and 141 grains, 141 and 142, and so on; such numbers represented by curves show at once where any particular varieties of the unit lie (see Naukratis, i. p. 83). This method is only applicable where there is a large number of examples; but there is no other way of studying the details. The results from such a study—of the Egyptian kat, for example—show that there are several distinct families or types of a unit, which originated in early times, have been perpetuated by copying, and reappear alike in each locality (see Tanis, ii. pl. 1.). Hence we see that if one unit is derived from another it may be possible, by the similarity or difference of the forms of the curves, to discern whether it was derived by general consent and recognition from a standard in the same condition of distribution as that in which we know it, or whether it was derived from it in earlier times before it became so varied, or by some one action forming it from an individual example of the other standard without any variation being transmitted. As our knowledge of the age and locality of weights increases these criteria in curves will prove of greater value; but even now no consideration of the connexion of different units should be made without a graphic representation to compare their relative extent and nature of variation.
5. Transfer of Units.—The transfer of units from one people to another takes place almost always by trade. Hence the value of such evidence in pointing out the ancient course of trade, and commercial connexions (17). The great spread of the Phœnician weight on the Mediterranean, of the Persian in Asia Minor, and of the Assyrian in Egypt are evident cases; and that the decimal weights of the laws of Manu (43) are decidedly not Assyrian or Persian, but on exactly the Phœnician standard, is a curious evidence of trade by water and not overland. If, as seems probable, units of length may be traced in prehistoric remains, they are of great value; at Stonehenge, for instance, the earlier parts are laid out by the Phœnician foot, and the later by the Pelasgo-Roman foot (26). The earlier foot is continually to be traced in other megalithic remains, whereas the later very seldom occurs (25). This bears strongly on the Phœnician origin of our prehistoric civilization. Again, the Belgic foot of the Tungri is the basis of the present English land measures, which we thus see are neither Roman nor British in origin, but Belgic. Generally a unit is transferred from a higher to a less civilized people; but the near resemblance of measures in different countries should always be corroborated by historical considerations of a probable connexion by commerce or origin (Head, Historia Numorum, xxxvii.). It should be borne in mind that in early times the larger values, such as minæ, would be transmitted by commerce, while after the introduction of coinage the lesser values of shekels and drachmæ would be the units; and this needs notice, because usually a borrowed unit was multiplied or divided according to the ideas of the borrowers, and strange modifications thus arose.
6. Connexions of Lengths, Volumes, and Weights.—This is the most difficult branch of metrology, owing to the variety of connexions which can be suggested, to the vague information we have, especially on volumes, and to the liability of writers to rationalize connexions which were never intended. To illustrate how easy it is to go astray in this line, observe the continual reference in modern handbooks to the cubic foot as 1000 ounces of water; also the cubic inch is very nearly 250 grains, while the gallon has actually been fixed at 10 ℔ of water; the first two are certainly mere coincidences, as may very probably be the last also, and yet they offer quite as tempting a base for theorizing as any connexions in ancient metrology. No such theories can be counted as more than coincidences which have been adopted, unless we find a very exact connexion, or some positive statement of origination. The idea of connecting volume and weight has received an immense impetus through the metric system, but it is not very prominent in ancient times. The Egyptians report the weight of a measure of various articles, amongst others water (6), but lay no special stress on it; and the fact that there is no measure of water equal to a direct decimal multiple of the weight-unit, except very high in the scale, does not seem as if the volume was directly based upon weight. Again, there are many theories of the equivalence of different cubic cubits of water with various multiples of talents (2, 3, 18, 24, 33); but connexion by lesser units would be far more probable, as the primary use of weights is not to weigh large cubical vessels of liquid, but rather small portions of precious metals. The Roman amphora being equal to the cubic foot, and containing 80 libræ of water, is one of the strongest cases of such relations, being often mentioned by ancient writers. Yet it appears to be only an approximate relation, and therefore probably accidental, as the volume by the examples is too large to agree to the cube of the length or to the weight, differing , or sometimes even . All that can be said therefore to the many theories connecting weight and measure is that they are possible, but our knowledge at present does not admit of proving or disproving their exactitude. Certainly vastly more evidence is needed before we would, with Böckh (2), derive fundamental measures through the intermediary of the cube roots of volumes. Soutzo wisely remarks on the intrinsic improbability of refined relations of this kind (Étalons Ponderaux Primitifs, note, p. 4).
Another idea which has haunted the older metrologists, but is still less likely, is the connexion of various measures with degrees on the earth's surface. The lameness of the Greeks in angular measurement would alone show that they could not derive itinerary measures from long and accurately determined distances on the earth.
7. Connexions with Coinage.—From the 7th century B.C. onward, the relations of units of weight have been complicated by the need of the interrelations of gold, silver, and copper coinage; and various standards have been derived theoretically from others through the weight of one metal equal in value to a unit of another. That this mode of originating standards was greatly promoted, if not started, by the use of coinage we may see by the rarity of the Persian silver weight (derived from the Assyrian standard), soon after the introduction of coinage, as shown in the weights of Defenneh (29). The relative value of gold and silver (17, 21) in Asia is agreed generally to have been 13 to 1 in the early ages of coinage; at Athens in 434 B.C. it was 14 : 1; in Macedon, 350 B.C., 12 : 1; in Sicily, 400 B.C., 15 : 1, and 300 B.C., 12 : 1; in Italy, in 1st century, it was 12 : 1, in the later empire 13·9 : 1, under Justinian 14·4 : 1, and in modern times 15·5 : 1, but at present 23 : 1,—the fluctuations depending mainly on the opening of large mines. Silver stood to copper in Egypt as 80 : 1 (Brugsch), or 120 : 1 (Revillout); in early Italy and Sicily as 250 : 1 (Mommsen), or 120 : 1 (Soutzo), under the empire 120 : 1, under Justinian 100 : 1; at present it is 150 : 1. The distinction of the use of standards for trade in general, or for silver or gold in particular, should be noted. The early observance of the relative values may be inferred from Num. vii. 13, 14, where silver offerings are 13 and 7 times the weight of the gold, or of equal value and one-half value.
8. Legal Regulation of Measures.—Most states have preserved official standards, usually in temples under priestly custody. The Hebrew "shekel of the sanctuary"
