For obvious reasons, more measuring devices and measurable structures survive from the Roman world than from any other ancient culture.  Yet nobody has ever been able to exactly define what was intended to be the standard length of the Roman foot.  This would be the measure adopted by the Roman bureaucracy as the national reference.  (Although a vast amount of alternative standards, apart from the variable "Roman" foot, were in concurrent use both in Rome itself and throughout the Empire).  Researchers have believed the number of variations in the national standard was due to poor regard toward the maintenance of accuracy, but this is not the case.  Because the identical range of variations to which the Roman measures were subject, are detectable in the measurement systems of all other nations.  Luco Petto, a Renaissance antiquarian, argued intelligently, that although rules varied in a general sense, if any of them exactly agreed, then this would imply an intentional standard.  When subjected to this scrutiny, so many of the Roman rulers achieve such a level of correspondence that the conclusion that must be drawn is that the variations are indeed fully intentional. 

Not only are the Roman variations in their measuring devices intentional, it would seem that they are constructed to a greater degree of accuracy than are modern rules.  When purchasing modern devices across the counter, either foot rules, tape measures or metre sticks, the variations may be as much as .3%.  The ancient devices would seem to be subject to much lesser variations from their intended lengths, from .15% at a maximum.  In the examples that follow, it is difficult to assess how accurate are the reported lengths; did those who made the physical measurements use agreeable standards?  What were their criteria for the intended length, such as demarcation points, etc?  All one may do is to take the reported lengths, usually given in millimetres, and make an accurate conversion by using the metre taken as 3.2808427ft.  With so many references to compare, a statistically accurate picture will emerge. 

In the book, All Done With Mirrors, the variety of measures are each given descriptive names as briefly described in the essay on the Greek Foot.  But for now, the values of the Roman feet, which are accepted as being 24 to 25 of the Greek feet, are here listed in their ten potential values in two rows, separated by the fraction 440 to 441, as letters of the alphabet.  The fraction between each measure across the two rows is 175-176

The natural log e 2.718281... is integral to the Roman foot .9732096 through the harmonic 82944:

Mediaeval scholars who studied ancient metrology knew by tradition that there were 75 Roman miles in one degree of latitude. However, they had no method of identifying which value of the Roman foot gave the correct solution, and no longer did they have the technical ability to accurately measure the degree, which is around 69 statute miles in length. At the three longest values of the original table, marked e, i and j, the degrees are exactly seventy five 5000ft Roman feet miles at the latitude of 10°, the latitude of 38° and that of the average degree at 51°.
 

Close inspection of Harleston's plans of the city, whereupon all distances are notated in hunabs, reveals that there is little doubt that this was a vitally important measurement in the overall plan. Canonical modules repeatedly occur; numbers such as 144, 288, 216 720 etc., but the number which occurs most frequently is a distance of 378 hunabs and it did not escape Harleston's notice that this was a geodetic value. It is very accurately the 100,000th part of the mean perimeter of the earth. However, where there are fractured or irrational numbers in the significant distances which he noted, almost invariably these become integral and rational in terms of directly related measures, such as the Greek, Roman, Mycenaean and particularly the vara, which is the Megalithic Yard. Unfortunately, Harleston never connected his standard unit to those of other ancient systems, he continued to view the value as exclusively an American contrivance and invariably expressed it in metres. 

As well as his masterly interpretation of the architect's numerical design through the measures, he went much further in explaining practical reasons for this layout of temples and pyramids. He noted that from the vantage point of the pyramid summits, a range of celestial bearings, extreme moon and sun declinations and certain stellar alignments were indicated by prominent foresights. In reverse, the pyramids could also be used as foresights to these phenomena from distant locations, these outlying observation points were clearly indicated by carved stones at the precise positions which he was able to predict, and in addition, were distanced in regular numbers of his standard unit.

These findings alone could have prompted serious archaeological investigation and eventual recognition of his valuable work. After all, these were observations of a similar nature to those noted by a host of other investigators in relation to ancient monuments throughout the world. But Harleston went much further. He noted ratios relating to phi, e, the speed of light and distance ratios to the planets, including those invisible to the naked eye in the architectural layout of Teotihuacan, and much more. His overall conclusions infer that the builders had as great, or a greater, grasp of the laws of physics than does modern man. And however that may be, it was far too great a concept to be rationally debated, and as a consequence the Society of Americanists continues to ignore all of his claims. Even the well founded ones, such as the identification of the standard unit. Harleston is endowed in courage and vision; it is such a pity he went public with too much. 

Aspects of what has been covered concerning Central American metrology are more detailed in All Done With Mirrors, including how the modules of construction and their classification values may be decoded from the simple ratios of the pyramid dimensions. 

(Sent via e-mail October 3, 2004)

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