Complete Works of Frontinus

by Frontinus

  [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] 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] 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 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] 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] 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] 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 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 quinariae 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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.

  BOOK II

  [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] 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] 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.

  [67] In the records Marcia is credited with the quantity of 2,162 quinariae. Gauging it at the intake, I found 4,690 quinariae, — 2,528 quinariae more than appear in the records. There were delivered, before it reaches the settling-reservoir, 95 quinariae; and 92 quinariae were given to supplement Tepula; likewise 164 to Anio. The total delivered before the settling-reservoir is reached, was 351 quinariae. The quantity which is computed at the reservoir from the gauges set up there, along with what is carried around the reservoir and received in the same channel on arches, is 2,944 quinariae. The aggregate of what is delivered above the reservoir or is received on arches is 3,295 quinariae, — more than is set down in the scheduled capacity by 1,133 quinariae, and less than given by the gaugings made at the intake by 1,395 quinariae. After passing the reservoir, it delivered 1,840 quinariae, — 227 quinariae less than we said was set down in the scheduled capacity, and 1,104 quinariae less than is taken from the reservoir upon the arches. The aggregate of what was lost either between the intake and the reservoir or downstream from the reservoir, was 2,499 quinariae, the diversion of which, as in case of the other aqueducts, we discovered at several places. For that there is no lack of water is manifest also from the fact that at the intake, besides the volume which we noted that we found from the capacity of the conduit, over 300 quinariae are wasted.

  [68] Tepula is credited in the records with 400 quinariae. This aqueduct has no springs; it consists only of some veins of water taken from Julia. Its intake is therefore to be set down as beginning with the Julian reservoir, for from this it first receives 190 quinariae; then immediately thereafter 92 quinariae from Marcia, and further from New Anio at the Epaphroditian Gardens 163 quinariae. This makes in all 445 quinariae, — more than the records show by 45 quinariae, — which appear in the
delivery.

  [69] Julia is credited in the records with a measure of 649 quinariae. At the intake the gaugings could not be made, because the intake is composed of several tributaries. But at the sixth mile-stone from the City, Julia is wholly taken into the settling reservoir, at which place its volume, according to the plainly visible gauges, amounts to 1,206 quinariae, — more than set down in the records by 557 quinariae. Besides this, near the City, behind the Gardens of Pallas, it receives from Claudia 162 quinariae, making the whole number of quinariae received by Julia 1,368. Of this amount, it discharges 190 into Tepula, and delivers on its own account 803 quinariae; from this we get a total of 993 quinariae which it delivers, — more than the records credit by 344 quinariae; less than we set it down as having at the reservoir by 213, which is precisely the amount we found diverted by those who were taking water without a grant from the sovereign.

  [70] Virgo is credited in the records with a measure of 652 quinariae. I could not take a gauging of this at the intake, because Virgo is made up of several tributaries, and enters its channels with too slow a current. Near the City, however, at the seventh mile-stone, on the land which now belongs to Cejonius Commodus, where Virgo has a greater velocity, I made a gauging, and it amounted to 2,504 quinariae, — 1,852 quinariae more than was set down in the records. The correctness of our gauging is very easily proved; for Virgo discharges all the quinariae which we found by gauging, that is, 2,504.

  [71] The measure of the capacity of Alsietina is not set down in the records, nor could it be accurately arrived at under present conditions, because [it receives] from Lake Alsietinus, and afterwards in the vicinity of Careiae from Sabatinus as much water as the water-men arrange for. Alsietina delivers 392 quinariae.