| digit | 10=lichas | ||||
| 96............. | =orguia | 10=amma, | 10=stadion. | ||
| ·76 inch | 7·6 | 72·9 | 729 | 7290 | |
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 unciæ, 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 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 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= 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 feet of 11·68 across, and the same is found in one or two other cases. 11·60 also appears as the foot of some mediæval English buildings (25).
We now pass to units between which we cannot state any connexion.
25·1.—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 inches, 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 mediæval 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 inches. 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 cubic inches, this would show a cubit of 25 inches. The corrupt text in Chronicles of 3000 baths would need a still longer cubit; and, if a lesser cubit of 21·6 or 18 inches 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 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 inches; and the Persian guerze at present is 25, the royal guerze being 1 times this, or 37 inches. 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 feet (U), and from the actual size the U is therefore 10·806 inches. Hence the recorded series of measures on the Senkereh 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 | 7,776 | 223,280 |
Other units are the suklum or U=5·4, and cubit of 2U=21·6, which are not named in this tablet. In Persia (24) the series on the same base was—
| vitasti, | 2=arasni | 360=asparasa, | 30=parathañha, | 2=gãv; |
| 10·7 inches | 21·4 | 7704 | 231,120 | 462,240 |
probably
| yava, | 6=angusta, | 10=vitasti; | and gama | = arasnl; | also bazu | = 2 arasni. |
| ·18 inch | 1·07 | 10·7 | 12·8 | 21·4 | 42·8 | 21·4 |
The values here given are from some Persian buildings (25), which indicate 21·4, or slightly less; Oppert's value, on less certain data, is 21·52. The Egyptian cubits have an arm at 15 digits or about 10·9 marked on them, which seems like this same unit (33).
This cubit was also much used by the Jews (33), and is so often referred to that it has eclipsed the 25·1 cubit in most writers. The Gemara names 3 Jewish cubits (2) of 5, 6, and 7 palms; and, as Oppert (24) shows that 25·2 was reckoned 7 palms, 21·6 being 6 palms, we may reasonably apply this scale to the Gemara list, and read it as 18, 21·6, and 25·2 inches. There is also a great amount of mediæval and other data showing this cubit of 21·6 to have been familiar to the Jews after their captivity; but there is no evidence for its earlier date, as there is for the 25-inch cubit (from the brazen sea) and for the 18-inch cubit from the Siloam inscription.
From Assyria also it passed into Asia Minor, being found on the city standard of Ushak in Phrygia (33), engraved as 21·8, divided into the Assyrian foot of 10·8, and half and quarter, 5·4 and 2·7. Apparently the same unit is found (18) at Heraclea in Lucania, 21·86; and, as the general foot of the South Italians, or Oscan foot (18), best defined by the 100 feet square being of the jugerum, and therefore = 10·80 or half of 21·60. A cubit of 21·5 seems certainly to be indicated in prehistoric remains in Britain, and also in early Christian buildings in Ireland (25).
22·2.—Another unit not far different, but yet distinct, is found apparently in Punic remains at Carthage (25), about 11·16 (22·32), and probably also in Sardinia as 11·07 (22·14), where it would naturally be of Punic origin. In the Hauran 22·16 is shown by a basalt door (British Museum), and perhaps elsewhere in Syria (25). It is of some value to trace this measure, since it is indicated by some prehistoric English remains as 22·4.
20·0.—This unit may be that of the pre-Semitic Mesopotamians, as it is found at the early temple of Muḳayyir (Ur); and, with a few other cases (25), it averages 19·97. It is described by Oppert (24), from literary sources, as the great U of 222 susi or 39·96, double of 19·98; from which was formed a reed of 4 great U or 159·8. The same measure decimally divided is also indicated by buildings in Asia Minor and Syria (25).
19·2.—In Persia some buildings at Persepolis and other places (25) are constructed on a foot of 9·6, or cubit of 19·2; while the modern Persian arish is 38·27 or 2×19·13. The same is found very clearly in Asia Minor (25), averaging 19·3; and it is known in literature as the Pythic foot (18, 33) of 9·75, or of 19·5, if Censorinus is rightly understood. It may be shown by a mark (33) on the 26th digit of Sharpe's Egyptian cubit = 19·2 inches.
13·3.—This measure does not seem to belong to very early times, and it may probably have originated in Asia Minor. It is found there as 13·35 in buildings. Hultsch gives it rather less, at 13·1, as the "small Asiatic foot." Thence it passed to Greece, where it is found (25) as 13·36. In Romano-African remains it is often found, rather higher, or 13·45 average (25). It lasted in Asia apparently till the building of the palace at Mashita (620 A.D.), where it is 13·22, according to the rough measures we have (25). And it may well be the origin of the dirá‘ Stambuli of 26·6, twice 13·3. Found in Asia Minor and northern Greece, it does not appear unreasonable to connect it, as Hultsch does, with the Belgic foot of the Tungri, which was legalized (or perhaps introduced) by Drusus when governor, as longer than the Roman foot, or 13·07; this statement was evidently an approximation by an increase of 2 digits, so that the small difference from 13·3 is not worth notice. Further the pertica was 12 feet of 18 digits, i.e., Drusian feet.
Turning now to England, we find (25) the commonest building foot up to the 15th century averaged 13·22. Here we see the Belgic foot passed over to England, and we can fill the gap to a considerable extent from the itinerary measures. It has been shown (31) that the old English mile, at least as far back as the 13th century, was of 10 and not 8 furlongs. It was therefore equal to 79,200 inches, and divided decimally into 10 furlongs, 100 chains, or 1000 fathoms. For the existence of this fathom (half the Belgic pertica) we have the proof of its half, or yard, needing to be suppressed by statute (9) in 1439, as "the yard and full hand," or about 40 inches, evidently the yard of the most visual old English foot of 13·22, which would be 39·66. We can restore then the old English system of long measure from the buildings, the statute-prohibition, the surviving chain and furlong, and the old English mile shown by maps and itineraries, thus:—
| foot, | 3=yard, | 2=fathom, | 10=chain, | 10=furlong, | 10=mile. |
| 13·22 | 39·66 | 79·32 | 793 | 7932 | 79,320 |
Such a regular and extensive system could not have been put into use throughout the whole country suddenly in 1250, especially as it must have had to resist the legal foot now in use, which was enforced (9) as early as 950. We cannot suppose that such a system would be invented and become general in face of the laws enforcing the 12-inch foot. Therefore it must be dated some time before the 10th century, and this brings it as near as we can now hope to the Belgic foot, which lasted certainly to the 3d or 4th century, and is exactly in the line of migration of the Belgic tribes into Britain. It is remarkable how near this early decimal system of Germany and Britain is the double of the modern decimal metric system. Had it not been unhappily driven out by the 12-inch foot, and repressed by statutes both against its yard and mile, we should need but a small change to place our measures in accord with the metre.
