The Broch that Modelled the Earth


In the picture above [1] the inner profile of the thick-walled Iron-Age broch of Dun Torceill is the only elliptical example, almost every other broch having a circular inner court. Torceill’s essential data was reported by Euan MacKie in 1977 [2]: The inner chamber of the broch is an ellipse with axes nearly 23:25 (and not 14:15). The actual ratio directly generates a metrological difference, between the major and minor axis lengths, of 63/20 feet. When multiplied by the broch’s 40-foot major axis, this π-like yard creates a length of 126 feet which, multiplied again by π as 22/7, generates 396 feet. If each of these feet represented ten miles, this number is an accurate approximation to the mean radius of the Earth, were it a sphere.

The two ratios involved, 22/7 and 63/20, each an approximation to π, become 9.9 (99/100) when they are multiplied together, as an approximation to π squared.  Figure 1 shows that these two ratios, if 22/7 differently used as its reciprocal 7/22, also generates the ratio between the mean and polar radii of the Earth, since 63/20 x 7/22 = 441/440. The ancient Meridian length could be calculated from 396 when multiplied by using the most accurate rational π noted by Fibonacci as 864/275. The 396 units, of 10 miles per foot, was a practical distance to have realized in the megalithic without arithmetic, to store the 3960 mile mean radius of the earth, since the mile of 5280 feet is 4/3 of 3960; that is, 396 x 4/3 equals 528, implying that this model was conceived of within a decimal framework but without the base-10 positional notation of arithmetic. We show that the methods of calculation used can only have seen numbers-as-lengths as being composed of factors of just the first five prime numbers {2 3 5 7 11} and that this limitation upon numbers created a metrology in which fractional units of measure could manipulate lengths to multiply and divide them through addition and subtraction of the powers of these primes.

Marc Calhoun’s picture from the Island (picture from his blog)


  1. Summary
  2. Introduction.
  3. Main Thesis.
  4. Pre-arithmetic Calculation using Powers of {2 3 5 7 11}
  5. Combining Prime Number Composites.
  6. Appendix 1 Extract from Science and Society in Prehistoric Britain.
  7. Appendix 2: Preface: The Metrology of the Brochs.
  8. Metrological Bibliography.
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Walking on the Moon

There are plans to walk again on the moon (above is a NASA visualization), but there is a sense in which the surface of the moon belongs to the surface of the earth, since the earth’s circumference is 4 times the mean diameter of the earth, minus the moon’s circumference.

The Earth and Moon were formed out of an early collision which left the two bodies in an unusual relationship to one another, in more ways than one. Here we discuss the diameter (and circumference) of each body as a sphere as being in the ratio 11 to 3. The diameter of the Moon is 2160 miles so that the common unit is 720 miles (the harmonic constant) and the diameter of the spherical mean earth would be 7920 miles.

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Recalibrating the Pyramid of Giza

Once the actual height (480 feet) and actual southern base length (756 feet) are multiplied, the length of the 11th degree of latitude (Ethiopia) emerges, in English feet, as 362880 feet. However, in the numeracy of the 3rd millennium BC, a regular number would be used. In the last post, it was noted that John Neal’s discovery of such rectangular numbers to define degrees of latitude, multiplied the pyramid’s pointed height (481.09 feet) by the southern base length (756 feet) to achieve the length of the Nile Delta degree of latitude and, repeating Neal’s diagram relating the key latitudinal degrees of the ancient Model as figure 1, the Ethiopian degree is 440/441 of the Nile Delta degree. As shown above, the length of the 756 foot southern base is changed, when re-measured in the latitudinal feet for Ethiopia; it becomes the harmonic limit of 720 feet of 1.05 feet – normally called the root Persian foot.

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Ethiopia within the Great Pyramid

My last posting mentioned John Neal’s creative step of not averaging the Great Pyramid of Giza’s four sides, as had routinely been done in the past – as if to discover an idealized design with four equal sides. Instead, Neal found each length to have intensionally been different. When multiplied by the pyramid’s full height, the length of four different degrees of latitude were each encoded as an area. The length of the southern side is integer as 756 feet, and this referred to the longest latitude, that of the Nile Delta, below 31.5 degrees North. Here we find that the pyramid’s reduced height also indicated the latitude of Ethiopia.

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Silbury Hill: Metrological Key to the Model of the Earth between Stonehenge & Avebury

Archived: 11 August 2012

The exact location of Silbury Hill is as mysterious as the purpose of the Hill itself, a thirty degree cone, only recently with a flat top, overlooking Avebury and the surrounding hills. The Hill figures in John Michell’s model of the Earth between Stonehenge and Avebury in which one quarter of a degree of latitude, between the two henges, appears to have been measured by a type of Persian foot so as to make the number of feet, in between, equal numerically to that required to perfectly model the Earth using 864:866:867 double triangle.

The double triangle model of the size of the Earth between Stonehenge and Avebury

There are 86400 Persian feet of 1.056 feet (south to north) between Stonehenge and Avebury Ridgeway enabling the Avebury henge to be 86600 of these Persian feet from Stonehenge, then to represent the Mean Earth radius (see Initial Article – missing link). The Avebury henge appears to have been specifically tied to the distinct Latitude of 360/7 degrees.

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