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QUADRANTAL, or AMPHORA QUADRANTAL, or AMPHORA only, was the principal Roman measure of capacity for fluids. All the Roman measures of capacity were founded on weight, and thus the amphora was originally the space occupied by •eighty pounds of wine (Festus, s.v.).
There is also preserved to us by Festus (s.v. Publica Pondera p246, Müller), a plebiscitum (the Sillian) of unknown origin, regulating the weights and measures, to the following effect:— Ex ponderibus publicis, quibus hac tempestate populu oetier solet, uti coaequetur sedulum, uti quadrantal vini octoginta pondo siet: congius vini decem p. (i.e. pondo) siet: sex sextari congius siet vini; duodequinquaginta sextari quadrantal siet vini:— that is, that the quadrantal should contain •80 pounds of wine,1 and the congius 10; and that the sextarius should be ⅙th of the congius, and 1⁄48th of the quadrantal. The quadrantal was subdivided into 2 urnae, 8 congii, 48 sextarii, 96 heminae, 192 quartarii, 384 acetabula, 576 cyathi, and 2304 ligulae.a As compared with the Roman dry measure, the quadrantal was three times the modius. The only measure larger than the quadrantal was the culeus of 20 amphorae, which was used, as well as the amphora itself, in estimating the produce of a vineyard. [Culeus: comp. Amphora sub fin.]
The quadrantal was connected with the measures of length, by the law, that it was the cube of the foot, whence its name quadrantal, or, as other writers give it (using the Greek κύβος instead of the Latin quadrantal) amphora cubus (Cato, R. R. 57; Gell. I.20; Priscian. Carm. de Mens. et Pond. vv. 59‑63:—
"Pes longo in spatio latoque altoque notetur:
Angulus ut par sit, quem claudit linea triplex Quatuor et medium quadris cingatur inane: Amphora fit cubus, quam ne violare liceret, Sacravere Jovi Tarpeio in monte Quirites." 
A standard model of the Amphora was kept with great care in the temple of Jupiter in the Capitol, and was called amphora Capitolina (Priscian, l.c.; Capitolin. Maximin. 4). There still exists a congius which professes to have been made according to this standard. [Congius.] For a full account of this congius, see H. Hase, Abhandl. d. Ber. Akad. 1824.
There are two questions of very great interest connected with the Roman quadrantal; namely, (1) whether the equality to the cubic foot was originally exact, or only approximate, and (2) whether there was any exact ratio between the Roman and the Grecian measures. The full discussion of these questions would be inconsistent both with the limits and with the chief object of this work. A general statement of the matters in dispute will be found under Mensura, p754. It may here be added that, whether there was or was not originally any precise ratio been the Greek and Roman measures of capacity, they were at least so nearly related to one another, that, when the two systems came to exist side by side, it was found easy to establish the following definite ratios. Of the liquid measures; the Roman amphora, or quadrantal, was 2/5ths of the Aeginetan, and 2/3rds of the Attic amphora or metretes; and the congius of the Roman system was equal to the χοῦς of the Attic. Again, comparing the Roman liquid with the Greek dry measures, the quadrantal was 1‑3rd of the Aeginetan, and one half of the Attic, medimnus. Consequently, of the dry measures, the modius (which was 1‑3rd of the quadrantal) was 1‑9th of the Aeginetan, and 1‑6th of the Attic, medimnus. The connecting subordinate unit in all these sets of measures is the Roman sextarius, or sixth part of the congius, which was introduced into the Greek system under the name of ξέστης, and which stands to the several measures now mentioned in the following relations:—
1. Liquid Measures.


The Roman quadrantal  =  48 sextarii 
The Attic metretes  =  72 sextarii 
The Aeginetan metretes  =  120 sextarii 
2. Dry Measures.


The Roman modius  =  16 sextarii 
The Attic medimnus  =  96 sextarii 
The Aeginetan medimnus  =  144 sextarii 
The ξέστης, or Roman sextarius, is not to be confounded with the genuine Attic ἕκτευς or sixth of the medimnus, which was equal to the Roman modius. (On the whole of this part of the subject, see Böckh, cc. III, XI, XVXVII.)
From the preceding remarks it will be seen that the only safe mode of computing the content of the amphora in terms of our own measures of capacity is by deducing it from the value already assigned to the Roman pound, on the authority chiefly of the coins. That value may be taken, in round numbers, at 5050 grains. Now the imperial gallon contains 70,000 grains. Therefore p980 the Roman amphora = (5050 × 80⁄70000) = •5·77 imperial gallons, or a little more than 5¾ gallons, or than 5 gallons and 6 pints. If we were to make the computation directly from the congius of Vespasian, we should have a somewhat higher value; which, as has already been shown under Pondera, arises probably from a source of error. On the other hand, the computation from the Roman cubic foot gives a somewhat lower value [Pondera]; but, as already intimated, it is very doubtful whether the true content of the amphora was exactly a cubic foot, and in fact, if Böckh be right, it was a little more. At all events, the value of •5 gallons 6 pints is quite near enough to the truth for all the purposes of the classical student. (See the Tables.) On the other hand, if we were to reckon the quadrantal at exactly 6 gallons, and consequently the sextarius, which is the small unit of the system, at exactly 1 pint (instead of ·96) we should obtain a system so extremely simple, and with so small a limit of error (namely less than 4⁄100 in a pint), that it would probably be allowable to adopt it in the ordinary reading of the classic authors; indicating, however, the small error, by prefixing in each case the words a little less than; and correcting it, when the numbers are large, by taking from the result 1/25th of itself.
1 The Romans were aware that there is a difference in the specific gravity of wine and of water, and in the different sorts of each, but, for the sake of simplicity, they regarded them as of the same specific gravity; when, however, they wished a very exact determination, they used rain water (Böckh, c3).
a . . . 384 acetabula, 576 cyathi, 2304 ligulae: These numbers seem needlessly arbitrary and involved, but they are an artifact of simple progressions by 2 and 3. Working in an American kitchen, you will use a gallon subdivided into 4 quarts, 8 pints, 16 cups, 256 tablespoons, 768 teaspoons. (Working in the metrically superior European kitchen, you will have measuring cups graduated in a dozen scales by weight for water, oil, cheese, sugar, etc.; a grossly inconvenient system providing much scope for error. To each our own lunacy.)
Ligula (q.v.) is the Latin word for a spoon; the attentive reader — I prefer to think that's a pleonasm rather than an oxymoron — will find that those ligulae are equivalent to ⅔ Tbp., or 2 Tsp., in U. S. kitchen measurement.
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