by Frontinus
[21] Anio Vetus citra quartum miliarium infra Novum, qui a Via Latina in Labicanam inter arcus traicit, et ipse piscinam habet. Inde intra secundum miliarium partem dat in specum qui vocatur Octavianus et pervenit in regionem Viae Novae ad hortos Asinianos, unde per illum tractum distribuitur. Rectus vero ductus secundum Spem veniens intra Portam Esquilinam in altos rivos per urbem diducitur.
[21] Old Anio, this side the fourth milestone, passes under New Anio, which here shifts from the Latin to the Labican Way; it has its own catch-basin. Then, this side the second milestone, it gives a part of its waters to the so-called Octavian Conduit and reaches the Asinian Gardens in the neighbourhood of the New Way, whence it is distributed throughout that district. But the main conduit, which passes Spes Vetus, comes inside the Esquiline Gate and is distributed to high-lying mains throughout the City.
[22] Nec Virgo nec Appia nec Alsietina conceptacula, id est piscinas, habent. Arcus Virginis initium habent sub hortis Lucullanis, finiuntur in Campo Martio secundum frontem Saeptorum. Rivus Appiae sub Caelio monte et Aventino actus emergit, ut diximus, infra Clivum Publicii. Alsietinae ductus post Naumachiam, cuius causa videtur esse factus, finitur.
[22] Neither Virgo, nor Appia, nor Alsietina has a receiving reservoir or catch-basin. The arches of Virgo begin under the Lucullan Gardens, and end on the Campus Martius in front of the Voting Porticoes. The conduit of Appia, running along the base of the Caelian and Aventine, emerges, as we have said above, at the foot of the Publician Ascent. The conduit of Alsietina terminates behind the Naumachia, for which it seems to have been constructed.
[23] Quoniam auctores cuiusque aquae et aetates, praeterea origines et longitudines rivorum et ordinem librae persecutus sum, non alienum mihi videtur, etiam singula subicere et ostendere quanta sit copia quae publicis privatisque non solum usibus et auxiliis verum etiam voluptatibus sufficit, et per quot castella quibusque regionibus diducatur, quantum extra urbem, quantum in urbe, et ex eo quantum lacibus, quantum muneribus, quantum operibus publicis, quantum nomine Caesaris, quantum privatis usibus erogetur. Sed rationis existimo, priusquam nomina quinariarum centenariarumque et ceterorum modulorum, per quos mensura constituta est, proferamus, et indicare quae sit eorum origo, quae vires et quid quaeque appellatio significet, propositaque regula, ad quam ratio eorum et initium computatur, ostendere qua ratione discrepantia invenerim et quam emendandi viam sim secutus.
[23] Since I have given in detail the builders of the several aqueducts, their dates, and, in addition, their sources, the lengths of their channels, and their elevations in sequence, it seems to me not out of keeping to add also some separate details, and to show how great is the supply which suffices not only for public and private uses and purposes, but also for the satisfaction of luxury; by how many reservoirs it is distributed and in what wards; how much water is delivered outside the City; how much is used for water-basins, how much for fountains, how much for public buildings, how much in the name of Caesar, how much for private consumption. But before I mention the names quinaria, centenaria, and those of the other ajutages by which water is gauged, I deem it appropriate to state what is their origin, what their capacities, and what each name means; and, after setting forth the rule according to which their proportions and capacities are computed, to show in what way I discovered their discrepancies, and what course I pursued in correcting them.
[24] Aquarum moduli aut ad digitorum aut aut unicarum mensuram instituti sunt. Digiti in Campania et in plerisque Italiae locis, unciae in pApula cita hunc observatur. Est autem digitus, ut convenit, sextadecima pars pedis, uncia duodecima. Quemadmodum autem inter unciam et digitum diversitas, ita et ipsius digiti non simplex observatio est. Alius vocatur quadratus, alius rotundus. Quadratus tribus quartisdecumis suis rotundo maior, rotundus tribus undecumis suis quadrato minor est, scilicet quia anguli deteruntur.
[24] The ajutages to measure water are arranged according to the standard either of digits or of inches. Digits are the standard in Campania and in most parts of Italy; inches are the standard in … Now the digit, by common understanding, is 1/16 part of a foot; the inch 1/12 part. But precisely as there is a difference between the inch and the digit, just so the standard of the digit itself is not uniform. One is called square; another, round. The square digit is larger than the round digit by 3/14 of its own size, while the round is smaller than the square by 3/11 of its size, obviously because the corners are cut off.
[25] Postea modulus nec ab uncia nec ab alterutro digitorum originem accipiens inductus, ut quidam putant, ab Agrippa, ut alii, a plumbariis per Vitruvium architectum in usum urbis exclusis prioribus venit, appellatus quinariae nomine. Qui autem Agrippam auctorem faciunt, dicunt, quod quinque antiqui moduli exiles et velut puncta, quibus olim aqua cum exigua esset dividebatur, in unam fistulam coacti sint; qui Vitruvium et plumbarios, ab eo quod plumbea lammina plana quinque digitorum latitudinem habens circumacta in rotundum hunc fistulae modulum efficiat. Sed hoc incertum est, quoniam cum circumagitur, sicut interiore parte adtrahitur, ita per illam, quae foras spectat, extenditur. Maxime probabile est, quinariam dictam a diametro quinque quadrantum, quae ratio in sequentibus quoque modulis usque ad vicenariam durat, diametro per singulos adiectione singulorum quadrantum crescente: ut in senaria, quae sex quadrantes in diametro habet, et septenaria, quae septem, et deinceps simili incremento usque ad vicenariam.
[25] Later on, an ajutage called a quinaria came into use in the City, to the exclusion of the former measures. This was based neither on the inch, nor on either of the digits, but was introduced, as some think, by Agrippa, or, as others believe, by plumbers at the instance of Vitruvius, the architect. Those who represent Agrippa as its inventor, declare it was so designated because five small ajutages or punctures, so to speak, of the old sort, through which water used to be distributed when the supply was scanty, were now united in one pipe. Those who refer it to Vitruvius and the plumbers, declare that it was so named from the fact that a flat sheet of lead 5 digits wide, made up into a round pipe, forms this ajutage.º But this is indefinite, because the plate, when made up into a round shape, will be extended on the exterior surface and contracted on the interior surface. The most probable explanation is that the quinaria received its name from having a diameter of 5/4 of a digit, a standard which holds in the following ajutages also up to the 20-pipe, the diameter of each pipe increasing by the addition of ¼ of a digit. For example the 6-pipe is six quarters in diameter, a 7-pipe seven quarters, and so on by a uniform increase up to a 20-pipe.
[26] Omnis autem modulus colligitur aut diametro aut perimetro aut areae mensura, ex quibus et capacitas apparet. Differentiam unciae, digiti quadrati et digiti rotundi, et ipsius quinariae ut facilius dinoscamus, utendum est substantia quinariae, qui modulus et certissimus et maxime receptus est. Unciae ergo modulus habet diametri digitum unum et trientem digiti; capit plus, quam quinaria, quinariae octava, hoc est sescuncia quinariae et scripulis tribus et besse scripuli. Digitus quadratus in rotundum redactus habet diametri digitum unum et digiti sescunciam sextulam; capit quinariae dextantem. Digitus rotundus habet diametri digitum unum; capit quinariae septuncem semunciam sextulam.
[26] Every ajutage, now, is gauged either by its diameter or circumference, or by its area of clear cross-section, from any of which factors its capacity becomes evident. That we may distinguish the more readily between the inch ajutage, the square digit, the circular digit, and the quinaria itself, use must be made of the value of the quinaria, the ajutage which is most accurately determined and best known. Now the inch ajutage, has a diameter of 1⅓ digits. Its capacity is [slightly] more than 1⅛ quinariae, i.e., 1½ twelfths of a quinaria plus 3/288 plus ⅔ of 1/288 more. The square digit, reduced to the circle is 1 digit plus 1½ twelfths of a digit plus 1/72 in diameter; its capacity is 10/12 of a quinaria. The circular digit is 1 digit in diameter; its capacity is 7/12 plus ½ twelfth plus 1/72 of a quinaria.
[27] Ceterum moduli, qui a quinaria oriuntur, duobus generibus incrementum accipiunt. Est unum, cum ipsa
multiplicatur, id est eodem lumine plures quinariae includuntur, in quibus secundum adiectionem quinariarum amplitudo luminis crescit. Est autem fere tum in usu, cum plures quinariae impetratae, ne rivus saepius convulneretur, una fistula excipiuntur in castellum, ex quo singuli suum modum recipiunt.
[27] Now the ajutages which are derived from the quinaria increase on two principles. One principle is that the quinaria itself is taken a given number of times, i.e., in one orifice the equivalent of several quinariae is included, in which case the size of the orifice increases according to the increase in the number of quinariae. This principle is regularly employed, whenever several quinariae are delivered by one pipe and received in a reservoir, from which consumers receive their individual supply, — this being done in order that the conduit may not be tapped too often.
[28] Alterum genus est, quotiens non ad quinariarum necessitatem fistula incrementum capit, sed ad diametri sui mensuram, secundum quod et nomen accipit et capacitatem ampliat: ut puta quinaria, cum adiectus est ei ad diametrum quadrans, senariam facit. Nec iam in solidum capacitatem ampliat; capit enim quinariam unam et quincuncem sicilicum. Et deinceps eadem ratione quadrantibus diametro adiectis, ut supra dictum est, crescunt septenaria, octonaria usque ad vicenariam.
[28] The second principle is followed, whenever the pipe does not increase according to some necessary multiple of quinariae, but according to the size of diameters, in conformity with which principle they enlarge their capacity and receive their names; as for example, when a quarter [of a digit] is added to the diameter of a quinaria, we get as a result the senaria, but its capacity is not increased by a whole quinaria, for it contains a quinaria plus 5/12 plus 1/48. So on, by adding successive quarters of a digit to the diameter, as was said above, we get by gradual increases, a 7-pipe (septenaria), an 8-pipe (octonaria), and up to the 20-pipe (vicenaria).
[29] Subsequitur illa ratio, quae constat ex numero digitorum quadratorum, qui area, id est lumine, cuiusque moduli continentur, a quibus et nomen fistulae accipiunt. Nam quae habet areae, id est luminis in rotundum coacti, digitos quadratos viginti quinque, vicenum quinum appellatur: similiter tricenaria et deinceps pari incremento quinorum digitorum quadratorum usque ad centenum vicenum.
[29] After that we have the method of gauging which is based on the number of square digits contained in the cross-section, that is, the orifice of each ajutage, from which number of square digits the pipes also get their names. Thus those which in cross-section, that is, in circular orifice, have 25 square digits, are called 25-pipes. Similarly we have the 30-pipe (tricenaria), and so on, by a regular increase of 5 square digits, up to the 120-pipe.
[30] In vicenaria fistula, quae in confinio utriusque rationis posita est, utraque ratio paene congruit. Nam habet secundum eam computationem, quae in antecedentibus modulis servanda est, in diametro quadrantes viginti, cum diametri eiusdem digiti quinque sint; et secundum eorum modulorum rationem, qui sequuntur, aream habet digitorum quadratorum exiguo minus viginti.
[30] In the case of the 20-pipe, which is on the border line between the two methods of gauging, the two methods almost coincide. For according to the reckoning to be used in the first-named set of ajutages, it is twenty quarter digits in diameter, inasmuch as its diameter is 5 digits; while according to the computation to be applied to the higher ajutages, it has an area of 20 square digits, less a fraction.
[31] Ratio fistularum quinariarum usque ad centenum vicenum per omnes modulos ita se habet, ut ostendimus, et omni genere inita constat sibi. Convenit et cum is modulis, qui in commentariis invictissimi et piissimi principis positi et confirmati sunt. Sive itaque ratio sive auctoritas sequenda est, utroque commentariorum moduli praevalent. Sed aquarii cum manifestae rationi in pluribus consentiant, in quattuor modulis novaverunt, duodenaria et vicenaria et centenaria et centenum vicenum.
[31] The gauging of the entire series of ajutages from the 5-pipe (quinaria) up to the 120-pipe, is determined in the way I have explained, and in each class the principle adopted is adhered to for that class. It conforms also to the ajutages set down and verified in the records of our most puissant and patriotic emperor. Whether, therefore, computation or authority is to be followed, on either ground the ajutages of the records are of greater weight. But the water-men, while they conform to the obvious reckoning in most ajutages, have made deviation in the case of four of them, namely: the 12-, 20-, 100-, and 120-pipe.
[32] Et duodenariae quidem nec magnus error nec usus frequens est. Cuius diametro adiecerunt digiti semunciam sicilicum, capacitati quinariae quadrantem. In reliquis autem tribus modulis plus deprenditur. Vicenariam exiguiorem faciunt diametro digiti semisse et semuncia, capacitate quinariis tribus et quadrante et semuncia, quo modulo plerumque erogatur. Centenaria autem et centenum vicenum, quibus adsidue accipiunt, non minuuntur sed augentur. Diametro enim centenariae adiciunt digiti bessem et semunciam, capacitati quinarias decem semissem semunciam. Centenum vicenum diametro adiciunt digitos tres septuncem semunciam sicilicum, capacitati quinarias sexaginta sex sextantem.
[32] In case of the 12-pipe, the error is not great, nor is its use frequent. They have added 1/24 plus 1/48 to its diameter, and to its capacity ¼ of a quinaria. A greater discrepancy is detected in case of the three remaining ajutages. These water-men diminish the 20-pipe in its diameter by ½ plus 1/24 of a digit, its capacity by 3 quinariae plus ¼ plus 1/24; and common use is made of this ajutage for delivery. But in case of the 100-pipe and 120-pipe, through which they regularly receive water, the pipes are not diminished but enlarged! For to the diameter of the 100-pipe they add ⅔ plus 1/24 of a digit, and to the capacity, 10 quinariae plus ½ plus 1/24. To the diameter of the 120-pipe they add 3 digits plus 7/12 plus 1/24 plus 1/48; to its capacity, 66 quinariae plus ⅙.
[33] Ita dum aut vicenariae, qua subinde erogant, detrahunt aut centenariae et centenum vicenum adiciunt, quibus semper accipiunt, intercipiuntur in centenaria quinariae viginti septem, in centenum vicenum quinariae octoginta sex. Quod cum ratione approbetur, re quoque ipsa manifestum est. Nam et vicenaria, quam Caesar pro quinariis sedecim assignat, non plus erogant quam tredecim, et ex centenaria, quam ampliaverunt eque centenum vicenum certum est illos non erogare nisi ad artiorem numerum, quia Caesar secundum suos commentarios, cum ex quaque centenaria explevit quinarias octoginta unam semissem, item ex centenum vicenum quinarias nonaginta octo, tamquam exhausto modulo desinit distribuere.
[33] Thus by diminishing the size of the 20-pipe by which they constantly deliver, and enlarging the 100- and 120-pipes, by which they always receive, they steal in case of the 100-pipe 27 quinariae, and in case of the 120-pipe 86 quinariae. While this is proved by computation, it is also obvious from the facts. For from the 20-pipe, which Caesar rates at 16 quinariae, they do not deliver more than 13; and it is equally certain that from the 100-pipe and the 120-pipe, which they have expanded, they deliver only up to a limited amount, since Caesar, as his records show, has made delivery according to his grant, when out of each 100-pipe he furnishes 81½ quinariae, and similarly out of a 120-pipe, 98.
[34] In summa moduli sunt XX quinque. Omnes consentiunt et rationi et commenatriis, exceptis his quattuor, quos aquarii novaverunt. Omnia autem quae mensura continentur, certa et immobilia congruere sibi debent; ita enim universitati ratio constabit. Et quemadmodum verbi gratia sextarii ratio ad cyathos, modii vero et ad sextarios et ad cyathos respondet; ita et quinariarum multiplicatio in amplioribus modulis servare consequentiae suae regulam debet. Alioqui cum in erogatorio modulo minus invenitur, in acceptorio plus, apparet non errorem esse sed fraudem.
[34] In all there are 25 ajutages. They all conform to their computed and recorded capacities, barring these four which the water-men have altered. But everything embraced under the head of mensuration ought to be fixed, unchanged, and constant. For only so will any special computation accord with general principles. Just as a sextarius, for example, has a regular ratio to a cyathus, and similarly a modius to both a cyathus and sextarius, so also the multiplication of the qu
inariae in case of the larger ajutages must follow a regular progression. However, when less is found in the delivery ajutages and more in the receiving ajutages, it is obvious that there is not error, but fraud.
[35] Meminerimus omnem aquam, quotiens ex altiore loco venit et intra breve spatium in castellum cadit, non tantum respondere modulo suo sed etiam exuberare; quotiens vero ex humiliore, id est minore pressura, longius ducitur, segnitia ductus modum quoque deperdere; et ideo secundum hanc rationem aut onerandam esse erogatione aut relevandam.
[35] Let us remember that every stream of water, whenever it comes from a higher point and flows into a reservoir after a short run, not only comes up to its measure, but actually yields a surplus; but whenever it comes from a lower point, that is, under less pressure, and is conducted a longer distance, it shrinks in volume, owing to the resistance of its conduit; and that, therefore, on this principle it needs either a check or a help in its discharge.
[36] Sed et calicis positio habet momentum. In rectum et ad libram conlocatus modum servat, ad cursum aquae oppositus et devexus amplius rapit, ad latus praetereuntis aquae conversus et supinus, id est ad haustum pronior, segniter et exiguum sumit. Est autem calix modulus aeneus, qui rivo vel castello induitur; huic fistulae applicantur. Longitudo eius habere debet digitos non minus duodecim, lumen capacitatem quanta imperata fuerit. Excogitatus videtur, quoniam rigor aeris difficilior ad flexum non temere potest laxari vel coartari.