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Megalithic Mensuration 3. The Megalithic Inch.

3.3.1  Thom believed that the insistence on integrality in megalithic maths was a reflection of the trial-and-error approach to the development of the large range of designs. Rather than reduce mathematical explorations to precise formula or clear relationships more empiric methods were used to build 'libraries' of series of acceptable designs. This would demand exhaustive explorations, at small scale, which might have taken place on close turf, or sand, perhaps on beaches. To maximise this approach it is obvious that the chosen units of measurement should be very manageable and have simple scaling proportions to the larger version projects they must ultimately express. 3.3.2  The cup-and-ring marks. In groups of rock-cut designs in Scotland Thom claimed to have identified a sub-division of the Megalithic Yard. He termed this the Megalithic Inch, one 40th of the yard. 1/40th MY = 1 Megalithic Inch (MI) = 0.816 ins = 20.73 mm. and 1 Megalithic Rod = 100 MI.

A.Thom,'Megalithic Sites in Britain' p.112 It has been shown elsewhere that there existed in Britain in Megalithic times a widespread knowledge of geometry. We find designs drawn with the same conventions set out on the ground and inscribed on rocks and stones......

Auchnabreck cup-and-ring marked rock, Argyll.

.........In both there is the same insistence on integral lengths. The linear unit that we find on the rock designs is 0.816 inch or exactly one-fortieth of the Megalithic yard used in ground plans. The designer undoubtedly used a set of beam compasses with the distance between the inscribing points advancing by units or half units.This explains the preoccupation with integral lengths and the necessity of using triangles with sides of integral length satisfying the Pythagorean theorem.

These enigmatic rock cut cup-and-rings designs are to be found throughout the ranges of megalith building in Britain. Attempts at explaining them vary from rock-cut art, or territorial boundary markers to rites-of-passage activities. They are often carved on standing stones or walls of chambered cairns, but the most developed groups are found on living rock faces around Auchnabreck in the Kilmartin Glen, Argyllshire. Although these large groupings are in the vicinity of several major stone rows and chambered cairns there are no clear connections to these monuments. Thom believed he could identify, to parts of an inch, a quantum in the diameters of these rock carvings. 40 of these quanta make 1 Megalithic Yard, 100 make a Megalithic Rod.

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