Buildings in Assyria and Babylonia show 20-5 to 206. The Babylonian

system was sexagesimal, thus (18)— uban, s = qat, 6=ammat, 6 = qanu, 6o=sos, 3o=parasang, 3 = kaspu. 6g iBcli 3'44 2o'6 124 7430 223,000 446,000 Asia Minor had this unit in early times— in the temples of Ephesus 20-55, Samos 2062; Hultsch also claims Priene 2090, 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 arose to 20-76 in late Roman times, like the late rise in Egypt (25). It was specially divided into Jth, the foot of Iths being as important as the cubit. 12"4S in This was especially the Greek derivative of the 20-63 J cubit. It originated in Babylonia as the foot of that JX2075. gysfgni (24), in accordance with the sexarj' system applied to the early decimal division of the cubit. In Greece it is the most usual unit, occurring in the Propylaea at Athens 12-44, temple at Aegina 12-40, Miletus 12-51, the Olympic course 12-62, &c. (18); thirteen buildings giving^ an average of 12-45, mean variation -06 (25), =2 of 20-75, ni. var. - 10. The digit = i palaeste, = foot of 12-4; then the system is —

1. .

(IJ=cubit, 4 = orsuia 100= / ^-, j„ «> lio! =a caeiu, lo=plethron, 6=^ J stadion. 12-4 in. 187 747 124S 124S 7470 In Etruria it probably appears in tombs as 12-45 (25); perhaps in Roman Britain; and in medieval England as 12-47 (25). 13'8 in This foot is scarcely known monumentally. On three ~y

Eg>'ptian cubits there is a prominent mark at the 19th 5X207. cjigjt or 14 in., which shows the existence of such a measure (33). It became prominent when adopted by Philetaerus about 280 B.C . as the standard of Pergamum (42), and probably it had been shortly before adopted by the Ptolemies for Eg>-pt. 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-S (18). Fixed by the Romans at 16 digits (i3-j = Roman foot), or its cubit at i| Roman feet, it was legally =13-94 at 123 B.C. (42); and 7j Philetaerean stadia were = Roman mile (18). The multiples of the 20-63 cubit are in late times generally reckoned in these feet of f cubit. The name " Babylonian foot " used by Bockh (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 in. 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 There is, however, fair evidence for units of I7-30 and 5

l'730 or -jij of 20-76 in Persian buildings (25); and the jX20 76. same is found in Asia Minor as 17-25 or | of 20-70. On the Eg^'ptian cubits a small cubit is marked as about 17 in., which may well be this unit, as | 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 obser-ed 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. In the •727 in Dynasties IV. and V. in Eg^'pt the digit is found in tomb sculptures as -727 (27); while from a dozen e.amples 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, panicularly at Nimrud (25); and in Persia buildings show the lo-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 '^^^ pre-Greek examples of this cubit in Eg^'pt, men^ tioned by Bockh (2), give 18-23 as a mean, which is 25^'" 25 digits of -729, and has no relation to the 20-63 cubit. This cubit, or one nearly equal, was used in Judaea in the times of the kings, as the Siloam inscription names a distance of 1758 ft. as roundly 1200 cubits, showing a cubit of about 17-6 in. This is also evidently the Olympic cubit; and, in pursuance of the decimal multiple of the digit found in Egj'pt and Persia, the cubit of 25 digits was i of the orguia of 100 digits, the series being — old digit,) 1, ^*^

^Z (orguia, lo=amma, lo=stadioQ. •72Q inch 18-3 72-9 729 7296. Then, taking f of the cubit, or J of the orguia, as a foot, the Creeks 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 ft. wide, and apparently 225 ft. 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 i2-i6 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, Z2-16 inches xo=i^ethroa, 1216 which stand as -Jth of the other decimal series based on the digit. This is the agrarian sv-stem, 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 i6| digits, and a new digit was formed — longer than any value of the old digit —of Jj of the foot, or -760, so that the series ran dieit ^ io=Iichas ^

(96 =orguia, io=amma, io=stadlon. 76 inch 76 72-9 729 7296. This formation of the Greek system (25) is only an inference from the facts yet known, for we have not sufficient information to prove it, though it seems much the simplest and most likely history. 11-52 Seeing the good reasons for this digit having been exi6v-7 ->6 ported to the West from Egypt—from the presence of the IDA -7-0 . 18.23 cubit in Egypt, and from the -729 digit being the decimal base of the Greek long measures— it is not surprising to find it in use in Italy as a digit, and multiplied by 16 as a foot. The more so as the half of this foot, or 8 digits, is marked off as a measure on the Egyptian cubit rods (33). Though Queipo has opposed this connexion (not noticing the Greek link of the digit), he agrees that it is supported by the Egyptian square measure of the plelhron, being equal to the Roman actus (33). The foot of 11-6 appears probably first in the prehistoric and early Greek remains, and is certainly found in Etrurian tomb dimensions as 11-59 (25). Dorpfeld considers this as the Attic foot, and states the foot of the Greek metro logical relief at Oxford as 1 1 -6 5 (or 11-61, Hultsch). Hence we see that it probably passed from the Eagt through Greece to Etruria, and thence became the standard foot of Rome; there, though divided by the Italian duodecimal system into 12 unciae, it always maintained its original i6 digits, which are found marked on some of the foot-measures. The well-known ratio of 25:24 between the 12-16 foot and this we see to have arisen through one being % of 100 and the other 16 digits— 16|: 16 being as 25: 24, the legal ratio. The mean of a dozen foot-measures (1) gives 11 -616 ±-008, and of long lengths and buildings Ii-6o7=t-oi. In Britain and Africa, however, the Romans used a rather longer form (25) of about 11-68, or a digit of -730 . Their series of measures was — digitus, 4 = palmus, 4=pes. 5 = passus, i2S=stadium, 8 = mniiare; 726 inch 2"9o 11-62 581 7262 58,100 also uncia '968=1') pes, palmipes I4"s2 = s palmi, cubitus 17-43 = 6 pahnL Either from its Pelasgic or Etrurian use or from Romans, this foot appears to have come into prehistoric remains, as the circle of Stonehenge (26) is 100 ft. of 11-68 across, and the same is found in one or two other cases. 1 1 -60 also appears as the foot of somq medieval English buildings (25). We now pass to units between which we cannot state any connexion. 251. — The earliest sign of this cubit is in a chamber at Abydos (44) about 1400 B.C .; there, below the sculptures, the plain wall is marked out by red designing lines in spaces of 25-l3=fc-03 in., which have no relation to the size of the chamber or to the sculpture. They must therefore have been marked by a workman using a cubit of 25-13. Apart from medieval and other very uncertain data, such as the Sabbath day's journey being 2000 middling paces for 2000 cubits, it appears that Josephus, using the Greek or Roman cubit, gives half as many more to each dimensiori of the temple than does the Talmud; this shows the cubit used in the Talmud for temple measures to be certainly not under 25 in. Evidence of the early period is given, moreover, by the statement in i Kings (vii. 26) that the brazen sea held 2000 baths; the bath being about 2300 cub. in., this would show a cubic of 25 in. The corrupt text in Chronicles of 3000 baths would need a still longer cubit; and, if a lesser cubit of 21-6 or 18 in. be taken, the result for the size of the bath would be impossibly small. For other Jewish cubits see 18-2 and 21-6. Oppert (24) concludes from inscriptions that there was in Assyria a royal cubit of j the U cubit, or 25-20; and four monuments show (25) a cubit averaging 25-28. For Persia Queipo {33) relies on, and develops, an Arab statement that the Arab hashama cubit was the royal Persian, thus fixing it at about 25 in.; and the Persian guerze at present is 25, the royal guerze being I J times this, or 37J in. As a unit of 1-013, decimally multiplied, is most commonly to be deduced from the ancient Persian buildings, we may take 2534 as the nearest approach to the ancient Persian unit. 2r6. — The circuit of the city wall of Khorsabad (24) is minutely stated on a tablet as 24,740 ft. (U), and from the actual size the U is therefore 10-S06 in. Hence the recorded series of measures on the Senkerch tablet are valued (Oppert) as•18 inch 2o=fpa!m), 3 = U, 6=qanu, 2 = 5a, 5=fii). 12=us, 30>=lasbll. 777S 223.280 3-6 = U.60 10-80 648 129-6 643 Other units are the suklum or jU=5-4. and cubit of 2U = 2i-9,