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MENSU´RA (μέτρον). The simplest and probably most primitive measures are those derived from the various parts of the human body. Such was the view of the ancients themselves (cf. Heron Alexandr. Tab., τὰ μέτρα ἐξεύρηνται ἐξ ἀνθρωπίνων μελῶν ἤγουν δακτύλου κονδύλου παλαιστοῦ σπιθαμῆς πήχεως βήματος ὀργυιᾶς καὶ λοιπῶν; Vitr. 3.1, 5, “mensurarum rationes . . . ex corporis membris collegerunt, uti digitum palmum pedem cubitum” ). Among primitive and unmixed races, where all live under the same conditions, idiosyncrasies of stature are rare, and consequently the average sized foot will give a standard sufficiently accurate for all their purposes. When, however, peoples of different stocks come into contact, and different modes of life may cause differences in stature among the various classes of a single community, many variations of the foot or cubit will naturally be found.

The growth of the arts of civilisation will require greater accuracy in measurements of various kinds: accordingly the interrelations of various standards will be carefully ascertained by the use of some small natural object of uniform size, such as the barleycorn of the English system. Finally, with the advance of science, efforts will be made to get some more general units fixed with great accuracy, and probably to bring those into relation with the measures of capacity and standards of weight.

Measures of capacity are probably first obtained from natural products of a uniform size. The Hebrews and ancient Irish employed the hen's egg as their unit; at Zanzibar a small gourd is now employed as a general unit; and the Chinese use the joints of the bamboo in a similar fashion. The Roman cochlear (from cochlea, “a mussel” ), their smallest measure of capacity, and possibly the κύαθος of the Greeks (which perhaps originally meant “a gourd” ), indicate a like origin for standards of capacity. It is natural to expect many local variations in such measures, and it is only a strong centralised government which can introduce some universal standards, such as those established in this country by the Act of 1824. Of such regulation of standards in ancient times we have examples in the case of Pheidon of Argos, who, according to Herodotus, fixed the standard measures used by the Peloponnesians (τοῦ τὰ μέτρα ποιήσαντος Πελοποννησίοισι, 6.127); in Solon, who fixed the standards of weights and measures at Athens (Decret. ap. Andocid. 11, 25, νόμοις χρῆσθαι τοῖς Σόλωνος καὶ μέτροις καὶ σταθμοῖς), and in Augustus at Rome. It is possible that at such a time an effort may be made to fix cartain [p. 2.159]relations between the standards of length, capacity, and weight.

The Tables at the end of the volume give a general view of the various systems of measures of the ancients, setting forth as accurately as possible their value, according to modern standards. The following pages give a more detailed account of the different systems. A large mass of valuable information has reached us from the ancient metrologists, whose fragments have been collected by Hultsch (Metrologicorum Scriptorum reliquiae, Leipzig, 1864-6). The tables named after Heron, an Alexandrine mathematician, are of especial value, although they are probably of various dates; whilst the excerpts from the ancient lexicographers, such as Pollux, afford much important information.

The German metrologists have assumed that the Greeks and Romans, who derived theirs from the Greeks, borrowed their standards from the East: one school, that of Brandis and Hultsch, deriving them from the Chaldaeans, whilst that of Lepsius derives not merely the Greek, but also the Chaldaean from Egypt, although both alike admit the ultimate origin to be the parts of the human body. It is therefore a question worth considering how far like conditions of development may not have produced the close general approximation between the various systems.

Whilst admitting that measures of length were based on the parts of the human body, the German metrologists have sought outside Greece for the standards there in use. One school--that of Brandis and Hultsch--consider the standards of measures and weights to have been invented by the Chaldaeans: the other school--that of Lepsius (Längenmasse der Alten)--makes the Greeks to have borrowed their systems from the Egyptians. The latter had two cubits, one based on the average length of the fore-arm of a full-grown man, from the point of the elbow to the tip of the middle finger. This was fixed at 0.450 metre. Beside it was another cubit, evidently of later construction, which was about one-sixth larger than the natural cubit. The fact that it varies so much from nature shows that it is later in point of time. It may be fixed at 0.525 metre. This cubit is found not only in Egypt and in Palestine, but also in the regions of the Euphrates and Persia, although in the latter cases somewhat raised, as it may be fixed at about 0.532 metre. In both Egypt and Mesopotamia it is called the royal cubit, as we learn in the one case from the inscriptions on the measuring-rods, which have survived; in the other from the testimony of Herodotus (1.178). Whilst the natural cubit was used for the general purposes of life, according to Lepsius the royal cubit was exclusively used in building. It would seem, however, that our data are not yet sufficient to enable us to decide whether the Egyptians borrowed the royal cubit from the peoples of the Euphrates, or whether the latter borrowed it from the Egyptians. If the Egyptians came from Asia into the Nile Valley (as supposed by the best modern authorities), there is no reason why they should not have brought the royal ell with them from their early home. The Egyptian cubit was subdivided into six palms, each containing four fingers. But at Babylon the sexagesimal system influenced the subdivision of the cubit. The Chaldaeans made the cubit consist of six hands, each of which contained five fingers. The royal cubit thus contained thirty fingers, according to Lepsius. But there can be little doubt that Lepsius is wrong. Dörpfeld (Mittheil. 1883, p. 36) has shown from Hdt. 1.178, 7.117, that the μέτριος πῆχυς there mentioned is the common Greek cubit: but, as Herodotus says that the royal cubit is three fingers longer than the μέτριος ( δὲ βασιλήϊος πῆχυς τοῦ μετρίου ἐστι πήχεος μείζων τρισὶ δακτύλοισι), the royal cubit therefore = 27 δάκτυλοι.

In Greece proper at least three different foot-standards were employed,--Attic, Olympic, and Aeginetan. Dörpfeld has shown from the measurements of the cella of the Parthenon, called the Ξ̔κατόμποδον, that the Attic foot was 295.7 mill. The measurement of the stadion at Olympia has proved the Olympic foot to be 320.5 mill. Tradition said that this was the size of Hercules' foot. (Aul. Gel. 1.1.) The mythical connexion of Hercules with Olympia may indicate Oriental influence. The Aeginetan foot, according to the temple measurements, 333 mill. Other measures mentioned by the ancient writers are the Philetaerean foot (ποῦς φιλεταίρειος), which was probably so called from Philetaerus, king of Pergamus, shown by Dörpfeld to = 330 mill.; the Samian cubit, which Herodotus (2.168) regarded as the same size as the Egyptian.

In Western Europe we find three foot-standards: the Italian, proved from the writings of the Gromatici (Surveyors) and from buildings to be about 275 mill.; the Roman, known to us from actual measures to be 296 mill.; and the pes Drusianus, used by the Surveyors in Gaul and Germany = 333 mill.

It will be seen that the Attic and Roman standards are practically identical; that so also the pes Drusianus, the ποῦς Πιλεταίρειος, the Aeginetan foot, and Ionian foot are almost identical; whilst the Italian foot is almost identical with the Phrygian foot of 277.5 mill.

Method.--It is of course of the greatest importance that in metrological investigations a strictly scientific method should be followed. From the nature of the case it is necessary that we should obtain by means of actual measures, if they still survive, at least one of the units of measure mentioned by the ancient writers. As the tables of Heron and other writings give the comparative values of various units and standards, it follows that if we can obtain with accuracy one such unit, we can deduce from it all the rest. Linear units are of course the most important, as from them we can deduce the itinerary and superficial measures, and the most important of these is the Roman foot.

The Roman Foot.--There are five different ways of determining the length of the Roman foot. These are: (1) from ancient measures still in existence, including feet laid down on sepulchral monuments, and foot-rules found in the ruins of various cities of the Roman empire; (2) from measurements of known distances along roads, both between milestones and between places; (3) from measurements of buildings and obelisks; (4) from contents of certain measures of capacity; and (5) from measurements of a degree on the earth's surface.

(1) It might appear at first thought that [p. 2.160]ancient measures in actual existence would at once give the required information. But these measures are found to differ among themselves. They are of two kinds,--foot measures cut upon grave-stones, and brass or iron measures intended in all probability for actual use. From the nature of the case the latter would probably be more exact than the former, and in fact the measures on the gravestones are rudely cut, and their subdivisions are of unequal length, so that they have no pretensions to perfect accuracy, but on the other hand it would be absurd to suppose that they would have been made very far wrong. We may safely conclude that they would have about as much accuracy as a measure hastily cut on a stone by a mason from a foot-rule used by him in working. Three such measures are preserved in the Capitol at Rome, and one in the Capponi collection. They are called the Statilian, the Cossutian, the Aebutian, the Capponian feet. They have been repeatedly measured, but unfortunately the different measurements gave different results. Besides these, we have two models of feet cut on the rocks at Terracina. The bronze and iron foot-rules, of which several have been found at Pompeii, do not precisely agree in length. There was anciently a standard foot measure kept in the Capitol, called the pes monetalis, which was probably lost at the burning of the Capitol under Vitellius or Titus.

(2) The itinerary measurements are of two kinds, according as they are obtained by measuring the distance from one place to another, or the distance from one milestone to another on a Roman road. Both methods have the advantage of the diminution of error which always results from determining a lesser magnitude from a greater, but both are subject to uncertainties from turnings in the road, and from the improbability of the milestones being laid down with minute accuracy; and two other serious objections apply to the former mode, namely, the difficulty of determining the points where the measurement began and ended, and the changes which may have taken place in the direction of the road. Both methods have been tried: the former by Cassini, who measured the distance from Nîmes to Narbonne, and Riccioli and Grimaldi, who measured that between Modena and Bologna; and the latter by Cassini, between Aix and Arles.

(3) The measurement of buildings is rather a verification of the value of the foot as obtained from other sources than an independent evidence. (The method was first employed by Raper in his Enquiry into the Measure of the Roman Foot, Philosoph. Transact. 1760, who obtained a foot = 295.7 mill.) It is very seldom that we know the number of ancient feet contained in the building measured. We have one such example in the Parthenon, the cella of which was called the Hecatompodon, the hundred-footed (Plut. Per. 13; Cato, 5), but even in this case we could not have told exactly, till we knew something of the length of the Greek foot, to what part of the edifice this measurement applied. Furthermore, the measurement of the stadion at Olympia laid bare by the German excavations has enabled us to ascertain with accuracy the length of the Olympian foot; but in this case likewise, it would have been impossible to arrive at an accurate result had we not known already that this stadion was 600 feet long. Again, there are the obelisk in the Piazza del Popolo at Rome, and the Flaminian obelisk, the heights of which are given by Pliny (Plin. Nat. 36.71). But the actual heights of these obelisks as compared with Pliny would give a value for the foot altogether different from that obtained from other sources. Indeed, the numbers in Pliny are undoubtedly corrupt, and as they stand it is only the difference of height between the two that can be of any service, and even this gives a result by no means satisfactory. An ingenious emendation from Stuart would remove the difficulty, but it is obvious that a passage which requires a conjectural emendation cannot be taken as an independent authority. There is another mode of deducing the value of the foot from buildings of the dimensions of which we have no information. The building is measured, and the lengths thus obtained are divided by the supposed value of the ancient foot (as derived from other evidence), and if a remainder be left the value of the foot is corrected so that there may be no remainder. It is assumed in this process that no fractions were allowed in the dimensions of the building, and also that the plans were worked out with minute exactness, both of which assumptions are not very probable. In fact these measurements have given different values for the foot. Thus some metrologists have found by this method that two separate foot standards were employed in the temple at Aegina, a supposition which can scarcely be credited. Modern architects do not allow that such calculations could be depended on in modern buildings for determining the true length of the measures by which they were planned. Nor are the dimensions of the parts of mediaeval buildings in our own country, as churches and cathedrals, found to agree exactly, so as to give whole numbers of the standard measure. On the other hand these measurements, like those on roads, have the advantage of involving in all probability very small errors, and of the diminution of the error by division. It must however be borne in mind that buildings, like temples, were liable to have their dimensions conditioned by the nature of the site, and also that those which remain to us have been built on the foundations of older and smaller ones.

The results of these various methods are as follows: (1) The Roman foot as obtained from the measures varies between 295.6 and 296 mill. (2) The foot obtained from itinerary measures is 295.85 mill.; and (3) that obtained from the measurements of buildings at Pompeii by Nissen is 296 mill.

From these results we cannot be far from the truth in setting the Roman foot at 296 mill., or a little less than the English foot (301 mill.).

(4) Some have attempted to deduce the length of the Roman foot from the solid content of the congius of Vespasian. Since the congius was 1/8 amphora, and the content of the amphora was a cubic foot [QUADRANTAL], the process is to multiply the content of the congius by 8, and to extract the cube root of the product. But this method is very uncertain. Hultsch, for instance, will not allow that the measures of capacity were obtained from the linear unit, but rather [p. 2.161]from a certain weight of water or wine. Further, there is a doubt about the actual content of the congius; and even granting that the congius had been adapted to the foot with tolerable accuracy, there is a risk of error in reversing the process.

(5) Some French geographers have supposed that the ancient astronomers were acquainted with the dimensions of a great circle of the earth, and that they founded their whole system of measures on the subdivisions of such a circle. But we have no evidence of any sort to show that the ancients were acquainted with any such method.

The Greek Foot.--We have no ancient foot-rules surviving, so therefore we fix the Greek (Attic) foot from the testimony of ancient writers that it was about the same as the Roman, confirming this by the measurements of buildings, such as the Parthenon, from which Dörpfeld has shown the foot to be 295.7 mill. The Olympian foot is derived similarly from the testimony of ancient writers comparing it with other feet, and from the actual measurement of the stadium.

Greek Measures of Length.--In Homer the following measures are mentioned: δῶρον (=the later παλαιστή), ποῦς (in compound ἑκατόμποδος), πυγών (in adjective πυγούσιος), ὄργυια, πλέθρον (in form πέλεθρον). Theπυγὼν is a short cubit, being the distance from the point of the elbow to the knuckles (εἰ συγκάμψειας τοὺς δακτύλους, ἀπ᾽ ἀγκῶνος ἐπ᾽ αὐτοὺς πυγὼν τὸ μέτρον, εἰ δὲ συγκλείσειας, πυγμη). It is to be noted that the πῆχυς does not occur as the name of a measure in the poems. Homer makes mention also of a long measure, called simply μέτρου (ὥστ᾽ ἀμφ᾽ οὔροισι δυ᾽ ἄνερε δηριάασθον μέτρ᾽ ἐν χερσὶν ἔχοντες, Il. 12.422). It is impossible for us to say what was the length of this measuring-rod-whether it was the length of an ὄργυια, or of the κάλαμος or κάλαμος of later date. Of course there are no data for fixing the length of the Homeric ποῦς ὄργυια, and πέλεθρον.

Superficial Measure.--The unit of superficial measure in Homer is the γύης (found only in the compounds πεντηκοντόγυος and τετράγυος), which probably meant the space traversed by the plough in one day's work. It probably derived its name from the ancient form of the plough (called αὐτόγυον by Hesiod), and was thus somewhat analogous to the English ploughgate. The term was applied to the patches of ground in the common field (ἐπιξύνῳ ἐν ἀρούρῃ, Il. 12.422), which were separated from each other by land-marks (οὖρα) made of stones (Il. 12.421; 21.405), corresponding to Latin limes, “balk.” In such common fields or early communities the furrow was always of a customary length, hence our fur-long (furrow-long), which doubtless depended on the distance which a yoke of oxen could drag, and a man could steer, the plough without a rest. The breadth of the γύης was the distance between the οὖρα, which bounded each side. The Scholiast sets it at about 10 fathoms = 60 feet. But we know from Homer (Hom. Il. 10.351; Od. 8.124) that the distance between the οὖρα of mules--that is, the breadth of the patch ploughed by mules--was greater than that between those of oxen. Consequently the breadth (πλἑθρον) varied. Now the old name for the στάδιον was αὖλος, and its double was called δίαυλος, from which it is probable that the stadion represented the furrow-long (αὖλος being an old form of αὖλεξ). The stadion being 600 feet, is therefore ten times the breadth of the γύης, a ratio found to exist in similar land systems elsewhere.

Measures of Capacity.--Homer has but the word μέτρον to express the unit of both Dry and Liquid measure. Telemachus (Od. 2.355) takes 20 μέτρα of barley-meal as provision for his crew. Some have identified the μέτρον both in liquid and dry measure with the Hebrew saton, but it is more probable that in the μέτρον of barley-meal we have the μέδιμνος of later times. It is almost certain that the μέτρον used for liquids differed from that used for dry measure. The μέτρον of barley-meal is evidently a considerable amount, from the passage quoted above. But as the capacity of the various vessels offered as prizes by Achilles is given in μέτρα, it is not probable that the μέτρον by which their capacity is expressed is the same as that used for the barley-meal. On the other hand, it seems not improbable that the μέτρον used for wine was the same as the δέπας or cup of Od. 9.208-10: “ τὸν δ᾽ὅτε πίνοιεν μελιηδέα οἳνον ἐρυθρόν,
ἓν δέπας ἐμπλήσας, ὕδατος ἀνὰ εἳκοσι μέτρα

To suppose that the proportion was one cup of wine to twenty μέδιμνοι of water is absurd; whereas the proportion of one cup of wine to twenty cups of water is sufficiently marvellous to show the strength of the wine without falling into grotesque exaggeration. The word κοτύλη occurs occasionally in Homer (only in the Odyssey) in the sense of cup. It probably is the same as δέπας, and thus connects the Homeric δέπας with the κοτύλη of later times.

Greek and Roman Linear Measure.--The finger--breadth (δάκτυλος, digitus) was the. smallest measure employed in both systems, and was regarded as the unit (μονάς). Later writers, e. g. Isidorus, mention the use of the barleycorn as the unit, 5 barleycorns making a finger, 7 making a thumb (pollex).

The κόνδυλος, the middle joint of the finger, = 2 fingers.

The παλαιστή (later παλαιστής, in strict Attic παλαστή), δῶρον (Homer and Hesiod), or δοχμή (according to some writers), palmus, handbreadth = 4 fingers. This measure was in very common use with both Greeks and Romans.

The διχάς = 2 hands = 8 fingers, usually called ἡμιπόδιον.

The λιχάς, the space between the thumb (ἀντίχειρ) and forefinger (λίχανος), = 10 fingers.

Ὀρθόδωρον, space from the base of the hand to the finger-tips, = 11 fingers.

Σπιθαμή, span = 3 handbreadths = 12 fingers = 1/2 cubit. This measure, much used by the Greeks, was not employed by the Romans, who used instead the dodrans = 3/4 pes.

Ποῦς, pes, foot = 16 fingers. The Romans also used their national uncial system in dividing the pes, thus giving it 12 parts, which in later times passed into general use.

Πυγών (Homer, Hdt. 2.175, and some other isolated passages), the distance from the elbow [p. 2.162]to the first joint of the fingers, = 20 fingers. The Romans employed as its equivalent the palmipes = palmus + pes.

Πῆχυς, cubitus, cubit or ell, distance from the point of elbow to the point of the middle finger, = 24 fingers. Roman writers employ cubitus when following Greek sources; the native Roman term is sesquipes.

Βῆμα, gradus, pace, = 2 1/2 feet.

Passus, double pace or stride, = 5 feet. The later Greeks employed the ἄμπελος as its equivalent.

Ὄρεγμα (Heraclean Tables) = 4 feet (or, according to others, 5 feet).

Ὀργυιά, fathom, the space which a man can stretch with both arms, = 6 feet. The Romans had no corresponding term (although tensum is used in Low Latin), but occasionally used ulna to express it, although usually employing this term for the cubit.

Ἄκαινα (in late writers ἄκενα) = 10 feet. It probably means the goad used in driving the plough oxen, which was finally fixed at 10 feet and employed as the special land measure. To it corresponds the Roman pertica, or decempeda (ten-foot rod), the square of which formed the basis of all land measures. Hence the Roman agrimensores were sometimes called decempedatores.

Πλέθρον (πέλεθρον, Homer) probably was originally the breadth of the γύης or acre-strip, the space lying between the οὖρα or boundary stones, which form the longer sides of the patch. It = 100 feet; and its square became the regular limit of land measure with the Greeks of historical times. To it corresponds in size the vorsus, used by the Oscans and Umbrians, which properly means the “turning place” or headland (cf. αἱ στροφαὶ sc. τῶν βοῶν, Hesych.).

The Roman actus, = 120 feet, properly meant the “headland” (called actus minimus, 4 feet broad). It then came in later times to mean the distance which oxen can draw the plough at a single draught ( “sulcum autem ducere longiorem quam pedum centum viginti contrarium pecori est, quoniam plus aequo fatigatur ubi hunc modum excessit,” Col. 2.2, 27).

Itinerary Measures.--For the higher measures of length, although the continuity of the system was preserved by making them exact multiples of a foot, it is obvious that convenience would demand higher denominations, one of which would be regarded as a new unit. Nay, these higher measures may be viewed with respect to their origin, as in a certain sense independent of those smaller measures with which they were afterwards made to agree. For just as we have seen that the smaller measures of length are taken from natural objects, so we shall find that at an early period the larger measures were not derived artificially from the smaller, but from distances which occur in nature and in ordinary life. Thus Homer expresses distances by the cast of a stone (II. 3.12, ὅσον τ᾽ ἐπὶ λᾶαν ἵησι), and so even too in later times (Thuc. 5.65; Polybius, 5.6); of a quoit (Il. 23.431, ὅσσατε δίσκου οὖρα . . . πέλονται); of a spear (Il. 15.358, δουρὸς ἐρωή); by the distance which a man can reach with a spear (II. 10.357, δουρηνεκές); and by the still more indefinite expression, “as far as a man makes himself heard distinctly when he shouts” (Od. 5.400, 6.294 et alib., ὅσσον τε γέγωνε βοήσας); and again by standards derived from agriculture (It. 10.352, ὅσσον τ᾽ ἐπὶ οὖρα πέλονται ἡμιόνων), which from what we have seen above represents the breadth of the acre piece or γύης, the amount ploughed in one day: as mules are superior to oxen, the breadth ploughed in one day of a piece of ground of a fixed length would be greater than the breadth (πλέθρον) ploughed in the same time by a yoke oxen. (See Ridgeway's article in Journal of Hellenic Studies, 1885.) Of the longest distances time was made the measure, as in the case of the German Stunden: the journey of a day by an active traveller (εὔζωνος ἀνήρ), or of a day and a night, or on horseback, or with a merchant ship (ναῦς στρογγυλή, σλκάς), a method too frequently employed now as well as in ancient times to need illustration. (Comp. Ukert, Geograp. d. Griech. u. Röm. vol. i. pt. 2, pp. 54-5.) The system of measuring by stations or posts [MANSIO] should probably be referred to this head, as it is most likely that such distances would be fixed with reference to the powers of endurance of man and horse, before the trouble was taken actually to measure them out. Another plan was that which Herodotus several times adopts, and which is also familiar to all ages, the description of one distance by comparing it with another which is well known. It is true that in many cases the method is only general and indefinite, as when Herodotus describes the length of the Nile as equal to that of the Danube, but there are other cases in which the method was definite, and especially one case, in which it actually formed the foundation of the common system of itinerary measures in use among the Greeks. We refer of course to the stadion.

Στάδιον (σπάδιον, Doric), stadium = 600 feet. The Doric σπάδιον (from σπάω) indicates that it was the distance traversed in a single draught by the plough. It thus was probably the length of the γύης strip, just as the πλέθρον was its breadth. It always contained 100 orgyiae or 600 feet, no matter what the size of the foot might be. The Homeric γύης (vide supra) was in breadth 10 orgyiae: the stadion is thus ten times the breadth of the γύης. A similar proportion is found between the length (furlong) and breadth of English and Irish acre strips. The Germans regard the, stadion as of Babylonian origin. Brandis (Münz-, Mass-, und Gewichtswesen, p. 20) holds that the Babylonians determined the length of an hour of equinoctial time by the water-clock: in one hour the sun traversed a portion of the sky thirty times his own diameter; therefore every two minutes a portion equal to his apparent diameter. With this they equated the distance which an active walker can traverse on the earth in the same time: the stadion therefore is the distance traversed by an active walker in two minutes. As the Greeks had provided themselves with all the other measures by purely empirical means, it is not likely that they went to the East to borrow the stadion, but derived it from their own system of agriculture, which was not borrowed from the East. The Romans only employed the stadium in later times, and that only for distances by sea, where they simply followed the Greeks. The στάδιον in historical times was the distance of the racecourse, and was the regular unit of road measure, [p. 2.163]and was in later times the unit used by the astronomers and geographers.

Δίανλος (or διστάδιον), so named from αὖλος, the old name of the στάδιον, probably meant originally “double furrow,” and then came to mean a course up and down the stadion.

Ἱππικόν, the course for the horse-race, = 4 stades, as they ran twice up and down the στάδιον.

Μίλιον, miliarum. The Romans measured all long distances by milia passuum, or shortly milia. Strabo is the first Greek to use the borrowed μίλιον, and that only when speaking of distances which he had derived from the chorography of Agrippa. Miliarium is only a late word, as the good writers use lapis or lapis miliarius.

Παρασάγγης, a Persian road measure, used by Greek authors writing about Asia Minor, as Herodotus and Xenophon. It contained 30 stades, or 4 Roman miles. Modern metrologists assign it an origin similar to that of the στάδιον given above, regarding it as the distance traversed by an active walker in an hour of equinoctial time. It may have been so adjusted in a later and scientific age, but it is more probable that it had its origin long before the beginnings of scientific metrology.

Land Measures.--We have seen that a distinct source of some of the greater measures of length (e. g. the πλέθρον andστάδιον) arose out of the measures of surface, which must of necessity be employed from a very early period in every civilized community for determining the boundaries of land. Herodotus (2.109) mentions a tradition which assigns the invention of geometry to such a necessity which arose in Egypt in the reign of Sesostris. This tradition is of course now only referred to as an illustration, not as an expression of an historical fact. As in the other cases, the origin of the system lies far back beyond the reach of history, and all that can be done is to trace with some probability its successive steps as indicated by the names of the measures and by the statements of ancient writers. Here too, as in the itinerary distance, the original unit of the system was probably not a specific number of feet, but some natural quantity which was afterwards brought into accordance with the standard of the smaller measures. Also it is to be observed that these measures are from the nature of the case measures of surface, although in practice often used (as the stadium and plethrum) as measures of length. The precise fact seems to be that the first natural measure of the sort was a strip of ground of considerable length and moderate breadth, being the amount which could be ploughed in one day's work by a yoke of oxen. (See Homeric γύης, supra.) This is borne out by what we know of the Roman system. The Roman settlers in Further Spain called the actus quadratus by the name acnua, an old Latin term; the same people gave the name porca to a strip of land = 180 X 30 feet. They had evidently brought this customary unit from Italy, which was 60 feet longer than the actus as finally fixed by the land-surveyors. Now we know that the actus was originally the headland, where the plough was turned, and along which the cattle were driven; this was called by Varro (L. L. 5.3, 10.22) actus minimus, being only 4 feet wide. It is not then unreasonable to suppose that the length of the original furrow, that is, of the patch ploughed in one day, was shortened until the furrow became equal to the breadth of the strip, that is, to the headland or actus of 120 feet. This patch, the square of the headland, became the basis of the Roman land measure. The Gallic arepennis (French arpent), which according to Columella corresponded in size to the Roman actus, certainly meant originally the headland. We may not unreasonably assume a similar development for the Greek unit of 100 feet square, the plethrum, and also for the Oscan versus; namely, that it arose from a land unit of larger extent and oblong in shape, the breadth of which may have been originally about 60 feet, corresponding to the measure called clima (half of an actus) mentioned by Columella, and the breadth of the Homeric γύης.

The unit employed by the Greeks was the square of the πλέθρον, which=10,000 square feet. The Italians used similarly the square of the vorsus, which was of like size.

The γύης (or γύη) was the unit employed in Homer (supra).

On the Heraclean Tables (found at Heraclea in Lucania) the γύης probably represents a piece of land 100 feet broad and 5000 feet long that is, 50 plethra.

The σχοῖνος is another Heraclean measure = 120 feet square, corresponding to the actus. Each σχοῖνος was divided into 30 ὀρέγματα of 4 feet each.

Μέδιμνος: in two parts of Hellas we find a system which was common in many parts of the ancient and mediaeval world. The μέδιμνος at Cyrene and in Sicily means as much land as can be sown by a medimnus of seed. In Sicily this was equal to the Roman jugerum (Cic. Ver. 2.3, 112).

The Roman system of the agrimensores represents a later stage of development. The square foot (pes constratus or quadratus) was the unit of the system ( “modus omnis areae pedali mensura comprehenditur,” Col. 5.1). The system is partly decimal, partly duodecimal.

The scripulum = 1 decewpeda quadrata (square rod) = 100 sq. feet.

The clima = 36 sq. rods.

The actus quadratus = 144 sq. rods.

The jugerum = 288 sq. rods, being an oblong piece of ground, consisting of two actus. It means the amount ploughed by a yoke of oxen in one day ( “jugerum vocabatur quod uno jugo boum in uno die exarari posset,” Plin. Nat. 18.9).

The heredium = 2 jugera. So called (according to Varro) from two jugera being the birthright of every Roman citizen.

The centuria = 200 jugera generally, but varied, at times containing 50, 210, 240, or 400 jugera. From its name it is not improbable that it originally contained 100 jugera ( “centuria primo a centum jugeribus dicta est, post duplicata retinuit nomen,” Varro, R. R. 5.34).

The saltus = 800 jugera.

The term jugum was used in Spain to denote a day's work of a yoke of oxen (Varro, R. R. 1.10).

Acnua was the Latin name for the Roman actus quadratus (Varro, R. R. 1.10), likewise used by the farmers of the province of Baetica in Spain (Col. 5.1, 5). [p. 2.164]

Porca was the name given in Baetica to a piece of ground 180 X 30 feet.

Arepennis was a Gaulish unit of land measure, corresponding in size, according to Columella (5.1), to the Roman actus quadratus. Hence French arpent.

The Romans likewise applied the system of the as to land measure; regarding the juyerum as the as or unit, they carried out its subdivision on the rigid duodecimal system (vide Tables at the end of the volume).

Measures of Capacity.--The most important products of ancient agriculture are, on the one hand, wine and oil, on the other various kinds of corn. Hence naturally arose two kinds of measures, liquid and dry. The smaller units are common to both systems (ride Tables).

Liquid and Dry.--The κύαθος, cyathus (according to some connected with κύλιξ, and possibly originally meaning a kind of gourd), was the unit in common use. It contained about 4 centilitres = 0.08 English pint. A smaller measure = 1/4 cyathus, called ligula (spoon) or cochlear (mussel-shell), was sometimes employed.

Ὀξύβαφον, acetabulum, vinegar bottle, = 1 1/2 cyathi.

Quartarius, so called from being 1/4 sextarius, = 3 cyathi, has no Greek equivalent.

Κοτύλη, at Athens, was a kind of bowl, called τρύβλιον in other parts of Greece, and the same as the Sicilian ἡμίνα (the half mina = ἡμιμναῖον), which, borrowed by the Romans, = 1/2 sextarius = 6 cyathi.

Ξέστης, sextarius = 12 cyathi. Ξέστης is a loan word from the Roman sextarius, so named as the 1/2 of congius.

So far the measures are common to both systems, but they now diverge as follows:--

Liquid.--Χοῦς, congius (derived from κόγχη) = 12 κοτύλαι. Its half, the ἡμίχους (plur. ἡμίχοα), also is found: ἡμιάμφορον (or ἡμικάδιον), urna.

Ἀμφορεύς, amphora (ἀμφιφορεύς, Homer), the large wine jar with handles on both sides, as it was used for the storing of wine, was used as the chief unit of liquid measure. It was also called κάδος, cadus. The Roman amphora = 8 congii = 48 sextarii = 576 cyathi.

Μετρητὴς is commonly used as equivalent of ἀμφορεύς, but strictly was larger.

Culleus, tun, = 20 amphorae.

Dry.--The Greek (distinctively) dry measure starts from the κοτύλη, the Roman from the sextarius.

Χοῖνιξ (mentioned in Homer, Hom. Od. 19.28), a day's allowance for a man at Athens, = 4 κοτύλαι.

Ἡμίεκτον, semodius, the half of the following, = 4 χοίνικες.

Ξ̔κτεύς, or μόδιος, modius. The first name is the Old Attic, but the second is already used by Deinarchus. The former indicates that it is 1/6 of the chief unit, the medimnus.

Μέδιμνος at Athens = 8 modii. The Romans did not employ this measure, but only modius or its compounds, such as trimodium.

Ptolemaic.--To above we may add certain measures in use in Egypt under Ptolemaic and Roman rule, for which see also Tables.

Ξύλον = 3 royal cubits = 72 fingers.

Σχοῖνος, an itinerary measure, usually counted equal to the Persian Parasang (= 30 stades), but actually containing 32 stades of the common Greek standard. It was probably also in use among the Hebrews.

Ἄμμα = 10 fathoms = 60 feet. Its square was used as a land measure.

Σχοινίον was another name (probably the Greek one) of the (Egyptian) ἄμμα just described.

Σωκάριον, with the addition of δεκαόργυιον, was another name applied to the square ἄμμα, being a name derived from the amount of seed required to sow that amount of land.

Ἄρουρα was a piece of ground 100 cubits square, and which formed the regular Egyptian land unit from early times. (Hdt. 2.168, δὲ ἄρουπα ἑκατὸν πηχέων ἐστὶ Αἰγυπτίων πάντῃ).

Bibliography.--F. Hultsch, Metrologicorum Scriptorum Reliquiae, Lipsiae, 1864, 1866, and Griechische und römische Metrologie, 2nd ed., Berlin, 1882; J. Brandis, Das Münz-, Massund Gewichtswesen in Vorder Asien, Berlin, 1866; Vasquez Queipo, Essai sur les Systèmes métriques et monétaires des anciens Peuples, Paris, 1859; A. Boeckh, Metrologische Untersuchungen über Gewichte, Münzfusse und Masse des Alterthums in ihrem Zusammenhange, Berlin, 1838; Hussey, An Essay on the ancient Weights and Money, and the Roman and Greek liquid Measures, with an Appendix on the Roman and Greek foot, Oxford, 1836; W. M. Flinders Petrie, Inductive Metrology; R. Lepsius, Längenmasse der Alten, Berlin, 1884.


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