| Medieval Units of Measure
In the 1790s the French Metric Commission surveyed the existing units of measure used in France before creating the metric system. They found tens of thousands, with separate lengths and names for measuring cloth, tin, gold, firewood and scantling. Even within the one town there could be five separate units in use, often displayed on metal bars fixed to the jambs of the gates into the town.
The variety of units employed in the twelfth century may have been similar. Anyone trading in the medieval world had to handle proportional computation to survive. A merchant visiting Chartres from Florence could be buying in Pied du Roi with Livres minted locally, and calculating there would be a profit in Bracchia and Florins. We do something similar when we travel and convert pounds weight to grams and dollars to francs - but we have had years of schooling to equip us for this.
Though the records give us the names of medieval units, and occasional metal rods provide exact lengths, very little is known of most of the lengths being used. To clarify this while puzzling out the geometrical and proportional methods used by the medieval masters I drafted a book on my findings, but it remains unpublished.
Medieval measures were, on the whole, debased versions of the units used in Classical times. For the lengths of the ancient units of measure the most secure sources lie in the dimensions of buildings, in units marked on metal or stone rods, in distances between milestones, and the like. From these it appears there were less than a dozen distinct major systems of measure in Europe and the Middle East for many thousands of years before Christ.
During this time most of them remained remarkably stable. The Roman Foot, for example, is recorded within ±1.5 mm of 295.5 mm over two millennia. After the fourth century as central authority disappeared this unit became less exact and came to vary widely beyond these tolerances.
HOW TO FIND FOOT UNITS BY MEASURING A BUILDING
To do this we need to follow a rigorous method. The essential steps (from "The Ratio Hunter' and "The Contractors of Chartres") are:
1) determine the cutting and erection tolerances on each site,
2) accurately calculate every length in the chosen geometric system, and
3) compare it with the actual building measurements,
4) so that we accept only that geometric system in which all the calculations coincide with the measurements within the tolerances for that building.
The tolerances between the calculated geometry and the actual measurements of the element (be it window, tower, pillar etc) must be less than the cutting tolerances in the stones themselves. This is a very rigorous test.
For example, where a group of stones show a cutting error of ±1 mm, the difference between the average of these and the geometry as calculated and not drawn (to eliminate the errors that come from having a thick pencil) must be significantly less than ±1 mm. If they are not, then the geometry being tested is rejected and we start again. In over 250 geometric studies in "The Contractors of Chartres" I have followed this method. It is particularly important in the analysis of large items such as bays and buttresses.
Within the limits imposed by this methodology, one must discover the simplest arrangement, with the least number of steps and the least complex proportional system that would be consistent with what we know of current tools and methods.
One outcome will usually be to disclose the original foot from which the geometry was evolved. We can be sure of the original foot only when we have unearthed the whole of the geometry. Measuring only bay centres may be highly misleading, as the wall thicknesses and the epicentres of the buttresses are as important as the spaces between the piers, and all must be taken into account if the original geometric figure is to be found.
Then the geometry used to determine the bay must be consistent with that used for the parts, such as piers and windows. The masters of that time saw that the whole world had been created by God, and that every part should reflect that equally. They would refer to "extracting" an element or an elevation from the bolder figures set into the plan.
At Chartres each master used his own unit and only that unit. Occasionally he may have used more than one, but in each case the units had a clear proportional relationship to one another. Scarlet, the first master, used the Roman Foot and a unit called in Classical times the Ped Manualis. These were294.4 and 353.3 mm which form the ratio of 5:6. It is interesting that in spite of the great variation found in Roman measures at that time, Scarlet's foot unit was only 1 mm less than the average for the Roman foot described by Greaves and others.
Other foot units used at Chartres were 279.6, 282.5 and 285 mm. Another was close to the English foot of 305.7 and two were similar to the Pied du Roi at 322.9 and 325.8 mm, and one measuring between 336.8 and 337.1 was mentioned by the Commissioners as the Marseilles Foot. These lengths are calculated from the average of all occasions where they occurred in the cathedral, within a tolerance of no more than ±0.5mm.
I have had to conclude that each mason set out his buildings and created his templates from his own measure, and was not in the least concerned to share another's. Few measures are common to more than one builder. Seldom do any of them use the "official" royal measures, though they may have employed the units of their city, their quarry, or their lord.
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