tures. Just as a carpenter to-day might lose a two-foot rule in the wall of a house, so 3000 years ago an Egyptian stone mason lost his two-cubit rule in the wall of a temple at Karnak. Subsequent ruin and excavation brought it to light, and allowed a direct comparison with the temple dimensions. At the present day, in some parts of China, the first step toward building a house is making a measuring stick, according to which all materials are purchased and the dimensions determined. This method suffices for simple exchange.
Standards of quantity or weight seem to have developed in a still more arbitrary manner. The cuneiform tablets of Babylon tell of ‘vessels’ of oil and ‘skins’ of wine, the volume being as arbitrary as the ‘jar’ or ‘amphora’ of the Romans. For dry produce the term often means simply a heap, large or small. With the introduction of the balance, weighing became possible, and pondus appears, designating essentially ‘a weight.’ Many ‘steel yards’ and balances (see Balance) were unearthed amid the ruins of Pompeii. As the pondus seems to be a haphazard unit, so also is the stone (14 pounds), still used in England, and the base of such units as the hundredweight (cwt.) or 112 pounds (8 stone), and the ton of 2240 pounds or 160 stone, also the bushel of 56 pounds (4 stone), etc.
The earliest systems of linear units seem to be based upon either the cubit (20.62 inches = 52.4 centimeters) or the digit (0.73 inch, or 1.85 cm.), probably derived from the breadth of the finger. The cubit appears first in Egypt in the Fourth Dynasty, and the great pyramid yields the value above given. Nevertheless, as might be expected, considerable variation occurs, even in Egypt (20.5 inches to 20.7 inches). The cubit was divided into hundredths, but as incommensurate, approximate subdivisions the one-seventh, ‘palm,’ and one-twenty-eighth, ‘digit,’ were used. Several extant cubit rods give an average of 20.65 inches. At the Nilometers it is 20.75. As multiples of the cubit (mahi) the xylon, 3 cubits, walking staff, the neut, 4 cubits, and the khet of 40 cubits, are found along with the schoenus of 12,000 cubits. About the same time a similar unit appears in Babylon, especially as the half of 20.89 inches or span of 10.44 inches, or 16 digits of 0.653 inches. A cubit of 20.5 inches is derivable from various buildings in Assyria and Babylonia, where a sexagesimal system existed. In Asia Minor the cubit derived from temples appears as 20.55 inches at Ephesus, 20.62 inches at Samos, while the stadium at Laodicea gives 20.94 inches. Three-fifths of the cubit of 20.75 inches, a combination of the Egyptian decimal and the Assyrian sexary system, is the commonest of Greek derivatives (12.44 inches) occurring in the Propylæa, the Temple of Ægina, the Olympian course, etc. Other and less important derivations from the cubit occur in restricted localities or periods. The digit appeared about simultaneously with the cubit, and some confusion arose from the belief that it was one twenty-eighth of a cubit; in reality they appear to be incommensurate, although 10 digits were often indicated on cubit sticks as the ‘lesser span.’ Practically the same unit appears in Assyria, Persia, and Asia Minor. The common Egyptian small unit of volume was the hon = about 29 cubic inches. The artaba was the practical equivalent of the Attic metretes. The Egyptian unit of weight was the kat = 146 grains; 100 kat = 10 uten = 1 tema. In Babylonia the talent = 360 stone = 3600 shekels = 66.4 pounds. The stadion appears very early as equal to one-thirtieth of a parasang, or about 148 meters, or 485 feet, the parasang being 14,550 feet, or 2.76 miles. This is the old itinerary stadion, used in measuring distances from place to place. As examples of Greek measures of length the following may be given:
1 stadion = 6 plethra or length of a furrow.
1 plethron = 16⅔ orgyia, similar to the fathom, the distance from tip to tip of the outstretched arms.
1 orgyion = 4 pecheis, or cubits.
1 pechus = 1½ pous (foot).
1 pous = 1⅓ spithame (span) from tip to tip of outstretched thumb and finger.
1 spithame = 3 palaisté or handbreadth.
1 palaisté = 4 dactyloi or finger-breadth.
2 stadia = a diaylos, 4 a hippikon, and 12 a dolichos. This Attic or Olympian stadion = 184.97 meters or 606 feet.
The common Greek measure of area was the plethron or square, on the unit of length = 0.095 hectare or 0.235 acre.
Greek units of volume, Attic, were as follows for liquids:
1 metretes = 12 chous = 72 xestes = 144 kotylé = 288 tetarton = 570 oxybaphon = 864 kyathos.
1 metretes = 39.39 liters or 43.33 quarts. For dry materials.
1 medimnos = 6 hecteus (modios) = 12 hemihectons = 48 choinix = 96 xestes = 192 kotylé = 1152 kyathos; 1 medimnos = 52.53 liters or 57.9 quarts.
The Greek units of mass or weight were 1 talent = 60 minæ = 6000 drachmai = 36,000 oboloi = 288,000 chalkia = 26.2 kilograms = 57.7 pounds.
In the Roman system we find the foot of 29.57 centimeters or 11.64 inches, duodecimally subdivided with special names as quincunx = 512 foot. etc., also 1 pes (foot) = 4 palmi = 16 digiti = 4⁄5 palmines = 2⁄3 cubitus, used in building; for geodetic work we have 1 actus = 12 decempeda (pertica, perch) = 24 passus = 48 gradus = 120 pedas. In traveling the following were used: A Roman mile (mille passuum) = 8 stadia = 1000 passus = 5000 pedes. The Romans used the jugerum (as) as the fundamental unit of area = 0.252 hectare or 0.623 acre. As nuiltiples we have 1 saltus = 4 centuriæ = 400 heredia = 800 jugera; 1 jugerum = 2 actus = 8 clìma = 288 scripula (decempeda quadrata) = 28,800 pedes quadrati.
Roman units of capacity were for liquids: 576 cyathus = 384 acetabulum = 192 quartarius = 90 hemina = 48 sextarius = 8 congius = 2 urna = 1 amphora = 26.26 liters = 28.9 quarts. For dry materials, 192 cyathus = 128 acetabulum = 64 quartarius = 32 hemina = 16 sextarius = 2 semodius = 1 modius = 8.754 liter = 9.62 quarts. The Roman unit of weight, the pound, was subdivided duodecimally with special names as semis ½, bes ⅔, etc., into 12 unciæ each equal to 4 sicilici = 24 scripula = 48 oboli = 144 siliquæ = 27.29 grams = 1.04 ounces.
Passing over the details of mediæval European units, it appears that in England, up to 1400, an old building foot existed, about 13.22 inches,
