The Sources of the English and of the Rhineland
Foot

Commerce is the great conservator of standards. These may become altered by the ill-advised action of rulers, by municipal or parochial carelessness, even by the desire of profit on short measure, or occasionally, as seen to a slight extent in our old Bushel, by the faulty dimensions of a standard; but wholesale trade, supported, in weights at least, by the goldsmith and the apothecary, preserved the integrity of many standards during the Middle Ages and up to modern times. Commerce conveyed to the West the standards that had developed in the great Oriental Kingdoms, sometimes with the modifications due to Roman influence. Masons and architects also preserved the standards of length and, allowing for variations inevitable under the feudal system, the principal linear measures can generally be traced to their sources as surely as weights. But there are two, yea three, striking exceptions among the linear standards of the West: the English foot, and the Rhineland foot, and also the PÁn of Marseilles. These are quite unconnected with any ancient measures, and there is no record of their origin. The only clue to it is found in the simple relation of each to the corresponding weights and measures of capacity, the origin of which can be satisfactorily traced. This leads to the hypothesis that these linear measures were ‘involved,’ that is produced by a method of involution the inverse of that which had evolved the measures of weight and capacity.

1. The English Foot

There seem three hypotheses for the origin of the English foot.

1. That it was the Olympic foot = 12·16 inches, its standard diminished by the accidents of time.

But we know that the Romans established their measures in Britain, and our mile of 8 stadia and of 5000 feet (first Roman, then English) up to Tudor times, shows that it was originally 1000 Roman paces of 5 feet; and our early wine-bushel, of which the wine-gallon was 1/8, is referable to the cube of the English foot, not to that of the Olympic foot.

There is no trace of the Olympic foot in Northern Europe except the possibility (mentioned under Foreign Linear Measures) of the Amsterdam local foot, = 11·146 inches, being 11 inches of the Olympic foot.

2. It happens that the mean of the Roman foot = 11·67 inches, and of the Rhineland foot = 12·356 inches, gives 12·013 inches. But there is no instance of a new standard being formed from the mean of two older ones; moreover this hypothesis begs the question of the Rhineland foot.

3. The hypothesis which I consider the most likely is that the foot is the measure of the side of a cubical vessel containing 1000 Roman ounces of water. It seems likely that in early times, possibly under King Alfred by the advice of Italian moneyers or Jewish merchants, this measurement was effected in order to establish a foot and a cubic foot measure of capacity corresponding to a new talent of 1000 Roman ounces. There is no record of this, any more than there is a record of the standard taken for the Tower pound of the Norman and Plantagenet kings. All we know is that, during the times of these kings, the relation of Averdepois or Roman weight to our measures of capacity was utterly ignored until at last, in 1685, ‘some Gentlemen at Oxford determined the weight of a cubic foot of spring water, or 1728 solid inches, to be 1000 ounces averdepois.’ That the correct weight is not 1000 but about 998 ounces at 62° does not militate against the connexion of the weight and measure any more than the fact that a cubic decimetre of water, supposed to weigh 1000 grammes, only weighs about 998-1/2 grammes would disprove a connexion between the cubic decimetre and the gramme.

The difficulty of making a ‘quadrantal,’^[10] a vessel of exactly cubical form inside, is so great that the wardens of the Metric System abandoned the cubic decimetre of water as giving the standard, either of the litre for capacity, or of the kilogramme for weight. Even approximate accuracy was unattainable, and they were obliged to make the kilogramme an arbitrary standard of mass and the litre a vessel containing a kilogramme of water.

When it is seen that a difference of 1 in 2500 in the length of the foot taken as the inside measure of a quadrantal makes a difference of 3 cubic inches out of 1728 in its capacity, the material difficulties of constructing a vessel exactly cubical will be understood. However, a quadrantal being constructed, perhaps after many trials of sides as exactly equal as possible, and holding 1000 ounces of Roman ounces (= 437 grains) of water, the mean measure of its panels was taken as a foot, and the quadrantal as a cubic foot—the wine-bushel.

Let us take 1000 Roman ounces and divide the total number of grains weight by the statute number of grains in a cubic inch of water as determined by Captain Kater in 1824.

The dividend will be the number of cubic inches, and its cube root will be the foot—

of which the cube root is 12·0042 inches, a length differing by only 1/2400 from the actual Imperial foot.

I took the idea of this hypothesis from that by which Don V. V. Queipo inferred the BelÁdi cubit to be the double measure of the side of a cubical vessel containing a PtolemaÏc talent of water. Certainly it solves the question of the origin of our foot, and it happens that, applied to the equally obscure origin of the Rhineland foot, the results are equally satisfactory.

2. The Rhineland Foot

Let the same process of involution be applied to the side of a cubical vessel containing 1000 Troy ounces of water.

The standard of Troy weight varied very much, from the Danish value of a little over 481 grains in the ounce, to the French Troy value of 472·13 grains.

The Scots Troy weight, = 476·09 grains to the ounce, is nearly the same as the Amsterdam weight, = 476·68 grains.

These Troy weights may be taken at three main standards, high, medium, and low, represented by:

Let us apply to 1000 ounces of water, at the medium Amsterdam standard, = 10 Egyptian dirhems of 47·6 grains, the same measurement of a quadrantal made to contain them as exactly as possible.

and the cube root of the dividend gives 12·357 inches, exactly, to 1 in 20,000, the Rhineland foot as established in Prussia = 12·3564 inches. The Prussian standard of the Cologne pound (its ounce = 451·1 grains) was 1/66 of a Rhineland cubic foot of water at 65·75 F., and was fixed at 7217·9 grains. This was exactly 1/66 of 1000 Troy ounces of water at the standard of 476·38 grains. So 66 Prussian pounds were equal to 1000 Troy ounces, or to 62·5 Troy pounds at that standard.

The Rhineland cubic foot had, like the English cubic foot, long been the bushel standard of North Germany. The Himt, now, or until quite recently, the unit of corn-measure in Hanover and Brunswick, contained 6·852 gallons, or 68·52 lb. of water. It is probable that the Himt, which passed to Scotland in the fifteenth century as the firlot of that time, had risen slightly, and that it was originally = 68·05 lb., the true Rhineland cubic foot of water.

3. The PÁn of Marseilles

Marseilles, a city of Greek origin, always in extensive commercial relations with the Mediterranean countries using the Arabic system of weights and measures, had an almost perfect system of its own, entirely sexdecimal, and dating from about the tenth century. This system is still extant, so far as the French law can be evaded (see Chap. XXI: Old Weights and Measures of France). Wine and corn measures were in the usual Southern water-wheat ratio of 1 to 1·22, and the principal of these was the Escandau for wine and oil, and the Panau for corn. Now Escandau means ‘standard’; and this measure was 1/4 of the Mieirolo, the half wine-load or ‘wey’ which corresponded in water-wheat ratio to the half-load or wey of wheat. The load of wheat, the cargo, was the cubic cubit of Al-Mamun, brought from Egypt by the corn-trade. The unit of length was the Pan (pronounced pÁng), a word apparently similar to the palmo of Italy and Spain, but really different. Palmo becomes paume in ProvenÇal, while Pan is from L. pannus, a side, pane or panel;^[11] and the Marseilles Pan = 9·9 inches is exactly the measure of the side or pan of an Escandau of cubical form. The filiation of the Escandau is evident, while the Pan is not derived from any antecedent measure. That the Pan was the measure of the pan or panel of a cubical Escandau is supported by the name of the corn-standard, the Panau, corresponding to the fluid standard of the Escandau, and of the land-measure, L. Panalata, the peck-land, originally the extent usually sown with a Panau of wheat.

The evidence of the Pan seems to me to remove any doubt as to the medieval evolution of linear measures from imported standards of weight or capacity. The meaning of Pan as ‘side, panel’ is conclusive, especially when supported by the Panau measure and by other ProvenÇal derivatives:

Panard, a limping man, leaning to one side as he walks.

Lou Panard, the star Antares which, rising late and setting early, not appearing much above the horizon, is visible only on one side of it.

In the description of the ancient cubits and talents and of the Roman system derived from them, the filiation of the English system of weights and measures, and of the Scots and other cognate systems, is clearly seen. There was no taking of a King’s heel-to-toe as a foot, no pound imported from some unknown country at an unknown period, no wheat-quarter preserved in the dimensions of an Egyptian sarcophagus, not even a pint from the Roman sextarius; legend disappears, the course of evolution, and, at one point, of involution, is clear, and as thoroughly scientific as in any system invented by an Academy of Sciences. Here are the links of filiation of the English foot:

1. The Egyptian meridian cubit.

2. The royal cubit, increased from the meridian cubit.

3. The royal foot, two-thirds of the royal cubit.

4. The cubic royal foot.

5. The Alexandrian talent, the weight of a royal cubic foot of water.

6. The Roman ounce, 1/1500 of the Alexandrian talent.

7. The English talent, 1000 Roman ounces.

8. The volume of 1000 Roman ounces of water, the original wine-bushel.

9. The 1000-ounce Quadrantal becomes the cubic foot, its side giving the English foot.

For the Rhineland and Scots system we have:

1. The Egyptian meridian cubit.

2. The Arabic or Black cubit, 7 palms of the meridian cubit’s 6 palms.

3. The Arabic foot, two-thirds of the Arabic cubit.

4. The Arabic talent or Cantar, the weight of an Arabic cubic foot of water.

5. The Troy ounce, 1/1500 of the Cantar, and coinciding with 10 lesser dirhems of about 48 grains.

6. The Rhineland talent of 1000 Troy ounces Amsterdam standard.

7. The Quadrantal containing 1000 Troy ounces of water becomes the cubic Rhineland foot, its side giving the measure of the Rhineland foot.

For the ProvenÇal system we have:

1. The Egyptian meridian cubit.

2. The Arabic cubit, 7 palms of the meridian cubit’s 6 palms.

3. The Arabic cubit cubed, in the corn-measure of medieval Egypt, the Cargo of Marseilles, the Setier of Paris.

4. The half-cargo reduced to wine-measure in wheat-water ratio becomes the Mieirolo; of which one-fourth is the Escandau or Standard measure.

5. The Quadrantal containing an Escandau gives, as the measure of its side or panel, the PÁn of Marseilles.

The evolution of the English foot, of the Rhineland or Scots foot, of the PÁn of Marseilles, being now made clear, we can proceed to English and other linear measures. The origin of the Ounce, the foot, the cubic foot or wine-bushel is explained. That of Troy weight has been seen, and its predecessor, Tower weight, came from another ounce of the Arabic cantar. The origin of every measure and weight used in the civilised world will be found in the stories of the ancient cubits and talents.