Since the Penny Cyelopmdia ' appeared, we have examined several other figured feet ; for some of which see De Morgan, Arithmetical Books,' pp. 8, 9. The results accord very well with those given above and the mean of the whole gives a foot of 9.85 inches. But Ferrel and Stoffier are the best authorities, because they are the best names, have given the whole foot, and have taken the greatest pains with the sub divisions. The mean of their results, before allowance for shrinking, is 91 inches : that of the barley, presently mentioned, is 9.8 inches. The allowance for shrinking is, as above given, perhaps too great ; and 9'8 inches is, it may be, as good an estimate as can be given of this once well-known measure.
There is little reliance to be placed on the barley standard ; never theless, this addition to the Roman system of measures must have been made by some who had tried it : we can hardly suppose that writers would In all cases carefully state that four grains of barley placed aide by side give their first and lowest measure, unless they were at least repeating a well-established tradition, founded upon an actual mode of measurement. According to this mode, 04 grains, placed able by aide, ought to give their foot : we believe it will be found very difficult to make an7 barley of our day give more than 10 inches. On trying the first grams we obtained, we found that, by picking out the largest grains, 33 of them just gave more, and 32 less, than five inches : but that, taking the grains as they came, 3S gave only five inches. Not wishing however to trust to one trial, we procured the largest speci mens of barley which could be got from two different and distant parts of England, and from these specimens, already selected as choice samples, we picked out the largest grains. In a first sample, 33 grains placed aide by side gave five inches ; in a second, 33 grains gave five nchea and one-tenth ; in a third, 33 grains gave also 5 inches and one tenth. And yet these samples differed apparently in bulk ; but on examination we found that the lengths of the grains differed materially. their breadths very little. So that the ancient English standard which depended, or was said to have depended, upon the lengths of barley-corns placed end to end, was not founded upon so sure a method as that above described, which depended upon the breadths. The foot of 64 barleycorns derived from the average of the preceding (rejecting that from the smaller grains of the London sample) is 9 inches and eight-tenths of an ineh, rather smaller than might be supposed from the other methods of judging, which, however, it must be remembered, have been pushed to their utmost.
We feel persuaded from all that precedes, not only that at the beginning of the 16th century there was no distinction made between the measures of the learned and the Roman measures, but that the Roman foot, the foundation of all, was taken to be considerably shorter than the truth, having been probably recovered from the human body. Long after the introduction of sounder notions, we see traces of the same sort of thing. For instance, in the second edition of the mathe matical Lexicon of Vitalis (1690), the first edition (166S) being silent on the matter, an article on measures is introduced in which the only authorities alluded to are the 'Dies Geniales ' of Alexander ab Alex andre), in which there is nothing but description of ancient measures, and the work of George Agricola already cited. The Roman foot was recovered with tolerable ease as soon as it was looked for. Leonard di Portia, an Italian lawyer, gave its length from the Colotian foot here after noticed; and Lucas Pettus, another lawyer, wrote elaborately on the ancient weights and measures in 1573. Those who would see more of this subject in the 16th century must search for the writings of Alciatua, Alcasar, Geo. Agricola, Iludxua, Budelius, Capellus, Mon tanus, Mariana, Lebrixa (Nebrissensis), Neander, Pasi, Pettus, Portius, Villalpandus, &c.
As soon as tho middle period is past, the history of weights and measures down to our own time ceases to be European, and, with the exception of those of England and France, we need not, in so short a sketch as the present, give any very close account of the various national measures.
In England, it seems as if the standards were tolerably well settled and widely diffused at so early a period that the writers of this country took comparatively little notice of the system which the continental mathematicians used for their own communications. That the ear of
barley and of wheat were actually used in determining the standards, seems • to admit of no doubt. The statute 51 Henry Ill. (A.D. 1206) enacts," that an English penny,t called the sterling, round, without clipping, should weigh 32 grains of wheat, well dried and gathered out of the middle of the ear; and twenty pence to make an ounce, twelve ounces a pound, eight pounds a gallon of wino, and eight gallons of wine a bushel of London, which is the eighth part of a quarter." Again, 17 Edward II. (war. 1324) provides that three barley-corns, round and dry, make an inch,12 inches a foot, &c. And the interpreta tion of the older scientific writers on measures is agreeable to the common meaning of the words. " Look to the first grounde," says Oughtred, " and principle of our English measuring, from Barley cornea." But it is so difficult to know how much of the sharp end of a barley-corn must be cut or worn away before it becomes what was called " round," that this mode of measuring by the lengths of barley corns is very indefinite. Standards were made at early periods and enforced by various statutes; one of the earliest is one of Edward I. of uncertain date, which directs that a standard of bushels, gallons, and ells, shall be kept in every town, agreeing with the king's measure. With regard to the measure of length, this country has been fortunate, and its standards have, for commercial purposes, fully deserved the name. But the measure, of capacity [Gettos) remained various in spite of all acts of Parliament. In the year 1650 there were throe distinct modes of determining a wino gallon : 1, From general opinion, which gave 231 cubic inches, and with which, in fact, the gallons in common use agreed, as was proved by the measurements of Oughtred, Gunter, Brig,gs, and others. 2, The customary standard at the Guildhall, which, though not a legal standard, was considered as such, even by the law-officers of the crown, and which, though In reality only 224 cubic inches, was always taken to be 231 inches. 3, The real legal standard, preserved at the Treasury, containing 282 cubic inches. Oughtred says that the difference between the ale and wine gallons is, " that because of the frothing of the ale or beer, the quantity bwometh lease, and therefore such liquors as did not so yield froth, as wine, ogle, and the like, should in reason have a lesser measure." The Report of one of the oommittees states that the wine gallon had been gradually shrinking in capacity, until it was arrested at 231 cubic inches by a fiscal • definition. ''hat this value was laid down by the statute of 5 Anne, cap. 27, is certain ; and the origin of this (which is into a statute having nothing to do with weights and measures) seems to have been as follows :—A little after 1700, an information was tried in the Exchequer against one Barker, for having imported more of .Alicant wino than he had paid duty for. On the part of the crown it was contended that the sealed gallon at Guildhall (said to contain 231 cubic inches) was the standard. But the defendants appealed to the law which required that a standard gallon should be kept at the Treasury, proved that there was such a gallon at the Treasury containing 2S2 cubic inches, and established, by the evidence of the oldest persons in the trade, that the butte and hogsheads which came from Spain had always contained the proper number of the real standard gallons. A juror was withdrawn, and the law-officers of the crown took no further proceedings except procuring the above act. A better instance of confusion could hardly be imagined : the legal gallon had gradually been diminished more than 50 cubic inches ; the merchants in one particular trade continued to import and to pay duty by the real gallon, and were finally called to account by the attorney general, who, in common with the rest of the world, had forgotten what the real gallon was, and sued for penalties upon appeal to what was no more a legal standard than the measure in a private shop.