Some time ago back in July of 2020 I wrote a post on Newgrange and Le Menec. Not much else has been done with the subject since then, but Peter Harris recently mentioned Carnac in the context of the possible use of the Megalithic Foot there, which started me thinking about the subject of French Megalithic sites and whether I had done any work that supported the use of the Megalithic Foot in the region.
I’m generally not keen on working with the French Megalithic sites because I don’t know that we have ever had adequate data on the curious massive stone rows that we typically find in some of these places. There is an erratic nature to them that makes them seem if they could constitute entire libraries of significant mathematical values, but that seems like a very risky thing to just guess at.
However, at least the stone circles (cromlechs) that we find at some of these sites should be more easily fathomable, and better still, several of them were described by Professor Thom.
One reason the two subjects of Irish sites and French sites were lumped together in a single post is because there may be some important parallels in spite of the geography.
This rather rought sketch of Newgrange after Euan MacKie in The Megalith Builders shows that MacKie gave for the width of the outer ellipse a measure of 110 Megalithic Yards which is approximately 110 x 2.72 = 299.2 ft
I’ve annotated Thom’s diagram of the West cromlech of Le Menec so we can better see one of the parallels
The total length of the cromlech is 17 + 20 + 7 = 44 Megalithic Rods (the “Megalithic Rod” is something of a superfluous unit of measure since 1 Megalithic Rod = 2.5 Megalithic Yards)’ 44 x 2.5 = 110 Megalithic Yards = ~299.2 ft – so we can see that this unusual length was used in both Ireland and France.
In spite of David Kenworthy’s interpretation of this as simply 110 Megalithic Yards, as readers may be well aware, the number 11 is not in my vocabulary, for good reason, which I’ve recently gone into more detail about in my post about Exclusion of many whole numbers. One reason for this exclusion is because ratios like 22/7 = (11 x 2)/7 interfere with the use of the true Pi ratio, but perhaps even more importantly, the use of multiple units that the ancients demonstrably practiced is enough for metrological unit values to interfere with each other even with only a small number of units and with the pool of whole numbers already greatly diminished as in done in my work.
Add a couple more ancient units of measure or a few more whole numbers to the pool and good luck trying to figure out what units they were really using. Even Petrie himself was quite confounded by this, causing his Royal Cubit values to fluctuate almost beyond recognition, but of course that is one of the basic classic problems in ancient Egyptian metrology, the ease of conflation of Royal Cubits and Remens, which is probably one of the first things that has led Egyptologists to make an absolute mess of ancient Egyptian metrology.
I sometimes remark that Egyptologists with the Royal Cubit remind me of children who have just discovered ketchup or mustard who put it on everything – ice cream, birthday cake – which in a way is endearing, but for a parent who has to wash out all the resulting ketchup or mustard stains, sometimes it’s also downright exhausting.
At any rate, we will want to observe that “110” Megalithic Yards = 299.2 feet might likely be an attempt to reference the Jupiter Synodic Period fractionally; that is, 299.2 x (4/3) = 398.93333333, which puts us quite close to the “textbook” figure for Jupiter’s Synodic Period of 398.88 days, so that even in Imperial units (“modern” feet) we are still readily recovering important astronomical data from this measurement shared by both of these ancient monuments according to the data.
The East cromlech at Le Menec, from Thom, “Megalithic Remains in Britain and Brittany”. Here, the total length of the West cromlech, 44 Megalithic Rods, is repeated as a width of 44 Megalithic Rods = 110 Megalithic Yards = 299.2 ft.
I’m not at all certain yet what either of these two Le Menec cromlechs are really made of metrologically. In my experience I think it really is unheard of for any design to be made of a single unit, be it Royal Cubit, Megalithic Yard/Rod, or any other. That’s really why these multiple units of length measure exist in the first place. If we looked up “Ancient Egyptian Units of Measure” on Wikipedia and all that were these was the Royal Cubit, that would be one thing – but that’s not the way it works.
Even while I really know so little about what went into these designs, I wanted to bring up the subject again because I’m not at all certain that some important things got pointed out that may be somewhat more self-evident on examination.
For instance, note that according to Thom’s data, the perimeter of the West cromlech is 304.4 Megalithic Yards, and the perimeter of the East cromlech is 370 Megalithic Yards. What is the relationships between the two? Remarkably, it is
370 / 304.4 = 1.215505913
Is there anyone who isn’t going to immediately equate this first and foremost with the Egyptian Remen value in Imperial Units, of 1.216733603 feet?
Let’s attempt to examine this proposal just a little more closely.
Previously, it was proposed that the calculated 1006.4 ft perimeter for the East cromlech is a rather obvious “echo” of the 100.6036766 ft calculated mean perimeter of the Stonehenge sarsen circle.
If this is the case, it would make the perimeter of the Western cromlech, estimated at 827.968 ft to be, using the primary Remen value,
1006.036766 / 1.216733603 = 826.8340445 ft
Would this be a sensible proposal?
Well, it may be – starting with 826.8340445 / 2 = 413.4170223
Readers might recall that the amazing book by Harris and Stockdale identifies a “Unifying Value” of (Astronomy and Measurement in Megalithic Architecture, page 28) 413.42 days (15 Anomalistic Months and 14 Lunar Months, according to the text), which I believe to most likely be synonymous with 413.4170223 = (13.333333333 x (Pi^3).
Notice what happens if we use the value I use for the Megalithic Foot with this number
413.4170223 / 1.177245771 = 351.1739791, which is a number that we have been finding more often since beginning to examine the architecture of Egypt’s Faiyum Oasis, although it had long ago been found in the Great Pyramid model, where twice the perimeter of the now-missing apex section of the Great Pyramid would be 351.1730791 ft.
More importantly, 413.4170223 x 1.177245771 = 4866.934411, which is 100 times the 40 Remen inner diameter of the Stonehenge sarsen circle (40 x 1.216733603 = 48.66934411 ft).
In turn, 413.4170223 x (1.177245771^2) = 5729.577951, which is 100 times the Radian value of 57.29577951 (360 / (2 Pi) = 57.29577951), so we see that the Unifying Value of Harris and Stockdale appears to intimately related to and linked to both the Megalithic Foot and to the Stonehenge sarsen circle.
There is at least one other very noteworthy ratio that may be trying to leap out at us from the data – the length of the East cromlech is 52 Megalithic Rods, while while the width of the West cromlech is 34 Megalithic Rods
52 / 34 = 1.529411765 = 3.058823529 / 2
We may wish to recall at this point that the inner circumference of the sarsen circle calculates as 360 / (1 Megalithic Foot in feet 1.177245771) = 305.7985077, and that this very important number in fact appears to be incorporated into the basic proportioning of Thom’s Flattened Megalithic Rings.
Thom’s data for the Type A Flattened Megalthic Ring. The exact value for the perimeter / major diameter ratio Perimeter / MN = 3.0591 is thought to be 3.057985077. In a manner of speaking, what else would it be?
We hopefully know by now of course that circumference 305.7985077 / (2 Pi) = radius 48.66934411
This would be the same thing that we find often, that many Megalithic sites contain some of the same basic data that Stonehenge contains, although Stonehenge represents such an usually well-packaged bundled of this data that it’s very easy to see why it merited such a special architectural design to accompany such a special collection of numbers. There may really be nothing else quite like Stonehenge, architecturally or mathematically.
One way of looking at what is proposed here then, is that for
1006.036766 / 1.216733603 = 826.8340445 ft
Something it showing us is that a value in the ancient Egyptian Mystery Unit of 1.676727943 / the Remen = a value in another metrological unit.
I’m having a bit of trouble placing it, but this equation may well demarcate 826.8340445 as a metrological value, and it may be something of a Unifying Value metrologically speaking
For instance, a Megalithic Yard of 2.720174976 ft / a putative ancient Meter of 3.289868134 = 8.268340445 / 10. Likewise, the greater unifier of ancient metrological units, 2 Pi, turns 8.268340445 into
8.268340445 x 2 Pi = 51.95151515 = outer radius Stonehenge sarscen circle
Likewise, a value in Egyptian Sacred Cubits (see Thom Mid Clyth Quantum aka TMCQ) times Hashimi Cubits, will be in the same unidentified unit as is a vlue of 8.268340445
TMCQ / 2 = 3.872983357 ft; 3.872983357 x Hashimi Cubit = 1.067438159 = 8.268340445 / 2 = 4.134170224
So again, 4.134170224 may be a Unifying Value metrologically as well as a Unifying Value astronomically.
We may also wish to be observant that 4.134170224 / Remen 1.216733603 = 3.397761198, which is 4 Inverse Megalithic Feet
4 / 1.177245771 = 3.397761198, and this value (as 339.7761198 ft may have been built into Avebury partly for this reason, whereas Thom would have tended to identify it as 125 Megalithic Yards, again driving home the point about the risk of confusion of units even with a radically limited palette of ancient units and whole numbers. Once again, try and imagine what chaos this would be without such dramatic restrictive measures being in place.
While we are at it, why don’t we try and see if we can find out anything else about these subjects since it seems like on this occasion we may have spotted several things that were previously overlooked.
By the way, I am still experimenting with a value of 18.60376601 (6 x (Pi^3) / 100) as the number of years in the Lunar Nodal Cycle. This quantify may not have had a fixed value in ancient calendars- and it may not help that there is a variety of ways we can express the number of days in a year, but we might note that
18.60376601 / 4.134170224 = 45/10, so there is another possible facet of the Unifying Value form Harris and Stockdale’s book.
For the Le Menec West cromlech, with a perimeter (P) of an estimated 304.4 MY = 829.768 ft, and estimated length (L) and width 
of 44 MR = 299.2 ft and 17 x 2 = 34 MR = 231.2 ft respectively, (without yet converting the perimeter into Megalithic Rods to match the length and width values which are in Megalithic Rods because this way we may be able to generate a meaningful “second opinion”) we obtain ratios of
Pmy/Lmr = 304.4 / 44 = 6.918181818
Pmy/Wmr = 304.4 / 34 = 8.952941176
As well as a length / width ratio of
L/W = 44 / 34 = 1.294117647
All of these three ratios look challenging to identify at first glance; however a reciprocal check shows that 1 / 8.952941176 = 1.116951380 / 10. Normally things like this will turn out to be one of three things: 1.115419203, 1.116225960, or 1.117818629; 1.116225960 = (360 x (Pi^3) / (10^5) has been surprisingly rare, so the correct fintended figure may well be one of the other two.
(There is also 1.117441171 – this is connected to the standard value for polar circumference in miles: (1 / 360) / 1.117441171 = 24858.28047 / 10^n – textbook polar circumference value about 24860 miles – but although we can find 1.117441171 in the Great Pyramid, generally speaking it has also seemingly been rather rare).
The other two ratios from the West cromlech of Le Menec I am going to try to refrain from attempting to qualify for now, but I do want to go back to the figure and make what may be a new observation, which is that while 34 MR = 231.2 ft, the standard Megalithic Yard / Megalithic Foot ratio is 2.720174976 / 1.177245771 = 231.0626246 / 100 = 346.5939368 / (15/10).
To harmonize the perimeter / (lenght or widht) ratios then, we next convert the perimeter into Megalithic Rods, and discover that 304.4 MY / 2.5 = 121.76 Megalithic Rods, which greatly resembles 100 Remens = 121.6733603 feet, but we will have to be careful with that. Instead then let’s first use the values in feet to detimeter the true perimeter / (length or width) ratios
With a projected perimeter of 1006.036766 / 1.216733603 = 826.8340445 ft, a possible width of 231.0626246 ft, and an estimated length of 299.2 feet
826.8340445 / 231.0626246 = 3.578398047 = 1.789199023 x 2
826.8340445 / 299.2 = 2.763482869
I wrote a bit about 1.789199023 on my Megalithic Portal thread just yesterday. So far so good, if we are lucky.
I’m still at a loss for 299.2 means exactly. In accordance with some researchers, we might take it as 110 Megalithic Yards, with an adjustment of 110 to one of the more likely Indus / Northern Foot values (currently, Long Indus foot = 1.100874628 ft, Short Indus foot 1.100078967 ft, and that’s the way they’ve been ever since way back when I didn’t know what an Indus Foot was, but was trying to relate these values to the Royal Cubit at ratio of 1:64 — i.e., 110.0078967 / 64 – standard Royal Cubit 1.718873385 ft).
Starting with the most likely figures 1.100874628 x 2.720174976 = 299.4571616. However, 299.4571616 x 1.333333333 = 399.2762155, which is thought to be the C value for the Jupiter Orbital Period. They may have wanted to put a better foot forward than that here.
What they might have done at Newgrange and at Le Menec might be something they seem to have done at Callanish and elsewhere, which is switch the emphatic on the Megalithic Yard from the “AEMY” of 2.720174976 ft to the “IMY” of 2.719256444 for various practical purposes.
Hopefully they have not done something even more elaborate, but even Stonehenge does seem to represent a small variety of Megalithic Yard values.
A few paragraphs ago, I wrote, “304.4 MY / 2.5 = 121.76 Megalithic Rods, which greatly resembles 100 Remens = 121.6733603 feet, but we will have to be careful with that.” and I wrote that because we have a slight problem.
If we believe the perimeter value to be 826.8340445 ft, 826.8340445 / 2.5 = 330.7336178, and 330.7336178 = 2.720174976 x 1.215854203 x 100 ft, or 2.718208957 x 1.216733603 x 100.
If we conserve the Remen value at the Long Remen of 1.216733603 ft rather than the short Remen of 1.215854203, we get a Megalitihic Yard value of 2.718208957, which some readers may already know as a Megalithic Yard that is made out of Megalithic Feet (3.2 / 1.177245771 = 2.718208957) and which is the radial/diameteral unit to a circumferential unit of 1.067438159, as was discovered while following up on the remarkably insightful work of Geoffrey Bath.
Specifically, if for example the radius of a regular circle is 27.18208957 ft, the circumference will be radius 27.18208957 x 2 Pi = circumference = 170.7901058 ft = 160 x Hashimi Cubit 1.067438159.
Technically (in the “Inductive Metrology” sense where we should see whole numbers of units in “forward” rather than Inverse form), a Megalithic Yard is of 2.718208957 ft is the Megalithic Yard of the inner sarsen circle circumference of Stonehenge
305.7985077 / 2.718208957 = 1125 / 10
So we can see that by conserving the ideal Remen value, we haven’t gotten into any trouble we haven’t been in before at Stonehenge, so to speak.
Let’s go back to this now for a moment, “Starting with the most likely figures 1.100874628 x 2.720174976 = 299.4571616. However, 299.4571616 x 1.333333333 = 399.2762155, which is thought to be the C value for the Jupiter Orbital Period. They may have wanted to put a better foot forward than that here.”
If we take this equation and make one or more Megalithic Yard substitutions,
1.100874628 x 2.719256444 = 299.3560426 = 399.1413902 / 1.333333333
1.100874628 x 2.721223220 = 299.5725600 = 399.4300799 / 1.333333333
1.100874628 x 2.718208975 = 299.2407275 = 398.9876367 / 1.3333333331
IF we have the mechanics right and the measure in question is indeed linked to the Jupiter Synodic Period by 1.333333333 rather than by some other number such as 1.331433599 or etc, then conserving the more ideal Indus Foot value, either the IMY of 2.719256444 ft has been used as at Callanish (see also “Callanish Number,” etc), or the DMY (Draconic Megalithic Yard of 2.721223220 ft, representing Draconic Month of 27.212220815 days the most accurately of any of the known Megalithic Yard values).
Since the IMY is generally more useful all-round than the DMY, it may be more likely that the IMY has been used as at Callanish, with the result that the premiere A value for the Jupiter Synodic Period, 399.1413901, has been spelled out.
That’s still a long way from solving the puzzle of Le Menec’s West cromlech in total, but hopefully on revisiting the subject we have been able to chip away more of the mystery this time.
As I look at the diagram of the West cromlech that 17 MR = 115.6 feet stands out – it might tempt one somewhat to make the Egyptian Royal foot something like this rather than the more established ~115.3 / 100 value, but again, we have experimentally qualified the cromlech’s 17 x 2 = 34 MR = 231.2 ft width as probably (2.720174976 / 1.177245771) x 100 = 231.0626246 ft, thus “17 MR” = 231.0626246 / 2 = 115.5313123 ft, and the significance of this number has been discussed in some detail before (115.5313123 does not translate well into Megalithic Feet, but instead it becomes rather talkative when divided by Inverse Megalithic Feet exponentially).
115.5313123 / 10^n serves as a viable approximation of a rather important astronomical figure — in crude numbers, it is no less than “Tzolkin” 260 days / Venus Orbital Period 225 days = 1.155555555, hence it is important astronomical data, even while still in in “modern” “Imperial” feet.
Let’s go back here for a moment now
IF 304.4 MR = 826.8340445 ft and 44 MR = 299.3560426 ft and 34 MR = 299.3560426, then
826.8340445 / 299.3560426 = 2.7620422735 = 1 / 0.3620509394
IF 304.4 MR = 826.8340445 ft and 44 MR = 299.3560426 ft and 34 MR = 299.3560426, then
826.8340445 / 299.5725600 = 2.7600459952 = 1 / 0.3623128026
Either I have made some terrible mistake, or as often happens, the ancients are still five steps ahead of us with their remarkable mathematical prowess. The only one of these four numbers that I actually recognize is 3.620509394, and offhand I have no explanation for what it’s doing here.
We may not be seeing the Harris-Stockdale Unifying Value doubled to form the perimeter length pf the Western cromlech, although it would eminently sensible to find it here for the reasons described, and more.
If we’re forced to look for alternatives, perhaps it’s worth noting that in crude terms, Anomalistic Month 27.55 days x 3/4 of Jupiter’s Synodic Period (399 x (3/4) = 299.25 days) = 27.55 x 299.25 = 8244.3375 = 20.61084375 x 400, and the standard Royal Cubit in inches is 1.718873385 ft x 12 = 20.62648062 inches.
Thus, while once again it may be easy enough to see roughly what the ancients were up to, it can be a different thing to determine exactly what they were up to. Hence, while our understanding of he cromlechs may have grown by leaps and bounds, the jury may still be out on this one as a whole.
Before I “sign off” on this post, let’s have another look at the East cromlech again, shall we?
We think the perimeter may be 1006.036766 feet, or exactly ten times the mean diameter of the Stonehenge sarsen circle, with a width of ~44 MR = ~299.2 feet, and a length of ~52 MR = ~353.6 ft
This gives us internal ratios of about (using the raw value 1006.4)
P/L = 1006.4 / 353.6 = 2.846153846
P/W = 1006.4 / 299.2 = 3.363636363
L/W = 353.6 / 299.2 = 1.181818181
These too are potentially rather confusing. Perhaps the 4 most likely things for 1.181818181 to represent are the Megalithic Foot of 1.177245771, the Alternate Megalithic Foot of 1.1797781993, (57.29577951^2 x 36) / 1^n = 1.181810286, and (12 x (Pi^2)) / 100 = 1.184352528.
Before putting this back on the back burner, lets’ try looking at one more aspect for possible guidance.
For the West cromlech, l/w = ~44 / 34 = 1.294117647.
If 44 MR = 299.3560426 and 34 MR = 231.0626246, “44 / 34” = 299.3560426 / 231.0626246 = 1.295562374 and 1 / 1.295562374 = 0.7718655771; 299.5725600 / 231.0626246 = 1.296499425 and 1 / 1.296499425 = 0.77130770806
None of the four numbers thus generated are familiar and I can find no prior history on them.
Talk about a prime example that not just “any old thing” works!
One possibility here might be that they really did resort to using the C value for the Jupiter Synodic Period — note that 231.0626246 / 299.4571616 = 1.296, and that is something that we do recognize and which has considerable important.
Another possibility might be that because the Meg Yard of 2.720174976 may not be at a premium here, perhaps its a “faux paus” to use 231.0626246 which again has been conjugated from 2.720174976 / 1.177245771
Yet another possibility might be that a mistake has been in seeing Jupiter’s Synodic Period where perhaps we are actually seeing Venus’ Orbital Period.
I’m going to use for this demonstration a rarer form of the Venus Orbital Period that was discovered at Monte Alban in the Americas
(15 / 1.000723277)^2 x 10 = 224.6748781
224.6748781 / .75 = 299.5665042, while 299.5665042 / .75 = 399.4220056, just missing the current B value for the Jupiter Synodic Period of 399.4300799 days.
399.4300799 x .75 = 299.5725599 and 399.4300799 x .75 = 224.6748783, the F value for the Venus Orbital Period. The architects of this design may have navigated some of the most treacherous waters in the calendar system with this because the .75 ratio will try again and again to make us think it is working here, and exponentially — but is it, and did the ancients really go so far out on a limb to catch this one as an F value from the calendar tables? So far we really shouldn’t have to get any further out than the C group.
This may be in essence where the last attempt got fouled up as well.
There may even be other possibilities as to what’s gone seemingly wrong here. A particularly interesting one can be illustrated thus
399 x .75 = 299.25; 299.25 x .75 = 224.4375
Is anyone thinking what I’m thinking here? Do you happen to recall, dear reader, the Aubrey Number from experiments with the Aubrey Circle?
Remember that we can conjugate the Aubrey Number 224.4305459 as (1.315947254^2) x (360^2) = 224.4305459 x 10^n, although the .75^2 trick is apparently not going to serve this possibility either, at least not if one of the primacy values (values A-C) for the Jupiter Synodic Period is going to be honored. It’s a novel, very challenging problem, and exactly how the ancients got around it may require more understand that we currently have.
As always, ancient “rocket science” is by rights not necessarily any simpler than modern “rocket science” – but at least readers have been afforded the opportunity to see some of what can go into an effort to interpret ancient monuments.
In the long run, the usual rule should apply that since the “name of the game” is to record and communicate astronomical data, that whatever combination of possibilities best serves that purpose is going to quite likely be the right answer.
Once again, at least we can say for that for this brain-twisting exercise, we have advanced our understanding of the Le Menec cromlechs considerably. If the next effort manages to advance things any further, we should have the answer at last.
–Luke Piwalker
Luke Piwalker 