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even partly successful would have been formidable. Hawkins explains this by supposing that the Late Neolithic priests used the 56 Aubrey holes as a device for predicting many more eclipses. The basis of this suggestion is that 56 is almost exactly the number of years in three of the lunar cycles of 18.61 years. Such a 56 year cycle can be used to record the azimuthal swings of moonrise and moonset over several centuries before becoming inaccurate. Eclipses of course only occur at full and new moon and when the moon is near the ecliptic at those times and is thus in line with the earth and the sun. By moving up to six stones at set intervals apart regularly around the Aubrey circle at the rate of a hole a year many important eclipses can be foreseen. The details do not matter here: the fact is that it seems to be workable. The only objection, apart from a general disbelief that anything so advanced was possible at so early a date, is an archaeological one. Those Aubrey holes which have been excavated were apparently refilled with their own chalk rubble soon after they were dug: on some cases they were then emptied and filled again. There were cremation burials in most, sometimes in the primary refilling but more often in the later, and objects found with the bones were of Secondary (Late) Neolithic type. No sign of the holes having ever held stones was noted though presumably large posts would have served almost as well as markers of the sort required by Hawkins' theory. There seems to be no doubt that a circle of 56 holes could be used for eclipse prediction in the way Hawkins suggests. Whether the Aubrey holes at Stonehenge I were so used is another matter. It depends on what the sum total of the evidence about the cultural level of Late Neolithic Britain suggests was possible at the time. If a circle of 56 holes had been found in the floor of a contemporary Mesopotamian temple it would be quite reasonable to accept that the astronomers there, who are known to have been greatly concerned with eclipses, used it for prediction. Indeed a practical method for such prediction suitable for early times was not known until Hawkins set out his ideas. However Late Neolithic Britain seems at first sight an unlikely environment for such spectacular intellectual advances and this is indeed the crucial question. Are Hawkins' theories about Stonehenge I plausible against the background of our knowledge of the rest of Britain at that time? 500 stone circles have been accurately surveyed Here we turn to Megalithic Sites in Britain and in this we find the essential background to the problems of Stonehenge just discussed for Thom—an emeritus professor of Engineering Science at Oxford—has spent many years visiting and accurately surveying some 500 stone circles and allied sites in England, Wales and Scotland. The problems of Stonehenge when Plan of the Dinnever Hill, Cornwall, stone circle (NGR: SX/126800), reproduced with the kind permission of Professor A. Thom. This is one of Thorn's type A flattened circles, made of very small stones and 130 feet across, and the dotted lines show its probable geometrical construction. A large part is a true circle inscribed from the centre point. Part of the north side is a segment of a circle of twice the radius of the foregoing, drawn from the point on the circumference opposite. The flat northern section is joined to the rest by two sharp 'corners' formed of short segments of circles of half the radius of the main one. These were drawn from the intersections of the main and long radii at the extreme points of their respective arcs. discussed in isolation inevitably assume a certain air of unreality: too much hinges on too little evidence. However the formidable mass of accurate data on many comparable circles assembled by Thom has allowed him to extract from it by statistical analysis a startling amount of information which, considering the qualifications of the author, is scarcely likely to be challenged. The conclusions he draws about the circles are twofold and concern the geometry of their construction and their astronomical alignments and function. Many of the rings are true circles and were obviously laid out with a length of rope tied to a central peg. Many others however are clearly not circular and Thom shows, with a wealth of examples, how they must have been constructed. Many are laid out with circles of different diameter superimposed, whose centres are 282
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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. 283

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even partly successful would have been formidable.

Hawkins explains this by supposing that the Late Neolithic priests used the 56 Aubrey holes as a device for predicting many more eclipses. The basis of this suggestion is that 56 is almost exactly the number of years in three of the lunar cycles of 18.61 years. Such a 56 year cycle can be used to record the azimuthal swings of moonrise and moonset over several centuries before becoming inaccurate. Eclipses of course only occur at full and new moon and when the moon is near the ecliptic at those times and is thus in line with the earth and the sun. By moving up to six stones at set intervals apart regularly around the Aubrey circle at the rate of a hole a year many important eclipses can be foreseen. The details do not matter here: the fact is that it seems to be workable. The only objection, apart from a general disbelief that anything so advanced was possible at so early a date, is an archaeological one. Those Aubrey holes which have been excavated were apparently refilled with their own chalk rubble soon after they were dug: on some cases they were then emptied and filled again. There were cremation burials in most, sometimes in the primary refilling but more often in the later, and objects found with the bones were of Secondary (Late) Neolithic type. No sign of the holes having ever held stones was noted though presumably large posts would have served almost as well as markers of the sort required by Hawkins' theory.

There seems to be no doubt that a circle of 56 holes could be used for eclipse prediction in the way Hawkins suggests. Whether the Aubrey holes at Stonehenge I were so used is another matter. It depends on what the sum total of the evidence about the cultural level of Late Neolithic Britain suggests was possible at the time. If a circle of 56 holes had been found in the floor of a contemporary Mesopotamian temple it would be quite reasonable to accept that the astronomers there, who are known to have been greatly concerned with eclipses, used it for prediction. Indeed a practical method for such prediction suitable for early times was not known until Hawkins set out his ideas. However Late Neolithic Britain seems at first sight an unlikely environment for such spectacular intellectual advances and this is indeed the crucial question. Are Hawkins' theories about Stonehenge I plausible against the background of our knowledge of the rest of Britain at that time?

500 stone circles have been accurately surveyed

Here we turn to Megalithic Sites in Britain and in this we find the essential background to the problems of Stonehenge just discussed for Thom—an emeritus professor of Engineering Science at Oxford—has spent many years visiting and accurately surveying some 500 stone circles and allied sites in England, Wales and Scotland. The problems of Stonehenge when

Plan of the Dinnever Hill, Cornwall, stone circle (NGR: SX/126800), reproduced with the kind permission of Professor A. Thom. This is one of Thorn's type A flattened circles, made of very small stones and 130 feet across, and the dotted lines show its probable geometrical construction. A large part is a true circle inscribed from the centre point. Part of the north side is a segment of a circle of twice the radius of the foregoing, drawn from the point on the circumference opposite. The flat northern section is joined to the rest by two sharp 'corners' formed of short segments of circles of half the radius of the main one. These were drawn from the intersections of the main and long radii at the extreme points of their respective arcs.

discussed in isolation inevitably assume a certain air of unreality: too much hinges on too little evidence. However the formidable mass of accurate data on many comparable circles assembled by Thom has allowed him to extract from it by statistical analysis a startling amount of information which, considering the qualifications of the author, is scarcely likely to be challenged. The conclusions he draws about the circles are twofold and concern the geometry of their construction and their astronomical alignments and function.

Many of the rings are true circles and were obviously laid out with a length of rope tied to a central peg. Many others however are clearly not circular and Thom shows, with a wealth of examples, how they must have been constructed. Many are laid out with circles of different diameter superimposed, whose centres are

282

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