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Ancient FeetA.F.Whillock |
(We received an enquiry from an architect in Italy regarding the derivation of the English Foot and its relationship to other similar units. Our reply contained some interesting data worth recording here.)
Both the Roman and Belgic (northern) feet were in use at the Norman Conquest of 1066. The latter was dominant in the eastern half of the country where pre-Norman settlers were established. There was a pre-Roman unit used by the Celts (the Welsh foot) of about 9 inches, derived from the Greek Pythic foot, its anthropometric form. This was retained by the Welsh tribes as they were driven westwards by successive waves of invaders.
Linear measures in this country were unified by Edward I, in 1308 (see p. 94 of ref.6), who ordained that the inch was to be three grains of barley, dry and round, taken from the middle of the ear. This was possibly a compromise between the Roman foot and the larger Belgic/Drusian foot. The three barleycorn standard enabled anyone to obtain an inch with sufficient accuracy for the times. As mentioned by Skinner, three average grains gives a length slightly greater than our present inch, which archaeologist Flinders Petrie claims has maintained its value within 0.2% since its definition. Possibly, mediaeval barley grains were less well-developed than are modern ones because of our more effective fertilisers. Cereal-plant breeding has increased only the number of grains on a shoot, not their basic size.
Our foot is Graeco-Roman in origin and derived originally from Egypt, where practical measures were anthropomorphic, with units of the digit - or finger width - of about 3/4 inch. The practical cubit or forearm length was 18 inches divided into two feet of twelve digits, which became the Pythic foot of Greece. In that country it was increased by four digits to form the Attic foot, later adopted by the Romans who divided it into twelve uncia (inches).
The foot is divided into twelve inches for general use. The inch is a useful tactile unit in its own right, dividedinto binary fractions down to 64ths and into twelfths (ligns) with further binary division of these down to 96ths. Decimal division of the inch is used for precision engineering down to thousandths for an ordinary standard of accuracy. Another set of subdivisions is obtained by splitting a lign into six points (72 to the inch) and by making two ligns equal to a pica which is the standard single line-spacing for typewriters, stencils, etc. Points, of course, are used in printing. All these divisions are useful in design and layout work, enabling various proportions to be readily obtained. In particular, with binary divisions, mid- and quarter-points of a distance can be easily found - an important requirement on the drawing-board. Steel engineers' scales are sold in tool shops with all divisions, including metric. For surveying, the foot is divided decimally (though metric staffs are now 'de rigeur' in the belief that these are more 'scientific').
Multiples of the foot are the yard of three feet, which is a normal single-arm stretch and measuring step (the French surveyors used to count 100 steps and put down 90 metres), and the fathom, or furthest (double) arm stretch - six feet - which is a practical unit for inshore navigation: the length of a sounding-line can be easily estimated as it is hauled in. Longer distances for land measurement have different derivations but are equated to the foot. An interesting one is the rod of 16-1/2 feet or 5-1/2 yards. This is, in fact, fifteen northern or Saxon feet*. When the shorter unit was standardized by Edward I, existing land allocations had to be recognized in the new units. The furlong or furrow-length of 220 yards had been (roughly) detemined since early days as the distance an ox team could effectively pull a plough continuously (they could then have a rest while the plough was turned round). Elizabeth I defined our statute mile at 5280 feet (8 furlongs), putting land measurement on a binary basis with 64 square furlongs (= 640 acres) to the square mile. (5280 can be divided exactly by 2, 3, 4, 5, 6, 8, 10, 11, 12, 16....)
Those who are ignorant of, and indifferent to, their country's history mock these so-called 'illogical' measures without appreciating the reasons behind them The advantages of the metric system which covers a range from the very small to the very large in un-ergonomic steps are limited to a few specialized subjects and are attractive to administrators who don't have to use them. Machines are not designed in fractions of a furlong, nor is land usually measured in inches!
The early Russian unit of length was the archine of 28 inches, divided into 16 verschoks. The verschok was an arm-length (from armpit to finger-tip) known in Italy as the braccio - 30·7 inches in Rome, 23 inches in Florence - an erratic measure used for cloth. I suppose it varied as one was buying or selling! Peter the Great worked in English ship yards in 1697 while he was Czar, and made the English foot standard for his country on his return (and that led to our adoption of the Petrograd Standard of softwood measure: 165 cubic feet, or 120 pieces 12′ x 11″ x 1-1/2″). The metric system was enforced in Russia after their revolution, perhaps for the French reason, 'pour changer tout cela'.
The French foot or 'pied du roi' in the Système Ancien of 12·79 inches prooably relates to the Northern foot identified by Flinders Petrie from a statistical study of ouildings in eastern England (Ref.1). This was later traced to the Indus valley from excavations at Mohenjo-Daro (p.40 in ref.6) and brought to Europe by the Teutonic migrations. The desiccation ofcentral Asia caused large population movements in early days. It had ten divisions of 1·32 English inches which seems to have been the length of five wheat grains end-to-end. This would have been appropriate to farming communities, just as the Royal cubit of Egypt could be formed from 100 wheat grains side by side.
Since the northern foot was firmly established for land measurement by the Belgic tribes, General Drusus allowed its use. Divided into twelve parts it might have become the unit for Frankish tribes. Skinner says that, under Charlemagne, they adopted a foot larger than the Roman foot of aoout 11·7 inches as half the Arabic Hashimin cubit of 25·56 inches. This is likely to have come from the Indus valley via a southern route. The northern foot also went eastwards to become the mathematical foot of China.
A spacing of about a foot is effective in use because it subtends the maximum angle for comfortable viewing at a normal holding distance. For this reason it occupies a prominent position in all national measures. In metric, the decimetre is too small and the metre cannot be regarded without head movement.
Practical rulers are in 30cm/12in. lengths. Samples I bought in Italy and Portugal have English inches on one edge, the 'mesura per mechanici'. A 30cm 'foot' would be a way of co-ordinating the three major measuring systems in the world: metric, English and Japanese (shaku-sun). We could have an inch of 25mm and the Japanese a sun of 30mm.
The mathematical significance of our foot lies in its twelve divisions which allow the primary ratios of 2, 3 and 4 to be obtained and represented exactly. In a decimal system, one ratio in every three has to be approximate only. In other fields, the factor three would allow weighing and paying to be made with the minimum number of pieces.
Geometrically, spatial relationships are more easily defined oy the dozen. For the packaging of goods, twelve and its multiples offer a wide choice of arrangements: a quarter gross (36) of rectangular objects can be assembled in 36 ways to form a compact parcel, whereas a quarter-hundred has a choice of only six not-very-convenient forms. If packaging in tens is required to suit decimalized accounting, it is often cheaper to use a dozenal box and leave empty spaces. (See 'Boxes & Cans', Dozenal Journal Nos. 2 and 3).
The core of our argument is that primitive finger-counting methods are inadequate to deal properly with the complexity of modern scientific and social requirements.
Books on the subject of measurement, some of which are listed next, all quote the same material, but place different interpretations on it, sometimes attempting to deduce too much from small variations. I have mentioned the four basic systems of linear measurement that have evolved for our convenience over the ages; and inevitable changes must have occurred as they were transmitted from area to area. Once accepted by each city or authority, some method of stabilizing a unit had to be decided - which was surprisingly effective. Ref.3 lists various forms of the foot throughout the world.
*Berriman (qv) identifies the Northern foot with the Sumerian foot; the Sumerian cubit is one-tenth of a pole. The double foot is close to Berriman's "Cubit A" which he derives from the Earth's radius.