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Not all stone circles are circular: some are eclipses, some egg-shaped, some a special 'megalithic' shape.

in careful geometrical relation to one another, so that the curvature of the line of stones is sharper in some places than in others. Some are distinctly egg-shaped in that one half of the circle was inscribed from one point and the other half with segments of circles of large diameters. There are even a few ellipses, with two foci, anticipating by over 1,000 years the Greeks' studies of conic sections. One of the most interesting points to come out of the accurate measurement and statistical analysis of these circles was the existence of a unit of measurement—which Thorn calls the Megalithic Yard—which was uniform from the Outer Hebrides to southern England and which was equivalent to 2.72 ft. (2 ft. 8.65 in.). The implications of the use of such a unit over such a large area are profound. So close is the agreement between the units of length inferred for different parts of the country that standard rods must have been sent out from a single centre. Copying the rod from one district to the next would have resulted in cumulative errors and larger differences. Another surprising discovery is that the circle builders sometimes made use of Pythagorean right-angled triangles when setting out their figures, and this more than a millennium before Pythagoras.

The question of whether ordinary henge monuments with wooden posts were also laid out in such a sophisticated manner is partly answered by Thorn's investigation of Woodhenge. Far from being a huge roofed temple it seems that it could have been a form of mathematical experiment. The single axis of all the concentric flattened rings point towards the midsummer sunrise of c. 1800 B.C. The whole construction is laid out on the basis of a triangle measuring, in units of half megalithic yards, 122 + 352=372, the sixth in the list of perfect Pythagorean triangles. The circumferences of the rings are 40, 60, 80, 100, 140 and 160 Megalithic Yards. Thorn suggests that the whole set may have been 'an elaborate empirical determination of a geometrically constructed ring which would have as it were Pi equal to (exactly) three and at the same time have a circumference a multiple of 20 MY'.

Alignments point to sun, moon and stars

As the mass of information about the alignments of the circles and rings built up and was plotted on histograms Thom was able to see how the alignments clustered around certain well defined points. It became clear that the stone circles were used to define both lunar and solar phenomena and also the risings and settings of some stars, notably Capella. There are even suggestions that some sites had alignments to divide the year into sixteen months by a process of sub­

dividing the horizon between the solstitial sunrises. These months of course had nothing to do with the moon although there are separate indications that the four extremes of moonrise and moonset were marked at some sites.

Thorn's evidence suggests that the builders of the stone circles in Late Neolithic Britain could have had advanced geometrical and astronomical knowledge though, short of finding an inscribed clay tablet, it is hard to see how supporting evidence will ever be forthcoming from more traditional archaeological methods. In the light of Thorn's work it may seem that the builders of Stonehenge I are more likely to have possessed similar advanced knowledge though the question of whether they had reached the point of being able to predict eclipses is still an open one. Even apart from that, if the inferences drawn about the geometry and astronomical alignment of the circles are acceptable, it may be necessary to suppose that in Britain in the late 3rd and early 2nd millennia B.C. a situation existed similar to that in Central America in the first millennium A.D. There a class of astronomerpriests arose from the Neolithic background of the Maya people, lived in 'ceremonial centres' and achieved great things in astronomy and mathematics. However they left written records of their work, carved in stone.

Does the Megalithic yard still survive ?

Certainly the archaeological investigation of henges and stone circles in the light of Thorn's evidence would appear to be an important task. Similarly earlier Neolithic forerunners of the circle building period need to be sought. It has been suggested that the dimensions of the megalithic tombs may show how the unit of length evolved. In this context Thorn's suggestion that the Megalithic Yard (2.72 ft.) survives in the Iberian peninsula and in the Spanish New World as the vara is interesting. In Spain the modern vara is about 2.74 to 2.76 ft. Perhaps the Passage Graves need to be accurately measured and re-examined for any alignments. Surely also the south English 'causewayed camps' with their non-functional, rapidly silting ditches and many entrances could have been ceremonial sites and ancestral to the more formalised henges of a later stage. Perhaps we may yet find earlier figures outlined in post-holes in some of them. Alternatively they might belong to a stage before the intellectual achievements of the priestly elite had advanced very far and primitive religion was dominant.

In conclusion, I have to thank Dr. A. E. Roy of the Department of Astronomy in the University of Glasgow for reading this article and supplying some useful information.

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