Geometry, the Megalithic Yard and Astronomy Following Alexander Thom’s suggestion that modified stone circle designs are geometrical comes the thought that, if this be the case, then maybe the axis is also geometrical, that is, it’s a fraction of a revolution from one of the cardinal points of the compass. Here’s the tricky bit! If this be the case then it’s possible that the megalith builders practised a conceptual astronomy. The implication is that they could bring order to chaos or the random by applying geometry to the heavens and to the horizon. Apart from calendar, they might also be seen to be controlling the heavens, for example, by declaring that, with the proper incantations, the sun wouldn’t go beyond a certain point on the layout and disappear for good. With this in mind, a possible measured geometrical schema for Stonehenge has been developed for inclusion in a forthcoming publication. In the plan below, the circles are placed with the same centre, as I don’t know how far adrift they are and on what bearing. I assume that the Sarsen centre has an easterly bearing from the Aubrey centre.  
Figure 1: A Pure Geometrical Construction for Stonehenge Incorporating the Megalitic Yard. 

Geometry Meets Astronomy Ex hypothesi, that the axis is a rational (common) fraction of a revolution from a cardinal point, the axis of the Sarsen Circle here is aligned to oneninth of a revolution north of east (az.50) and the Heel Stone is aligned midway between Aubrey Holes 56 and 1, that is, sixfiftysixths (3/28ths) of a revolution north of east (az.51.4), which is oneseventh of a revolution east of north (8/56ths). It might be accepted that the builders were aware that the sun’s altitude appears not to rise above a certain point nor descend below another and that there’s a point in the sky midway between when the sun rises and sets due east and west. If they could measure the altitude of these key events then, presumably unwittingly, they’d have hit upon their latitude and the precession of the equinoxes. Assume they did measure the sun’s altitude. Could it be that they came up with a latitude equivalent (90  equinox altitude) of one seventh of a revolution (8/56ths, that is 51.4 degrees) and a precession range of 15/112ths of a revolution (48.2 degrees), and this explains why the Aubrey Ring is in 112ths of a revolution offset from the cardinal points of the compass? Astronomy is not my strong point, but it strikes me that the northern extents of the major and minor moon rise might also be expressed in 112ths of a revolution (15 and 9?) with the midpoint at az. 51.4 where the Heel Stone sits on this geometrical plan. Thus, the major standstill is assumed to occur through Aubrey Hole 55 and the minor through Aubrey Hole 2. Then, given the approximate position of Stone Hole '97', drawn here at az. 48.2 through Aubrey Hole 56, the midpoint of the gap between this and the Heel Stone could have been solstitial at 40.2 degrees north of east (25/224ths). Given the positions of the Station Stones visavis the Aubrey Holes, this could be the point they’re aligned to, with the angle subtended being 45 degrees, as shown. Such a schema would combine the movements of the sun and moon, which would thus have points in common on the conceptual geometry. As an aside, I have difficulty interpreting Mike Pitts’ data on Stone Hole '97' from the excavation report to get a reliable location (assuming the stone was erected rather than just dug up). On the plan, the gap would be 4.4m centre to centre, but some commentaries seem to suggest that’s too wide, the bulk of the stones occupying a large portion of this (in the figure, the gap between the stones would be about 2 metres). Also, some observers don’t show the stone hole to be on the same radius as the Heel Stone. As part of the geometry, the causeway postholes could be dividing a key segment of the arc described, though it's difficult to figure out why! A count pertaining to astronomy, perhaps?  
Figure 2: Geometrical Detail of the Stonehenge Causeway.  
Given the underlying bimetric hypothesis, the circle diameters from the Aubrey Ring outwards are all in multiples of 56 x 1MY/16 (9.52 feet, 2.9m). I was unable to survey at Stonehenge, so I’ve taken the data from published sources as best I could. According to this model, the distance between the centre of the Aubrey Ring and the Heel Stone would be 261.8 feet (96.25MY) which compares with 261.5 feet (96.125MY) if taking the Aubrey Ring diameter to be 105MY (87.05m) and using a [5,12,13] triangle to represent the angle of 22.5 degrees (deriving 1538 diametric units to my 1540), assuming they didn’t see, or use, the 45 degree shortcut (840 / 140 x 99): 840 x COS 22.5 / TAN 22.5  840 x SIN 22.5 840 / 13 x 12 / 5 x 12  840 / 13 x 5 = 1538 / 16 x 2.72 = 261.46 feet (79.7m). It is thus suggested that the Heel Stone (and potentially Stone Hole '97') was originally linked to the Aubrey Ring rather than the Sarsen Circle, which may be why it’s not dressed, and later in Phase 3 may have been used as a marker to place the Sarsen Circle, the summer solstice sunrise occurring to its left from the centre. A stone at Hole '97' may simply have been redundant or moved in order to redefine the location of the event. Note, the Heel Stone would be aligned upon Aubrey holes 18 and 39 at 45 degrees. 

© G.J. Bath 2020 
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