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The Geocentric Model of the cosmos with the earth at its centre, by Portuguese cosmographer and cartographer Bartolomeu Velho, 1568 (Bibliothèque Nationale, Paris) [Wikipedia]. This mapping of planetary and other layers of time resembles the form of Neolithic henges (see figure 1 below).

Finding the right picture of important information requires ingenuity. Map makers, for example, use the technique of providing an inset showing a larger map at a smaller scaling (say of North America) and then a detailed map (of say the Gulf of Mexico) at the greater scale, so as to show cities and other features whilst still seeing the greater whole. Megalithic astronomy similarly generated maps, but of time periods, which were drawn geometrically, using lines and circles where units of measure represented every day which (for example) was an day to an inch or a day to a foot. In this and later articles we show how the megalithic built circular structures, henges and stone circles, to express major time periods. They had measured these periods using (a) alignments on the horizon pointing to sun and moon events and (b) counting time between events in metrological units of time.

A previous article about the Thornborough triple henge in North Yorkshire, looked at its likely metrology as a time-factored artifact. It consists of three henges oriented rather like Orion's belt of stars. Its Central henge is of particular interest here, in a way only mentioned in passing before.

A Henge is a circular structure with a ditch and raised ring. At Thornborough, the three henges each have three distinct concentric rings, and ditches or flat areas between. This design for a henge is the norm in Yorkshire's other henges, and these other henges are also of a similar size, implying both their size and their design was shared and significant. An outer ring defines the henge whilst two inner rings display a given ratio to each other, of around twelve to nineteen******* units. In other words when one looks at their diameters as a ratio, the nearest simple integer ratio that fits is 12:19. Since the rings are quite thick, their thickness can be variable due to erosion of damage, and so may deviate from what was originally built.

******* This ratio is very interesting since it can be normalised through division of the shared difference into each of the two numbers. 12/7 = 1.7143 which (in feet) is the Royal cubit

whilst 19/7 = 2.7143 which is the megalithic yard

*Figure 1 (right) the similarity in form and size of North Yorkshire's henges and (left) the integer ratio to be found between the inner and middle rings in Thornborough's central henge. [composite of sections of figures 3.18 and 6.4 of Harding. 2013]*

From surviving engraved art near Carnac in Brittany, we can know that the megalithic counting of time (by 3500-3200 BC) had evolved inches to count days and the megalithic yard of 19/7 feet, the overrun of three solar years over three lunar years when counted in day-inches. In Gavrinis' stone C3 we see engravings using divisions of 12/7 inches, within an astronomical diagram. From the centre of C3, seven divisions (times 12/7 inches) show the (so-called) English foot as seven divisions of 12/7 inches, running downwards from the centre. Also shown are 5 extra divisions, culminating in a phallic design, to reach a radius of 12/7 feet, the (so-called) Royal foot of the Egyptians. The stone C3 appears as a whole to have been composed within a circular framework of 19/7 feet, the (so-called) astronomic megalithic yard.

*Figure 2 Stone C3 of Gavrinis annotated as to its metrology. [adapted from figure 5.10 of Heath. 2014]*

We therefore find at Gavrinis two distinct measures within the engraved art, these measures related by the ratio 12 to 19, numerators of the Royal cubit and megalithic yard over their common denominator of seven. My brother and I have already demonstrated how these measures emerged of astronomical necessity, through counting three years in day-inches and because of the relative time lengths found when lunar months per megalithic yard are counted (instead of day-inches) when geometrically comparing the three periods: the eclipse year, the lunar year and the solar year. This required a relatively simple step, of equating the lunar month to the megalithic yard as a length. The foot and the royal cubit naturally emerged from the fact that the solar year contains 12 and 7/19 lunar months (12.368), the lunar year 12 months and the eclipse year 11 and 12/19 months.

- We know that the Saros period is made up of 19 eclipse years and this is because

*19 x 12/19 = 12*

- We also know that the Metonic period is made up of 19 solar years and this because

*19 x 7/19 = 7*

The builders of the henges in figure 1, in building two rings in this proportion might have been referencing (a) the three years which are about twelve months long and (b) the Saros and Metonic periods which take nineteen of these years to complete.

*Figure 2 Central Henge of Thornborough with 12 to 19 ratio employing a scale of feet to inches for days. The two sets of concentric red circles are (smaller) the eclipse, lunar and solar years and (larger) the Saros period, 19 lunar years and the Metonic period [adapted from Figure 3.18 of Harding. 2013.]*

By this artifice of scaling in feet or inches per day it was possible for the years, and their anniversaries with the moon over nineteen years, to be shown in a single monument which could be used not only to store these time periods as lengths but also employ them for counting or geometrical purposes.

### Thornborough Henge(s)

### References

- Harding, Jan et al. Cult, Religion, and Pilgrimage: Archaeological Investigations Thornborough. Council for British Archaeology: York 2013.
- Heath, Richard. Sacred Number and the Lords of Time. Inner Traditions:Rochester 2014.

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goto Part One

Picture of Arbor Low from English Heritage page

A fairly crucial component of Peter Harris' booklet, *Astronomy & Measurement in Megalithic Archetecture*, and of John Barnatt's *Stone Circles of the Peak* is their refactoring of Thom's megalithic yard (TMY = 2.72 ft) as being 2.31 of a new type of "megalithic foot" (MF=1.177 ft). This then enabled measures known in TMY (and TMRods = 2.5 TMY ~= 6.8 ft), when seen in terms of these megalithic feet (MF), to reveal nearly exact numbers of day-MFs as lengths found employed in monuments. The subsequent success of the authors in converting megalithic dimensions into time units gave them validation of their megalithic foot (MF), as being a unit actually employed within monuments which were deliberately dimensioned according to astronomical time periods.

Such a result could be interpreted as evidence of an earlier and less developed metrology, in use prior to the advent of the ancient metrology found world-wide (c.f. Neal) and historically considered to have emanated from the Ancient Near East. However, is the metrology proposed based upon the English foot and inch which the authors use to measure their units throughout? Or are they, by implication, evolving their megalithic foot as a standard unrelated to the English foot? It is certainly true that their megalithic foot finds no accurate home within the module of the Russian foot within whose territory it belongs, except as a Standard Canonical Russian foot of 1.176 ft and also the authors usage of their foot can define its length as within a small range of variation.

The problem with metrology in general is that a longer dimension can be broken up in many different ways and especially diabolical is when a unit of measure and a measurement using it can be switched around. For example 2.5 x 3 = 7.5 but also equals 3 x 2.5; is 2.5 the unit or is 3? The answer then is that the unit can be a different aspect of the dimension to that first thought.

In the case of Arbor Low, the dimension is 150 TMY = 408 ft, is then interpreted by Harris as the eclipse year (of 346.62 days) in megalithic feet (MF). When 408 ft is divided by 346.62 the result is 1.177 (MF) and this MF made into a step (x 2.5) is then of equal length to the megalithic yard (TMY).

But, since the authors are quite at odds with Thom's averaged MY, what if one divides 150 megalithic yards of the sort found at Carnac (CMY) of 2.71875 ft (= 32.625 inches) i.e. 407.81 ft. This length is 441 Root Geographical Iberian (RGI) feet (0.924765 ft) which is also 440 Standard Geographical Iberian (SGI) feet (0.926866 ft). The step of 2.5 RGI feet equals the megalithic yard of 2.3119 feet, just as the TMY is said by the authors to be 2.31 of their megalithic feet (MF). Thus the magalithic yard can be seen as being 2.3119 megalithic feet (but why?) so as to see 150 TMY as 346.62 MF whereas 150 CMY can instead be seen as 441 RGI or equally well as 440 SGI since the Standard measure emerges as 441/440 larger and a larger UNIT give a proportionately lesser MEASUREMENT of the same DIMENSION.

440 SGI is 44 x 10 and so the radius can immediately be known as 7 x 10 units long when PI is taken as 22/7.

150 CMY is merely ten times 15 CMY, which is 44 SGI so that 6 megalithic rods "do the trick" of relating circumference to radius, once one is interested in seeing ancient metrology as being employed in the creation of Arbor Low rather than needing to have the monument express astronomical time lengths in a monument thought contemporanious with the Sarsen Circle of Stonehenge, where ancient metrology is strongly demonstrated.

### To Summarise

The above gives us two pairs of numbers which can work well together in a **Triangular Proximate** way: 150 CMY to 176 STEPS (shown above) and 346.62 MF to 407.8 feet. The first would have enabled rationality between a radius and its circumference whilst the latter, proposed by Harris, would have enabled the eclipse year to have been symbolised around the circumference but in a way not obviously useful for the purpose of counting.

The numbers 176 and 440 form part of John Neal's microvariations within ancient near eastern metrology and indeed are here revealing that 176 times the step ratio of 2.5 is 440. We note also that the ratio 2.31 representing the number of Harris & Barnatt's megalithic feet in a megalithic yard turns up again in the Step length of 2.317 feet above which divides into Arbor Low's circumference 176 times, indicating that the ratio can be part of a Unit or of a Measurement in ways quite hard to resolve, hence creating cul-de-sacs unless one continues to investigate alternative perspectives within the same data.

Part Three (to come) will return to what was said in *Sacred Number and the Lords of Time* book, pages 220-223,

about the 3:4:5 triangle between Stonehenge, Bry Celli Dhu

and Arbor Low, viz-a-vis its diameter.

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