrections incorporated, at the end of the 19-year cycle the solar "month" calendar would be slow by .398 day.

4 (4 x 1.25) + (2 x 1) + (1 x 2) = 24 days
24 - 23.602 = .398 day

Using the corrections as described, the solar "month" calendar is never slow by more than .969 day, and never fast by more than .398 day. (See Tables I and II.)

With the solar "month" calendar slow by .398 day for each 19-year cycle, this error would accumulate to 1.99 days after the completion of 5 19-year cycles. An additional correction to eliminate this error almost entirely can be incorporated by advancing the Sun marker stone to hole No. 2 a day early by skipping hole No. 56 at the end of the second and the fifth 19-year cycles. Since the Sun marker stone is already delayed 2 days at the end of each 19-year cycle, this additional correction means that, at the end of the 2nd and 5th 19-year cycles, the marker stone is delayed only one day in moving from hole No. 56 to hole No. 2.

Continuing on with this correction through 40 19-year cycles, a day would be dropped at the end of 19-year cycles 7, 10, 12, 15, 17, 20, 22, 25, 27, 30, 32, 35, 37, and 40. The calendar at the end of 5 19-year cycles would then be fast by .010 day, and at the end of 40 19-year cycles fast by .080 day.

So much for the corrections needed to keep the solar "month" calendar chronologically aligned with the solar year. Let us now take a look at the Sarsen Moon Circle which Wall has shown is capable of tracking the lunar month, which has a lunation of 29.5306 days, a lunation being defined as the time encompassed in one full cycle of lunar phases.

On pages 35-36 of his paper Wall says: "A year of 12 lunar months falls nearly 11 days short of the solar year and, since the latter determines the return of the seasons, there was need to adjust the calendar to the solar year. This was accomplished by the intercalation of an additional month 7 times within the 19-year period in such a manner that the full cycle consisted of 125 thirty-day months and 110 twenty-nine day months.

125 x 30 = 3750 days
110 x 29 = 3190 days       
6940.000 days
19-year cycle = 6939.602 days
Difference = .398 days or 9.55 hours."

To add the necessary 7 lunar months in the most advantageous manner, they should be spaced reasonably equal throughout the 19-year cycle to try to maintain an average approaching 12.37 lunar months per year. All of the additive months would be 30-day months; 125 30-day months are required and only 110 29-day months. If the 12 full lunar months for each year are divided so that there are 6 29-day months and 6 30-day months, then, to create the correct number of each type month, four of the years in the 19-year cycle would have to have a 29-day month converted to a 30-day month, so that those four years chosen would have 7 30-day months and 5 29-day months. This can be seen as shown below:

30-day months 6 x 19 = 114 + 7 = 121 + 4 = 125
29-day months 6 x 19 = 114 - 4 = 110

Now, how can these corrections to the calendar be accomplished in a logical and easily remembered manner? My suggestion would be the following:

The seven additional lunar months can be inserted individually beginning with year 2 in alternate 3 and 2-year intervals at the end of the 2nd, 5th, 7th, 10th, 12th, 15th, and 17th years. The four 29-day months that must be changed to 30-day months will be the last lunar month for the years 3, 8, 13, and 18. If we start each year with a 30-day month and then a 29-day month, and continue to alternate for the full 12 lunar months, we end the year with a 29-day month. It is this month, the last lunar month at the end of years 3, 8, 13, and 18, that is changed from a 29-day month to a 30-day month by adding a day. The lunar marker stone skips the last arch (No. 30) on 29-day months. (See Tables I and II.)

As shown earlier, 125 30-day lunations and 110 29-day lunations take exactly 6940 days, which is .309 day more than the accepted observed time for 235 lunations which is 6939.691 days. In order to keep the Sarsen Moon calendar in phase with the observed termination of 235 lunations, the lunar marker stone would have to be advanced 1 day at the end of every 3rd 19-year cycle.

.309 x 3 = .927 day

Since the last lunation of the 19-year cycle is a 29-day month, this is accomplished by having the marker stone skip the last arch, arch No. 29, and move directly to arch No. 1. The error of this correction gradually builds up, so that at the end of every 40th 19-year cycle the Sarsen lunar calendar would have gained almost a full day.

40 cycles
.073 day x   = .973 day
3 cycles

This one day can be added at the end of the 40th 19-year cycle by changing the last month of that cycle from a 29-day month to a 30-day month and thus having the marker stone stop for a day at arch No. 30. The remaining error is only .027 day slow every 40th 19-year cycle. (See Table III.)

Reviewing the corrections which I have shown to be necessary in order to make the Aubrey Sun Circle an accurate calendar of the year, and the Sarsen Moon Circle an accurate calendar of the lunar month, the question must be asked: "Are these correction systems accurate, and are they practical by standards of logic, simplicity, and ease of remembrance? "

The corrections have been shown to be very accurate as I detailed each correction. They are certainly logical if they produce an accurate calendar, and I believe they are about as simple as they could possibly be and still produce the desired accuracy. Whether they are easily remembered is a more nebulous question, but I have tried by simplicity and repetition to make them reasonably easy to recall.

The correction for the solar year is made at the end of each of the 19 years in the cycle and, except for the final 3-year period, is similar to our method today of introducing the leap year. The movement of the Sun marker stone is delayed one day in moving from Aubrey hole No. 56 to Aubrey hole No. 2, except at the end of every 4th year and at the end of the 19th year of the cycle, at which time it is delayed two days.

The correction for the Sarsen lunar year calendar has to be made in two ways. A lunar month of 30 days is added at the end of years 2, 5, 7, 10, 12, 15, and 17. Note that the interval separating adjacent years of those chosen for intercalation are 3 years and 2 years in an alternating sequence, and that the interval between every other intercalation year is 5 years.

The second correction required for the lunar year calendar is changing 4 lunar months from 29-day months to 30-day months. For consistency, I have also placed this correction at the end of the year. Starting with year 3, the year following year 2 where the previous correction of an additional seven lunar months began, and employing 5-year intervals, a day is added to the final month of years 3, 8, 13, and 18. I have chosen to start with year 3 so that this correction would never occur on the same year in which a lunar month is added, as that might prove confusing.

As one can see the easy-recall factor is not great, but it is the best I could work out.

Below, I have created three tables recording the corrections I have proposed. Together, these three tables show all of the corrections required in operating the Stonehenge Sarsen Moon Circle Calendar and the Stonehenge Aubrey Sun Circle Calendar to keep them accurately in tune with the actual periods of the Moon and the Sun, respectively, for at least a thousand years, barring catastrophic disturbances.

TABLE I
INTRA-YEAR CALENDAR CORRECTIONS FOR STONEHENGE CALENDAR

Sarsen Moon circle


Aubrey Sun Circle

Lunar
Month

Sarsen Circle
Corrections
(days)

Length of
Lunar Calendar Month
(days)


Solar
Month

Sarsen Circle
Corrections
(days)

Length of
Lunar Calendar Month
(days)

1


30


1


28

2

-1

29 *


2


28

3


30


3


28

4

-1

29 *


4


28

5


30


5


28

6

-1

29 *


6


28

7


30


7


28

8

-1

29 *


8


28

9


30


9


28

10

-1

29 *


10


28

11


30


11


28

12

-1

29 *


12


28



354


13


28







364**

*The establishment of alternating 30-day and 29-day months is a correction to make the average length of the lunar month 29.5 days rather than 30 days as laid out in the Sarsen Lunar Circle, so as to match closely the period of the Moon's orbit, which is now accepted as 29.5306 days. On 29-day months the Sarsen Lunar marker stone skips arch No. 30, moving directly from arch No. 29 to arch No. 1.

** The first correction for the Aubrey Sun Calendar is at the end of the first year (See Table II).

TABLE II
YEARLY CALENDAR CORRECTIONS DURING 19-YEAR CYCLE FOR STONEHENGE CALENDAR

Sarsen Moon circle


19-Year Cycle

364-DAY YEAR


Aubrey Sun Circle

No. of
30-Day
Lunar Month

No. of
29-Day
Lunar Months

Sarsen Circle
Corrections
(days)



Aubrey Circle
Corrections
(days)

Solar Year
Shown by
Calendar
(Days)

6

6



1


+1

365

7

6

+30


2 @


+1

365

7

5

+1


3 #


+1

365

6

6



4


+2

366

7

6

+30


5 @


+1

365

6

6



6


+1

365

7

6

+30


7 @


+1

365

7

5

+1


8 #


+2

366

6

6



9


+1

365

7

6

+30


10 @


+1

365

6

6



11


+1

365

7

6

+30


12 @


+2

366

7

5

+1


13 #


+1

365

6

6



14


+1

365

7

6

+30


15 @


+1

365

6

6



16


+2

366

7

6

+30


17 @


+1

365

7

5

+1


18 #


+1

365

6

6



19


+2

366

125
x30
3750
3190
6940

110
x29
3190






6940

@ Add a 30-day month at the end of the year indicated.
# Add 1 day at the end of the final month of the year indicated.
+ Add to calendar by delaying the movement of the marker stone, except in the case of the addition of the 30-day month when the Lunar marker stone would continue to move to count the 30 days of month added.
- Subtract from calendar one or more stations, thus hastening the movement of the marker stone.

TABLE III
19-YEAR CYCLE CORRECTIONS FOR STONEHENGE CALDENAR

Sarsen
Lunar Calendar
(Days)

No. of
19-Year Cycles

Aubrey
Solar Calendar



-1

1
2
3
4
5


-1


-1

-1


-1

6
7
8
9
10


-1


-1


-1


-1

11
12
13
14
15


-1


-1



-1

16
17
18
19
20


-1


-1

-1


-1

21
22
23
24
25


-1


-1


-1


-1

26
27
28
29
30


-1


-1



-1

31
32
33
34
35


-1


-1

-1

-1
+1

36
37
38
39
40


-1


-1

Note: All corrections are applied at the end of the 19-year cycle.

Now let us check to see if these corrections, as applied, make the Stonehenge calendar conform to the four -cycle points which, as Wall so clearly emphasized, are the only points during the entire 19-year cycle at which the Sun and Moon marker stones come into conjunction, and this consecutively, at each of the four -cycle points of the Aubrey Sun Circle and the Sarsen Moon Circle. Also, with the exception of the start position of the 19-year cycle, the Bluestone Year Horseshoe is included in these four conjunctions.

19-Year Year Aubrey Circle
(Days)
Sarsen
Moon Circle
(Days)
Bluestone
Year Horseshoe
(Years)
First Quarter 1
2
3
4
x 5
364           + 1 = 365
364 + 1 = 365
364 + 1 = 365
364 + 2 = 366
364 x = 273
1734
354 = 354
354 = 384
354 + 30 = 355
354 + 1 = 354
(354 +30) = 288
1735

1
1
1
1
 1 
5

Second Quarter x 5
6
7
8
9
x 10
(364 x ) + 1 = 92
364 + 1 = 365
364 + 1 = 365
364 + 2 = 366
364 + 1 = 365
364 x = 182
1734
(354+30) = 96
354 = 354
354 + 30 = 384
354 + 1 = 355
354 = 354
(354 +30) = 192
1735

1
1
1
1
 1 
5

Third Quarter 10
11
12
13
14
x 15
(364 x ) + 1 = 183
364 + 1 = 365
364 + 2 = 366
364 + 1 = 365
364 + 1 = 365
364 x = 91
1734
(354+30) = 96
354 = 354
354 + 30 = 384
354 + 1 = 355
354 = 354
(354 +30) = 192
1735

1
1
1
1
 1 
5

Fourth Quarter x 15
16
17
18
19
(364 x ) + 1 = 274
364 + 2 = 366
364 + 1 = 365
364 + 1 = 365
364 + 2 = 366
1734
(354+30) = 288
354 = 354
354 + 30 = 384
354 + 1 = 355
354 = 354
1735

1
1
1
1
 1 
5

19-Year Totals 6940 6940

10

Because the correction days are added to the end of the year, the first quarter of the 19-year cycle of the Aubrey Sun Circle tallies 1734 at 4 years, rather than 1735 days. Similarly, the fourth quarter tallies 1736 days, but the total number of days counted by the Aubrey year Circle correctly totals 6940 days. In the same way, the Bluestone Year Circle indicates the year for the whole 365-day period and can not be expected to count quarters of a year.

One essential component of the Stonehenge calendar appears to be missing, and that is a means of counting off the 13 months of the solar year. This might possibly have been accomplished by positioning at the exact center of the Stonehenge complex a large flat stone, similar to a millstone of Colonial times, having 13 stations for a marker stone to designate the 13 months sequentially through the year. Such a large stone would serve as an observational platform and also preserve the exact center of the complex. A possible design for such a stone is shown in Drawing No. 1. Such a center stone might have been an attractive target for early vandals.

[*!* Image] Drawing No. 1 Solar Month Center Stones. Note: a) Stone is orientated so that arrow points toward the Heel Stone. b) Months are counted counter-clockwise. See text.

Note that in the design of this "Solar Month Center Stone", I have chosen to count the solar months in a counter-clockwise manner. The reason for this is that such a sequential rotation of its marker stone establishes positions at the quarter points of the 19-year cycle which align with the conjunction positions of the Aubrey Sun Circle marker stone and the Sarsen Moon Circle marker stone, thereby enhancing the uniqueness of the four quarter points in the operation of the Stonehenge calendar. This is a most important factor since it proves the amazing extent of the astronomical knowledge of these ancient monument builders.

The position of the marker stone on the Solar Month Center Stone is indicated by the following calculation.

19- Year Cycle


0-Cycle

-Cycle

1/2-Cycle

-Cycle

0 mo.


61.75 mos.


123.50 mos.
185.25 mos.

0 mo. (4 yrs.) 52 (9 yrs.) 117.00 (14 yrs.) 182


-      -      -
0 yrs. 0 mo. 4 yrs. 9.75 mos. 9 yrs. 6.50 mos. 14 yrs. 3.25 mos.

In summary, this evaluation has been conducted in much detail, and in so doing I believe the following has been accomplished:

1) Evolved a system of precise corrections capable of maintaining accurate operation of Stonehenge as a calendar, measuring accurately Sun time in days, months, and years, Moon cycles and Moon phases, and the 19-year cycle, at the end of which the Sun and Moon regain the same relationship that existed at the start of the 19-year cycle.

2) Established readily understood tables of this correction system.

3) Demonstrated that these corrections do provide calendar accuracy both for the Sun and the Moon.

4) Suggested a practical design of a missing, but essential component, of the calendar, i.e., the Solar Month Center Stone, and made its operation at the quarter points of the 19-year cycle align with the conjunction positions attained by the marker stones of the Aubrey Sun Circle and the Sarsen Moon Circle at the same quarter points.

REFERENCES

1. A.Wall, "A Calendric View of Stonehenge", KRONOS VIII:2 (Winter 1983), pp. 35-46.

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