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How to create this prehistoric measurement unit for yourself
A guide distributed at Orkney Science Festival by Robert Lomas.
This article describes work carried out with Christopher Knight, whilst co-authoring the book, 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:
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:
Stage three - Constructing a megalithic
degree
A megalithic circle was divided into 366 equal parts, which is very likely to be 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. A megalithic
degree would thus be 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').
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. Make sure that you use a star as using a planet will introduce errors in the timing. This is because a star is a point source of light and will dissapear instantly when passing behind the marker. (This is called occulation) Planets are not point sources and having a disc they fade in and out of view, and so do not give an accurate time when appearing or dissappearing.
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.
There are two mechanical sources of error which limit the accuracy of this technique. These are:
1. Difficulty in estimating the centre of mass of the plumb weight.
The measurement of the working length of the pendulam has to be from the point of suspension to the centre of mass of the plumb weight. If the hole in the weight is not in the centre of mass of the weight then measuring the length to the hole will introduce an error, which will be doubled up as the half megalithic yard which has been created is used to creat a full megalithic yard measuring stick. This error can be shown experimentally by repeating the experiment using a number of differently shaped pendulams. It can be expected to produce systematic errors of the order of 2 -3 millimetres. The smaller your stone the less centre of mass error is introduced.
2. A Digitising Error produced by counting swings of the pendulam
When creating a megalithic yard you have to count 366 complete oscillations of the pendulam whilst observing the occulation of the choosen star. As only completed swings are counted it may well be that there is a a part completed swing in the count which is ignored. At worst this could give an error of 1/366th of a half megalitic in yard in the measured length. which is an error of 2 millimetres in the half megalithic yard you have created.
Consideration of these sources of error show that with reasonable care it is possible to produce a standard unit of length that is repeatable within an accuracy of around half a percent, or about 5mm in a metre. Considering that this is can be created with the absolute minimum of equipement and the method can be explained within minutes it is not surprising that it spread throughout the trading communities of the western Europe during the Neolithic period, as professor Thom discovered.
Some writers have suggested that "Until such a time as a Neolithic measuring rod is excavated, the theory remains unproved." This is a naive statement as any observer, interested enough in the movements of the sun to wish to create a calender to mark the time of planting (as all Neolithic farmers were) will easily be able to deduce the method given above. It also ignores the engineering reality that multiple copying of measuring rods would introduce far greater errors than simply creating a new measure from scratch. Any attempt to distribute measuring rods would not only be highly unlikely, as there would be not central organistaion to do it, but it would be doomed to failure as there was no accurate technology for copying such rods accuarately.
This technique is an excellent example of an algorythm, which is a method of conveying how to produce a standard unit of length, in a few simple words. It is not a basis for suggesting a archeological search for a non-extistent stone-age bureaucracy which created and dispenced 'measuring rods' throughout the Neolithic world!'
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. (Which is about the same order of magnitude as the standard error of creation of the unit). 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?
