 one and one half of these feet as a cubit would be the Arabic black cubit, also the Egyptian cubit of the Nilometer.
Variants and variables in the above descriptions are in no wise arbitrary regional fluctuations but follow a distinct
discipline. The extent of the variations covers a range of values that amounts to about one fortieth part. Immediately one can
see one of the prime difficulties in the identification of ancient modules, because some of the distinct foot values are
related by lesser fractions; the Roman is 48 to 49 of the common Egyptian and the common Egyptian is 49 to 50 of the
Greek/English. They therefore overlap at certain of their variations, in the course of comparisons this often results in the
lesser variation of a distinct measure -- that is essentially longer than the measure of comparison -- to be shorter in length
than the greater variations of the lesser measure. Metrologists continually confuse the Belgic, Frankish and Saxon/Sumerian,
the latter has also been appended Ptolemaic. But, the differences become distinctively identifiable at the lengths of the
pertica, chain, furlong, stadium, mile etc.
It would appear from most of the empirical evidence that the full range of the variations in a single module,
here given in terms of the variations of the Greek-English foot, (the English foot being one of the series of the Greek foot)
are as follows:
|.990916 ||.996578 ||1.002272 ||1.008 ||1.01376
The above terminology is used as descriptive in the classification of the values. It was realised from the beginning that
all of these variations were impossible to express in an ascending order. They must be tabulated in two rows, the fraction
linking each of the variations across the rows is 175:176, and each of the values in the top row is linked to the value directly
below as 440:441. "Root" prefixes the descriptive terminology from Least to Geographic in the top row and "Standard" in the
bottom row. For example, 1.008 is Standard Canonical and 1.0114612 is Root Geographic etc.
As well as these values being measurements, they are also regarded as the formulae by which any other module is classified.
That is, any of the listed feet could occupy the Root position in the above table, and all of its variants would be subject to
the multiplications of the tabulated values. As an example, the Persian foot when subjected to this process:
|1.040461 ||1.046406 ||1.052386 ||1.0584 ||1.064448
Thus, whichever of the measures shows a direct fractional link to the English foot, such as the one and one twentieth, as above,
is Root, then the maximum value of 1.064448ft is both the Hashimi foot and the original pied de roi, both could be
classified as a Standard Geographic Persian foot (1.05 x 1.01376). Or the given length of the Mycenaen foot at .910315ft could
be classified as a Root Geographic Assyrian foot (.9 x 1.0114612ft) and so forth. Then, whenever one is making cultural
comparisons of modules, the correct classification must be selected, Root Reciprocal to Root Reciprocal etc. otherwise one is
looking at a compound fraction, i.e. the fraction separating the distinctive foot plus the fraction of the variation(s), which
may then show no apparent rational relationship.
These fractional separations of the rows and columns have a practical purpose; they are designed to maintain integers in
circular structures and artefacts such as storage and measuring vessels. If a diameter is multiple of four or a decimal,
by using 22/7 as pi this results in a fractured number perimeter. Therefore 3.125 or 25/8 would be used to give an
integer or rational fraction for the perimeter. Accuracy is maintained by using the longer version -- by the 176th part -- of
the measure in the perimeter; this is because 25/8 differs from 22/7 as 175 to 176. Similarly, the fraction 441 to 440 maintains
integrity of number in diameter and perimeter, but of different modules. If one has a canonical perimeter number such as
360 English feet, then the diameter will be exactly 100 royal Egyptian feet, but, the royal Egyptian foot that is directly
re