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.
476·687/252·458 = 1886·9 cubic inches
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-Mamūn, 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.
Escandau = 16·096 litres = 3·54 gallons.
∛16096 = 25·24 centimetres, the Pan = 9·9 inches.
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.