The argument for the subdivision of the megalithic yard can be much simplified, as follows.
It goes without saying that every circle with an integer number of metres on the circumference will have that same number of an apparent unit of 1m/pi (318.3mm) on the diameter.
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In the same way, any circle having an integer number of units with a length of 2.6m on the circumference will have that same number of Thom’s megalithic yard (829mm) on the diameter.
Such a circumferential unit of 2.6m might be appropriate for large circles but would be totally unsuited to small circles and would thus be ideally subdivided. The likely number of divisions can be deduced logically from a subset of well defined stone circles.
Assume that the Aubrey Ring at Stonehenge has an integer number of perimetric units in each of its 56 arcs (gaps). The diameter is 105 megalithic yards, so there would be 105 corresponding perimetric units of 2.6m on the circumference. So, each arc would be 1.875 such units. However, to make this an integer it should be multiplied by 8 to make 15. Thus, there would be 840 perimetric units of 325.5mm on the circumference of the Aubrey Ring and the megalithic yard in this case would be subdivided into eight units of 103.625mm on the diameter which would be 840 such diametric units in length.
Machrie Moor V on the Isle of Arran, Scotland, has two concentric circles both with diameters in megalithic yards. The ratio between them is, perhaps significantly, 14:22 with the inner circle having eight equal divisions. The diameter of this circle would be 112 derived diametric units and the circumference would thus be 8 x 14 corresponding perimetric units.
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However, assuming that the outer circle uses the same unit of measure results in there being a half unit on this circumference, suggesting that the megalithic yard is, in fact, divided into 16 units of 51.8mm (2.04 inches) with a corresponding perimetric unit of 162.8mm (6.4 inches). Analysis of stone circles further afield, including Ireland, bears this out.
The existence of such a perimetric unit is supported by the circles at Stennes (37.5MY diameter) and Balbirnie (17.5MY), in Scotland. The excavation reports suggest that these are not properly equally divided, but it can be appreciated that at each there was a potential tallying error in a multiple of the suggested perimetric unit. At Stennes, the gaps are in multiples of ten units, at Balbirnie they are in multiples of four.
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If it be assumed that the system used at the Aubrey Ring (and also across Scotland, as above) was used at the Sarsen Circle, despite the huge difference in ages, then each of the thirty arcs formed by the lintels would be an integer number of units. However, none of the three obvious circumferences (inner, middle, outer) has a diameter in megalithic yards.
Nonetheless, it so happens that the inner circumference of the Sarsen Circle is 1800 diametric units of 51.8mm, one-sixteenth of a megalithic yard, meaning that each lintel has an inner curve of 60 such units - presumable they were cut from blocks of about 64 units by 22 units, making the effective depth about 20 units (1m).
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This might suggest that there were two physical units, a diametric unit for lateral measure and a perimetric unit for curvilinear measure. This would also remove problems with the incommensurability of pi, as a given number of diametric units on the diameter would produce that same number of perimetric units on the circumference.
The ratio of the circumference of the Aubrey Ring to the circumference of the Sarsen Circle would be 11:4 outer and 44:15 inner (in the diametric unit with pi as 22/7). At this, the diameters would be 29.7m (97.4 feet) and 31.7m (103.9 ft).
Analysis of over 100 stone circles with acceptable archaeology suggests that Thom’s megalithic yard (and the assumed corresponding perimetric unit) varies by about 2% either side of the mean (829mm), far greater than Thom claimed.
Over 300 circles were surveyed, divided into three groups based on confidence levels (high, medium, low). The distribution of diameters is negatively skewed, and Scotland and Ireland may very well be bi-modal
It goes without saying that every circle with an integer number of metres on the circumference will have that same number of an apparent unit of 1m/pi (318.3mm) on the diameter.
In the same way, any circle having an integer number of units with a length of 2.6m on the circumference will have that same number of Thom’s megalithic yard (829mm) on the diameter.
Such a circumferential unit of 2.6m might be appropriate for large circles but would be totally unsuited to small circles and would thus be ideally subdivided. The likely number of divisions can be deduced logically from a subset of well defined stone circles.
Assume that the Aubrey Ring at Stonehenge has an integer number of perimetric units in each of its 56 arcs (gaps). The diameter is 105 megalithic yards, so there would be 105 corresponding perimetric units of 2.6m on the circumference. So, each arc would be 1.875 such units. However, to make this an integer it should be multiplied by 8 to make 15. Thus, there would be 840 perimetric units of 325.5mm on the circumference of the Aubrey Ring and the megalithic yard in this case would be subdivided into eight units of 103.625mm on the diameter which would be 840 such diametric units in length.
Machrie Moor V on the Isle of Arran, Scotland, has two concentric circles both with diameters in megalithic yards. The ratio between them is, perhaps significantly, 14:22 with the inner circle having eight equal divisions. The diameter of this circle would be 112 derived diametric units and the circumference would thus be 8 x 14 corresponding perimetric units.
However, assuming that the outer circle uses the same unit of measure results in there being a half unit on this circumference, suggesting that the megalithic yard is, in fact, divided into 16 units of 51.8mm (2.04 inches) with a corresponding perimetric unit of 162.8mm (6.4 inches). Analysis of stone circles further afield, including Ireland, bears this out.
The existence of such a perimetric unit is supported by the circles at Stennes (37.5MY diameter) and Balbirnie (17.5MY), in Scotland. The excavation reports suggest that these are not properly equally divided, but it can be appreciated that at each there was a potential tallying error in a multiple of the suggested perimetric unit. At Stennes, the gaps are in multiples of ten units, at Balbirnie they are in multiples of four.
If it be assumed that the system used at the Aubrey Ring (and also across Scotland, as above) was used at the Sarsen Circle, despite the huge difference in ages, then each of the thirty arcs formed by the lintels would be an integer number of units. However, none of the three obvious circumferences (inner, middle, outer) has a diameter in megalithic yards.
Nonetheless, it so happens that the inner circumference of the Sarsen Circle is 1800 diametric units of 51.8mm, one-sixteenth of a megalithic yard, meaning that each lintel has an inner curve of 60 such units - presumable they were cut from blocks of about 64 units by 22 units, making the effective depth about 20 units (1m).
This might suggest that there were two physical units, a diametric unit for lateral measure and a perimetric unit for curvilinear measure. This would also remove problems with the incommensurability of pi, as a given number of diametric units on the diameter would produce that same number of perimetric units on the circumference.
The ratio of the circumference of the Aubrey Ring to the circumference of the Sarsen Circle would be 11:4 outer and 44:15 inner (in the diametric unit with pi as 22/7). At this, the diameters would be 29.7m (97.4 feet) and 31.7m (103.9 ft).
Analysis of over 100 stone circles with acceptable archaeology suggests that Thom’s megalithic yard (and the assumed corresponding perimetric unit) varies by about 2% either side of the mean (829mm), far greater than Thom claimed.
Over 300 circles were surveyed, divided into three groups based on confidence levels (high, medium, low). The distribution of diameters is negatively skewed, and Scotland and Ireland may very well be bi-modal