is familiar; the standard volume of the apet was secured in the dromus of Anubis at Memphis (35); in Athens, besides the standard weight, twelve copies for public comparison were kept in the city; also standard volume measures in several places (2); at Pompeii the block with standard volumes cut in it was found in the portico of the forum (33); other such standards are known in Greek cities (Gythium, Panidum, and Trajanopolis) (11, 33); at Rome the standards were kept in the Capitol, and weights also in the temple of Hercules (2); the standard cubit of the Nilometer was before Constantine in the Serapæum, but was removed by him to the church (2). In England the Saxon standards were kept at Winchester before 950 A.D., and copies were legally compared and stamped; the Normans removed them to Westminster to the custody of the king's chamberlains at the exchequer; and they were preserved in the crypt of Edward the Confessor, while remaining royal property (9). The oldest English standards remaining are those of Henry VII. Many weights have been found in the temenos of Demeter at Cnidus, the temple of Artemis at Ephesus, and in a temple of Aphrodite at Byblus (44); and the making or sale of weights may have been a business of the custodians of the temple standards.
9. Names of Units.—It is needful to observe that most names of measures are generic and not specific, and cover a great variety of units. Thus foot, digit, palm, cubit, stadium, mile, talent, mina, stater, drachm, obol, pound, ounce, grain, metretes, medimnus, modius, hin, and many others mean nothing exact unless qualified by the name of their country or city. Also, it should be noted that some ethnic qualifications have been applied to different systems, and such names as Babylonian and Euboic are ambiguous; the normal value of a standard will therefore be used here rather than its name, in order to avoid confusion, unless specific names exist, such as kat and uten.
All quantities stated in this article without distinguishing names are in British units of inch, cubic inch, or grain.
Standards of Length.—Most ancient measures have been derived from one of two great systems, that of the cubit of 20.63 inches, or the digit of .729 inch; and both these systems are found in the earliest remains.
20.63 ins.—First known in Dynasty IV. in Egypt, most accurately 20.620 in the Great Pyramid, varying 20.51 to 20.71 in Dyn. IV. to VI. (27). Divided decimally in 100ths; but usually marked in Egypt into 7 palms or 28 digits, approximately; a mere juxtaposition (for convenience) of two incommensurate systems (25, 27). The average of several cubit rods remaining is 20.65, age in general about 1000 B.C. (33). At Philæ, &c., in Roman times 20.76 on the Nilometers (44). This unit is also recorded by cubit lengths scratched on a tomb at Beni Hasan (44), and by dimensions of the tomb of Ramessu IV. and of Edfu temple (5) in papyri. From this cubit, mahi, was formed the xylon of 3 cubits, the usual length of a walking-staff; fathom, nent, of 4 cubits, and the khet of 40 cubits (18); also the schœnus of 12,000 cubits, actually found marked on the Memphis-Faium road (44).
Babylonia had this unit nearly as early as Egypt. The divided plotting scales lying on the drawing boards of the statues of Gudea (Nature, xxviii. 341) are 12 of 20.89, or a span of 10.44, which is divided in 16 digits of .653, a fraction of the cubit also found in Egypt. Buildings in Assyria and Babylonia show 20.5 to 20.6. The Babylonian system was sexagesimal, thus (18)—
| uban, | 5=qat, | 6=ammat, | 6=qanu, | 60=sos, | 30=parasang, | 2=kaspu. |
| .69 inch | 3.44 | 20.6 | 124 | 7430 | 223,000 | 446,000 |
Asia Minor had this unit in early times, in the temples of Ephesus 20.55, Samos 20.62; Hultsch also claims Priene 20.90, and the stadia of Aphrodisias 20.67, and Laodicea 20.94. Ten buildings in all give 20.63 mean (18, 25); but in Armenia it rose to 20.76 in late Roman times, like the late rise in Egypt (25). It was specially divided into 15th, the foot of 35ths being as important as the cubit.
12.45 ins.
35 of 20.75. This was especially the Greek derivative of the 20.63 cubit. It originated in Babylonia as the foot of that system (24), in accordance with the sexary system applied to the early decimal division of the cubit. In Greece it is
the most usual unit, occurring in the Propykea at Athens 12.44, temple at Ægina 12.40, Miletus 12.51, the Olympic course 12.62, &c. (18); thirteen buildings giving an average of 12.45, mean variation .06 (25), = 35 of 20.75, m. var. .10. The digit = 14 palæste, = 14 foot of 12.4; then the system is
| foot, | 112=cubit, | 4=orguia. | ........................................ | 100= | stadion. | |||
| 10............. | ............... | =acæna, | 10=plethron, | 6= | ||||
| 12.4 inch | 18.7 | 74.7 | 124.5 | 1245 | 7470 |
In Etruria it probably appears in tombs as 12.45 (25); perhaps in Roman Britain; and in mediæval England as 12.47 (25).
13.8 ins.
23 of 20.7. This foot is scarcely known monumentally. On three Egyptian cubits there is a prominent mark at the 19th digit or 14 inches, which shows the existence of such a measure (33). It became prominent when adopted by Philetærus about 280 B.C. as the standard of Pergamum (42), and probably it had been shortly before adopted by the Ptolemies for Egypt. From that time it is one of the principal units in the literature (Didymus, &c.), and is said to occur in the temple of Augustus at Pergamum as 13.8 (18). Fixed by the Romans at 16 digits (1313=Roman foot), or its cubit at 145 Roman feet, it was legally =13.94 at 123 B.C. (42); and 712 Philetærean stadia were = Roman mile (18). The multiples of the 20.63 cubit are in late times generally reckoned in these feet of 23 cubit. The name "Babylonian foot" used by Böckh (2) is only a theory of his, from which to derive volumes and weights; and no evidence for this name, or connexion with Babylon, is to be found. Much has been written (2, 3, 33) on supposed cubits of about 17–18 inches derived from 20.63,—mainly, in endeavouring to get a basis for the Greek and Roman feet, but these are really connected with the digit system; and the monumental or literary evidence for such a division of 20.63 will not bear examination. 17.30
56 of 20.76. There is, however, fair evidence for units of 17.30 and 1.730 or 112 of 20.76 in Persian buildings (25); and the same is found in Asia Minor as 17.25 or 56 of 20.70. On the Egyptian cubits a small cubit is marked as about 17 inches, which may well be this unit, as 56 of 20.6 is 17.2;
and, as these marks are placed before the 23rd digit or 17.0, they cannot refer to 6 palms, or 17.7, which is the 24th digit, though they are usually attributed to that (33).
We now turn to the second great family based on the digit.
This has been so usually confounded with the 20.63 family, owing
to the juxtaposition of 28 digits with that cubit in Egypt, that it
should be observed how the difficulty of their incommensurability has been felt. For instance, Lepsius (3) supposed two primitive cubits of 13.2 and 20.63, to account for 28 digits being only 20.4 when free from the cubit of 20.63, the first 24 digits being in some cases made shorter on the cubits to agree with the true digit standard, while the remaining 4 are lengthened to fill up to 20.6.
.727 ins. In the Dynasties IV. and V. in Egypt the digit is found in tomb sculptures as .727 (27); while from a dozen examples in the later remains we find the mean .728 (25). A length of 10 digits is marked on all the inscribed Egyptian cubits as the "lesser span" (33). In Assyria the same digit appears as .730, particularly at Nimrud (25); and in Persia buildings show the 10-digit length of 7.34 (25). In Syria it was about .728, but variable; in eastern Asia Minor more like the Persian, being .732 (25). In these cases the digit itself, or decimal multiples, seem to have been used.
18.23
25 × .729. The pre-Greek examples of this cubit in Egypt, mentioned by Böckh (2), give 18.23 as a mean, which is 25 digits of .729, and has no relation to the 20.63 cubit. This cubit, or one nearly equal, was used in Judæa in the times of the kings, as the Siloam inscription names a distance of 1758 feet as roundly 1200 cubits, showing a cubit of about 17.6 inches. This is also evidently the Olympic cubit; and, in pursuance of the decimal multiple of the digit found in Egypt and Persia, the cubit of 25 digits was 14 of the orguia of 100 digits, the series being
| old digit, | 25=cubit, | 4= | orguia, | 10=amma, | 10=stadion. | ||
| 100................= | |||||||
| .729 inch | 18.2 | 72.9 | 729 | 7296 | |||
Then, taking 23 of the cubit, or 16 of the orguia, as a foot, the Greeks arrived at their foot of 12.14; this, though very well known in literature, is but rarely found, and then generally in the form of the cubit, in monumental measures. The Parthenon step, celebrated as 100 feet wide, and apparently 225 feet long, gives by Stuart 12.137, by Penrose 12.165, by Paccard 12.148, differences due to scale and not to slips in measuring. Probably 12.16 is the nearest value. There are but few buildings wrought on this foot in Asia Minor, Greece, or Roman remains. The Greek system, however, adopted this foot as a basis for decimal multiplication, forming
| foot, | 10=acæna | 10=plethron, |
| 12.16 inches | 121.6 | 1216 |
which stand as 16th of the other decimal series based on the digit. This is the agrarian system, in contrast to the orguia system, which was the itinerary series (33).
Then a further modification took place, to avoid the inconvenience of dividing the foot in 1623 digits, and a new digit was formed—longer than any value of the old digit—of 116 of the foot, or .760, so that the series ran
