being the 7th part of the Roman oz., they came now to be the 8th part: and therefore 96 were coined out of the Roman libra, whereas before, under the consuls, 84. From Vespasian to Alex. Severus, as far as he had observed, the silver continued at a kind of stay in respect of weight, excepting only such coins as on some extraordinary occasion, both then, and in the first Emperors time, were stamped, either in honour of the Prince, or of the Empress and Augusta familia, or else in memory of some eminent action. These last most usually were equal to the denarii consulares, and many of them had these characters Ex. s. c, or else S. P. Q. R. Under Severus and Gordianus, the denarii began to recover their primitive weight, but most commonly with a notable abasement, and mixture of allay." Eisenschmid has given the like account of the imperial denarius, and says, he found its weight from Nero to Sept. Severus, to be to the consular denarius, in the proportion of 7 to 8.

The denarius continued to be the current silver money of the empire, till Constantine substituted the Miliarensis in its stead. The price of gold had been increasing a considerable time before his reign, which made a new regulation of the money necessary. For this purpose, Constantine divided the pound of gold into 72 solidi, which was a more commodious number than either 40 or 45, as it divided the ounce and half ounce without a fraction. He likewise altered the weight of the silver coin, and fixed the price of the pound of gold at 1000 pieces of his new silver, which were thence called miliarenses. This he seems to have done in imitation of the ancient coinage; for when the aureus of 40 in the pound passed for 25 denarii, the pound of gold passed for 1000. But it was attended with this inconvenience, that his solidus could not be exchanged for its true value in silver; for 1000 divided by 72 is 13; but it passed for 14, which was more than it was worth, and made 2 prices of gold at the same time; one the legal price of 1000 miliarenses for the pound; the other, the current price, of 14 for the solidus, which must have occasioned disputes in the payment of small sums. To remedy this inconvenience, it was thought proper to alter the weight of the silver money, and having fixed the price of the pound of silver, at 5 solidi, to coin 60 pieces out of it; which retained the name miliarenses, though the pound of gold was worth only 864.

A scholiast on the basilics tells us, that "One siliqua [of gold] is worth 12 folles [of copper], or half a miliarensis: therefore 12 siliquas are half a solidus, for the whole solidus is worth 12 miliarenses, or 24 siliquas." The Roman pound contained 1728 siliquas, therefore there were 72 of these solidi in the pound; and each of them being worth 12 miliarenses, the pound of silver, which was valued at 5 solidi, must have contained 60 miliarenses. How many miliarenses Constantine coined out of the pound of silver is no where said; but if the price of gold was nearly the same in his reign, as when 5 solidi were worth a pound of silver, the pound must have been worth 14 pounds of silver; and

1000 divided by 14, gives 69 for the number of miliarenses coined out of the pound. Therefore it is probable Constantine's number was either 69 or 70. If the former, each piece should weigh 73 Troy grs.; if the latter, 72% Eisenchmid found the larger silver of Constantine to come up to 90 Paris grs., or 73 Troy; but the smaller, which should be its half, seldom amounted to 40 Paris grs., or 32 troy; which leaves it uncertain whether 69 or 70 of these miliarenses were coined out of the pound. If 69, the proportion of gold to silver was almost 14 to 1; if 70, 14% to 1.

4. Of the Value of Gold in Greece and Rome.

Herodotus reckons the value of gold to silver in the proportion of 13 to 1. Plato, who wrote about 50 years after him, says it was 12 times the value of silver; and Xenophon, Plato's contemporary, relates, that Cyrus paid Silanus the Ambraciot 3000 darics for the 10 talents he had promised him; which being Babylonian talents, agrees with Plato's estimate.

After the conquest of Asia by Alexander, the immense treasures of the Kings of Persia circulating in Asia and Greece, reduced the price of gold to 10 times its weight in silver, at which it seems to have continued 200 years, or more.

The Romans did not coin gold till above 100 years after the death of Alexander. That the Romans kept their accounts in copper sesterces of 2 asses, long after the silver sesterce passed for 4, appears from what Pliny says of the pay of the army, that notwithstanding the silver denarius passed for 16 asses, it was paid to the soldier for 10: which implies that the quæstor's accounts were kept in copper money, as all the public accounts probably were. Cæsar is said to have doubled the pay of the soldiers, and it appears from the account Tacitus gives of the mutiny of the legions in Pannonia, that at the accession of Tiberius to the empire, their pay was but 10 asses a day; and they demanded a denarius, not on pretence that the legionary soldiers had ever received so much, but that 10 asses were not an equivalent for the dangers and hardships a soldier underwent. Hence 5 asses appear to have been their pay before Cæsar raised it; but if this was their pay on the quæstor's book, they actually (according to Pliny) received a quinarius of 8 asses, and Cæsar only nominally doubled it; which is more probable than that their pay at the time he raised it, should be under two pence three farthings English a day. Polybius tells us, that in his time the pay of a Roman foot soldier was two oboles a day; that of a centurion twice as much; and that of a horseman a drachm or denarius. This must be understood of what they received, not of their nominal pay on the quæstor's book. The foot soldier, therefore, was paid at the rate of 5 asses a day, which, in a country where a traveller might have his lodging and all necessaries on the road for half an as, would be great pay, had not their cloathing, arms, and tents, been deducted out of it, as they were. But both the public and private riches of the

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Romans were increasing very fast when Polybius wrote, and the prices of all the necessaries of life must have increased in proportion, therefore it is probable that the soldier's pay was raised to 5 asses on the quæstor's book, for which they received a quinarius, before Cæsar augmented it.

If the pound weight of gold was worth 900 denarii, 84 of which were coined out of the pound of silver, the value of gold to silver must have been in the proportion of 900 to 84, or as 10 to 1. And if this was the value of gold at Rome 62 years after their first coinage of silver, it proves that no fewer than 84 denarii were then coined out of the pound. Now by an article in the treaty with the Etolians, about 18 years after this first coinage of gold at Rome, that people were permitted to pay one-third of their tribute in gold, at the rate of one pound of gold for ten of silver. Therefore gold was then but 10 times the value of silver in Greece; and it could not be much higher at Rome, where silver was esteemed the more useful metal, as appears by the limitation of the sum to be paid in gold, to one-third of the whole; and Pliny observes, that the Romans always required the tribute they imposed on conquered countries should be paid in silver, not in gold; therefore it is not probable that gold should bear a much higher price at Rome than elsewhere, as it would, according to this account of its first coinage, if fewer than 84 denarii were coined out of the pound of silver.

From a passage in Tacitus, compared with Suetonius, we learn that in Galba's time the aureus passed for 25 denarii. But 100 nummi were equal to 25 denarii; therefore when 40 aurei were coined out of the pound of gold, and 84 denarii out of the pound of silver, the pound of gold, passing for 1000 denarii, was worth 111 pounds of silver. When the aureus of 45 in the pound passed for 25 denarii of 96 in the pound, the proportional value of gold to silver was as 375 to 32, or a little under 11 to 1. Suetonius tells us, that Cæsar brought so great a quantity of gold from Gaul, that he sold it throughout Italy and the provinces for 3000 nummi the pound. 3000 nummi make 750 denarii; and 750 is to 84, as 8 to 1. This was its price as merchandise, when the market was overstocked, and the seller in haste to dispose of his goods; but what effect it had on the coin, is not known. By the diminution of the aureus for above half a century before the reign of Constantine, the price of gold appears to have been rising, till it came to above 14 times its weight in silver; for 5 solidi of 72 in the pound, being valued at a pound of silver, the proportion between the two metals was as 144 to 1.

SV. Of the Value of the Ancient Greek and Roman Money.

It does not appear that either the ancient Greeks or Romans allayed their money, but coined the metals as pure as the refiners of those times could make them: for though Pliny mentions two instances of the contrary at Rome, the example was not followed, till the late Emperors debased the coin: and his

expression, miscentur æra falsæ monetæ, shows he thought the practice illegal. Though the ancients had not the art of refining silver, in so great perfection as it is now practised, yet, as they mixed no base metal with it, and esteemed what they coined to be fine silver, Mr. R. values it as such.

Sixty-two English shillings are coined out of 11 ounces 2 dwt. Troy of fine silver, and 18 dwt. of allay. Therefore, the Troy grain of fine silver is worth of a farthing. Hence the Attic drachm of 66 grains will be found worth a little more than 9 pence farthing; the obole, a little more than 3 half-pence; and the chalcus, about of a farthing. But, for the reduction of large sums to English money, the following numbers are more exact.

Hence the mina expressed in pounds sterling and decimals of a pound will be 3.8697. the talent 232.157.

The Romans reckoned by asses before they coined silver, after which they kept their accounts in sesterces. The word sestertius is an adjective, and signifies 2 and a half of any substantive to which it refers. In money matters its substantive is either as or pondus; and sestertius as, is 2 asses and a half; sestertium pondus, 2 pondera and a half, or 250 denarir. When the denarius passed for 10 asses, the sesterce of 2 asses was a quarter of it; and the Romans continued to keep their accounts in these sesterces long after the denarius passed for 16 asses; till, growing rich, they found it more convenient to reckon by quarters of the denarius, which they called nummi, and used the words nummus and sestertius, indifferently as synonymous terms, and sometimes both together, as sestertius nummus; in which case, the word sestertius, having lost its original signification, was used as a substantive; for sestertius nummus was not 2 nummi and a half, but a single nummus of 4 asses.

They called any sum under 2000 sesterces so many sestertii, in the masculine gender; 2000 sesterces they called duo or bina sestertia, in the neuter; so many quarters making 500 denarii, which was twice the sestertium; and they said dena, vicena, &c. sestertia, till the sum amounted to 1000 sestertia, which was a million of sesterces. But, to avoid ambiguity, they did not use the neuter sestertium in the singular number, when the whole sum amounted to no more than 1000 sesterces, or one sestertium. They called a million of sesterces decies nummum, or decies sestertium, for decies centena millia nummorum, or sestertiorum, in the masculine gender, omitting centena millia, for the sake of brevity: they likewise called the same sum decies sestertium (in the neuter gender), for decies centies sestertium, omitting centies for the reason above-mentioned; or simply decies, omitting centena millia sestertium, or centies sestertium; and with

the numeral adverbs, decies, vicies, centies, millies, and the like, either centena millia, or centies, was always understood. The Constantinopolitans kept their accounts in solidi, which are reduced to pounds sterling, by multiplying the given. number by 58648, and cutting off 5 figures on the right hand for decimals.

Conclusion. The Greeks had no money at the time of the Trojan war; for Homer represents them as trafficking by barter, and Priam, an Asiatic, weighs. out the 10 talents of gold, which he takes to ransom his son's body of Achilles. This ponderal talent was very small, as appears from Homer's description of the games at the funeral of Patroclus, where 2 talents of gold are proposed as an inferior prize to a mare with foal of a mule. Whence Mr. R. concludes it was the same that the Dorian colonies carried to Sicily and Calabria; for Pollux tells us, from Aristotle, that the ancient talent of the Greeks in Sicily contained 24 nummi, each of which weighing an obole and a half, the talent must have weighed 6 Attic drachms, or 3 darics; and Pollux elsewhere mentions such a talent of gold. But the daric weighed very little more than our guinea; and if 2 talents weighed about 6 guineas, we may reckon the mare with foal worth 12; which was no improbable price, since we learn from a passage in the Clouds of Aristophanes, that, in his time, a running horse cost 12 ininas, or above 46 pounds sterling. Therefore this seems to have been the ancient Greek talent, before the art of stamping money had introduced the greater talents from Asia and Egypt.

Herodotus tells us that the Lydians were reputed to be the first that coined gold and silver money; and the talent, which the Greeks called euboïc, certainly came from Asia. Therefore the Greeks learned the use of money from the Asiatics. The Romans took their weights and their money, either from the Dorians of Calabria, or from Sicily; for their libra, uncia, and nummus, were all Doric words, their denarius was the Sicilian AxiTgov; and Pollux tells us, from Aristotle, that the Sicilian nummus was a quarter of the Attic drachm; and the Romans called a quarter of their denarius by the same name.

The great disproportion between the copper and silver money, when the Romans first coined the latter, has induced many to believe that the first denarii must have been heavier than the 84th part of their pound; thinking it incredible that silver should ever be valued at 840 times its weight of copper. But they can produce no ancient author of credit, in support of this opinion. But we are little interested in the weight of the denarius for the first 60 years after it was coined; and it has been shown that when the Romans began to coin gold, it did not exceed the 84th part of their pound.

XLIX. Description of a Method of Measuring Differences of Right Ascension