Regional Examples: Some Derbyshire Stone Circles
It should be noted that the sites illustrated below are in central England in which country statistical analysis subsequent to that presented by Alexander Thom deemed the Megalithic Yard not to be present. 1. Notes on Plans The plans presented, though surveyed to scale, are strictly illustrative, being intended to provide only a representation of the site rather than a close depiction. The orthostats are represented by ellipses illustrating dimensions either side of a perceived axis and bearing and thus defining a centre. This provides a constant centre point to facilitate inputs to routines to determine circles of fit and to have fixed points for automated analysis and comparison between sites. 2. Format Specification Ring designs in this work are described as arcconstructs being classified as Flattened, Oval, Elliptical, Compound or Complex, and described by use of a format specification indicating the design type and the parameters required for construction. This takes the form of a text string providing input to a computer program that embodies the general rules of arcconstruct design. The first element signifies the design type (F=Flattened, O=Oval etc.) Further parameters depend on the type, but represent either angles or fractions. Thus, ‘F,240,[1/2]’ represents Thom’s Type A flattened design the primary arc being twothirds of a revolution with the radius divided in two from the centre. A brief introduction to arcconstruct designs is provided in Appendix 2. Note that in this work, the term ‘ellipson’ has been created to describe a twodimensional construction, formed of four arcs, that approximates an ellipse. 3. Group 1 The first two circles discussed lie within 20 kilometres of each other and are very similar in size and orthostat distribution. Bamford Moor Southeast The Bamford Moor SE ring, near the foot of Stanage Edge, requires a moderate walk from the nearest convenient road, half of which is uphill. From the end of the tree line at the top of the hill head in the direction of the two leftmost of several prominent vertical outcrops projecting from the Edge.  
Figure 6: Bamford Moor Southeast. 

As at left in Figure 6, the ring is assumed to be a Flattened construct with a Bridging Arc of onetenth of a revolution, perhaps having a format of F,180,36 in favour of F,180,30. The axis is due south.
At centre, the gaps are shown measured in degrees on the Originating Circle, and it may be appreciated that all are multiples of 12 degrees, that is, one thirtieth of a revolution. One might therefore anticipate a diameter that is a multiple of this number of diametric units. The diameter is 7.8 metres which is 150 units and a multiple of the expected 30. The perimetric dimensions based on the Originating Circle are shown at right in the figure. On this basis, the imputed site Megalithic Yard would be 832mm (7.8m ÷ 150 × 16).  
Doll Tor
Doll Tor is a particularly small ring on the edge of a woodland setting, fairly close to the road, downhill from the Anvil Stone, a short way from the principal entrance to the Stanton Moor megalithic complex.  
Figure 7: Doll Tor. 

As can be seen from the plan at left in Figure 7, the ring is elliptical with the Originating Circle divided into gaps that are multiples of oneeighteenth of a revolution (20 degrees). The axis at the stone numbered 2 bears approximately at 78 degrees (12 degrees north of east). This might suggest a diameter that is a multiple of 90 diametric units (4.66m), four degrees being common to the gaps and axis.
The ring is assumed to be an Ellipson external to the Originating Circle with a Defining Circle half its diameter and a formative angle of 90 degrees at the apex, having the format specification E,90,[1/2], as at centre. The minor axis is 4.6 metres which is 89 diametric units being the expected multiple of 90 units. The distribution at this is shown in the diagram at right in the figure. Thus, the implied site Megalithic Yard would be 818mm (4.6m ÷ 90 × 16). It may be noted that this distribution of 4 x 60 degrees, plus 80 degrees plus 40 degrees, is similar to that found at another Derbyshire circle (see Bamford Moor SE, above), some 20km distant, which is divided as 4 x 60 degrees, 72 degrees and 48 degrees. The difference between the axial bearings of the two rings is 72 degrees (onefifth of a revolution).  
4. Group 2 The next three circles are within one kilometre of each other, two of which appear to be akin to Thom’s flattened modified ring design. Barbrook Northeast Barbrook NE (Barbrook III) can be reached by two access paths from roadside parking. The ring is a few hundred metres north of the juction of these paths.  
Figure 8: Barbrook Northeast. 

At left in Figure 8, the ring is shown as a Flattened circle of one of two possible formats. The inner has a Bridging Arc of 30 degrees (F,180,30) and the outer a Bridging Arc of 36 degrees (F,180,36) this appearing the more likely at first sight due to the two stones either side of the axis at east.
It can be seen from the Model at centre that the stones are distributed in four quadrants, three of which are divided in six with gaps of onetwentyfourth of a revolution (15 degrees) with the southeast quadrant being divided with seven gaps. This suggests a diameter divided into 24 equal parts, at minimum, though the southeast quadrant would require a division into a particularly large 168 parts and a diameter a multiple of this number of diametric units (8.7m) for the hypothesis to hold true. The diameter is 26.2 metres (3 x 8.7m) which is 506 diametric units suggesting 504 units (31.5 MY) as the nearest multiple of 168, and might be seen as producing 24 gaps of 21 perimetric units as at right in the figure. The southeast quadrant is assumed to be 7 gaps of 18 perimetric units and thus providing for 25 stones. However, were there no stone on the axis at east (possibly an entrance) then this would produce a stone count averaging gaps of 21 units. Many of the stones appear to be fallen. There is a stone at an apparent break in the enclosing bank at az.50 which may be solstitial. The axis is taken to be oneeighteenth of a revolution north of west (az.290) which is consistent with a diameter of 504 diametric units (as the circumference or perimeter would divide by 18). The size would also tend to suggest a preferred format of F,180,30 (as 504 divides by 12 not 10). The site Megalithic Yard would be 832mm.  
Barbrook Centre
The restored Barbrook Centre circle (Barbrook II) can be reached by a short walk on the moor over the rise above Barbrook SW (below), but also by continuing along the footpath and striking off uphill at a right angle when locating the modern engraved marker stone to the left of the path.  
Figure 9: Barbrook Centre. 

At left in Figure 9, the gaps are shown expressed in degrees with the azimuths of four stones. This might give an indication that the circle is divided into 120 equal parts, but it is felt that the Model at centre might indicate the original intent. This suggests a division into 40 parts, though the entrance, at az.42 degrees (48 degrees north of east), still hints at 120.
The inner bank is 14.4 metres which is 278 diametric units suggesting 280 as a multiple of 40 and the outer bank has a maximum diameter of 18.5 metres which is 357 diametric units suggesting 360 as a multiple of 120. At this, the site Megalithic Yard would be 823mm. The gaps are shown in perimetric units at right in the figure. It seems that there could have been an error of three perimetric units in the placing of Stone 6 if measured on the outer face of the bank (about 2.7 units on the inner).  
Barbrook Southwest
Barbrook SW (Barbrook I) is a short walk from limited parking on the main road along an established footpath from which the most prominent stone at south can be easily seen.  
Figure 10: Barbrook Southwest. 

The ring is taken to be a Flattened circle with a Bridging Arc of onetenth of a revolution (F,180,36) as at left in Figure 10. The axis is assumed to be oneeighth of a revolution north of east (az.45).
In the Model at centre, the gaps on the Primary Arc are shown in degrees from which it can be seen that the circle would divide into 72 equal parts. There is a stone at due east and the most prominent stone lies at the southernmost point of the ring due south of the design point at the intersection of the Bridging Arc and the crossaxis. The diameter is 14.6 metres which is 282 diametric units suggesting 288 units (18 MY) as the nearest multiple of 72 and a site Megalithic Yard of 811mm. At right, the gaps on the modified face (southwest) are measured, unusually, on the perimeter, much as on the Primary Arc, in multiples of four perimetric units. The perimeter is 271 units for a total of 272, potentially having 13 stones, six at north and seven at south, When simplified, the northwest half is divided as 5 x 6 + 4 and the southwest could have been 6 x 5 + 4 except that it may have been important to place the largest stone due south of the design point.  
5. Group 3 The final two circles are within a few hundred metres of each other, one being embanked and with very few stones extant. The Nine Ladies The Nine Ladies ring sits at the north of the Stanton Moor megalithic complex just off the main track. There is a small outlier, the King Stone, about 40 metres westsouthwest of the centre. The ring is one of a small group of stone circles that seem not to make a seamless transfer between component arcs.  
Figure 11: The Nine Ladies. 

The problem can be seen in John Barnatt’s suggested outline as shown by Figure 11a (top left inset) that consists of four arcs none of which makes a smooth transition from one to the next. The suggested answer to this is to acknowledge that this objective probably cannot be achieved and that the northeast and southwest arcs may be connected purely geometrically, which is to say that the arcs are logically connected but not intended to be physically so.
The Model at Figure 11b (centre inset) is one such construct in which the northeast arc is the Primary Arc at fivetwelfths of a revolution (150 degrees) upon the Originating Circle and the southwest arc is a disembodied arc of the same angle on a circle within a square inside the Originating Circle. The axis is drawn at oneeighth of a revolution north of east (az.45) and the gaps are all multiples of three degrees, so a diameter that is a multiple of 120 units (6.2m) might be expected. It may be appreciated that the generally stated dimensions may belie the true size. Burl’s 11.5 metres by 10.5 metres is accurate enough when measuring between the stones but would not take account of the extents of the design shown. On this basis, the diameter of the Originating Circle would be 240 diametric units (15 MY, 12.4m) as the nearest multiple of 120. On this basis, the site Megalithic Yard would be 827mm. This is shown in the main diagram which could have been divided as 10 gaps of 24 perimetric units on the Originating Circle, but, here, as at a few sites elsewhere, the number of stones appears to be (n  1). It is possible that the sunken slab marked at position 3a could be a fallen stone and with one stone potentially missing at location 4a. At southwest, there is a twovalue distribution featuring the original multiple (24). At northeast, it appears that the quadrant is split in three with a twovalue distribution. Why sixteen units was chosen at the axis is unclear  why not 3 x 20? The gaps are all measured on the Originating Circle.  
Figure 12: Nine Ladies Spirals. 
It may be observed that there could be a smooth transition from the inner circle to the outer simply by bridging employing a spiral as at Figure 12. 
Stanton Moor North
The Stanton Moor North circle is north of the Nine Ladies on a path leading off the main track to the right shortly after leaving that circle. This leads to a gate, but continue on the path for about 60 metres, where it runs almost parallel to the main track, and the circle is immediately off to the right.  
Figure 13: Stanton Moor North. 
The circle is embanked and in poor condition, having just a few stones outlining the entrances, but differs from the neighbouring embanked rings in being nearcircular. It is elongated at the north, presumably emphasising an entrance where there is a sizeable prostrate stone. There may have been an inner setting, apparently elliptical, now hollowed out and with small stones scattered about its outline.
As can be seen at Figure 13, the two openings to the interior appear to subtend angles of about 20 degrees and the axis is about onetwelfth of a revolution west of south. The outline of the bank is irregular with the outer ring between 13.5 and 14.5 metres and the inner ring between 9.8 and 10.2 metres (thus, 14 and 10 metres, as a guide). For the most part, the top of the bank at east and west has a diameter of about 11.9 metres. The inner ring appears to fit within a square within an outer ring, which would make the ratio between the circles the square root of two to one. Given the dimensions, it is possible that the outer ring has a diameter of 272 diametric units and the inner ring of 192 units (14.1m x 10m) with a site Megalithic Yard of 828mm. The ratio 17:12 would thus represent √2, and perhaps in a similar way at the Nine Ladies stone circle some 200 metres to the south. 
The Megalithic Yard implied across these seven sites ranges from 811mm to 832mm with a mean of 824mm. The two smallest sites average 815mm, leaving two Barbrook rings at 827mm and the remaining three at 829mm. 
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