Let me see what else is my recent notes that might be worth offering to posterity?
Oh, I might have made a discovery about the geodetic use of the Megalithic Yard? My notes suggest that 1 / (Incidental Megalithic Yard) x (Radian^3) is a geodetic function. Interestingly, the Draconic Megalithic Yard is also involved in this, but the “AEMY” Megalithic Yard is not, so I still don’t know how well this would fit into the tentative metrology tables I made.
Euan MacKie has a diagram of Newgrange on page 72 of The Megalith Builders in Thom’s style. I don’t know how reliable it is, but there may be some interesting things in the numbers and I can hope to work up a presentation.
I had to hastily salvage it but there are still some apparent issues with proportion in the section which contains the passage, and there might be several issues with MacKie’s diagram including that the origins of the arcs defining this section of the plan don’t seem clear to me, but his numbers do seem to add up, so perhaps (hopefully) there isn’t an error in the data itself.
I did do a previous work up of this very recently, but I lacked confidence in it and wanted to see if anything new might come to light that might make these figures more compelling. Following this effort, I’ll attempt to find the earlier one and see if anything was overlooked this time around.
This is a risky thing for me to do, both since MacKie’s model may or may not be a good match for other diagrams of Newgrange, which feature a sort of heart shape with concavity outside the entrance passage, and because Newgrange has historically undergone some alternations for various reasons that could interfere with the integrity of interpretations. It’s really just an experiment to try to see just what’s in MacKie’s data.
I should point out that at least MacKie seems to be a respected and trusted archaeologist, and I’m very grateful that he has also been an open-minded one who was both willing to entertain the idea of a Megalithic Yard, and its possible relatedness to ancient Egyptian units of measure, which to be fair seems to reinforce the sense of the legitimacy of the Megalithic Yard as ancient unit. All of this except MacKie’s endorsement is also the case with the Megalithic Foot of Harris and Stockdale.
The estimates:
19 MY x 2.72 = 51.58 ft
24 MY x 2.72 = 65.28 ft
26 MY x 2.72 = 70.72 ft
36 MY x 2.72 = 97.92 ft
44 MY x 2.72 = 119.68 ft
62 MY x 2.72 = 168.68 ft
72 MY x 2.72 = 195.84 ft
104 MY x 2.72 = 282.88 ft
110 MY x 2.72 = 299.2 ft
130 MY x 2.72 = 353.6 ft
275.36 MY x 2.72 = 748.9792 ft
309.58 MY x 2.72 = 842.0576 ft
A few comments: First, I could point out how the inner maximum diameter 104 MY = 282.88 ft resembles the Lunar Year written backwards: 1 / 282.88 = 353.067873, while the outer maximum diameter 130 MY = 353.6 resembles the Lunar Year written forwards, and how this is reminiscent of the “inversion” that seems to go on at Stonehenge.
The inner max / min diameter ratio: 104 / 72 = 1.444444444
The outer max / min diameter ratio: 130 / 110 = 1.181818182
The inner perimeter / diameter ratios
Perimeter 275.36 / Major diameter 104 = 2.647692308
Perimeter 275.36 / Minor diameter 72 = 3.824444444
The outer perimeter / diameter ratios
Perimeter 309.58 / Major diameter 130 = 2.831384615
Perimeter 309.58 / Minor diameter 110 = 2.814363636
The outer / inner perimeter ratio
Outer perimeter 309.58 / Inner perimeter 275.36 = 1.124273678 = 2.248547356 / 2
The other / inner perimeter difference
Outer perimeter 309.58 – Inner perimeter 275.36 = 34.22 = 17.11 x 2, faintly suggestive of Royal Cubits but perhaps not possible in this circumstance. 16 Hashimi Cubits = 17.07901054
Some resemblances and observations to note:
Perimeter 275.36 MY is approaching 10 times the lunar Anomalistic Month of 27.55 days. Perimeter 309.58 MY resembles
10 x (sqrt 960) = 10 x 2 x (sqrt 240). Sqrt 240 is thought to be rather important and the Stonehenge inner sarcen circle circumference can be built from sqrt 240 and Pi. It will be interesting to see if either suggestion is really possible.
2.814363636 is approximately 1/80th of the Venus Orbital Period — using 224.8373808, 224.8373808 / 80 = 2.810467260.
1.444444444 x 24 = 346.66666666 / 2. There may be a reference to the Eclipse Year of 346.62 days in there?
The estimates again with some comments:
19 MY x 2.72 = 51.58 ft – near to 30 Royal Cubits = 515.6620155 ft
24 MY x 2.72 = 65.28 ft – plausible number of Megalithic Yards?
26 MY x 2.72 = 70.72 ft – near to 60 Megalithic Feet = 70.63474626 ft = (224.8373808 x Pi) / 10
36 MY x 2.72 = 97.92 ft – plausible number of Megalithic Yards?
44 MY x 2.72 = 119.68 ft – 200 inverted units of 1 / 1.676727943 = 119.2799350 ft = 1177.245771 / (Pi^2) – good number.
62 MY x 2.72 = 168.68 ft – 180 inverted units of 1 / 1.067438159 = 168.6280357 ft = 1.216733603 x (1.177245771^2) x 100
72 MY x 2.72 = 195.84 ft – plausible number of Megalithic Yards but resembles 196.2076285 which should be explored
104 MY x 2.72 = 282.88 ft = ~(1 / Lunar Year) x 10^n
110 MY x 2.72 = 299.2 ft – David Kenworthy: 299.2 x 3 = 897.6, see Aubrey Circle
130 MY x 2.72 = 353.6 ft = ~(1 / Lunar Year) x 10^n
275.36 MY x 2.72 = 748.9792 ft = 117.6493776 x 2 Pi = ~117.7245771 x 2 Pi = 739.6853331 = 100 Squared Munck Meg Yards
309.58 MY x 2.72 = 842.0576 ft
(10 x sqrt 960 = 309.8386677) x 2.720174976 = 842.8153905 = 1685.630781 / 2
(10 x sqrt 960 = 309.8386677) x 2.719256444 = 842.5307937 = 1685.061587 / 2
(10 x sqrt 960 = 309.8386677) x 2.721223218 = 843.1491765 = 1686.280353 / 2 (see 62 MY)
(10 x sqrt 960 = 309.8386677) x 2.718208958 = 842.2062419 = 1684.412571 / 2
It may be that this was specifically chosen so that it homes on in the Draconic Megalithic Yard specifically, in a self-referential manner, rather than accommodating a variety of different Megalithic Yard values, in contrast to at least parts of Stonehenge? That is only a first impression, but in the long run it could be the correct answer.
There are still a lot of questions, though. There are some unusual numbers here, including that the very obvious but long-awaited 119.2799350 of course has that status because somehow it’s been unusual.
Another question would be why we are seeing 1686.280353. Even if it’s used to indicate the Draconic Megalithic Yard, we should hope that there was more rationale for its appearance than simply that, but relatively little may be known about 1686.280353 at present because it too is an unusual number to encounter.
Really then this is just scratching the surface of MacKie’s data for Newgrange.
Newgrange had come up several times recently because Aubrey Burl seems to have championed a suggestion by Anthony Powell of a “Beaker Yard”, a unit of 13.1 m used at Newgrange, one of several units discussed by Burl that apparently unbeknownst to him, can be taken as the Royal Cubit in the Megalithic Landscape, helping provide the indication of other Egyptian measurements there that may lend support for the Megalithic Yard, which is geometrically related to Egyptian units.
Also, DavidK recommended Howard Crowhurst’s work on the basis of some Newgrange measurements, including one that I think I was able to effectively interpret as being in Remens, which if valid might provide more support for ancient Egyptian units accompanying the Megalithic Yard.
DavidK also commented: “Crowhurst’s work at Newgrange is astonishingly correct and this is fitting because it records the 2919.60 day Venus cycle the Goddess of the Heavens recorded by Stonehenge.”
The 2919.60 figure is still under consideration (by me, at least). It’s extremely close to 2400 Remens (2919.60 / 2400 = 1.2165, with the usual perfected value being given at 1.216733603 ft), but DavidK could be right and there might be something else afoot here.
Again, all of this work on Newgrange is just an experiment.
I also decided it was about time I have a look at Le Menec. I don’t aspire to being able to comprehend much concerning the stone rows. To my reckoning, an array like that might represent a vast data bank of important mathematical constants expressed through metrology, but I don’t know if the data is really out there somewhere to explore that question. We would probably want to know the individual spaces between stones in order to put this to the test as a hypothesis.
If this impression is correct and the data is indeed lacking, that would be by far the bulk of the site’s data that may be currently be completely inaccessible.
However, there is a Megalithic Egg at each end (east and west) of the aligned rows for which Thom provides data that can be experimentally interpreted.
Curiously, like at Newgrange, a value of 44 Megalithic Yards appears in association with the Cromlech at the East End of the Le Menec Rows, as does a value of approx 1.181818182 which for Le Menec is obtained from the ratio Major Diameter 52 MY / Minor Diameter 44 MY = 1.181818182, whereas for Newgrange it was obtained as “outer max / min diameter ratio: 130 / 110 = 1.181818182”.
This means that the suggestion of the rare figure of 119.2799350 ft = 1177.245771 / (Pi^2) is also seen at Le Menec, which makes it a very timely subject in case Newgrange and Le Menec can help promote the understanding of each other. Perhaps this may also help provide some confidence that even though they are strange, perhaps MacKies figures for Newgrange may not be in error.
The 52 Meg Yards used in obtaining the ratio at Le Menec of 52 MY / 44 MY = 1.181818182 is in feet 52 x 2.72 = 141.44, looking rather like 120 Megalithic Feet. The main, or the exclusive, Megalithic Yard in use there may then the “Incidental” Megalithic Yard (IMY) of 2.719256444 ft, which provides
(120 x 1.177245771) / 2.719256444 = 51.95151515, the outer sarsen circle radius of Stonehenge.
Thom gives the perimeter of the West end Cromlech of Le Menec as 370 MY; 370 x 2.72 = 1006.4, which bears considerable resemblance to ten times the 100.6036766 ft mean sarsen circle diameter at Stonehenge.
Regarding the figure 1.181818182, there is a valid figure of (Radian 57.29577951)^2 x 360 = 1.181810286 which belongs to Munck’s numbers. Michael Morton worked with this number and was fond of it. He associated with with one of the Draco stars, Alpha Draconis, in his “Archaeo-Sky Matrix”, which I mention because even if the “ASM” as he called it was an idea that didn’t pan out, some of his interesting thoughts on this number itself and its relationships to other important numbers may still be available on the Internet.
I also worked extensively with the number because I sincerely wished to off Michael all the support I could with his premise, although I’ve forgotten much of what was involved. For me it was one of those numbers that just when you’re about to give up on it, it does another amazing thing to prevent being discarded hastily. However, it does not seem to turn up often, and is frequently overshadowed by its neighbors like 12 x (Pi^2) = 1.184352528 or even 1.177245771.
I have a note on paper from a few recent experiments with this data that 1.181810286 “is SMMY fodder”, which may be of particular importance in the Megalithic Landscape where the Squared Munck Megalithic Yard seems notably prevalent.
Perhaps something of the same may be said for 100.6036766 or 1006.036766. which is near the middle of a SMMY series to about SMMY^7 that runs down to 1006.036766 / (2.719715671^2)^3 = 24858.38047 / 10^n, the standard value I use for the Earth’s Polar circumference in miles.
The Cromlech at the West end of Le Menec has according to Thom, a perimeter of 304.4 Megalithic Yards x 2.72 = 827.968 ft. This may be a reciprocal value of inverted units of 1.676727943
(1 / 72) x (1 / 1.676727943) = 828.3328817; alternately there is possibly a metrological composite at work, such as 1 Megalithic Rod x 1 Remen
(2.720174976 x 2.5) x 1.216733603 = 827.4320748 / (10^n)
Or perhaps 1 Petrie Stonehenge Unit / 1 Megalithic Yard
224.8373808 / 2.720174976 = 826.5548459
Thus far (1 / 72) x (1 / 1.676727943) = 828.3328817 may be the least departure from Thom’s data.
Thom’s diagram of the West Cromech, taken from an article by Dmitrios Dendrinos
https://www.researchgate.net/publicatio … ercomputer
It’s noted in my notes that 360 / 304.4 MY = 1.182654412. If this were a reinforcement of the possible 1.181810286 ratio at Le Menec, 304.4 MY would be 360 / 1.181810286 = 304.6174198 = 8283.328817 / 2.719256444, surprisingly enough.
The Maximum Diameter / Minumum Diameter Ratio for the Western Cromlech is apparently 42.5 MY / 31 MY = 1.370967742 = ~5 / 364.7058824, which may help to guide our efforts, and likewise with the ratio between the two perimeter values given by Thom:
Circumference East Cromlech 370 MY / Circumfernce West Cromlech 304.4 = 1.215505913, looking very much like the Remen in feet as ratio once again.
For the West Cromlech, the perimeter / diameter ratios are estimated at
Perimeter 304.4 / Major Diameter 42.5 = 7.162352941
Perimeter 304.4 / Minor Diameter 31 = 9.819354839
For the East Cromlech,
Perimeter 370 / Major Diameter 52 = 7.115384615
Perimeter 370 / Minor Diameter 44 = 8.409090909
Some unusual numbers may be at work here that may take some careful thought to unravel, but 9.819354839 does seem to resemble 117.7245771 / 120 = 9.810381425
In my notes there are some rumblings about whether 7.115384615 could have been meant as the reciprocal of 1.424280286 = 1 / 1.424280286 = 7.02108995, or perhaps better yet 14.24280286 / 2 = 7.121401428, but I think that is still purely speculative at this point.
That’s probably enough for one post but for now, I’d like to take the opportunity, since in the Le Menec diagrams I’m looking at a measure of 15 MY x 2.72 = 40.8 ft.
Perhaps it might be a clue to the identity and nature of some approximations of the 6793 day lunar Nodal Precession Cycle that the Cube of 4.08 is 4.08^3 = 6791.7312 / 100.
–Luke Piwalker
Luke Piwalker 