The dividend will be the number of cubic inches, and its cube root will be the foot—
437,000/252,458 = 1729·8 cubic inches,
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:
| English | Troy, | its | ounce | = 480 | grains |
| Amsterdam | „ | „ | „ | = 476·68 | „ |
| French | „ | „ | „ | = 472·13 | „ |