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 arose 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 in
35×20·75This 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 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),＝35 of 20·75, m. var.
·10. The digit＝14 palaeste,＝14
foot of 12·4; then the system is—
| foot, | 112＝cubit, | 4＝orguia | . . . . . . . . . . . . . . . . . . | 100＝ | stadion. | |
| 10 . . . . . . . . . . . . . . . . | ＝acaena, | 10＝plethron, | 6＝ | |||
| 12·4 in. | 18·7 | 74·4 | 124·5 | 1245 | 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
23×20·7This foot is scarcely known monumentally. On three
Egyptian cubits there is a prominent mark at the 19th
digit 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 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 Philetaerean 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 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 in
56×20·76There 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 in., 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. In the ·727 in 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×·729The 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 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 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 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 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＝acaena; | 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
| digit, | 10＝lichas | |||
| 96 . . . . | ＝orguia, | 10＝amma, | 10＝stadion. | |
| ·76 inch | 7·6 | 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.
11·62
16×·726.Seeing the good reasons for this digit having been exported
to the West from Egypt—from the presence of the
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 plethron, 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). Dörpfeld considers
this as the Attic foot, and states the foot of the Greek metrological
relief at Oxford as 11·65 (or 11·61, Hultsch). Hence we see
that it probably passed from the East 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 16 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 16 of 100
and the other 16 digits—1623 : 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 11·607±·01. 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, | 125＝stadium, | 8＝milliare; | |
| ·726 inch | 2·90 | 11·62 | 58·1 | 7262 | 58,100 | |
| also | ||||||
| uncia ·968＝112 pes, | palmipes 14·52＝5 palmi, | cubitus 17·43＝6 palmi. | ||||
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. 11·60 also appears as the foot of some 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 25·13±·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 dimension 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 1 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 76 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 112 times this, or 3712 in. As a unit of 1·013, decimally multiplied, is most commonly to be deduced from the ancient Persian buildings, we may take 25·34 as the nearest approach to the ancient Persian unit.
21·6.—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 10·806 in. Hence the recorded series of measures on the Senkerch tablet are valued (Oppert) as—
| susi, | 20＝(palm), | 3＝U, | 6＝qanu, | 2＝sa, | 5＝(n), | 12＝us, | 30＝kasbu. |
| 60. . . . . . . | ＝U, | 60. . . . . . . . . . | ＝(n), | ||||
| ·18 inch | 3·6 | 10·80 | 64·8 | 129·6 | 648 | 7776 | 223,280 |
Other units are the suklum or 12U＝5·4, and cubit of 2U＝21·9,
