The surveyor of megalithic monuments in Britain, Alexander Thom (1894 – 1985), thought the builders had a single measure called the Megalithic Yard which he found in the geometry of the monuments when these were based upon whole number geometries such as Pythagorean triangles. His first estimate was around 2.72 feet and his second and final was around 2.722 feet. I have found the two megalithic yards were sometimes 2.72 feet because the formula for 272/100 = 2.72 involved the prime number 17 as 8 x 17/ 100, and this enabled the lunar nodal period of 6800 days to be modelled and and the 33 year “solar hero” periods to be modelled, since these periods both involve the prime number 17 as a factor. In contrast, Thom’s final megalithic yard almost certainly conformed to ancient metrology within the Drusian module in which 2.7 feet times 126/125 equals 2.7216 feet, this within Thom’s error bars for his 2.722 feet as larger than 2.72 feet.

This suggests Thom was sampling more than one megalithic yard in different regions or employed for different uses. Neal [2000] found for Tom’s statistical data set having peaks corresponding to the steps of different modules and variations in ancient metrology, such as the Iberian with root 32/35 feet and the Sumerian with root 12/11 feet. It is only when you countenance the presence of prime numbers within metrological units that one breaks free of the inevitably weak state of proof as to what ancient units of measure actually were and, more importantly, why they were the exact values they were and further, how they came to be varied within their modules. However, the megalithic yard of 2.72 appears to outside the system in embodying the prime number 17 for the specific purpose of counting longer term periods which themselves embody that prime number.

The discipline of using only the first five primes {2 3 5 7 11} must have been accompanied by the perception that only if primes were dealt with could certain ends be served. This is crystal clear when we come to musical ratios in which the harmonic primes alone are used of {2 3 5} with an occasional “passenger” of the prime {7} as in 5040 which is 7 x 720, the harmonic constant.

## Using 2.72 feet to count the Nodal Period

The first remarkable characteristic of 2.72 feet is that 8 x 17 in the numerator means that the approximation to π of 25/8 = 3.125 can, in (conceptually) multiplying a diameter, provide an image of 25 units on the circumference of a stone circle. For example a diameter of 2 MY would suggest 17 MY on the circumference, which is quite remarkable. Further to this, we know that the 6800 days of nodal cycle is factored as 17 x 400 and that the MY was shown (acceptably) to have been made up of 40 digits (in conformance to the general tradition within metrology that there are 16 digits per foot and 40 for a step of 2.5 feet, which a MY traditionally is). The circumference of 17 MY is then 17 x 40 digits which means that a diameter of 20 MY would give a circumference of 17 x 400 digits equalling 6800 digits as a countable circumference in digits per day.

This highlights how prime number factors played a role, in the absence of arithmetical methods, in solving the astronomical problems faced by the late stone age when counting time periods in days.

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