A book was published by Oxford University Press in 1967. Later editions were
published up to 1976. Perhaps there were later editions as well, but I did not
know about them as my copy was a 1976 edition. The book's title is Megalithic
Sites in Britain and was written by A. Thom. As of 1976, A. Thom
had written one other book with the title Megalithic Lunar Observatories.
(1). According to A. Thom, there are thousands of Megalithic sites in Britain, stones aligned
in egg-shaped, elliptical, and circular arrangements. About 300 of these sites were
surveyed by Thom. . He found them to be constructed according to a linear dimension
he calls the megalithic yard which equates to 2.72 feet. The accuracy of measurement
found in these circles exceeds the limits of most surveyors in the sense that even
stretching a measuring tape exceeds the limit of the accuracy of the engineers who created
the alignments (accuracy given as approaching 1 in 1,000). This led to the conclusion
that the megalithic yard was a standard of measure at the time these alignments were created
that was employed with an accuracy of one percent throughout the whole of Britain.
(2). Most of the arrangements were not circular. The ellipses and eggs were more dominant.
However, all alignments were perfectly symmetrical with a circumference that was
always a multiple of 2.5 megalithic yards (MY).
(3). "Vara" is a Spanish word for "measuring stick".
The old "vara" was 2.766 feet long in Burgos, 2,7425 feet long in Madrid, 2.749 feet long
in Mexico, 2.778 feet long in Texas and California, and 2.75 feet long in Peru.
(4). The MY is 2.72 feet (using today's foot) with an accuracy of .1 percent throughout Britain.
There is also a megalithic fathom made of two megalithic yards (5.44 feet).
The fathom was a unit of diameter and the yard was a unit of radius. The megalithic
yard was sometimes halved to make a megalithic cubit when stones were formed in elliptical
or egg-like shapes. One MY equals 2.27 feet plus or minus .003 feet.
(5). All circle circumferences were multiples of 2.5 megalithic yards (MY), and usually of 12.5 MY. Most circles had diameters of 8 or 16 with a circumferences of 25 or 50. Sometimes pi was used as 3 1/8, and sometimes as 22/7. Some circles were very accurately laid out and at other times, accuracy does not appear to have been necessary.
(6). Sometimes eggs and ellipses were given multiples of 10 for perimeters and the
diameters were sacrificed.
(7). Right triangles were used in the construction of "circles", and it is obvious
that at least
the first few of this family (of right triangles) were known. More may have been
known but the first few are the easiest to use for measuring.
(8). In Secrets of the Great Pyramid, the old geographic foot of ancient Mesopotamia was 1.0101 times the foot of today. One hundred feet were equal to one second of arc on the earth's surface. The circumference of the earth was 129,600,000 feet (36 squared = 1296). 1296 reduces to 18 and then 9. The number 36 is often used as a synonym for the pentagram (see The Five-Pointed Star found herein).
1 + 2 + 9 + 6 = 18 1 + 8 = 9
and 1 + 2 + 9 + 6 = 9 + 9 which can be used as 99 on occasion according to the old codes.
Thirty-six degrees is the smallest angle found in the pentagram, often simply notated as 36.
(9). In the circle circumscribing the pentagram, the circumference is 81.6140899, using the
actual value of pi, and 81.7142857 when using 22/7. In this circle, the diameter
is 26. The circumscribed pentagram is the symbol for the Life Force and the circle
is the symbol for the Eternal.
(10). The ratio of the volume of a sphere circumscribing a cube to the volume of the cube itself is 2.720699. The volume of the sphere is 4/3 pi r cubed.
Volume of sphere = (4/3)(pi)r3
Let r = 31/2 / 2 = .8660254
(31/2 / 2)2 = 3/4
(4/3)(pi)r3 = (4/3)(pi)[(31/2 / 2)3] = (4/3)(pi)(3/4)(31/2 / 2) = (pi)(31/2 / 2)
(pi)(31/2 / 2) = 2.720699
(11). Let 2.720699 equal R for Ratio. Then
R x 12 inches x 2.5 = 81.6209838 inches. This is the length of the unit used in the circumferences - see (5) above. See also how this relates to (9) above.
If the old foot of Mesopotamia is used, the value is 80.8048425. If 2.72 is used
for R with the modern foot, the value is 81.60000000. If 2.72 is used for R with
the old Mesopotamian foot, the value is 80.7840808.
(12). The circumference of the megalithic circles of multiples of 2.5 MY must have been referring to the original pentagram circle of half a year (2 seasons) as the full year would have been a circle of a diameter of 52.
26pi = 2.5 MY in inches
(13). It would appear that the R of 2.72 must have been the ratio of the volumes of the
circumscribing sphere over the cube, which is the symbol for earth.
(14). In The Monuments of Mars by Hoagland, 2.72 was said to refer
to the areas of a sphere and a tetrahedron where the sphere is circumscribing the tetrahedron.
Hoagland (or the man from whom he took the information) also mentioned that "e", the
base for natural logarithms, is 2.71828. Somehow, this seems less likely to be the
key to the 2.72 ratio, although it is interesting that 2.72 is very close to the average of
"e" and the true ratio of 2.2706990. Their average is 2.71949 or .00051 off of 2.72.
(15). (2.72)(12)(2.5) = 81.6
26pi = 81.68
(26)(22/7) = 81.714286
(16). The two prevalent angles found on Mars were 22.5 and 19.5 degrees. It was mathematically proven that the beings who did the work on Mars were using a circle of 360 degrees.
19.5 / 22.5 = .8666667
e / pi = .8652554
31/2 / 2 = .8660254
2.72 / (22/7) = .8654545
2.72 / pi = .8658029
2.7206690 / pi = .8660261
If the circumscribing sphere is a planetary surface, and assuming that one point of a circumscribed tetrahedron is at a pole, 19.5 is the angle of the other points of the circumscribed tetrahedron to the equator - this would be the latitude.
But there is something that I do not believe Hoagland knew. The ancients considered the cube to be circumscribed by the sphere rather than the tetrahedron. This is a bit more difficult to visualize. However, if the long interior diagonal of the cube is placed as the axle of the earth as it turns, two points of the cube will be at the poles, and the other points will touch at 19.5 degrees of latitude - three as north latitudes and three as south latitudes. Furthermore, if the volumes of the sphere and cube are used - see (10) above - the same ratio of 2.720699 is found. This makes the circumscribed cube at least as good a candidate as the circumscribed tetrahedron for illustrating the action of magma within the earth. Frankly, after all I have learned of the ancient scientists, I trust their interpretation more than I do Hoagland's.
22.5 is the tilt angle of the face on Mars.
Hoagland's book is well worth reading and contains too much to even begin to summarize here.
(17). e = 1 + 1/1 + 1/(1)(2) + 1/(1)(2)(3) + 1/(1)(2)(3)(4) .....
(18). One of the oldest Pagan traditions gives a cord length for a ceremonial robe
of 65 5/16 inches which is 1/32 of an inch shorter than the megalithic fathom.
The number 65 is 5 times 13. This points directly to the circumscribed pentagram
with five points and a radius for its circle of 13. Moreover, the fathom is
traditionally a measure of the human body from fingertip to fingertip with its arms
outstretched to the sides and the fingers fully extended. It is also the approximate
height of the the same body with arms outstretched. This could well have been the
dimensions of the average high priestess at the time (1600 to 2400 BCE).
(19). The megalithic yard (MY) is 32.64 inches. The number 32 is 2 to the
fifth power, and 64 is 2 to the 6th power. Phi squared multiplied by 6/5 is pi.
(20). The number 65.28, the actual megalithic fathom in modern inches, is .51 times 128.
The number .51 stands for both 5 and 6 as it contains 5 and reduces to 6.
128 is 2 to the 7th power.
(21). The ratio known as phi, and the diameter of the circle of a circumscribed
pentagram (26) both occur on the zodiac circle at the summer solstice.
(22). Using the math found in The Music of the Spheres found herein, the table
of frequencies found in The Oldest Magic was constructed. Using this table
we find the following.
The circumference, 81.6, of a circle of a circumscribed pentagram, occurs at
Aquarius (the fixed sign for mankind).
(23). The dimensions of the old Irish Merlin rod of Blackthorne have been kept through
the generations. It has a sighting fork at the top that is
precisely one megalithic fathom from the bottom end to the line of sight through the fork
at the top.
(24). Using the system in (22) above, we find the following.
One MY of 32.64 is opposite red of the zodiac circle.
2.5 MY (81.6) is opposite yellow on the zodiac circle.
12.5 MY (408) is opposite blue on the zodiac circle.
Red, yellow, and blue are the primary colors.
(25). Common perimeters of the megalithic circles were 25 and 50 MY,
diameters 6, 16, 7, 14, and 21.
(26). Phi = 1.6180339 13/8 = 1.625 Using the system in (22) above, the summer solstice = 1.6339155