Complete Works of Frontinus

by Frontinus

  [36] But the position of the calix is also a factor. Placed at right angles and level, it maintains the normal quantity. Set against the current of the water, and sloping downward, it will take in more. If it slopes to one side, so that the water flows by, and if it is inclined with the current, that is, is less favorably placed for taking in water, it will receive the water slowly and in scant quantity. The calix, now, is a bronze ajutage, inserted into a conduit or reservoir, and to it the service pipes are attached. Its length ought not to be less than 12 digits, while its orifice ought to have such capacity as is specified. Bronze seems to have been selected, since, being hard, it is more difficult to bend, and is not easily expanded or contracted.

  [37] Formulas modulorum qui sunt omnes viginti et quinque subieci, quamvis in usu quindecim tantum frequentes sint, derectas ad rationem de qua locuti sumus, emendatis quattuor, quos aquarii novaverant. Secundum quod et fistulae omnes, quae opus facient, derigi debent aut, si haec fistulae manebunt, ad quinarias quot capient computari. Qui non sint in usu moduli, in ipsis est adnotatum.

  [37] I have described below all the 25 ajutages that there are (although only 15 of them are in use), gauging them according to the method of computation spoken of, and correcting the four which the water-men have altered. To these specifications all ajutages in use ought to conform, or if those four remain in use, they ought to be gauged by the number of quinariae which they contain. The ajutages that are not in use are so referred to.

  [38] Uncia habet diametri digitum unum et trientem digiti; capit plus quam quinaria, quinariae sescuncia et scripulis tribus et besse scripuli. Digitus quadratus in latitudine et longitudine aequalis est. 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 et semiunciam sextulam.

  [38] The inch ajutage is 1 digit plus ⅓ of a digit in diameter; it contains more than a quinaria by 1½ twelfths of a quinaria plus 3/288 plus ⅔ of 1/288. The square digit has the same height as breadth. The square digit converted into its equivalent circle is 1 digit plus 1½ twelfths of a digit plus 1/72 in diameter; it measures 10/12 of a quinaria. The circular digit is 1 digit in diameter; and measures 7/12 plus 1½ twelfth plus 1/72 of a quinaria in area.

  [39] Fistula quinaria: diametri digitum unum = Ò , perimetri digitos tres S = = Ò ‘ III, capit quinariam unam.

  [39] The quinaria: 1 digit plus 3/12 in diameter; 3 digits plus ½ plus 5/12 plus 3/288 in circumference; it has a capacity of 1 quinaria.

  [40] Fistula senaria: diametri digitum unum semis, perimetri digitos IIII S = £ ‘ II, capit quinariam I = = Ò ‘ VII.

  [40] The 6-pipe: 1½ digits in diameter; 4 digits plus ½ plus 2/12 plus 1/24 plus 2/288 in circumference; it has a capacity of 1 quinaria plus 5/12 plus 7/288.

  [41] Fistula septenaria: diametri digitum I S = Ò , perimetri digitos V S, capit quinariam I S = = Ò £ ; in usu non est.

  [41] The 7-pipe: 1 digit plus ½ plus 3/12 in diameter; 5 digits plus ½ in circumference; it has a capacity of 1 quinaria, plus ½ plus 5/12 plus 1/24; is not in use.

  [42] Fistula octonaria: diametri digitos duos, perimetri digitos sex = Ò ‘ X, capit quinarias II S £ ‘ quinque.

  [42] The 8-pipe: 2 digits in diameter; 6 digits plus 3/12 plus 10/288 in circumference; it has a capacity of 2 quinariae plus ½ plus 1/24 plus 5/288.

  [43] Fistula denaria: diametri digitos duos et semis, perimetri digitos septem S = = ‘ VII, capit quinarias IIII.

  [43] The 10-pipe: 2½ digits in diameter; 7 digits plus ½ plus 4/12 plus 7/288 in circumference; it has a capacity of 4 quinariae.

  [44] Fistula duodenaria: diametri digitos III, perimetri digitos VIIII = = Ò ‘ III, capit quinarias quinque S = Ò ‘ III; in usu non est. Apud aquarios habebat diametri digitos III £ ‘ VI, capacitatis quinarias sex.

  [44] The 12-pipe: 3 digits in diameter; 9 digits plus 5/12 plus 3/288 in circumference; it has a capacity of 5 quinariae plus ½ plus 3/12 plus 3/288; is not in use. But with the water-men it measured 3 digits plus 1/24 plus 6/288 in diameter, containing 6 quinariae.

  [45] Fistula quinum denum: diametri digitos III S = Ò , perimetri digitos XI S = Ò ‘ X, capit quinarias novem.

  [45] The 15-pipe: 3 digits plus ½ plus 3/12 in diameter; 11 digits plus ½ plus 3/12 plus 10/288 in circumference; it has a capacity of 9 quinariae.

  [46] Fistula vicenaria: diametri digitos quinque, perimetri digitos XV S = = ‘ VI, capit quinarias sedecim. Apud aquarios habebat diametri digitos IIII S, capacitatis quinarias duodecim S = = Ò £.

  [46] The 20-pipe: 5 digits plus 1/24 plus 1/288 in diameter; 15 digits plus ½ plus 4/12 plus 6/288 in circumference; it has a capacity of 16 quinariae plus 3/12 plus 1/24. With the water-men it measured 4 digits plus ½ in diameter, holding 13 quinariae.

  [47] Fistula vicenum quinum: diametri digitos quinque S · Ò £ ‘ V, perimetri digitos decem et septem S = £ ‘ VII, capit quinarias XX = = ‘ VIIII; in usu non est.

  [47] The 25-pipe: 5 digits plus ½ plus 1/12 plus 1/24 plus 5/288 in diameter; 17 digits plus ½ plus 2/12 plus 1/24 plus 7/288 in circumference; it has a capacity of 20 quinariae plus 4/12 plus 9/288; is not in use.

  [48] Fistula tricenaria: diametri digitos sex = ‘ III, perimetri digitos decem et novem = = Ò , capit quinarias viginti quattuor = = Ò ‘ quinque.

  [48] The 30-pipe: 6 digits plus 2/12 plus 3/288 in diameter; 19 digits plus 5/12 in circumference; it has a capacity of 24 quinariae plus 5/12 plus 5/288.

  [49] Fistula tricenum quinum: diametri digitos sex S = ‘ II, perimetri digitos XX S = = Ò £ V, capit quinarias XXVIII S ‘ III; in usu non est.

  [49] The 35-pipe: 6 digits plus ½ plus 2/12 plus 2/288 in diameter; 20 digits plus ½ plus 5/12 plus 1/24 plus 4/288 in circumference; it has a capacity of 28 quinariae plus ½ plus 3/288; is not in use.

  [50] Fistula quadragenaria: diametri digitos septem Ò £ ‘ III, perimetri digitos XXII = = Ò , capit quinarias XXXII S Ò .

  [50] The 40-pipe: 7 digits plus 1/12 plus 1/24 plus 3/288 in diameter; 22 digits plus 5/12 in circumference; it has a capacity of 32 quinariae plus ½ plus 1/12.

  [51] Fistula quadragenum quinum: diametri digitos septem S £ ‘ octo, perimetri digitos XXIII S = Ò ‘ X, capit quinarias XXXVI S = £ ‘ octo; in usu non est.

  [51] The 45-pipe: 7 digits plus 1/12 plus 1/24 plus 8/288 in diameter; 23 digits plus ½ plus 3/12 plus 1/24 in circumference; it has a capacity of 36 quinariae plus ½ plus 1/12 plus 1/24 plus 8/288; is not in use.

  [52] Fistula quinquagenaria: diametri digitos septem S = = Ò £ ‘ quinque, perimetri digitos XXV £ ‘ VII, capit quinarias XL S = £ ‘ V.

  [52] The 50-pipe: 7 digits plus ½ plus 5/12 plus 1/24 plus 5/288 in diameter; 25 digits plus 1/24 plus 7/288 in circumference; it has a capacity of 40 quinariae plus ½ plus 2/12 plus 1/24 plus 5/288.

  [53] Fistula quinquagenum quinum: diametri digitos octo = = ‘ decem, perimetri digitos XXVI = Ò £ , capit quinarias XLIIII S = Ò £ ‘ II; in usu non est.

  [53] The 55-pipe: 8 digits plus 4/12 plus 10/288 in diameter; 26 digits plus 3/12 plus 1/24 in circumference; it has a capacity of 44 quinariae plus ½ plus 3/12 plus 1/24 plus 2/288; is not in use.

  [54] Fistula sexagenaria: diametri digitos VIII S = £ ‘ novem, perimetri digitos XXVII = = Ò £, capit quinarias XL octo S = = ‘ XI.

  [54] The 60-pipe: 8 digits plus ½ plus 2/12 plus 1/24 plus 8/288 in diameter; 27 digits plus 5/12 plus 1/24 in circumference; it has a capacity of 48 quinariae plus ½ plus 4/12 plus 11/288.

  [55] Fistula sexagenum quinum: diametri digitos novem Ò ‘ III, perimetri digitos XX octo S Ò, capit quinarias quinquaginta duas S = = £ ‘ octo; in usu non est.

  [55] The 65-pipe: 9 digits plus 1/12 plus 3/288 in diameter; 28 digits plus ½ plus 1/12 in circumference; it has a capacity of 52 quinariae plus ½ plus 3/12 plus 1/24 plus 8/288; is not in use.

  [56] Fistula septuagenaria: diametri digitos novem = = Ò ‘ sex,
perimetri digitos XXIX S = , capit quinarias LVII ‘ V.

  [56] The 70-pipe: 9 digits plus 5/12 plus 6/288 in diameter; 29 digits plus ½ plus 2/12 in circumference; it has a capacity of 57 quinariae plus 5/288.

  [57] Fistula septuagenum quinum: diametri digitos novem S = Ò ‘ sex, perimetri digitos XXX S = ‘ VIII, capit quinarias LXI Ò ‘ II; in usu non est.

  [57] The 75-pipe: 9 digits plus ½ plus 3/12 plus 6/288 in diameter; 30 digits plus ½ plus 2/12 plus 8/288 in circumference; it has a capacity of 61 quinariae plus 1/12 plus 2/288; is not in use.

  [58] Fistula octogenaria: diametri digitos decem Ò ‘ II, perimetri digitos XXXI S = £ , capit quinarias LXV =.

  [58] The 80-pipe: 10 digits plus 1/12 plus 2/288 in diameter; 31 digits plus 1/12 plus 2/12 plus 1/24 in circumference; it has a capacity of 65 quinariae plus 2/12.

  [59] Fistula octogenum quinum: diametri digitos decem = = £ ‘ septem, perimetri digitos XXXII S = ‘ IIII, capit quinarias LXVIIII = £ ; in usu non est.

  [59] The 85-pipe: 10 digits plus 4/12 plus 1/24 plus 7/288 in diameter; 32 digits plus ½ plus 2/12 plus 4/288 in circumference; it has a capacity of 69 quinariae plus 3/12; is not in use.

  [60] Fistula nonagenaria: diametri digitos decem S = ‘ X, perimetri digitos triginta tres S Ò £ ‘ X, capit quinarias septuaginta tres = = £ ‘ V.

  [60] The 90-pipe: 10 digits plus ½ plus 2/12 plus 10/288 in diameter; 33 digits plus ½ plus 1/12 plus 1/24 plus 2/288 in circumference; it has a capacity of 73 quinariae plus 3/12 plus 1/24 plus 5/288.

  [61] Fistula nonagenum quinum: diametri digitos X S = = Ò £ ‘ VIIII, perimetri digitos XXXIIII S £, capit quinarias LXXVII = = £ ‘ II; in usu non est.

  [61] The 95-pipe: 10 digits plus ½ plus 5/12 plus 1/24 plus 9/288 in diameter; 34 digits plus ½ plus 1/24 in circumference; it has a capacity of 77 quinariae plus 4/12 plus 1/24 plus 2/288; is not in use.

  [62] Fistula centenaria: diametri digitos XI = Ò ‘ VIIII, perimetri digitos XXXV = = Ò £ , capit quinarias octoginta unam = = £ ‘ X. Apud aquarios habebat diametri digitos XII, capacitatis quinarias nonaginta II.

  [62] The 100-pipe: 11 digits plus 3/12 plus 9/288 in diameter; 35 digits plus 5/12 plus 1/24 in circumference; it has a capacity of 81 quinariae plus 5/12 plus 10/288. With the water-men it had a diameter of 12 digits; having a capacity of 92 quinariae.

  [63] Fistula centenum vicenum: diametri digitos duodecim = = ‘ VII, perimetri digitos XXXVIII S = = , capit quinarias LXXXXVII S = Ò . Apud aquarios habebat diametri digitos XVI, capacitatis quinarias centum sexaginta tres S = = Ò , qui modus duarum centenariarum est.

  SIGNORUM CONSPECTUS:

  * * * (lacuna)

  Ò (uncia)

  = (sextans)

  £ (semuncia)

  ‘ (scripulum)

  [63] The 120-pipe: 12 digits plus 4/12 plus 6/288 in diameter; 38 digits plus ½ plus 4/12 in circumference; it has a capacity of 97 quinariae plus ½ plus 3/12. With the water-men it had a diameter of 16 digits, having a capacity of 163 quinariae plus ½ plus 5/12, which is the measure of two 100-pipes.

  LIBER SECUNDUS

  BOOK II

  [64] Persecutus ea quae de modulis dici fuit necessarium, nunc ponam, quem modum quaeque aqua, ut principum commentariis comprehensum est, usque ad nostram curam habere visa sit quantumque erogaverit; deinde quem ipsi scrupulosa inquisitione praeeunte providentia optimi diligentissimi Nervae principis invenerimus. Fuerunt ergo in commentariis in universo quinariarum decem duo milia septingentae quinquaginta quinque, in erogatione decem quattuor milia decem et octo: plus in distributione quam in accepto computabatur quinariis mille ducentis sexaginta tribus. Huius rei admiratio, cum praecipuum officii opus in exploranda fide aquarum atque copia crederem, non mediocriter me convertit ad scrutandum, quemadmodum amplius erogaretur, quam in patrimonio, ut ita dicam, esset. Ante omnia itaque capita ductuum metiri adgressus sum, sed longe, id est circiter quinariarum decem milibus, ampliorem quam in commentariis modum inveni, ut per singulas demonstrabo.

  [64] Having detailed those facts which it was necessary to state with reference to the ajutages, I will now set down what discharge each aqueduct, according to the imperial records, was thought to have up to the time of my administration, and also how much it actually did deliver; then the true measure, which I reached by careful investigation, acting on the suggestion of that best and most industrious emperor, Nerva. Now there were, in the aggregate, 12,755 quinariae set down in the records, but 14,018 quinariae actually delivered; that is, 1,263 more quinariae were reported as delivered than were reckoned as received. Since I considered it the most important function of my office to determine the facts concerning the water-supply, my astonishment at this state of affairs stirred me profoundly and led me to investigate how it happened that more was being delivered than belonged to the property, so to speak. Accordingly, I first of all undertook measurements of the intakes of the conduits and discovered a total supply far greater — that is, by about 10,000 quinariae — than I found in the records, as I shall explain in connection with each aqueduct.

  [65] Appiae in commentariis adscriptus est modus quinariarum octingentarum quadraginta unius. Cuius aquae ad caput inveniri mensura non potuit, quoniam ex duobus rivis constat. Ad Gemellos tamen, qui locus est infra Spem Veterem, ubi iungitur cum ramo Augustae, inveni altitudinem aquae pedum quinque, latitudinem pedis unius dodrantis; fiunt areae pedes octo dodrans, centenariae viginti duae et quadragenaria, quae efficiunt quinarias mille octingentas viginti quinque; amplius quam commentarii habent quinariis nongentis octoginta quattuor. Erogabat quinarias septingentas quattuor; minus quam in commentariis adscribitur quinariis centum triginta septem, et adhuc minus quam ad Gemellos mensura respondet quinariis mille centum viginti una. Intercidit tamen aliquantum e ductus vitio, qui cum sit depressior, non facile manationes ostendit, quas esse ex eo apparet quod in plerisque urbis partibus probata aqua observatur, quae ex ea manat. Sed et quasdam fistulas intra urbem inlicitas deprehendimus. Extra urbem autem propter pressuram librae, cum sit infra terram ad caput pedibus quinquaginta, nullam accipit iniuriam.

  [65] In the records Appia is credited with 841 quinariae. A gauging of this aqueduct could not be taken at the intake, since there it consists of two channels. But at The Twins, which is below Spes Vetus, where it joins with a branch of Augusta, I found a depth of water of 5 feet, and a width of 1¾ feet, making an area of 8¾ square feet, twenty-two 100-pipes plus a 40-pipe, which makes 1,825 quinariae, — more than the records would have it by 984 quinariae. It was delivering 704 quinariae, — 137 quinariae less than credited in the records; and, furthermore, 1,121 quinariae less than given by the gauging at The Twins. A considerable amount of this, however, is lost by leaks in the conduit, which, being deeply buried, does not clearly exhibit them. And yet their presence is plainly indicated by the fact that in very many parts of the City excellent water is met with, which leaks from that aqueduct. But we also detected some illicit pipes within the City. Outside the City, however, on account of the depth of the level, which at the intake is 50 feet underground, the conduit suffers no depredations.

  [66] Anioni Veteri adscriptus est in commentariis modus quinariarum mille quingentarum quadraginta unius. Ad caput inveni quattuor milia trecentas nonaginta octo praeter eum modum qui in proprium ductum Tiburtium derivatur, amplius quam in commentariis est quinariis duobus milibus octingentis quinquaginta septem. Erogabantur antequam ad piscinam veniret quinariae ducentae sexaginta duae. Modus in piscina, qui per mensuras positas initur, efficit quinariarum duo milia trecentas sexaginta duas. Intercidebant ergo inter caput et piscinam quinariae mille septingentae septuaginta quattuor. Erogabat post piscinam quinarias mille trecentas quadraginta octo; amplius quam in commentariis conceptionis modum significari diximus quinariis sexaginta novem; minus quam recipi in ductum post piscinam posuimus quinariis mille decem quattuor. Summa quae inter caput et piscinam et post piscinam intercidebat quinariae duo milia septingentae octoginta octo, quod errore mensurae fieri suspicarer, nisi invenissem ubi
averterentur.

  [66] Old Anio is credited in the records with the amount of 1,541 quinariae. At the intake I found 4,398 quinariae, exclusive of the quantity which is diverted into the special conduit of the Tiburtines, — 2,857 quinariae more than is recorded. There were distributed 262 quinariae, before the aqueduct reaches its settling-reservoir. The quantity at the reservoir, determined from the gauges placed there, was 2,362 quinariae, so that 1,774 quinariae were lost between the intake and the reservoir. Down-stream from the settling-reservoir, 1,348 quinariae were delivered, — more than we have stated to be the capacity according to the records by 69 quinariae, but less than we have shown was received into the conduit from the settling-reservoir by 1,014 quinariae. The total which was lost between the intake and the settling-reservoir, amounted to 2,788 quinariae, which I should have suspected resulted from an error of measurement, had I not discovered where it was diverted.