The Megalithic Yard: A Mathematical Consequence

of Circumferential Distribution?

G.J. Bath


Analysis of over 300 megalithic rings suggests that many stone circle perimeters are rationally divided, that is, the gaps between orthostats at any given circle all appear to be multiples of a common number of degrees, suggesting the presence of a circumferential unit.

Further analysis of equally-divided circles from the north, west and east of Scotland and the south of England indicates the potential for a circumferential unit common to all which is related to the Megalithic Yard by a factor of π, and it appears that a unit of this magnitude may have been in widespread use. Thus, the Megalithic Yard could be present on diameters mathematically even if it never actually existed.

In combination, these observations would permit the determination of an imputed Megalithic Yard at any reasonably-defined stone circle. This exercise suggests that the implied Megalithic Yard employed at sites throughout Britain and Ireland would potentially have varied by at least three percent either side of the mean. From the author’s surveys and analysis, this derived apparent unit would be marginally less than 83cm (32.7 inches) much as found by Alexander Thom by way of statistical analysis (Thom, 1955, 1961).
Rational Distribution Loch Buie
Rational Distribution at Loch Buie, Mull: The circle in degrees, 48ths and potential circumferential units.

Rational distribution becomes apparent when the gaps at stone circles are expressed in degrees. A circle rationally divided in a multiple of 60 equal parts has gaps that are all multiples of 6 degrees, a circle divided in a multiple of 48 equal parts has gaps all multiples of 7.5 degrees, and if in 72 equal parts the gaps are all multiples of 5 degrees. Clearly, the corollary is also true. This occurs in so many cases across Britain, Ireland, Germany and Scandinavia that it would seem perverse to attribute it entirely to chance.

The procedure also reveals that pattern and balance of distribution about an axis appear to be present at all reasonably defined megalithic rings. Given this, it follows that even the axis of a truly circular site might be identified.

The Megalithic Yard is not immediately apparent in all stone circle diameters because of the above-mentioned variance and the fact that many diameters would appear to be multiples of one-quarter of a Megalithic Yard, and very occasionally one eighth, this being identifiable by the rational division of the circumferences. It is considered possible that the presence of fractions of the Megalithic Yard upon diameters having a variance of three percent or more about the mean may have affected the statistical analyses conducted by Kendall (1974) and Freeman (1976) that led to rejection of a common unit by archaeologists.

A more flexible approach to stone circle design than that proposed by Thom might also be considered in conjunction with the suggested measuring system. In this respect, all the modified layouts (Flattened, Egg-shape, Ellipse, Compound) may well have common design principles - all belonging to the same family and having the same geometrical roots. In this way, it is suggested that there is potentially a single design process underlying all modified rings rather than Thom’s four different.

The above would provide an explanation as to why the Megalithic Yard is present in stone circle diameters. Circumferences appear to be rationally divided and a likely common unit emerges, though with a potentially significant variance, this being related by π to the Megalithic Yard.

The results of an analysis of 230 circles in Britain and Ireland used in the descriptive statistics is referred to herein.

Source: Bath G.J. (2021) Stone Circle Design and Measurement Vol.2. KeyPress.
© G.J. Bath

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