## Stone Circles

Stone circles in Britain marked a move away from henges of circular banks and ditches. They were only widely surveyed for the first time by Alexander Thom and some of his surveys are provided here. Thom's geometrical ideas for these circles, whilst still contested, provide clear evidence of advanced horizon astronomy, "sacred" geometry and landscape geodesy often linking sites. Arguments as to whether ropes were used or whether alignments really existed prove fatuous unless based on efforts to understand such ancient skills without prejudice.

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Almost all of the different types of megalithic building [1] were evolved in the fifth millennium (5,000-4,000 BC), in the area around Carnac on southern Brittany's Atlantic coast. This includes the stone circles later extensively built in the British Isles. When Alexander Thom surveyed these, between 1934 and 1978, he found them to be remarkably technical constructions, involving sophisticated geometrical ideas. It was only in the mid-seventies, when Thom came to Carnac, that the same geometries were found applied within Carnac's stone circles though at that time it was not known that Carnac's monuments preceded those of Britain by at least a thousand years.

[1] Megalithic building types include standing stones, stone circles, stone rows, dolmen, chambered and other cairns.

After an initial enthusiasm for Thom's work, in the late 1960s and early 1970s, British archaeologists chose, with very few exceptions, to refute the entire notion that the Neolithic could have been constructing such technical geometries which, as far as our History would have it, would only have become possible after the development (over two thousand miles away in the ancient near east) of a functional mathematics which culminated in Euclid's classical work on analytic geometry, Elements. Thom's use of geometry therefore seemed anachronistic to archaeologists and to accept it would have required a revolution in our thinking about the megalithic; for this there was little appetite. It was easier to falsify Thom's hypothesis with new work concluding that, for example, "stone circles were distorted so that the audience could see all the rites; and the principals could occupy visually focal positions facing the spectators.", clearly indicating the current "comfort zone" within archaeology in which unquestioned ideas about superstitious rites are used to supersede Thom's accurate and well founded proposals, of a megalithic technical capability, as being overly technical. The problem with inventing such ancient rites as being the primary purpose for stone circle construction is that, whilst refuting Thom's proposal, it definitely cannot be proved, cannot be disproved; Talk of rites as being the reason for stone circles is not delivering a scientific theory and Thom's proposals are not disproved by such ideas.

Figure Thom's site plans of two of Britain's finest surviving Flattened Circles, Castle Rigg (Type A) and Long Meg (Type B). Castle Rigg points (within a degree) to Long Meg, on a bearing which follows the diagonal of a two by one (east by north) rectangle, as if (despite some Lake District mountains in between) the two sites were related when built and hence contemporaneous.

Unlike most of his detractors, Thom physically engaged with stone circles, by surveying them, and through this activity he was to create the first and only extensive corpus of stone circle site plans. Through this he left a vitally important legacy by, at the very least, preserving their layout against natural and man-made degradation. The geometrical overlays and typology found within Thom's site plans have been dismissed as unlikely, on spurious technical grounds [*], usually by people with insufficient technical background in the technical issues within his work. Despite this, Thom's later work in Carnac has proven critical in providing further alternative explanations as to how the megalithic actually constructed these stone circle geometries without Euclidian geometrical methods, using instead the system of multiple squares found to be in use in the megalithic structures around Carnac; this in the late 1970's [note on AAK and Howard Crowhurst], and after Thom's surveying seasons there.

Such a system of squares avoids the arcing of ropes used by Thom to explain the construction of different stone designs. Instead, a grid of squares can establish the few key points on the perimeter of a flattened circle. This would eliminate one of the main objections to Thom's stone circle geometries: that a Euclidian geometrical process, of lines and arcs, is anachronistic in the context of a megalithic three to four thousand years before Euclid.

Figure The geometries of Flattened Circles (left to right) called Types A, B and D

In the case of the Type A (flattened) stone circles proposed by Thom, I demonstrate below that accepting Thom's identification of its geometry is a necessary stepping stone to understanding how this could be achieved by a pre-arithmetic megalithic of the fifth millennium BC. By the Middle Kingdom, the Egyptians had put stylus to papyrus, to describe their mathematics in the document now called the Rhind Manuscript. This recorded a system of geometry based around pre-Ptolemaic ideas, that included the use of a grid of multiple squares.

At Carnac, the angular extremes of sunrise and sunset, on the horizon during the year, followed the lesser angle of a 3-4-5 triangle whilst in the Rhind Manuscript one finds a "canevas" [*] or grid-based diagram, in which both of the acute angles of this triangle are shown to be generated by the summed diagonal angles of either; two double squares or two triple squares. The resulting grid is then 14 squares by 14 squares, and this is exactly the grid upon which the Type A stone circles are most easily constructed if one excludes the use of ropes, stakes and measuring rods to construct these designs.

*Figure of Rhind diagram showing evolution of a 3-4-5 triangle within a 14 by 14 grid of squares*

However, such a use of squares to construct a stone circle geometry immediately raises the question of the side length used, since they all need to be identical and so an ability to create identical lengths almost certainly points to an accurate system of measures, a metrology. This leads us into another quite bitter dispute, concerning Alexander Thom's ideas for the existence of a megalithic yard as primary unit of measure, maintained accurately by the megalithic builders throughout the British Isles and Brittany. Unfortunately, Thom did not know enough about historical metrology to see that the megalithic yard might well have been accompanied by systematic variations applied to its length or indeed, other measures might also have evolved. His proposal of an accurate megalithic yard, like that of exact stone circle geometries, therefore came to be rejected since his detractors, who also knew very little about historical metrology [*], could point to cases where, in fact, the actual presence of other measures had muddied any proof of there had only been a singular measure in megalithic Britain.

*[Historical metrology is a scattered remnant of the metrological system employed within the British stone circles and also within the Egyptian pyramids. It is this latter application of metrology in the ancient near east which spread metrology, though such an idea has also been opposed by archaeologists working in the near east.]

NEXT: Generating Flattened Circles using a Grid of Squares

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### Drone Flight by Iain Petrie

Long Meg and her Daughters by Drone from Iain Petrie on Vimeo.

### Alexander Thom L1 / 7 Class III Survey

Construction: Type B flattened circle (Li/7). Diameter 359 ft = 131.9 my. Perimeter 390.0 my = 156.0 mr. The flow of the earth down the slope may have displaced the stones, leaving the more deeply set stones slightly behind. Long Meg as seen from the construction centre indicates the setting midwinter Sun and seen from the same centre the stones at Little Meg (Li/8) indicate the Sun rising at May Day/Lammas.

*Alexander Thom Site Plan from BAR**see photos and site visits at http://www.megalithic.co.uk/article.php?sid=101*

### Aubrey Burl (Cumberland 23)

This is one of the largest British rings. It is in State care. It was built on a slope at 100 m O.D., 2 1/4 miles N of Langwathby. It is about 359 x 305 ft (109 x 93 m) in diameter.

Some 70 local porphyritic stones remain of a ring flattened at the N. 2 massive blocks stand at the E and W of the circumference. There are traces of a bank at the SW. 2 large stones at the SW define an entrance. 25 m beyond this is Long Meg* a red sandstone pillar possibly brought from the Eden valley i| miles away. Its SE face has several carvings of rings and spirals on it.

John Aubrey reported that 2 large cairns stood at the centre of the ring. William Stukeley noticed remains in 1725 but they have now gone.

There is a tradition that the ring has been disturbed and rebuilt.

### Bibliography

W. Stukeley. Itinerarium Curiosum II, 1776, 47. J. Y. Simpson. Archaic Sculpturings..., 1867, 19-21. C. W. Dymond, TCWAAS 5, 1881, 39. T. Clare, TCWAAS 75, 1975, 7.

J. Aubrey. 'Monumenta Britannica1, 1670-97, c. 24, 72-3.

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The Geocentric Model of the cosmos with the earth at its centre, by Portuguese cosmographer and cartographer Bartolomeu Velho, 1568 (Bibliothèque Nationale, Paris) [Wikipedia]. This mapping of planetary and other layers of time resembles the form of Neolithic henges (see figure 1 below).

Finding the right picture of important information requires ingenuity. Map makers, for example, use the technique of providing an inset showing a larger map at a smaller scaling (say of North America) and then a detailed map (of say the Gulf of Mexico) at the greater scale, so as to show cities and other features whilst still seeing the greater whole. Megalithic astronomy similarly generated maps, but of time periods, which were drawn geometrically, using lines and circles where units of measure represented every day which (for example) was an day to an inch or a day to a foot. In this and later articles we show how the megalithic built circular structures, henges and stone circles, to express major time periods. They had measured these periods using (a) alignments on the horizon pointing to sun and moon events and (b) counting time between events in metrological units of time.

A previous article about the Thornborough triple henge in North Yorkshire, looked at its likely metrology as a time-factored artifact. It consists of three henges oriented rather like Orion's belt of stars. Its Central henge is of particular interest here, in a way only mentioned in passing before.

A Henge is a circular structure with a ditch and raised ring. At Thornborough, the three henges each have three distinct concentric rings, and ditches or flat areas between. This design for a henge is the norm in Yorkshire's other henges, and these other henges are also of a similar size, implying both their size and their design was shared and significant. An outer ring defines the henge whilst two inner rings display a given ratio to each other, of around twelve to nineteen******* units. In other words when one looks at their diameters as a ratio, the nearest simple integer ratio that fits is 12:19. Since the rings are quite thick, their thickness can be variable due to erosion of damage, and so may deviate from what was originally built.

******* This ratio is very interesting since it can be normalised through division of the shared difference into each of the two numbers. 12/7 = 1.7143 which (in feet) is the Royal cubit

whilst 19/7 = 2.7143 which is the megalithic yard

*Figure 1 (right) the similarity in form and size of North Yorkshire's henges and (left) the integer ratio to be found between the inner and middle rings in Thornborough's central henge. [composite of sections of figures 3.18 and 6.4 of Harding. 2013]*

From surviving engraved art near Carnac in Brittany, we can know that the megalithic counting of time (by 3500-3200 BC) had evolved inches to count days and the megalithic yard of 19/7 feet, the overrun of three solar years over three lunar years when counted in day-inches. In Gavrinis' stone C3 we see engravings using divisions of 12/7 inches, within an astronomical diagram. From the centre of C3, seven divisions (times 12/7 inches) show the (so-called) English foot as seven divisions of 12/7 inches, running downwards from the centre. Also shown are 5 extra divisions, culminating in a phallic design, to reach a radius of 12/7 feet, the (so-called) Royal foot of the Egyptians. The stone C3 appears as a whole to have been composed within a circular framework of 19/7 feet, the (so-called) astronomic megalithic yard.

*Figure 2 Stone C3 of Gavrinis annotated as to its metrology. [adapted from figure 5.10 of Heath. 2014]*

We therefore find at Gavrinis two distinct measures within the engraved art, these measures related by the ratio 12 to 19, numerators of the Royal cubit and megalithic yard over their common denominator of seven. My brother and I have already demonstrated how these measures emerged of astronomical necessity, through counting three years in day-inches and because of the relative time lengths found when lunar months per megalithic yard are counted (instead of day-inches) when geometrically comparing the three periods: the eclipse year, the lunar year and the solar year. This required a relatively simple step, of equating the lunar month to the megalithic yard as a length. The foot and the royal cubit naturally emerged from the fact that the solar year contains 12 and 7/19 lunar months (12.368), the lunar year 12 months and the eclipse year 11 and 12/19 months.

- We know that the Saros period is made up of 19 eclipse years and this is because

*19 x 12/19 = 12*

- We also know that the Metonic period is made up of 19 solar years and this because

*19 x 7/19 = 7*

The builders of the henges in figure 1, in building two rings in this proportion might have been referencing (a) the three years which are about twelve months long and (b) the Saros and Metonic periods which take nineteen of these years to complete.

*Figure 2 Central Henge of Thornborough with 12 to 19 ratio employing a scale of feet to inches for days. The two sets of concentric red circles are (smaller) the eclipse, lunar and solar years and (larger) the Saros period, 19 lunar years and the Metonic period [adapted from Figure 3.18 of Harding. 2013.]*

By this artifice of scaling in feet or inches per day it was possible for the years, and their anniversaries with the moon over nineteen years, to be shown in a single monument which could be used not only to store these time periods as lengths but also employ them for counting or geometrical purposes.

### Thornborough Henge(s)

### References

- Harding, Jan et al. Cult, Religion, and Pilgrimage: Archaeological Investigations Thornborough. Council for British Archaeology: York 2013.
- Heath, Richard. Sacred Number and the Lords of Time. Inner Traditions:Rochester 2014.

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