feature picture: Broch of Mousa. The broch on the island of Mousa is the best-preserved of the many brochs in northern Scotland. It is thought to be some 2000 years old

credit: Anne Burgess / *Broch of Mousa* / CC BY-SA 2.0

I wrote this preface for Euan MacKie who had resurrected his work on measures found within the brochs of Scotland. Euan was almost a lone voice in support of Alexander Thom’s work on metrologyThe application of units of length to problems of measurement, design, comparison or calculation. in the megalithic, and also the long distance alignmentsA name special to Carnac's three successive groups of parallel rows of stones, starting above Carnac called Le Menec, Kermario, and Kerlescan and another found near Erdevan. in the Western Isles of Scotland. When he met John Neal at the latter lecture in Glasgow, at which I was present, they appear to have entered into a review of the data and John Neal came back with an interesting theory which would make a full range of historic measures to have been employed in one area of northern Scotand, in the Iron Age. I sent Euan a summary of what ancient metrology appeared to be as a system of ratios and why Neal’s finding within MacKie’s data would be important. It became the preface for the article called *The Roundhouses, Brochs and Wheelhouses of Atlantic Scotland c.700 BC-AD 500: Orkney and Shetland Isles Pt. 1: Architecture and Material Culture (British Archaeological Reports British Series) *which I have recovered from a partial proof copy.

**Preface**

###### by Richard Heath

John Neal has demonstrated elsewhere [*All Done With Mirrors*, John Neal, 2000] that ancient metrology was based upon a “backbone” of just a few modules that each related as simple rational fractions to the “English” Foot. Thus a Persian foot was, at its root value, 21/20 English feet, the Royal foot 8/7 such feet, the Roman, 24/25 feet and so on. By this means, one foot allows the others to be generated from it.

These modules each had a set of identical variations within, based on one or more applications of just two fractions, Ratio A = 176/175Ratio crucial to maintaining integers (see geometry lesson 2) between radii and circumference of a circle, and crucial to the micro-variation of foot modules in ancient metrology. and Ratio B = 441/440. By this means ail the known historical variations of a given type of foot can be accounted for, in a table of lengths with ratio A acting horizontally and ratio B vertically, between adjacent measures.

In the context of what follows, this means that each of the differently-sized brochs analysed by Neal appear to have used a foot from one or other of these ancient modules, in one of its known variations. That is, the broch builders seem to have chosen a different unit of measure rather than a différent measurement, as we would today, when building a differently sized building. Furthermore, these brochs appear to have been based upon the prototypical yet accurate approximation to pior π: The constant ratio of a circle's circumference to its diameter, approximately equal to 3.14159, in ancient times approximated by rational approximations such as 22/7. of 22/7The simplest accurate approximation to the π ratio, between a diameter and circumference of a circle, as used in the ancient and prehistoric periods., so that – providing the broch diameter would divide by seven using the chosen module – then the perimeter would automatically divide into 22 whole parts.

Thus, John Neal’s discovery that broch diameters divide by seven using a wide range of ancient measures implies that the broch builders had – (a) inherited the original system of ancient measures with its rational interrelations between modules and variations within these, from which they could choose, to suit a required overall size of circular building, often the foundations available: (b) were practicing a design concept found in the construction of stone circles during the Neolithic period.

These measures, used in the brochs, are not often found elsewhere in Britain, but are historically associated with locations hundreds if not thousands of miles distant. This suggests that the historical identification of such measures is only a record of the late use of certain modules in different regions, after the system as a whole had finally been forgotten, sometime after the brochs were constructed.

Such conclusions, if correct, are of such a fundamental character that they present a compelling case for ancient metrology and its forensic power within the archaeology of ancient building techniques.

—x—

Throughout Scotland and the Scottish islands there are in excess of 200 major broch sites. The following analysis is taken from, what I believe to be, the accurately measured inner diameters of 49 of them as supplied by Professor Euan MacKie. The modules are expressed in English feet although the original measurements were taken in metres and converted to feet at the rate of 3.2808427 feet to the metre. The range of diameters extends from the smallest, at Mousa, 18.897654ft, to the greatest at Oxtrow at 44.816311ft. John Neal’s original work on this can be found in this article, from this website’s earlier incarnation which also included a version of Appendix 2 of *Sacred Number and the Origins of Civilization* – soon also to be added, for reference.

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