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. Footnote 10: Quadrantal, the Roman standard of capacity, a cubic vessel measuring one foot on each of its inside panels. 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— 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.