Ancient Measurement Systems: Their fractional integration
From the beginning of the 20th century the study of ancient metrology
has faded into the background of academic research. Before this, it was a topic of lively debate among the scientific and
archaeological communities. It was considered important to clearly define the ancient modules in order to interpret
architectural intentions in the ancient monuments, understand itinerary distances, the statements of the classical writers and
even biblical descriptions that abound with reference to measures.
Interest in the subject was briefly revived during the 1960s by the claim of
who asserted that the builders of the Megalithic structures had consistently used a common unit of measure throughout the British
Isles and Brittany. The claim, to this day, has been neither confirmed nor disproved.
This is entirely due to the fact that there is a prevailing ignorance of the subject of ancient metrology.
The statisticians who number-crunched the Megalithic data,
and dozens of highly qualified authors, simply failed to recognise the modules that their analyses produced. None of them had
made a detailed study of ancient systems and methods of mensuration.
At first glance, the subject seems formidable, causing one learned academic to exclaim that
"[Ancient] metrology is not a science, it is a nightmare."
It may seem so, there were a great many modules that were commonly used, various
spans, feet, digit multiples such as pygme,
remen, cubit and feet multiples -- step, yard, pace, fathom, pertica and various
bracchia; intermediate measures of the various
furlongs and stadia and the itineraries of
miles, leagues, schoenus etc.
However, the approach to the subject may be simplified by simply considering the basic measure of each system, which is
invariably the foot.
Augustus De Morgan
gave a broad hint at this method of assessment in 1847, he stated:
There runs through all these national systems a certain resemblance in the measures of length; and, if a bundle of rods
were made of foot rules, one from every nation, ancient and modern, there would not be a very unreasonable difference in the
lengths of the sticks.
It was simply by comparing the foot lengths of the different national systems that a very elegant order was perceived,
leading to the conclusion that all of these "national systems" formed a single organisation. It has become customary for
us to name a unit from the society in which it is found to have been used, but most often, the bureaucracies have adopted
particular units during the historical period. Obviously a universal system had been fragmented into these various cultures.
The difficulties of research are compounded by the lack of agreement as to nomenclature, for example, what are universally known
as Roman feet are often called Attic, and at one of its variations, Pelasgo.
Which brings us to the most confusing of all the aspects of metrology -- the variations. In all ancient societies, there is a
quite broad variation throughout the modules, which has been wrongly regarded as slackness in the maintenance of standards.
It would seem that the range of variations and the fractions by which they vary, are not merely similar from nation to nation,
but identical. Once these fractions == and the simple mathematical reasons for them == had been established, it became possible
to then classify these dissimilarities of the same module. The feet of the various national standards could then be compared at
their correct relationships. By seeing the fractional integration through the basic foot structure, many modules could be
discarded for comparative purposes, until very few Root feet remained. In fact, there are probably only twelve distinct feet
from which all other "feet" are extrapolated. For example the Pythic foot is a half Saxon cubit, and many modules attributed to
different cultures are in fact variations of the same basic foot, such as Saxon and Sumerian, or
pied de roi and Persian. These feet in
ascending order, in terms of the English foot are as follows:
- .9ft -- W