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The metrological systems of the Greeks and Romans, and the methods pursued in the determination of their standards, have been regarded with interest by those curious in antiquarian researches. While the relations of the various parts of each system have been satisfactorily ascertained, the values which have been assigned to their units, whether of length, capacity, or weight, when referred to those of modern times, exhibit considerable discrepance. This may not excite surprise when it is considered that these values have been deduced from observations, made with different degrees of nicety, upon models possessing conflicting claims to perfection. A learned professor of Stutgard" has reviewed the labours of his predecessors in these inquiries with masterly skill, and has imparted to his investigations a precision which entitles them to reliance. . His results have been adopted, and his mode of procedure exhibited in the following pages. In consormity with his plan, and for the reason that we possess more numerous specimens of the Roman standards than of those of the Greeks, which furnish more accurate data for the estimate of both, the former will be first treated of.

§ 1. Roman MEAsures of LENGTH.

The Romans, like other nations of antiquity, derived their measures of length from the different members of the human body, the unit of which was the foot. Their Pes was divided both into 12 uncia and 16 digiti. The first division, by which it was recognised as the tAs or unit, and its parts expressed by uncia, was generally adopted. Thus, when authors make mention of pes uncialis, they understand the To of pes; thus, also, pes dodrantalis means #, bessalis #, quincunqualis so trientalis #, quadrantalis #, and semiuncialis or of pes. The second division, into 16 digiti, is the more natural, and was principally used by architects and land surveyors; and, though it latterly came into more general use, is seldom found in the specimens of the pes, unaccompanied by the first. Palmus, the palm, or the width of the hand, is the Tañatorff of the Greeks, and was invariably received by the Romans as the fourth of pes; but St. Jeroine, in his comments on Ezechiel (cap. 40), has assumed it as the three fourths, by which admeasurement it nearly answers to the Greek artôauń, and the modern Italian Palm. Cubitus is sesquipes or 1% pedes, and is seldom met with except when it is used in translating

* J. F. Wurm. His determinations are given in the old French measures, weights, &c., and have been reduced to the English and American standards by a comparison of the o Mani". Poids et Mesures" of M. Tarbé, and Mr. Hassler's able report to the Treasury Department in 1832. Other works have been consulted, of which may be mentioned those of Greaves, Hooper, and Arbuthnot, the papers of Raper in the Philosophi:as transactions of the Royal Society of London for the years joo on. To and the profound report of President Adams to the senate of the United States in 1821.

i see the section on Roman Weights.

the Greek trixvo. It is sometimes improperly confounded with Ulna. Ulna is the Greek Špyva ("dicta ulna årö Tāv &Aévov, id est a brachus; proprie est spatium in quantum utraque extenditur manus.”—Servius ad Virg., Ecl., 3, 105.) Pes sestertius=2} ped. is rendered by Boëthius and Frontinus gradus or “step,” a term, however, not sound in any classical writer. Passus (“a passis pedibus") was a pace, equal to five pedes. Decempeda or Pertica (modern Perch) was employed in measuring roads, buildings, land, &c. Actus is the length of a furrow, or the distance a plough is sped before it turns, and corresponds to our Furlong : it equalled 120 ped. The Itinerary unit, by which the Romans assigned the length of their own roads, was milliare (mille passuum)=5000 ped. ; that by which they expressed the valuation of maritime distance, or that between places situated in Greece, was the stadium=125 passus=725 ped. ; and that employed in measuring the roads of the Gauls was the leuca or leuga (whence our League is derived, though more than double in value)=1 milliaria. - to ro § 2. Roman MEAsures of rxrks.

The unit of extent was Jugerum (nearly # of our acre), which was also distributed into uncia : Columella describes it as being 240 pedes in length and 120 in breadth=28,800 pedes quadrati; and, consequently, uncia=2400, Siciliquus=600, Sextula–400, and Scrupulum=100 ped, quad. ; which last is evidently a decempeda quadrata. These were used by surveyors; but those more commonly mentioned by writers on husbandry were Clima, Actus, Jugerum, Heredium, Centuria, and Saltus. Clima is a square whose side is 60 ped. (Columella, 5, 1.) Actus quadratus (“in quo bores agerentur cum aratro, cum impetu justo.”—Plin., 18, 3) is thus explained by Columella: “Actus quadratus undique finitur pedibus 120, et hoc duplicatum facit jugerum, et ab eo, quod erat junctum, nomen jugeri usurparit.” (Colum., l. c.) Actus minimus or simplex was 120 ped in length and four in breadth. Varro (R. R., 1, 10) thus describes the Heredium, Centuria, and Saltus : “Bina. Jugera, qua, a Romulo primum divisa ducebantur viritim, quod heredem sequerentur, heredium appellarunt. Heredia centum centuria dicta. Ha porro quatuor centuriae conjunctae, ut sint in utramgue partem binae, appellatur in agris viritim divisis publice salius.” Versus=10,000 ped, quad, answers to the Greek toč0

pov. § 3. Roman MEAsures of capacity.

1. For liquids. The standard measure of capacity was the Quadrantal or Amphora (derived from the Greek áudoproc), being a cubic vessel each of whose sides was a Roman foot; and, according to an old decree of the people preserved by Festuo; " contained 80 libra (Roman pounds) of wine. * freuently makes cadus synonymous with it, and by the

reeks it was called kepáutov, duopoptic, and perpmroç Tražukóc. The greatest liquid measure was the Culeus or Culleus=20 amphora. The divisions of the amphorae are easily inferred from the plebiscitum just mentioned, and from the following passage of Volusius Maecianus: “Quadrantal, quod, nunc plerique amphoram vocant, habet urnas 2, modios 3, semimodios 6, congios 8, sertarios 48, heminas 96, quartarios 192, cyathos 576.” The Urna was so called, according to Varro, “ab urinando, quod in aquà hauriendá, urinat, hoc est mergitur, ut urinator.” Congius was the cube of half a pes; one of Vespasian's is still extant, marked with the letters P. X., which denote pondo decem, ten being the number of pounds it contained by law. Congii of wine or oil were given to the people by the emperors and chief magistrates on holydays, which gifts were hence called congiarii, and persons frequently derived surnames from the number of congii of wine they were in the habit of drinking at a draught; hence Cicero's son was called Bicongius, and Novellus Torquatus, a Milanese, Tricongius. (Plin., 14, 22.)

Sertarius was # of the congius=2 hemina–4 quartarii=12 cyathi; hence the sextarius, from the fact of its containing 12 cyathi, was regarded as the as or unit of liquid measures, and its uncia, or cyathi were denominated, according to their numbers, sextans, quadrans, &c. It may be remarked that the ancients, at their entertainments, were in the habit of drinking as many cyathi as there were letters in the names of their mistresses. (Martial, Epig., 9, 93; 1, 72.) There were two kinds of sertarii, the castrensis and urbicus, the former being double of the latter, or common sextarius. Acetabulum was half the quartarius, and was so called, in imitation of the Greeks (to whose b;ü6apov it corresponded), from acetum, since it was first used for holding sauce for meat. Ligula or lingula at first simply signified a spoon, but was afterward regarded by the Latin physicians as a fourth of the cyathus; Pliny and Columella make cochlear or cochleare synonymous with it.

2. For things dry. The unit of this measure was the modius, which contained two semimodii, and was # of the amphora, as is apparent from the passage of Volusius Maecianus above quoted. The remaining measures, sextarius, hemina, &c., bear the same relation to the amphora in the dry as in the liquid In easure,

§ 4. DETERMINATIon of The Roman MEAsures.

The measures of Length, Extent, and Capacity are so intimately connected that the determination of their values will easily be deduced from that of the pes. Various measurements have been made, and various modes of investigation been É." for the purpose of assigning the value of the Roman foot, which, from the impersection of instruments, the want of accuracy of observation, and of attention paid to the degree of injury which the specimens examined may have sussered, differ considerably in their results. We shall give a brief account of most of these observations, and, as far as possible, assign to each its proper degree of credence. All that has served as a means of calculating the value of the Roman foot may be arranged under the following classes: (a) Specimens of the pes found on tombstones. (b) Foot-rules. (c) Milestones. (d) Distances of places. (e) Congii. (f) Dimensions of ancient buildings at Rome. (a) There remain four celebrated specimens of the Roman foot represented on tombstones, which have been . named the Statilian, Cossutian, AEbutian, and Capponian feet. 1. The Statilian foot was discovered in the 16th century in the Vatican Gardens at Rome, on the tombstone of a certain Statilius: though in a state of good preservation, it is of clumsy workmanship, and carelessly subdivided. Greaves

found it .972 feet, which measurement, however accurately it may have been determined, can now be of little use, inasmuch as the present standard foot is greater than that employed by him, by an excess not easily ascertained, though it has been estimated by Raper at son, which, applied as a correction, would give the Statilian foot .970056 ft. Auzout, according to Raper, found it .96996 ft., and Revillas .96979 st The mean value of the Statilian foot deduced from these observations is then 11.639224 inch.-2. The Cossutian foot was found on the tombstone of Cn. Cossutius (probably the same with a celebrated architect mentioned by Vitruvius), and dug up about the same time with the Statilian, in the gardens of Angelo Colozzi, from whom it has taken the name of Colouan; the divisions are scarcely perceptible; Greaves found it .967 ft., which, corrected, is .965066 ft.—3. The AEbutian foot was discovered on the monument of M. AEbutius, in the Villa Mattai; it is but rudely divided into palmi, and its mean length is 11.6483 inch–4. The Capponian foot was found on a marble without inscription in the Via Aurelia, and presented by the Marquis Capponi to the Capitoline Museum, where it is preserved with the three others. Revillas found it 11.625 inch. The value of the pes, if considered as the mean of these four feet, is 11.623326 inch. (b) From the foot-rules we might expect to derive a result more worthy of reliance, since they were constructed for the direct purpose of measurement, those on the marble .."...; intended to explain the profession of the individuals to whose memory they were erected. The soot-rules were bars of iron or brass, of the length of a pes. Those most celebrated are the three discovered by Poetus, equal in length, of which a model, cut in marble, was placed by him in the Capitol, whence the foot has been styled the Capitoline, and has been generally considered as the true Roman foot. From the numerous measurements it has undergone, it has sensibly increased, so that its value must be assumed=128.695 Par. lin., its original determination by Poetus, reduced to the French standard by Wurm. Now the Paris line being (according to the mean value of the toises of Canivet and Lenoir, as given by Mr. Hassler) equal to .007401829 English feet, the 3. foot equalled. 95258 feet. Besides the Paetian, other foot-rules remain, not, however, celebrated; their values are mostly between.967 and .97 ft. (c) The distances between the milestones might furnish a correct determination of the Roman foot, were it not that none are now standing within'30 miles of Rome, and, therefore, none to be much relied on as having been originally measured off with accuracy. ... however, a celebrated Italian philosopher and mathematician of the 17th century, from the distances of the milestones on the Appian road, deduced the Roman foot=130.6 Par. lin.-11.600.15 inch. (d) The measures of the public roads recorded in the Itinerary of Antoninus and in the Peutinger Table, can be of little assistance in our inquiry, since those records not only omit fractions, which must have existed, but are srequently at variance with each other. Besides, it is not known whether the distances are reckoned from the market-places or from the gates; and an error of half a mile in sixty, being equivalent to an error of the tenth part of an inch in a foot, no exact value of the Roman foot could be hence derived, even though the mensurations of Cassini, Riccioli, and others were totally unexceptionable. (e) In the description of the measures of capacity, it was stated that the congius, in accordance with a plebiscitum (the Silian law), contained ten Roman pounds of wine or water. By the determination of the libra, which is given in section v., the congius weighed 50495.3064 grs. ; now as a cubic inch of distilled water, at maximum density, weighs 252.633

grs, the congius contains 199.876921 cubic inches, and, consequently, its side is 5.8468 inch. But the side of the congius was half the Roman foot; hence the value of the Roman foot, as deduced from the congius, is 11.6936 inch. Though this result is very near the correct one, much reliance cannot be placed on this mode of arriving at it, in consequence of the weight of the ancient wine (80 libra of which were contained in the congius) being unknown. But, as Rhemnius Fannius informs us that the ancients accounted no difference to exist in the specific gravities of wine and water, we have considered them equal, and supposed distilled water of maximum density to be of the same specific gravity with that employed by them, which was very probably pure rain-water. There remain two congii, of which the most celebrated was placed by Vespasian in the Capitol, as its inscription imports, and is commonly called the Farnesian ; the other is preserved at Paris. These have been filled with water and weighed by Paetus, Villalpandus, Auzout, and others, who have hence sought to determine the libra and pes; but the results of their experiments are so much at variance as to render any inferences drawn from them objectionable. (f) The last method we shall notice, and which leads to the most satisfactory conclusion, consists in the measurement of the ancient buildings now standing at Rome; and though many have ascertained the length of some single parts of them, yet no one has compared the measures of the principal parts with so much assiduity and success as Mr. Raper. Having carefully examined the work entitled “Les Edifices antiques de Rome,” by M. Desgodetz, he very ingeniously deduced the value of the Roman foot from 65 dimensions=.97075 ft. From this value of the pes, which is the one now generally adopted in Germany and France, are easily deduced all the measures of length. (See Tables I. and II.) The jugerum being 28800 pcd. quad., equals 27139 sq. ft.=2 roods, 19 poles, and 187 ft. ; whence the superficial measures in Tables III., IV., and W. have been calculated. The amphora being the cube of the pes, equals 1580.75 cub. inch. ; but as a cubic inch of distilled water at maximum density weighs 252.632 grs., and a gallon 10 lbs. avoirdupoise or 70,000 grs., the amphora equals 5 galls., 2 qts., 1.64 pts. ; whence the Capacious measures in Tables VI. and VII. have been computed.

§ 5. Roman weights.

The unit of weight was originally denominated As, and subsequently Libra or As Libralis. It corresponded nearly with our Troy pound. Its multiples were Dupondius (2 pondo or librae), Sestertius (2} asses), Tressis (3 asses), Quatrussis, Quinquessis, and so on till Centussis. The term as, though properly applied to a piece of copper of the weight of a Roman pound, was extended not only to all the Roman measures expressing their units, but also denoted the entire amount of inheritances, interest, houses, farms, and all things which it was customary to divide; and reference being constantly made by authors to it and its subdivisions, it is important that they should be thoroughly understood. The following table exhibits the relations subsisting between the as and its several parts.

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The Romans made their weights of marble, iron, or brass. A few specimens of these are now extant, and have been weighed by Rome de l'Isle and Eisenschmid, whose results vary from 4900 to 5100 grs. Others have attempted the determination of the libra from the relation existing between it and the congius, the latter having been determined to contain 197.6 cub. inch. nearly. If we assume the weight of a cubic inch of water=253 grs., a congius of water would weigh 49992 grs., and the libra would equal 4999.2 grs. ; but if we suppose a cubic inch of the Roman wine, which was employed in the adjustment of the libra and congius with regard to one another, to weigh 256 grs, the value of the libra would be 5058.5 grs. It is then evident that, from our ignorance of the specific gravity of the ancient wine, we can arrive at no more accurate conclusion with regard to the value of the libra from a knowledge of the exact dimensions of the congius, than from the weight of those rough specimens just noticed. This assertion may be substantiated by mentioning the valuations given by different metrologists, who have employed either the congius or the specimens as the basis of their calculations. Budaeus makes the libra–5904 grs., Rome de l'Isle 4958, Auzout 5105, Eisenschmid 5097, Paucton 5175, and Arbuthnot 5245; grs. The mode of investigation founded on the hypothesis that the ancients exercised at least a tolerable degree of nicety in standarding their moneys, has been justly recommended as the most perfect we can employ. It consists in ascertaining the value of the scrupulum, and hence that of the libra, from certain aurei which are extant, and which were coined of the weight of a certain number of scrupula, indicated by the stamp they bear. Letronne, whose accurate and laborious experiments on the ancient coins have entitled him to implicit reliance, from the weight of 54 aurei deduced the scrupulum=21.4 Par. grs. ; hence 288 scrupula or the libra–6163.2 Par. grs. We may safely put the Roman pound, as Letronne advises, =6160 Par. grs., since an error of the hundredth part of a grain in the value of the scrupulum just assigned would produce one of 2.88 grs. in that of the libra. The li. bra then equals 6160 Par. grs.=5049.53 mint-pound grs.,” and the remaining weights are hence easily calculated. (See Tables VIII. and IX.)

§ 6. Roman Moneys.

Festus informs us that the Romans during the reign of Romulus had not established.coined money as a medium of exchange, but used for this purpose leather, painted wood, and pieces of metal, the values of which were determined by weight. That Numa caused copper to be cut into rough pieces (arra rudia) of the weight of a libra, is asserted by some authors, while others are of opinion that leather, &c., were still used in the time of Numa, and that Servius Tullius first ordered round pieces of copper to be made, of a pound weight, called asses librales, with the images of cattle (pecudes) rudely sketched on them, and that hence the term pecunia was applied to money. Copper continued to be in general circulation till A.U.C. 485, when silver was first coined at Rome, though foreign coins of this metal had been previously introduced; the coinage of gold followed 62 years after. The temple of Juno Moneta was appropriated as the general depository of standards, and the coins were issued from it, having been previously inspected by Nummularii or assaymasters. The entire mint was under the general superintendence of three men, appointed by the people at the Comitia Tributa, denominated Triumviri Monetales. The Romans counted by asses, sestertii, denarii, and aurei. The as (originally assis, from aes), or assipondium, was at first libralis, and bore the impression of Janus geminus, or bifrons, on one side; on the reverse, the rostrum of a ship, and was at first, as we have noticed, libralis; but in the first Punic war, in consequence of the scarcity of money, the re[. ordered asses to be struck weighing 2 uncia, y which, as Pliny informs us, it gained ; and discharged its debt; it was subsequently reduced, when Hannibal invaded Italy, to the weight of an uncia, and lastly by the Papirian law to that of a semiuncia; and though this rapid diminution of its weight was required by the necessities of the commonwealth, it would eventually have been accomplished by the increasing abundance of silver and gold. The as thus reduced was, in reference to its original weight, denominated libella, and the older coins are distinguished from it by later writers when they speak of as grave. Besides the as, its subdivisions, viz., semisses, trientes, quadrantes, sertantes, stipes unciales, semiuncia, and sextulae (the sinallest of the Roman coins according to Varro), and its multiples, dupondii, quatrusses, and decusses, were coined; specimens of which remain at the present day, and are to be found in the most valuable collections of ancient coins. But those pieces less than the as which were most frequently coined, were the semissis and quadrans, bearing the impress of a boat instead of the rostrum of a ship; the former was also named sembella (quasi semilibella), the latter teruncius. The sestertius, quinarius, and denarius were silver coins, and called bigati or quadrigati, from the impression of a chariot drawn by two or four horses, which they bore on one side, that on the reverse being the head of Roma with a helmet. The sestertius (or semistertius) was so called by a figure borrowed from the Greeks, and equalled 2+ asses; its symbol is H. S., abbreviated from L. L. S., the initials of libra, libra, semis. The sestertium,

* The Paris grain equals .819729 mint-pound grs, or 820072 Troughton's grs. ; since the French Kilogram equals 18827.15 Par. grs., 15433.159 mint-pound grs., or 15439.6.19 Troughton's grs. It may be here remarked, that we have employed the mint-pound grs. of Philadelphia, of which the mint-pound contains 7000, in assigning the values of the Greek and Roman weights, and those who wish to obtain them in Troughton's grs. can effect their object by o: those we have given by 1.0004184, (See Mr. Hassler's Report.)

or 1000 sestertii, was expressed by the symbol HS; it was not a coin, but was employed by the Romans, together with the sestertius, in computing large sums of money. Their method of notation was effected by combining the symbols with their numeral characters; thus HS, MC. indicates 1100 sestertii; but if the numerals have a line over them, centena millia or

100,000 is understood ; thus HS. M.C. means 110 millions of sestertii. When the numerals are separated by points into two or three orders, the 1st on the right hand denotes units, the 2d, thousands, the 3d, hundred thousands; thus, III. XII. DC. H.S. denotes 300,000+12,000+600=312600 sestertii. The following illustration may be also added. Pliny says, that seven years before the first Punic war there were in the Roman Treasury “auri pondo XVI. DCCCX. ; argenti pondo XXII. LXX.; et in numerato LXII. LXXV. CCCC.” (33, 3); that is, 16.810 pounds of gold, 22,070 pounds of silver, and 6,275,400 sestertii of ready money. The quinarius was equal to 5 asses, and marked V ; by the Clodian law it was imo. with the figure of Victory, and hence called

ictoriatus. The denarius, at its first institution, equalled 10 asses, and was stamped with the numeral

X or ; But when the Romans were pressed by Har

nibal, A.U.C. 537, the as having been made uncialis, the denarius passed for 16 asses, the quinarius for 8, and the sestertius for 4 ; and when the as was made semiuncialis the same proportion was retained, except in the payment of the soldiers, with whom the denarius preserved its original value. The denarius was not used as a weight until the Greek physicians came to Rome, who, finding it nearly equal to their

drachm, prescribed by it; it was then considered, as we are informed by Corn. Celsus, as the 3 of an uncia. But it gradually diminished in weight under the Caesars (see Table XII.); and having subsequently regained its original weight, though with a considerable abasement of its purity, it continued to be the current silver money of the empire till Constantine substituted the miliarensis in its stead. , Letronne having carefully weighed 1350 consular denarii, deduced the weight of the denarius=73 Par. grs.=59.84 mint-pound grs. Now its purity being .97, its value is easily calculated =8d. 2.17 far.—15 cts., 4.7 mills. (See Tables X. and XI.) The golden coins of Aurei were issued A.U.C. 546, weighing 1 or more scrupula, the scrupulum of gold passing for 20 sestertii. Some few remain with the numerals XX. and XXXX., which indicate their values to be respectively 20 and 40 sesterces. They have the head of Mars and the numerals denoting their value on one side, and on the reverse an eagle standing on a thunderbolt. Afterward it was thought proper to coin 40 aurei out of the pound, each valued at 25 denarii; their mean weight is 125.62 grs. The aureus gradually diminished in weight during the time of the emperors (see Tab. XII.), till in Pliny’s time 45 were struck out of the pound. The Emperor Severus coined semisses and tremisses of gold, whence the aureus, being considered the integer, was denominated Solidus. Soon aster, the cóinage, becoming irregular, was entirely remodelled by Constantine, who coined 72 solidi out of the pound, each ...; then 4 scrupula or 70.13 grs., and made the pound of gold equal to 1000 miliarenses; so that the solidus equalled 13% miliarenses, though it passed for 14. The ratio of gold to silver during the republic and the twelve Caesars is given in Tab. XII.

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