## Megalithic Mensuration

From a study of the dimensions of megalithic monuments throughout the British Isles, Alexander Thom (1967/ 1971/1973/1978) concluded that standard units of scale were employed. Some practitioners call this the "quantum hypothesis." Among the units were what Thom called the Megalithic Inch (MI) equal to 0.82 in or 21mm, and the Megalithic Yard (MY) equal to 2.720 ± 0.003 ft or 0.829 m (the precision cited is Thom's). The data, methods, and results have all come under careful scrutiny with the result that most investigators subsequent to the Thoms have concluded that marginal evidence exists for the Megalithic Yard, but not as uniform a measure as Thom's estimates would imply. It is important to reexamine the evidence to see how this conclusion was reached and, regardless of established opinion, to see if the quantum hypothesis may, nevertheless, be true regardless of rigid tests of significance.

The quantum, or the smallest basic unit of any quantity, can be determined from two basic conditions: It can be no larger than the smallest measured quantity and all larger quantities must be integral multiples of it. This can be considered the case if and only if no more than one such similar-scale unit was being used by different groups in the area. One can indeed question whether it is reasonable to expect a culture that has left no accepted evidence of writing ("cup and rings" notwithstanding) to be able to systematize their units of scale so that the same value is derived for each site. Leaving that question aside, what are the bases for the claims that these units were in use among the megalith builders?

They are the scale of markings on the stones in the case of the MI and the scales of the geometric figures created by the placements of the stones in the cases of larger units. Thom identified the Megalithic Inch to be about 1/40 MY on the basis of a histogram of frequencies of occurence of diameters of markings under 12 inches; the histogram shows that there is an apparent clumpiness of diameters near integral units of the Megalithic Inch. The case for the Megalithic Inch was subjected to Broadbent's lumped variance test2 by Thom and found to be significant. Heggie (1981b, p. 48) subjected the data to more stringent testing, which did not show significant clumping. On the latter basis, there does not seem to be a unique unit that provides a clearly better histogram than any other. Basically, the situation is this: If one assumes a value of the MI (e.g., 1/40 MY), one gets an indication of significance, but this does not prove that that unit alone was significant. Similar arguments have cropped up for the larger units.

With respect to the Megalithic Yard, the studies have been more positive, but the strictest tests suggest marginal significance only. Again, the evidence is for that unit in the form of a histogram of the frequencies of the diameters of stone "circles" (these are often not circular, as we discuss below). The diameters yield significant results for the existence of the MY once a unit is suggested. The same is true for a number of subsets investigated by Thom and others. There is somewhat greater significance for the more flattened variety of circles and for the Scottish circles than for the more nearly circular configurations and for the English and Welsh circles. Supporting evidence for the quantum hypothesis comes from other measurements [(such as the separations of individual stones, cf. Thom (1964/1971/1973/1978)] and from different types of structures, such as stone "fans." The separation of stones yields a common unit of 0.5 MY to a significance level of 0.97, meaning that the probability of the clumping being produced randomly is only 3%. An example of a stone fan is seen at Mid Clyth, where the convergent rows of stones march up (or down) a hillside (Figure 6.2).

The quantum found here, however, was not the Megalithic Yard, but a value 7.743 ft. = 2.360 m (2.843 - 20/7MY). Work on sites at Carnac and elsewhere has shown marginally significant results. There are notable examples of a failure to confirm the existence of the MY: In the Irish stone circles examined by Barber (1972) and in rings of the "Sanctuary" near Avebury in Wiltshire (Heggie 1981b, p. 42, based on Burl 1979), there does not seem to be evidence for the Megalithic Yard. This has led to suggestions that the integral values of diameters may be suggesting merely "popular" values, or that units were used in some cases and were randomly selected in others.

Supposing the existence of the MY, the measures of accuracy with which it can be obtained have been studied by Heggie (1981b, 56ff). The diameter of the highly circular Ring of Brogar at Orkney (cf. Figure 6.3, which shows also a portion of a comparably large site, Avebury) was determined by Thom and Thom (1973, p. 171) to be 340.02 ± 0.60 ft or 103.64 ± 0.18 m.

This is close to 125 MY. If that were the intended value, the error in the MY would be -0.005 ft. The uncertainty is small enough in whatever unit was intended. And it was most probably the Megalithic Yard as suggested by Thom. The variations from site to site suggest that it may have been some aspect of human dimensions—such as foot pacing— which can be done with high precision yet the resulting structure will vary slightly in dimensions from site to site with the builders.3 This was the hypothesis of Kendall (1974, p. 258), although it was challenged by Thom (1974, p. 179).

Thom's metrical and geometrical hypotheses were supported by subsequent analysis of the Breton site of Crucuno. Although the site is composed of moderately large standing stones, it is a simple rectangle and not impressive compared with many other sites in the region. This Megalithic site is, nevertheless, one of the most important, as a glance at Figure 6.4 reveals.

A considerable number of the stones of the site are known to have been reset. This led Hadingham (1976, p. 162) to declare, "Unfortunately, the enclosure was restored in the last century, so that no reliance can be placed on these remarkable facts." Such a statement ignores the fact that the rectangle is one of the easiest shapes to restore with substantial accuracy. Moreover, the stones are large enough to make a great deal of natural movement unlikely. In 1882, only 9 of the 22 stones were standing but a plan of 1867 offers strong support for the view that the reconstruction was done very carefully (Burl 1985, p. 133). If the alignments of the stones are even roughly authentic, displacements along the lines would not greatly affect the remarkable properties of this rectangle. The short sides of the rectangle measure 30 MY, the long sides, 40 MY, and thus the diagonals, 50 MY. These are the proportions of the classic "Pythagorean triangle," which, Thom has maintained, is basic to the construction of most megalithic structures. The absolute values conform with the unit of the Megalithic Yard as worked out by Thom from data of more complicated sites in Britain. The simple rectangle (the existence of the triangle is hypothetical but the rectangular is a manifest description) is in a way the best support yet published for the existence of that unit with a value very close to that given by Thom. The rectangle also possesses astronomical alignments, as it defines solar alignments at both solstices and equinoxes. The long sides are aligned east-west, and the short sides, north-south. Thus, the long sides point to both rising and setting Sun at both equinoxes. At this latitude (~47.5°), the diagonal line from the northwest points to the rising of the midwinter Sun, and the diagonal from the northeast points to the setting Sun on the same date. The diagonal from the southwest points to the rising of the midsummer Sun, and the diagonal from the southeast points to the setting of the midsummer Sun. The dimensions of the features of the Crucuno monument are matched to its latitude if its purpose was to provide solar alignments. Hence, the Crucuno monument furnishes simple but strong evidence of a deep megalithic involvement in astronomy. In terms of our understanding, this interpretation is both straightforward and complex. It suggests complete understanding of the regularities in the correspondence of the figure with the apparent movements of the Sun. It seems

2 See Broadbent (1955). The test involves the average of the squares of deviations.

3 The modern inch, span, fathom, and foot all have such anthropological origins.

Figure 6.2. A sketch of the mega-lithic fan-shaped configuration of stones at Mid Clyth in Caithness, in northern Scotland: From Thom (1964), who finds in such constructs evidence of stone grids used for lunar calculations. For discussion of the functioning of the site, see §6.2.15. Drawing by Sharon Hanna.

Figure 6.2. A sketch of the mega-lithic fan-shaped configuration of stones at Mid Clyth in Caithness, in northern Scotland: From Thom (1964), who finds in such constructs evidence of stone grids used for lunar calculations. For discussion of the functioning of the site, see §6.2.15. Drawing by Sharon Hanna.

Figure 6.3. (a) The Ring of Brogar, Orkney, northern Scotland: Photo courtesy of Sharon Hanna. (b) Avebury in the SW,

The monument has a diameter of 103.6 m, surrounded by a cir- looking SE: Large entrance stones marking the South entrance cular ditch with diameter of 142 m. These dimensions make it are on the right. Photo by David H. Kelley. one of the largest of the stone rings, comparable to Avebury.

Figure 6.3. (a) The Ring of Brogar, Orkney, northern Scotland: Photo courtesy of Sharon Hanna. (b) Avebury in the SW,

The monument has a diameter of 103.6 m, surrounded by a cir- looking SE: Large entrance stones marking the South entrance cular ditch with diameter of 142 m. These dimensions make it are on the right. Photo by David H. Kelley. one of the largest of the stone rings, comparable to Avebury.

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