"Arbor low 274167 560a8cc3" by Michael Allen. Licensed under CC BY-SA 2.0 via Commons

"Arbor low 274167 560a8cc3" by Michael Allen. Licensed under CC BY-SA 2.0 via Commons - https://commons.wikimedia.org/wiki/File:Arbor_low_274167_560a8cc3.jpg#/media/File:Arbor_low_274167_560a8cc3.jpg

The large Arbor Low site was shown by my brother to form the right angle of a very large 3:4:5 triangle between it, Stonehenge to the south and Bryn Chelli Dhu to the west (in Anglesey, north Wales). In my last book, on megalithic techniques, I showed (p 221-223) that the units, whilst those of 24/7 miles (John Michell's "geodetic unit"), had been altered in an interesting way - incidentally revealing that the polar radius and equatorial are in ratio through the combined microvariations of 440/441 x 176/175 (so that all three key radii of the earth are present in John Neal's system of microvariations of historical measures), see Part 2 (yet to come).

I recently bought Peter Harris' booklet Astronomy & Measurement in Megalithic Architecture from Northern Earth Books, based in part on John Barnatt's work Stone Circles of the Peak (District), in which Barnatt questioned Thom's megalithic yard and came to prefer 1/4 of it as a likely unit. Peter Harris (and Norman Stockdale) felt that the type of standard unit in use in the moors was not based upon the megalithic yard and seemed to find a new type of foot (unrelated to Neal's metrology), then called a "megalithic foot" (a MF = 1.177 ft), which divided into the circumference of Arbor Low so as to equal the number of days in an eclipse year (EY = 346.62 days).

"At Arbor Low, Barnatt (1978:81) stated that the circumference is approximately 60 of Thom's Megalithic Rods (MR). This distance, as at Avebury, equals exactly 346.62 [MF], i.e. the days in an eclipse year." Harris, page 18.

The circumference is thought (being ruinous) to be 150 of Thom's averaged megalithic yard (TMY = 2.72) so that Harris' proposal equates 150 TMY with 346.62 MF with the idea that having an eclipse year around the circumference would be useful or symbolic for megalithic astronomers.

Circumference ArborLow RE PeterHarris

This would tie in with the notion of countable structures being used in the megalithic to track important time periods such as the lunar orbit, solar year, lunar year, eclipse years, Saros period (of 19 EY) and the moon's nodal cycle (of 18.618 years or more practically 6800 days). 

But how would one find the foot unit (the MF) needed to divide up Arbor Low's perimeter into 346.62 parts, without using arithmetic? The answer lies in how right angled triangles were used in the megalithic culture to re-proportion an existing unit into a unit that would divide up a given dimension into the desired number of units, using a process called here Triangular Proximation (TP). The two numbers to be translated, one to the other, must be sufficiently similar in magnitude to form a reasonably acute angle as hypotenuse and base. This would have been done by using 408 units on the hypotenuse and 346.62 units on the base. Triangular Proximation recognises that any dimension is made up of a measurement and the units used from that measurement, and that by enlarging the unit used, the measurement is reduced whilst the dimension does not. In arithmetic, this is like division of the whole into so many parts and by reducing the length of the parts (the units), one is multiplying (rescaling) to a larger measurement, and by increasing units one is dividing to a smaller measurement, without arithmetic.

TriangularProximationAt ArborLow

If one uses ANY unit to build a right triangle embodying these numbers, then any English foot on the 346.62 side will be enlarged by 1.177, to become the megalithic foot proposed by Barnatt. This foot will then divide the circumference of Arbor Low (if it was 408 ft) by 346.62 day-feet. Such a division by a known time would be (a) symbolic or

(b) of some utility if and when counting by days around Arbor Low: one would start at a lunar eclipse and then reach the opposite point of the circle in 173.3 days, then reaching the next period during which another visible lunar eclipse (at a different lunar node) is possible. Returning to the beginning after 146.62 days the same lunar node may create another lunar eclipse. However possible this may have been, it seems unlikely to me.

One notices that fractions are not being handled by this technique, with the effect that the framework of days is "on the move", with each day-foot becoming displaced with every rotation. Then one comes to the fact that, if the megalithic foot (MF) declared by Barnatt existed at all in megalithic times, it was derived from the megalithic yard (MY). That is, why should it have been an original unit. And today, through arithmetic, the MF can be used to interpret monuments as time factored, but isn't this just a consequence of having made numbers of megalithic yards divide by an MF that suits the purpose of finding an astronomical period in the first place?

Part Two returns to the metrology of Arbor Low as demonstrating an application of Triangular Proximation, then Part 3 (to come) relates to what was said in my Sacred Number and the Lords of Time book, about the triangle between Stonehenge, Bry Celli Dhu and Arbor Low.