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and inches are lunations better!
[Robin Heath is the author of four books - including 'Sun, Moon & Stonehenge - a 256 page, fully illustrated, exploration of the megalithic landscape and its implications for modern culture (ISBN 0 9526151-7-7 £12.99 from any bookshop or tel. 01239 613224). Once a senior lecturer in mathematics and engineering, he now writes and lectures widely on matters megalithic, living in West Wales. It is a privilege to publish this article, specially written for BWMA, that summarizes his latest researches.]
I have for many years been involved in the surveying, geometry and structure of Stone Circles, which were built throughout what are now the British Isles and NW France between c.5,000 and 3,500 years ago. In this, I followed in the footsteps of the late Professor Alexander Thom, who discovered and proved the existence of the 'Megalithic Yard' (MY), a unit of 2.72 ft. 2½ of these define a 'Megalithic Rod' of 6.8 ft., so that 5 MY = 2 MR. Perimeters and the internal geometry of non-circular stone rings were commonly found by Thom to measure in whole numbers of MR. In addition to the metrology of stone rings, Thom pioneered what he came to term megalithic science, a subject embracing accurate astronomical alignments and an apparent obsession with numerical patterns held by Neolithic man.
Alexander Thom was Professor of Engineering Science at Oxford University from 1945-61. He refined the value of MY throughout the last 40 years of his working life, until shortly before his death in 1985. He defined the unit in the first of three major works published by Oxford University Press ('Megalithic Sites in Britain'), following detailed surveys of over 500 sites in person from Shetland to Brittany. Statistical analysis showed that 2.72 ft was accurate plus-or-minus 0.003 ft
In my book, 'Sun, Moon & Stonehenge', I show that if one assumes that 1 MY represents a lunation period - the time between two new moons - then the length of 1 imperial foot marks the required calendrical period between the end of the lunar year (12 lunations, which take 354.367 days) and the end of the solar year of 365.242 days. This discovery was so astonishing as to justify spelling out again: if the lunar year is represented by 12 MY then 1 ft corresponds precisely to the extra 10.875 days to coincide with the end of the solar or seasonal year. Furthermore, the period between the end of the solar year and 13 lunations - 18.656 days - is represented by another unit of length from antiquity, the 'Royal Cubit' of 20.63" or 1.72 ft. The Royal Cubit is indeed a most ancient measure, known to Newton who, drawing on the work of the metrologist Greaves, deduced that a value of 20.63" would make the King's Chamber within the Great Pyramid exactly 20 x 10 of this same measure. In the 1880's, Sir William Flinders Petrie accurately measured the Great Pyramid, using a 10" Gambay theodolite, and identified 20.63" as a primary unit of length also within other Egyptian dynastic buildings.
Hence the equally astonishing revelation that 1 MY = 1 ft + 1 RC. Assuming that the MY was the primary unit, then the derivative foot and cubit appear to have formed a logical and essential part of the astronomical and calendrical researches of our Neolithic ancestors. If, however, the foot preceded the MY in time - and here we must remember that 1/1,000th of a degree of arc around the equatorial circumference of the Earth is just 365.244 ft in length! - then knowledge of the roundness of the Earth must have predated use of the MY…i.e. well before 3,000BC. There are no other choices readily apparent! It would have been logical for the key calendrical period - the 10.875 days between the ends of the lunar and solar years - to have been represented by an existing length, and it does appear that the foot of 12.00 inches was adopted as that length.
My story doesn't end there, for there are 12.368 lunations in a full year, of which the fractional part (0.368) is almost exactly 7/19 (0.36842104). Using decimal fractions totally obscures the astronomic wisdom hidden in twelve and seven nineteenths. As a vulgar fraction, 12.368421 = 235/19, immediately informing an astute astronomer of a nineteen year synchronicity between lunar and solar cycles. Thus, 235 lunations will last exactly nineteen years. The correspondence is astoundingly accurate - a mere 2 hours in 19 years - and it is termed the Metonic cycle.
Let's take it even further. A length of 0.368 MY = 1 ft. Again assuming that 1 MY represents 1 lunation, then, totting up the exact number of lunations in the year, all one has to do is add 1 inch to 1 MY each one observes a new moon, because these extra inches will add up to 0.368 lunations, the required over-run. When demonstrating accurate calendrical predictions with my student groups over the years, I use a plastic Woolworth's foot ruler, marked in inches, to predict lunations and eclipses to the day, years in advance. Not very megalithic but highly accurate and apparently using those same measures of antiquity now ironically rendered illegal by the government of the same lands that originally built most of these great circles and invented the mathematics.
Many of the greatest metrologists of our age have suggested that the primary units of length were derived from units of time. To quote that greatest metrologist, Stecchini, who died only in 1999: "…all serious scholars of ancient and mediaeval measures have always known that measures of volume and weight are derived from the units of length." During the late 19th century, two other eminent scholars, the aforementioned Flinders Petrie and Carl-Friedrich Lehmann-Haupt, each concluded that ancient measures were so rigorously organized that they must have a basis on some absolute natural measure. I suggest that this absolute natural measure was the lunation period.
It now appears to me, therefore, that the Megalithic Yard may be considered a calendrical analogue of the lunation period, and that the foot and the cubit are proportioned within it to reveal the duration of the solar year, following the twelfth lunation or lunar year. The conclusions of this research have enormous implications for archaeology and human pre-history as well as for metrology and mathematics generally. For a start they confirm the primary connection between the science of measurement and the Moon. They also clearly offer one plausible explanation as to the historical basis for the foot and its twelve-fold division into inches, contrary to the popular impression that the foot and the inch were merely random evolutions from the anatomical foot and thumb-width, or derivatives respectively from Roman and Saxon measures. Our system of customary measures is not only coherent - it is also almost certainly celestial. Feet and inches are lunations better!
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