measure is mostly guess-work. Hence, except in a few cases, we shall not here consider any units of the Middle Ages. A constant difficulty in studying works on metrology is the need of distinguishing the absolute facts of the case from the web of theory into which each writer has woven them,—often the names used, and sometimes the very existence of the units in question, being entirely an assumption of the writer. Therefore we shall here take the more pains to show what the actual authority is for each conclusion. Again, each writer has his own leaning: Böckh, to the study of water-volumes and weights, even deriving linear measures therefrom; Queipo, to the connexion with Arabic and Spanish measures; Brandis, to the basis of Assyrian standards; Mommsen, to coin weights; and Bortolotti to Egyptian units; but Hultsch is more general, and appears to give a more equal representation of all sides than do other authors. In this article the tendency will be to trust far more to actual measures and weights than to the statements of ancient writers; and this position seems to be justified by the great increase in materials, and the more accurate means of study of late. The usual arrangement by countries has been mainly abandoned in favour of following out each unit as a whole, without recurring to it separately for every locality.
The materials for study are of three kinds. (1) Literary, both in direct statements in works on measures (e.g., Elias of Nisibis), medicine (Galen), and cosmetics (Cleopatra), in ready-reckoners (Didymus), clerk's (kátib's) guides, and like handbooks, and in indirect explanations of the equivalents of measures mentioned by authors (e.g., Josephus). But all such sources are liable to the most confounding errors, and some passages relied on have in any case to submit to conjectural emendation. These authors are of great value for connecting the monumental information, but must yield more and more to the increasing evidence of actual weights and measures. Besides this, all their evidence is but approximate, often only stating quantities to a half or quarter of the amount, and seldom nearer than 5 or 10 per cent.; hence they are entirely worthless for all the closer questions of the approximation or original identity of standards in different countries; and it is just in this line that the imagination of writers has led them into the greatest speculations, unchecked by accurate evidence of the original standards. (2) Weights and measures actually remaining. These are the prime sources, and, as they increase and are more fully studied, so the subject will be cleared and obtain a fixed basis. A difficulty has been in the paucity of examples, more due to the neglect of collectors than the rarity of specimens. The number of published weights did not exceed 600 of all standards a short time ago; but the collections in the last three years from Naucratis (28),[1] Defenneh (29), and Memphis (44) have supplied over six times this quantity, and of an earlier age than most other examples, while existing collections have been more thoroughly examined; hence there is need for a general revision of the whole subject. It is above all desirable to make allowances for the changes which weights have undergone; and, as this has only been done for the above Egyptian collections and that of the British Museum, conclusions as to the accurate values of different standards will here be drawn from these rather than Continental sources. (3) Objects which have been made by measure or weight, and from which the unit of construction can be deduced. Buildings will generally yield up their builder's foot or cubit when examined (Inductive Metrology, p. 9). Vases may also be found bearing such relations to one another as to show their unit of volume. And coins have long been recognized as one of the great sources of metrology,—valuable for their wide and detailed range of information, though most unsatisfactory on account of the constant temptation to diminish their weight, a weakness which seldom allows us to reckon them as of the full standard. Another defect in the evidence of coins is that, when one variety of the unit of weight was once fixed on for the coinage, there was (barring the depreciation) no departure from it, because of the need of a fixed value, and hence coins do not show the range and character of the real variations of units as do buildings, or vases, or the actual commercial weights.
Principles of Study.—(1) Limits of Variation in Different Copies, Places, and Times.—Unfortunately, so very little is known of the ages of weights and measures that this datum—most essential in considering their history—has been scarcely considered. In measure, Egyptians of Dynasty IV. at Gizeh on an average varied 1 in 350 between different buildings (27). Buildings at Persepolis, all of nearly the same age, vary in unit 1 in 450 (25). Including a greater range of time and place, the Roman foot in Italy varied during two or three centuries on an average 1400 from the mean. Covering a longer time, we find an average variation of 1200 in the Attic foot (25), 1150 in the English foot (25), 1170 in the English itinerary foot (25). So we may say that an average variation of 1400 by toleration, extending to double that by change of place and time, is usual in ancient measures. In weights of the same place and age there is a far wider range; at Defenneh (29), within a century probably, the average variation of different units is 136, 160, and 167, the range being just the same as in all times and places taken together. Even in a set of weights all found together, the average variation is only reduced to 160 in place of 136 (29). Taking a wider range of place and time, the Roman libra has an average variation of 150 in the examples of better period (43), and in those of Byzantine age 135 (44). Altogether, we see that weights have descended from original varieties with so little intercomparison that no rectification of their values has been made, and hence there is as much variety in any one place and time as in all together. Average variation may be said to range from 140 to 170 in different units, doubtless greatly due to defective balances.
2. Rate of Variation.—Though large differences may exist, the rate of general variation is but slow,—excluding, of course, all monetary standards. In Egypt the cubit lengthened 1170 in some thousands of years (25, 44). The Italian mile has lengthened 1100 since Roman times (2) ; the English mile lengthened about 1300 in four centuries (31). The English foot has not appreciably varied in several centuries (25). Of weights there are scarce any dated, excepting coins, which nearly all decrease; the Attic tetradrachm, however, increased 150 in three centuries (28), owing probably to its being below the average trade weight to begin with. Roughly dividing the Roman weights, there appears a decrease of 140 from imperial to Byzantine times (43).
3. Tendency of Variation.—This is, in the above cases of lengths, to an increase in course of time. The Roman foot is also probably 1300 larger than the earlier form of it, and the later form in Britain and Africa perhaps another 1300 larger (25). Probably measures tend to increase and weights to decrease in transmission from time to time or place to place; but far more data are needed to study this.
4. Details of Variation.—Having noticed variation in the gross, we must next observe its details. The only way of examining these is by drawing curves (28, 29), representing the frequency of occurrence of all the variations of a unit; for instance, in the Egyptian unit—the kat—counting in a large number how many occur between 140
