From a hundred and one upwards, the larger number is usually put first, either without or (except distributives) with a conjunction, e. g. ducentos (et) qvadraginta (et) qvattuor, qvingentesimum (et) qvinqvagesimum (et) octavum, duceni septuageni, centies (et) qvadragies; but with a conjunction the smaller (cardinal or ordinal) number sometimes is found preceding, e.g. qvinqvagintā et ducentă, septimum et qvinqvagesimum ac centesimum. So also ducentos et mille, mille et ducentos.

For eighteen, nineteen, twenty-eight, twenty-nine, &c., the subtractive forms (e. g. duodeviginti, undeviginti, undetrigesimus, &c.) are most common, but compound forms are also found, e. g. decem octo, decem et octo (frequently), octodecim (rare); novem et triginta, qvinqvaginta octo, triginta novem (Liv.), octavo decimo (Tac.), octoni deni (Liv.).

v. Use of classes of Numerals.

The ordinal, not the cardinal, is used in giving the date, e.g. In the year 1869 is anno millesimo octingentesimo sexagesimo nono. The distributives are used

(1) to denote that the number belongs to each of several persons or things, e.g. Cæsar et Ariovistus denos comites ad colloqvium adduxerunt, took ten companions each; pueri senum septenumve denum annorum, boys of sixteen or seventeen years old, i.e. each was 16 or 17; ambulare bina millia passuum, to walk two miles each time; tritici modius erat sestertiis ternis, corn was at three sesterces the (i.e. each) bushel. If singuli is expressed with the persons, &c., the cardinal number may be used with the things numbered, e.g. singulis denarii trecenti imperabantur, each avas required to pay three hundred pence. In this use terni, not trini, is used.

(2) in expressions of multiplication, e.g. bis bina, twice two; ter novena virgines, thrice nine girls; decies centena millia, ten times a hundred thousand. In these expressions the distributive numerals, e. g. decies centena millia, do not mean a million to each person, but a hundred thousand taken each of ten times.

(3) with nouns which have no singular, e.g. bina castra, the two camps; trinis hostium spoliis, with three sets of spoils from the enemy. (In this use uni not singuli; trini not terni is used.)

(4) Poets use distributives as merely equivalent to cardinals, e.g. centum quoi brachia dicunt centenasque manus (Verg. A. x. 565), i.e. a hundred hands in all, not a hundred in each arm. also post-Augustan writers use trinus (not ternus).

So

(5) In the singular the distributives are sometimes used, chiefly

by poets, e.g. centauri corpore bino, a double body; centenaque arbore fluctum verberat assurgens (Verg.), with an hundred-fold shaft, i.e. a hundred oars; novena lampade, with nine torches (a torch repeated nine times).

Every other is expressed by alterni; e.g. alternis diebus, every second day.

vi. Expression of Fractions1.

Fractions are expressed in words in several ways:

1. All fractions, with 1 for numerator, are denoted by ordinal numbers, with or without pars, e.g., dimidium (not dimidia) or dimidia pars;, tertia or tertia pars;, qvarta, &c.

2. All fractions with a numerator less by one than the denominator are denoted by the cardinal with partes simply, e.g. 2, duæ partes; 2, tres partes;, qvattuor partes; §, qvinque partes.

3. All fractions with 12, or its multiples for a denominator, are denoted by the parts of an as, which is taken as the whole and is equal to 12 unciæ. (See below, § viii.) Hence heres ex asse, heir to the whole inheritance: ex triente, to a third; ex dimidia et sextante, to two thirds (a half and a sixth).

4. Other fractions, not expressible by one of the above methods, are denoted by the cardinal for a numerator, and the ordinal (as in subsection 1) for the denominator, e.g., quattuor septime; 3,

septem ncnæ.

5. Some fractions are denoted by resolution into their components, e.g. 3, dimidia et quarta; 3, pars dimidia et sexta; &, pars tertia et nona; 1, pars tertia et septima.

6. Sometimes further division is resorted to, e.g., dimidia qvinta. And dimidia tertia is used for sexta; dimidia qvarta for octava.

7. Sesqui, 1, is used only in compounds, see § 987 (p. 386).

vii. Money coinage.

(Chiefly from Hultsch, see below, p. 451.)

Coined money was not used at Rome till the time of the Decemviral legislation (303 U.C.=451 B.C.). The coin was called an as, and was supposed to weigh a pound; hence called in distinction from the subsequent as, as libralis or librarius. Coins also existed for the semis, triens, qvadrans, sextans, and uncia. The real weight (of unworn pieces now found) was 9 to 11 unciæ and may be taken

1 Chiefly from Gossrau, Lat. Sprachlehre, § 125.

therefore at 10 unciæ. The coinage was of copper (as), alloyed with tin and lead. Analysis of these pieces gives 7°16 to 7.66 per cent. of tin; and 19:56 to 29°32 per cent. of lead.

In 485 U.C. (=269 B.C.), shortly before the first Punic war, silver was first coined, and at the same time the as was reduced to the weight of 4 uncia (and then gradually before the end of the 1st Punic war to 2 uncia) instead of an actual ro, nominal 12, unciæ. Three silver coins were introduced, the denarius (often stamped with a biga, or quadriga, and thence called bigatus or quadrigatus) =10 (reduced) asses; the qvinarius=5 asses; the sestertius=2 asses. The coin equivalent to the reduced as was of copper and called libella; the half of this was sembella; the quarter (of the libella) was teruncius. The double as was coined and called dupondius; other coins were tressis = 3 asses; decessis = 10 asses. The denarius was probably pound of silver.

In the year 537 U.C. (=217 B.C.) the copper as was reduced to the weight of one uncia, and to the value of denarius or sestertius. Probably at the same time the denarius, which had been gradually losing, was reduced so as to be equal to pound of silver. The as eventually sunk to the value of uncia.

A new silver coin called victoriatus, because stamped on the reverse with a figure of Victory, was introduced probably about the year 228 B.C. At first it was 3 denarius, afterwards by the Clodian law, 104 B.C., it was reduced to be = denarius, and as such was known to Varro, Cicero, &c.

In the time of Nero the denarius was again reduced to pound of silver, and remained at this until Marcus Aurelius. At the same time Nero debased the silver, which hitherto had been fine, by an admixture of 5 to 10 per cent. of alloy. Under Trajan, about the year 100, the alloy was 15 per cent., under Hadrian nearly 20 per cent., under Marcus Aurelius 25 per cent., under Commodus 30 per cent., under Septimius Severus 50 to 60 per cent.

Copper coinage was dropped from about 84 to 74 B.C. until 15 B.C. (Except that some coins by Antony are found.) Then the silver sesterce being given up, a four-as piece was coined instead; and a piece of half the value of the new sesterce, viz. the dupondius. Both these were of brass (the proportions being not quite zinc to more than copper). The as, semis and qvądrans were of copper.

Gold was first coined in 217 B.C.; but sparsely until Sulla, Pompey and Cæsar. Cæsar's coin called aureus was fixed as equivalent to 25 denarii or 100 sesterces.

The value of these different coins is as follows according to Hultsch. Hultsch's values are reduced to English money on the basis of 1 silver groschen = Izd. sterling.

Aureus (gold) = 25 denarii = 100 sestertii

Hence the following amounts are deduced:

175.

In intrinsic value the denarius is reckoned by Hussey at 8.62 pence; the aureus, in terms of the English sovereign, at £1. Is. Ild. If the value of the denarius (fixed at the twenty-fifth of the aureus) is deduced from this value, it would, of course, be considerably higher than that given above.

viii. Expression of sums of money.

The denarius which was the silver coin in most currency was little used in reckoning. The ordinary unit of reckoning was the sestertius, or nummus, or, in full, sestertius nummus.

Up to 2000, the cardinal numbers are prefixed, e.g. centum sestertii, ducenti sestertii. But for higher numbers, in thousands up to a million, a neuter substantive in the plural number was used, sestertia, e.g. duo or septem sestertia for duo or septem millia sestertium (the short form of the genitive plural being taken for a neuter substantive); sestertium sexagena millia, sestertium sexagena millia nummum, sestertium nummum qvinqve millia.

For sums of a million and upwards numeral adverbs are resorted to, e.g. decies centum (or centena) millia sestertium. Usually the numeral adverb and sestertium are put alone, e.g. decies sestertium; similarly duodecies sestertium (1,200,000), ter et vicies (2,300,000). In these expressions again sestertium was taken to be a neuter substantive, and described as such, but in the singular number only, e.g. (nom.) sestertium qvadragies relinqvitur (4,000,000); (acc.) sestertium qvadragies accepi; (abl.) sestertio decies fundum emi, in sestertio vicies egere (to be poor in the possession of 2,000,000 sesterces). Occasionally, when the context is clear, the adverb alone is put, and sestertium omitted. Sometimes other parts of the full

1 But intrinsically worth from 1'97 to 093 silv. gr.

expression are omitted, e.g. decies centena millia, decies centena. (cf. § v. 2.) As an instance of a composite expression may serve, Accepi vicies ducenta, triginta qvinqve milia, qvadringentos decem et septem nummos (C. Verr. Lib. I. 14), 2,235,417 sesterces1.

The sign for a denarius was X, for a qvinarius V, for an as I, for a dupondius II, for a sestertius IIS (for duo + semis). Sometimes a line is drawn through the middle of these signs, and hence printers have substituted for IIS HS. Hence IIS decem = IO Sesterces; IIS decem millia = 10,000 sesterces; IIS decies = 10,00,000. If the numbers were not written in full but denoted by letters an ambiguity might arise, which was however obviated by adding (see § ii.) a top line for thousands IIS; and top and side lines for hundred-thousands when the sum was equal to a million or more2; e. g. Plin. 33. 3, 17, §§ 55, 56 (ed. Jan.). Auri in aerario populi Romani fuere sex Julio L. Aurelio coss. septem annis ante bellum Punicum tertium, pondo xvII.CCCCX., argenti XXII.LXX. et in numerato LXI.Xxxv.cccc.; Sex. Julio d. Marcio coss. hoc est, belli socialis initio, auri XVI.XX.DCCCXXXI.: i.e. There was in the Roman treasury in the year 157 B.C., in weight 17,410 (pounds) of gold, 22,070 (pounds) of silver, and in count (i.e. in coin) 6,135,400 sesterces; in the year 91 B.C. 1,620,831 (pounds?) of gold.

The as3 consisted originally of 12 unciæ, and there were distinct names and signs for each multiple of the uncia and for some fractions of it.

1 Madvig, Lat. Gr. Append. II.

2 Marquardt, Röm. Alterth. Th. III. Abth. 2, p. 32.

3 See Volusius Mæcianus in Metrol. Script. 11. p. 61 sqq.; Hultsch's Preface to same, pp. xxv. to xxviii.; Prolegom. pp. 17—22; Marquardt, Röm. Alt. 111. 2, pp. 41-44, V. I, p. 102.

4 This term must either have been formed when the as was equal to 4 unciæ; or be short for two-thirds of an as (cf. § vi. 2).