The Megalithic Yard - A Long Time Before King Edward I!April 2 2005 at 9:56 AM
|Tony Bennett |
To: Beranger and others.
How old is the yard? Will the Stone Age do? - see below:
The Mystery of the Megalithic Yard Revealed
How to create this prehistoric measurement unit for yourself
A guide created by Robert Lomas and Christopher Knight, authors of Uriel's Machine.
This articles uses some research data developed in conjunction with Alan Butler.
For detail see Uriel's Machine in the Books section.
"And I saw in those days how long cords were given to two angels
'Why have they taken those cords and gone off?' And he said to me, 'They have gone to measure'" - The Book of Enoch
The discovery of the Megalithic Yard
When the late Professor Alexander Thom surveyed over a thousand megalithic structures from Northern Scotland through England, Wales and Western France he was amazed to find that they had all been built using the same unit of measurement. Thom dubbed this unit a Megalithic Yard (MY) because it was very close in size to an imperial yard, being exactly 2 feet 8.64 inches (82.966 cm). As an engineer he could appreciate the fine accuracy inherent in the MY but he was mystified as to how such a primitive people could have consistently reproduced such a unit across a zone spanning several hundreds of miles.
The answer that eluded the late Professor lay not in the rocks, but in the stars.
The MY turns out to be much more than an abstract unit such as the modern metre, it is a highly scientific measure repeatedly constructed by empirical means. It is based upon observation of three fundamental factors:
The orbit of the Earth around the sun
The spin of the Earth on its axis
The mass of the Earth
Making your own Megalithic Yard
These ancient builders marked the year by identifying the two days a year when the shadow cast by the rising sun was perfectly aligned with the shadow of the setting sun. We call these the spring equinox and the autumn equinox that fall around the 21st of March and 21st September respectively. They also knew that there were 366 sunrises from one spring equinox to the next and it appears that they took this as a sacred number.
They then scribed out a large circle on the ground and divided it into 366 parts. All you have to do is copy the process as follows:
Stage one - Find a suitable location
Find a reasonably flat area of land that has open views to the horizon, particularly in the east or the west. You will need an area of around forty feet by forty feet with a reasonably smooth surface of grass, level soil or sand.
Stage two - Prepare your equipment
You will need the following items:
Two stout, smooth rods approximately six feet long and a few inches diameter. One end should be sharpened to a point.
A large mallet or heavy stone.
A short stick with neatly cut ends of approximately 10 inches. To make life easier this should have small cuts made into it to mark out five equal parts.
A cord (a washing line will do) approximately forty feet in length.
A piece of string about five feet long.
A small, symmetrical weight with a hole in its centre (e.g. a heavy washer).
A straight stick about three feet long [Special Memo to Beranger...that is, er, one yard]
A sharp blade.
Stage three - Constructing a megalithic degree
A megalithic circle was divided into 366 equal parts, which is almost certainly the origin of our modern 360 degree circle. It seems probable that when mathematics came into use in the Middle East they simply discarded 6 units to make the circle divisible by as many numbers as possible. The megalithic degree was 98.36% of a modern degree.
For purposes of creating a Megalithic Yard you only need to measure one six part of a circle, which will contain 61 megalithic degrees. This is easy to do because the radius of a circle always bisects the circumference exactly six times. (Interestingly, the geometrical term for a straight line across a circumference is a 'chord').
So, go to a corner of your chosen area and drive one of the poles vertically into the ground. Then take your cord and create a loop that can be slipped over the rod.
Originally the megalithic builders must have divided the sixth part of the circle into 61 parts through trial and error with small sticks. It is highly probable that they came to realise that a ratio of 175:3 gives a 366th part of a circle without the need to calibrate the circle.
Your next step is to make sure that your cord is a 175 units long from the centre of the first loop to the centre of a second loop that you will need to make (the length of the units does not matter). For convenience use a stick of about 10 inches in length to do this, but to avoid an over-large circle mark the stick into five equal parts (you can cheat and use a ruler for this if you want). Next use the stick to measure out 35 units from loop to loop, which will give you a length of approximately thirty feet.
Now place the first loop over the fixed rod and stretch out the cord to its full length in either a westerly or easterly direction and place the second rod into the loop. You can now scribe out part of a circle in the ground. Because we are using the ratio method there is no need to make out an entire sixth part of a circle; a couple of feet will do.
Next take your piece of string and tie it neatly to the weight to form a plumb line.
You can then drive the rod into the ground using the plumb line to ensure that it is vertical. Then take your measuring stick and mark out a point on the curve that is three of the units away from the outer edge of the rod. Return to the centre and remove the first rod, marking the hole with a stone or other object to hand. This rod has now to be placed on the spot that you have marked on the circle, making sure that it is vertical and that its outer edge is three units from the corresponding edge of the first rod.
Return to the centre of the circle and look at the two rods. Through them you will be able to see exactly one 366th part of the horizon.
Stage four - Measuring time
You have now split the horizon so that it has the same number of parts as there are sunrises in the course of one orbit of the sun. Now you need to measure the spin of the Earth on its axis.
You will have to wait for a clear night when the stars are clearly visible. Stand behind the centre point and wait for a bright star to pass between the rods. There are twenty stars with an astronomical magnitude of 1.5, which are known as first-magnitude stars.
The apparent movement of stars across the horizon is due to the rotation of the Earth. It follows that the time that it takes a star to travel from the trailing edge of the first rod to that of the second, will take a period of time exactly equal to one three hundred and sixty-sixth part of one rotation (a day).
There are 86400 seconds in a day and therefore a 366th part of the day will be 236 seconds, or 3 minutes 56 seconds. So your two rods have provided you with a highly accurate clock that will work every time.
When you see a first magnitude star approaching the first pole take your plumb line and hold the string at a length of approximately sixteen inches. Swing the weight like a pendulum and as the appears from behind the first rod count the pulses from one extreme to the other.
There are only two factors that effect the swing of a pendulum; the length of the string and gravity - which is determined by the mass of the earth. If you swing a pendulum faster it will move outwards further but it will not change the number of pulses.
Your task now is to count the number of pulses of your pendulum whilst the star moves between the rods. You need to adjust the length until you get exactly 366 beats during this period of 3 minutes 56 seconds. It is likely to take you several attempts to get the length right so be prepared to do quite a bit of star gazing.
Stage five - Making your Megalithic Yard measure
One you have the correct length of pendulum mark the string at the exact point that it leaves your fingers. Next take the straight stick and place the marked part of the string, place it approximately in the centre and pull the line down the stick. Mark the stick at the point in the centre of the weight and then swing the pendulum over to the other side of the stick, ensuring that the marked part of the string stays firmly in place. Then mark the stick again to record the position of the centre of the weight.
Discard the pendulum and cut the stick at the two points that corresponded with the position of the weight.
Congratulations, you now have a stick that is exactly one Megalithic Yard long.
It is interesting to note that the curious British measurement unit known as a 'rod' or a 'pole' is equal to 6 megalithic yards to an accuracy of one percent. There are 4 rods to a chain and 80 chains to a mile. Could it be that the modern mile of 1760 yards is actually based on the prehistoric measure of the Megalithic Yard?
All content © Robert
The Celtic Rod, Pole or Perch - Stonehenge and Before (and that neolithic yard as well)
|April 2 2005, 10:02 AM |
Ancient measures in Celtic and other traditons - more follows:
THE MEGALITHIC YARD, THE POLE, STONEHENGE AND THE CIRCUMFERENCE OF THE EARTH - by Peter Sain ley Berry
Various writers have suggested that Stonehenge was laid out using the Megalithic yard of 2.72 feet as the base unit. This paper puts forward the alternative suggestion that the pole was used as the base unit of measure and shows how four major circles at Stonehenge could have been constructed using this measure. The paper also traces the pole's relationship to other ancient measures and to the circumference of the earth.
The Pole, the Acre, the Celtic League, the Earth's Circumference
The author has demonstrated that there is evidence to suggest that Neolithic builders in South Wales used the pole as a base measure (3). This measure (the pole) is one eight millionth of the circumference of the earth and also forms the basis of the Celtic League (500 poles) a measure in daily use in Western Britain until approximately the mid-eighteenth century (1).
The pole is also the basis for the area measure the acre - one acre being 160 square poles - a number easy to divide up when sharing land, for instance. Before the Statute mile was fixed in the late middle ages, reducing the length of the mile from 10 to 8 furlongs, there were 1,000 acres in a square (old English) mile. There are today 640 acres to a square Statute mile.
Moreover, the relationship between acre and pole is such that the number of acres to the land and marine surface of the earth is 100,000 times the radius of the earth expressed in poles. There is no 'magic' to this: it is the result of two formulae that reduce to 4 (or 400,000) over o . This relationship to the acre helps to confirm the pole's status as a true measure derived from the earth's circumference.
Nor is the pole the only ancient measure derived from the circumference of the earth. The digit of 0.729 inches - one of the two principal units used in the construction of the Great Pyramid (1) represents one hundred thousandth of a minute of arc at the earth's circumference, if this is taken as 39,996 kilometres.
The other unit used in the construction of the Great Pyramid is the cubit of 20.63 inches (1). This measure is 28.3 digits in length - a multiple that been the cause of some perplexity. The two units are in fact linked: the hypotenuse of a right-angled isosceles triangle measures one cubit if the other two sides of the triangle each measure 20 digits. The digit is based on rational numbers representing fractions of the earth's circumference. The cubit is based on the irrational square root of 2.
The Egyptians evidently used one unit for the sides of the Pyramid and another for the diagonals. This is interesting as it suggests that their command of decimals and of measuring in fractional units was not complete. Why otherwise have two systems? This indication that the ancients might not have worked in decimals is significant in the context of Stonehenge and other Neolithic structures. There is some evidence - see later in this paper - that the ancients in Britain had a similar difficulty in working with decimals and complex fractions and avoided them.
But to revert to the pole. This is fixed in the imperial system of measurement at 198 inches - a quarter of a chain of 22 yards. There is however evidence that suggest that the pole was fractionally shorter in Neolithic times - around 196.8 inches.
This evidence is twofold. First, if we accept that there are 8 million poles to the earth's circumference then a pole of 196.8 inches gives a better 'fit' than the pole of 198 inches; (39,990 kilometres as opposed to 40,234 kilometres). Secondly, the spacing between numerous ancient sites in South Wales - and between sites and geographical features - are frequently found to be 'whole number' - that is 1,000; 2,000; 3,000 etc - distances when measured using this slightly shorter pole of 196.8 inches (3).
Many people have difficulty in believing that the ancients could conceive of living on a spherical planet, let alone in measuring it. This casts doubt on their own (modern) intelligence rather than that of the ancients who were of course no inferior in their powers of intuitive reasoning to anyone alive today. In fact there is good reason to believe that the myth of a flat earth is of relatively recent provenance.
Anyone who observes the moon and the sun, who views the curved horizon, who watches ships appear and disappear over the ocean, who watches the sun shining on a sphere or an ovoid, who thinks of the consequence of a flat earth and what would happen to the sea and so forth, must conclude that we live on the surface of a globe and that the sun and moon are globes as well.
As for measuring the earth's circumference - there are a number of ways this could have been done. At any given time on any given day the shadow cast by a vertical stick will be a function of latitude. The difference in the length of shadow in two places due north of one another and a known distance apart can be used as the basis of a calculation of the earth's circumference. Another and perhaps simpler way would be by triangulation across the surface of a lake or the sea using a heliograph shone across an estuary or channel at low tide.
The Bristol Channel, running as it does east west and with a width of some 20 -25 kilometres would have been ideal for such measurement using a north-south shining heliograph. Setting the heliograph on the south shore at sea level the observer on the north bank would experiment in order to find the elevation at which it was just possible to see over the curve in the sea caused by the earth's circumference.
Progress of Civilisations
A frequent objection to accepting that such technology - such as measuring the circumference of the earth - was available to the ancients is that it does not seem to be written up in Roman literature and certainly did not begin to be thought feasible in modern times until after the Renaissance. If the ancients had had these skills, why did they not pass them on to their successors?
This is only an objection if one believes that civilisation progresses in a straight line - ever onward and upward. But is this really so? Mankind has been around for 100,000 years according to some estimates. There is no reason to think we were less intelligent then than we are now. Societies have however been wiped out, and their civilisations extinguished, by famine, disease, conquest, inundation - a multitude of reasons. And when civilisations have been lost so their knowledge and technology has been lost too. It is only perhaps in the last 500 years, and with the widespread use of writing and printing, that civilisation has progressed in something like linear fashion. Even then one has only to glance at a 100 year old encyclopaedia to see the scope of the technology and skills of yesteryear that have since been abandoned and lost.
The Megalithic Yard
Various writers measuring ancient sites have concluded that the builders used a unit called the Megalithic yard, generally but perhaps not universally held to be 2.72 feet. This may or may not be a real measure in its own right. Burl suggests that local variations exist among British stone circles (4) and at Stonehenge some measurements suggest a measure of 2.73 feet rather than 2.72 (but this may depend anyway on how accurately - see below - the site has been measured).
One real problem with the Megalithic yard is that there are, apparently, no other measures that relate to it. Nor does it relate to the circumference of the earth. There are no sub-divisions of the Megalithic yard - at least that have come down to us, nor are there any multiples. It is hard to conclude therefore that it is an independent measure at all.
However, if the pole is taken as 196.8 inches and the Megalithic yard as 2.73 feet then the correspondence between one pole and six Megalithic yards is so close (0.2 inches) as to be within measuring tolerance. Which brings us to the subject of accuracy.
Accuracy - or rather Spurious Accuracy
There are a number of reasons why any measurement of ancient sites that we may make today, such as the distances between standing stones, for example, or the diameter of henges, is likely to be no more than an approximation of what the ancient designers had in mind. At least five factors are likely to distort the true picture.
First, in order to measure something we have to interpret what it is that we are measuring. The distance between two stones may seem straightforward - but are we measuring between the inner faces, or the outer faces, or from some notional mid-point? Recognising that the surface of a stone is not perfectly flat do we measure from the deepest indentation, the highest projection, or do we try to take an average?
Do we measure at ground level, or some height above ground - and if so what height?
If one stone is leaning should we correct for this and if so how? Different people will answer these questions differently. This factor becomes even more complex when measuring, let's say, the diameter of a stone circle, or trying to ascertain the theoretical mid-point of a church built on an ancient site. Using a map is no substitute for the problem then just devolves to the map-maker.
Secondly, no measure we make - even between two points over which no ambiguity exits - can be perfect. All measurements are approximations and some will be more approximate than others, particularly where measuring has to be done over any significant distance.
Thirdly, since an ancient site was laid out there may have been small movements in the earth. The land may have shifted by a fraction as a result of an earth tremor or subsidence. Coastal sites will have been subject to erosion. Clearly the UK is not subject to significant earthquakes, but small ones do occur.
Then there is the possibility that over time, and as one building on an ancient site has succeeded another, the apparent centre of the site may have shifted. An extension built to a church will alter the theoretical mid point even though the original building may have been accurately positioned. Another factor altering the mid-point of sites will be erosion or even weathering, which may occur to a greater extent on one side of a site or stone than another.
Fourthly, while the ancients where undoubtedly clever those who had the task of constructing their sites were only human - and humans make errors. Two builders working from an identical set of plans will not construct two buildings of precisely the same size. Subtle differences creep in. Can we assume that Neolithic builders would have been any better? We surely have to assume construction inaccuracies.
Lastly, even were builders able to build with absolute accuracy there is still the question of how to interpret the designers' plans. The source of inaccuracy here is the reverse of the first source above. If the Neolithic Grand Wizards or High Priests request two stones to be set 100 poles apart, from which points on the stones should we measure exactly?
These different sources of inaccuracy may cancel each other out. Alternatively the errors may be cumulative. If we allow only a quarter of one percent for each of these inaccuracies then that suggests that what we measure on the ground today could be as much as 1.25% bigger or smaller than what the designers intended.
Within this margin measuring an ancient site must be a matter of opinion. It is a work of detection to fathom what the designers were really after, as the following example may demonstrate.
David Furlong's 666
In his fascinating book, the Keys to the Temple, David Furlong draws attention to a circle of ancient sites in the neighbourhood of Stonehenge. He gives the radius of this as 9.576 kilometres and says that the dimensions of the circle are such that when multiplied by the 'enigmatic' number 666 they equal the circumference of the earth. The number 666 is mentioned in the Book of Revelations from whence - at least in part - derives its enigma, says Furlong.
It is quite true that the dimensions of the circle (as given by him) are indeed this fraction of the earth's circumference. But is it the case that the multiplication relies on an unrealistic degree of accuracy both in the construction and measurement of the circle and of the measurement of the circumference of the earth? Albeit using maps, David Furlong gives the radius of the circle to 1 metre in nearly 10 kilometres - that is 1 in 10,000. Is this level of accuracy achievable?
Similarly, the figure for the earth's circumference generated by multiplying a circle of this radius by 666 is 40,077 kilometres - the exact measurement of the earth's equatorial circumference. This agreed measure of the circumference has only been reached in comparatively modern times. The kilometre - derived in the late eighteenth century - was based on a supposed circumference of 40,000 kilometres.
It is reasonable to assume both a 1 per cent margin of inaccuracy in the measurement of the circle and in the measurement of the earth. But if we do this then the 'enigmatic' number 666 becomes an unenigmatic 665 or 667 or some figure in between.
There is another reason for doubting the significance of 666. There do not appear to be other instances of the ancients using such complicated multiples. The evidence (such as it is) seems to be the reverse - that they didn't work with complicated fractions and nor did they work with decimals.
Nevertheless, I do believe that David Furlong's is broadly correct. His circle is indeed related to the earth's circumference and via the number 666. Except that this (I suggest) is not six hundred and sixty-six but one thousand times two-thirds. To see how we must first make the assumption that the builders of David Furlong's enigmatic circle were measuring in poles.
If we take the earth's circumference as 8,000,000 poles and divided this by 2000/3 (one thousand times two-thirds) as above, then the result is 12,000 poles - or one and a half times a thousandth part of the earth's circumference.
12,000 poles is 59.98 kilometres (taking the pole at 196.8 inches) which yields a circle of radius 9.542 kilometres (taking o as 22/7). The difference between this and David Furlong's radius of 9.576 is approximately one third of one per cent - easily within the tolerance range of measuring accuracy.
The conclusion is therefore that Furlong's circle is yet another ancient site measured in round numbers of poles. The radius of this circle is approximately 1,900 poles and the circumference is - or was intended to be - 12,000 poles. There is no need to evoke any number like 666 except as two-thirds of a thousand.
The Stonehenge site also appears to be laid out using the pole, although traditionally it has been measured in Megalithic yards. Not only does the pole give a better 'fit,' with more rational (round whole) numbers, but we can see that the principal concentric circles at Stonehenge have been planned not only on a linear basis but to give round whole numbers in terms of area (acres) as well. Moreover, using no more than some rope, pegs and a single one pole measure it would appear to be quite possible to lay out the major circles at Stonehenge - Heel Stone, Aubrey, Sarsen and Bluestone.
Robin Heath's book 'Stonehenge (2) gives the major measurements in feet and in Megalithic yards - and provides much detail about the potential use of the site as a solar and lunar calendar. The book does not, however, address the question of why the circles at Stonehenge might be the size they are.
There are four principal concentric circles at Stonehenge. The outer circle - what might be called the Heel Stone circle for this stone lies on its circumference - has a radius of some 80 metres. Inside this is the so-called Aubrey circle of post-holes; this has a radius of some 43 metres. Inside this again is the famous Sarsen circle of (originally) 30 uprights and 30 lintels, which has a radius of some 15 metres. Inside this is the circle of bluestones with a radius of approximately 11.5 metres. There are other circles, ellipses and horseshoes at Stonehenge. I have not looked at these, but the probability must be that they too are based on the pole.
Taking each of these circles in turn we can see how the pole 'fits' their measurement
as well or better than the Megalithic yard and how these circles might have been constructed. We do however need to be aware of the limitations of accurate measurement as discussed above.
The Heel Stone Circle
For instance, Robin Heath indicates that the radius of the outer Heel Stone circle is the same as the length of the long side of the Station Stone rectangle (part of the Aubrey circle). He gives this as 79.59 metres or 12 measures of a unit of 8 Megalithic yards. This equates to 15.92 poles (taking the pole as 196.8 inches).
If we allow a tolerance here of 8 parts in 1600 or half a percent - well within the likely margins of error - we can suggest that this outer circle might have had - or might have been intended to have - a radius of 16 poles.
If so this would have had some distinct advantages. For a circle whose radius is 16 poles has a circumference of (to within half a percent) 100 poles and is 5 acres in area. Such round dimensions are unlikely to occur by chance.
Nor is 16 any arbitrary whole number - for measures relating to the pole (apart from the 500 pole Celtic league) seem based on the number 4. Thus there are 4 poles to a chain, 40 poles to a furlong, 160 square poles to the acre and 8 million poles to the earth's circumference.
If we use Megalithic yards to describe this circle then we have: radius 96, circumference 603. We do not know of any units of area based on the Megalithic yard. We have to ask why the designers did not make the radius 100, or the circumference 600?
It would be justifiable perhaps to say that the builders were aiming for a radius of 100 but were simply inaccurate although this then would require the (somewhat improbable) assumption of a four per cent error. But a radius of 100 would give a circumference of 628 - not an obvious number. Then there is the question of area. We know of no measures of area based on the Megalithic yard and taking this as one sixth of the pole gives us 5,760 square Megalithic yards to the acre - again an improbable figure.
The pole therefore certainly seems then to be a better fit here. Moreover, the Heel Stone circle could be marked out simply by measuring a 16 pole length of rope, pegged at one end and describing a circle around it.
The Aubrey Circle
Now the Aubrey Circle. This has two key features. First, around the circumference are 56 evenly spaced 'post-holes,' presumably to allow posts to be inserted and removed as the sun or moon tracked across the sky. Secondly, four stones known as the Station Stones (of which two are now missing) located on the circumference of the Aubrey Circle define a rectangle - the Station Stone rectangle - that is thought to have been used for purposes associated with the calendar. The dimensions of this rectangle appear to be important.
Unlike the Heel Stone Circle, for which no great accuracy would have been needed, the Aubrey Circle with its postholes and Station Stones would require constructing with great accuracy if it were to be used for the purpose for which they appear to have been built.
The key measurements of the Aubrey circle and Station Stone rectangle (as given by Robin Heath) are as follows: circumference 271 metres; diameter 86.22 metres; radius 43.11 metres; long side of rectangle 79.58 metres; short side of rectangle 33.16 metres. Distance between post-holes: 4.84 metres; area: 23,364 sq. metres.
Translated into Megalithic yards these become: circumference 326.9; diameter 104; radius 52; long side of rectangle 96; short side of rectangle 40; distance between post holes 5.84; area: 33, 993 sq. Megalithic yards.
Translated into poles these are: circumference 54.2; diameter 17.24; radius 8.62; long side of rectangle 15.92; short side of rectangle 6.632; distance between post holes: 0.97; area: 5.84 acres.
It would appear at first that the Megalithic yard wins hands down on this circle - but looked at more critically a number of questions occur. If the Aubrey Circle really was constructed in Megalithic yards, why choose such odd numbers - a radius of 52, a diameter of 104? Such units could not have been intrinsically easy to work with.
Again we may want to consider that these measurements may not be accurate or exactly what the designers intended - the radius might have been 50 for instance - though again this would requires an improbable adjustment of 4 per cent. The problem however is that reducing the radius would make the rectangle sides shorter and the 96 would then become just over 92 - even further from a round '100.'
Then we have to think why the post-holes were constructed in the first place. We believe they were dug in order to let people move posts around a circle to mark the days or months or lunar cycles or whatever. Surely, in this case the designers would have specified a circle in terms of the distance between the post-holes rather then in terms of a circle radius? And would that distance then not have been some simple and straightforward distance?
Then we have to think how Neolithic builders might have set to work to construct a circle of a radius of 52 Megalithic yards with great accuracy and to produce a rectangle inside it that was again perfectly accurate? Achieving a length of 16 poles is relatively easy - we just double a single unit four times - but half of 52 is 26 and half of 26 is 13 - not an easy number to work with.
Last we must ask - how accurate are the measurements quoted by Robin Heath? If the Megalithic yard is used as the unit the measurements seem suspiciously exact. For an intended diameter of 104 we might have expected to record 103.9, for instance, or 104.1 rather than 104 on the nail.
Let us see what happens if we assume that the figures quoted by Robin Heath are just a half per cent too small. The measurements in poles now become: circumference 54.47; diameter 17.33; radius 8.66; long side of rectangle 16; short side of rectangle 6.66. Distance between post-holes: 0.973; area: 1.48 acres.
What we now have is very interesting. The long side of the rectangle has become 16 poles exactly. The same unit that was used to construct the Heel Stone circle. The short side appears to be an odd number - 6 ? - but the diagonal of the rectangle (also, of course, the diameter of the circle) is odd as well - 17 ?. A dd these two figures together and we have 24 - a nice round number - 16 units and one half of 16 units - easy to construct!
Now using a piece of rope 16 poles long (which was already marked out in constructing the Heel Stone circle) we can construct not only the Station Stone rectangle but the Aubrey Circle as well.
First the rectangle. The diagonal of the Station Stone rectangle divides it into two Pythagorean triangles with sides in the ratio 5:12:13. It is easy enough to construct a right angle by drawing intersecting arcs and we already have the 16 pole length for the long side of the rectangle. With a 16 pole length of rope it is easy enough to produce a 24 pole length of rope. This length of rope can be used to lay out the short side and the diagonal of the rectangle. From the diagonal, the unit 17.333 poles can be established and a rope this length divided in two will give the necessary 8.667 pole radius for drawing the Aubrey Circle.
It is not easy to see how one could do the same thing in Megalithic yards with the same accuracy.
Note also how by using the pole we obtain a post-hole spacing of 0.97 poles - almost one pole exactly (as opposed to 5.84 Megalithic yards). If the main reason for the circle was the post-holes, then it is likely that the designers would have specified a set distance between the holes rather than anything else. And what would be more natural than to specify a circle of 56 holes with a distance of just one pole between each?
However, a strict spacing of 1 pole would have entailed a circle with a diameter of 17.82 poles - a radius of 8.91. The station stone rectangle would then have been then 6.85 poles x 16.45 poles. The builders might well have shaken their heads. Without decimals or accurate measuring techniques, constructing such a circle would have been impossible.
Let's suppose the head builder proposed making the circle a little smaller so that the long side of the rectangle became 16 poles. As we have seen this length would have been bread and butter to a Neolithic builder. Moreover, it is only 16 times his basic unit (as opposed to 96 if one measures in Megalithic Yards). And from this - as we have seen above, both the rectangle and the circle could be constructed with relative ease and accuracy.
But instead of being a pole apart the post-holes would now be 0.97 of a pole apart. Clearly a builder might have had difficulty in computing 0.97 of a pole. We can't know exactly what happened but it is worth noting that the radius of a circle with a 56 pole circumference is 8.91 poles. This is exactly a quarter of a pole greater than the actual 8.66 radius of the Aubrey Circle.
Now a quarter of a pole would not be difficult to measure. So it would have been possible to describe a second circle outside the first and on this to measure the 56 necessary one pole spacings. It would have then been a simple matter to transfer these settings to the inner circle - the gap between the two circles being about 120 centimetres - reducing the spacings fractionally at the same time.
The Aubrey Circle occupies 1.475 acres - that is rather less than two per cent short of a round 1.5 acres. For all practical purposes this should surely be counted as a 'whole' number. (Note: in these measurements of area the acre is being taken as 160 square poles where the pole is being taken as 196.8 inches, rather than the 'imperial' pole of 198 inches on which the present day acre (though still 160 square poles) is based).
We can therefore reasonably conclude that the Aubrey Circle was laid out in poles rather than Megalithic yards.
The Sarsen Circle
We now pass to the great Sarsen circle of 30 uprights and lintels. This circle has a radius of some 15 metres. Its median diameter (that is to the centres of the uprights) is given by Robin Heath as 100.8 feet (30.72 metres) that is 6.15 poles or 37.06 Megalithic yards of 2.72 feet.
The outer circumference, around the external perimeter of the lintels, he gives as 327.6 feet. This is 120.4 Megalithic yards of 2.72 feet or 120 exactly if the Megalithic yard is taken as 2.73 feet rather than 2.72. It is also 19.98 poles of 196.8 inches. It would appear that the circumference is the key measurement of the Sarsen circle.
Robin Heath gives the length of the Sarsen lintels as 10.92 feet - exactly 4 Megalithic yards of 2.73 inches, or 0.666 (that number again! - that is two-thirds) of a pole. The width of the lintel is given as 3.475 feet or 1.27 Megalithic yards or 0.21 of a pole. However the lintel is curved and the block needed to carve a lintel of these dimensions would need to have been thicker - approximately 1.50 Megalithic yards or 0.25 poles.
The lintel blocks could thus have been measured with equal ease in poles or in Megalithic yards. In poles they would have been two thirds of a pole by a quarter of a pole; and in Megalithic yards: four by one and a half. However, if the blocks are the size he suggests then almost certainly the outer circumference of the lintel circle would have been larger than the figure given here in order to allow some tolerance between the stones. With so many stones missing from the Sarsen circle no present day measurement can be considered wholly accurate.
We have seen how the length of 16 poles appears to be a key building block in the Heel Stone and Aubrey circles. A circle with a radius of one fifth of 16 poles - a fraction by no means impossible to measure - would have a radius of 3.2 poles and a circumference of 20.11 poles or 329.87 feet. The difference between this and the figure given by Robin Heath is just over 27 inches. At a little over half a per cent this is well within the tolerance level we should afford to these measurements. In practical terms it would mean a small gap of less than an inch between each of the lintels - just enough room to allow them to be manoeuvred into position and adjusted.
Something that helps to confirm 3.2 poles as the radius of the outer edge of the lintels is the area measurement of the circle thus described, which then becomes exactly one fifth of an acre.
What is now needed is a circle on which to locate the uprights. This has to be constructed with great accuracy. The radius needs to be 3.08 poles. The question thus becomes how to lay out this circle without sophisticated measuring instruments - just some rope, a pole rod and a few pegs. It might have been done this way.
A rope length of 16 poles can be folded without difficulty into an equilateral triangle and held with pegs. It is then easy to find the exact centre of the triangle. If the Stonehenge builders did this, it could then have been placed over the 'hub' of the Stonehenge complex. The circle that can be drawn around the three points of this triangle will then have a radius of 3.08 poles and a diameter of 6.16 poles. This is very similar to the diameter for the median circle (that is the circle through the centres of the uprights) given by Robin Heath (the equivalent of 6.15 poles).
Thus starting with one piece of rope 16 poles in length - the same length that provided the fundamental building block for the Heel Stone and Aubrey circles - we could now lay out both the circle for locating the Sarsen uprights and the lintel perimeter circle.
Robin Heath gives the height of the lintel circle as 'about 15 feet above the ground.' The Encyclopaedia Britannica already quoted gives the height as 16 feet. It seems probably that it may have originally been designed to be one pole (16.5 feet approximately) in height - another reason for believing that the pole has more claim to Stonehenge than the Megalithic yard.
The final circle in this tour is the Bluestone circle. This would appear to be constructed on exactly the same basis as the circle locating the Sarsen uprights, although at just three-quarters of the size. The circle would be laid out in the same way - apart from using a rope of 12 poles instead of 16 poles for the equilateral triangle - giving a circle of radius 2.31 poles and an area of a tenth of an acre (actually 0.105 acres). The circumference would have been 14.5 poles.
The spacing between the stones - Robin Heath suggests there were 59 or 60 - would have been 0.246 or 0.242 poles respectively. At just under a quarter of a pole we are seeing here the same phenomenon as we saw in both the Aubrey and Sarsen circles. Each circle is actually two circles with the spacing between the stones (or the posts) being calculated on the circumference of an outer circle just beyond the locating circle. If there were 60 stones, then this outer spacing circle would have a circumference of 15 poles with quarter pole spacings.
None of these figures look better in Megalithic yards and again the pole seems to win hands down.
Peter SAIN LEY BERRY
10 March 2004
Re: The Megalithic Yard - A Long Time Before King Edward I!
|April 2 2005, 6:16 PM |
Having ploughed through the verbiage about how to measure a megalityic yard, what the writer is trying to say is that a pendulum which beats 366 times in 236 seconds has a length of one megalithic yard.
Given that the formula for the period of a pendulum is
T = 2*pi*square_root(length/gravity)
Set T = 236/366 and gravity = 9.81.
The answer is 0.1033m which is a lot less than one megalithic yard.
Tony, where do you dig up this trash?
Re: The Megalithic Yard - A Long Time Before King Edward I!
|April 2 2005, 9:38 PM |
In what year did the late Professor Alexander Thom publish his work?
I believe it was 1955. He began his work in 1934.
The name "Megalitic Yard" may be younger than you!
Professor Thom also named another common distance found in stone circles the "Megalithic Rod" (2.5 Meg. Yds = 1 Meg. Rod)
So lets go the other way. If you divide the Meg. Yd. by 2.5, you get a figure of just over 13 inches.
Are we back to the Northern Foot of 13.2 inches again?
Anyway, I recently discovered a measuring stick in the back of a cupboard. It was nearly a metre long and was divided into 36 units.
I measured it. It is 0.9144 metres long. I think I will name it the Megalithic Metre!
The megalithic yard has the same relationship to the yard that the megalithic metre has to the metre (and the megalithic metre is a slightly more accurate when compared to the metre than the megalithic yard to the yard)
The CMS report states (at Section 8.9)
"We can go back at least to the Molmutine laws, devised and codified in around 390 B.C. by the then King of the Britons, Dyfnal Moel Myd (the laws were named after him). These laws used some of todays measures, such as feet, yards and acres, which go back well beyond even 390 B.C"
The more that Tony posts, the more he shows the above to be incorrect!
Re: The Megalithic Yard - A Long Time Before King Edward I!
|April 2 2005, 11:35 PM |
"Anyway, I recently discovered a measuring stick in the back of a cupboard. It was nearly a metre long and was divided into 36 units."
Did you, by chance, discover this yardstick in Scotland? If it really is about 1 m long, then it is probably an old northern yard, and thus has no need of renaming. But your point is taken ;)