Page:Frontinus - The stratagems, and, the aqueducts of Rome (Bennet et al 1925).djvu/427

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Aqueducts of Rome, I. 30–32

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.^[1]

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.^[2] 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.

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 1/4 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 1/2 plus 1/24 of a digit, its capacity by 3 quinariae plus 1/4 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^[3] regularly receive water, the pipes are not diminished but enlarged! For to the diameter of the 100-pipe they add 2/3 plus 1/24 of a digit, and to the capacity, 10 quinariae plus 1/2 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 1/6.

↑ By successive additions of a quarter of a digit to the diameter of a quinaria, the diameter of the vicenaria becomes five digits or twenty quarter digits. The number of square digits in the cross section, therefore, would be $\scriptstyle \pi \left({\frac {1}{2}}\right)^{2}=19\cdot 6$ (almost twenty) square digits.
↑ Trajan is meant.
↑ The water-men.

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[1] By successive additions of a quarter of a digit to the diameter of a quinaria, the diameter of the vicenaria becomes five digits or twenty quarter digits. The number of square digits in the cross section, therefore, would be $\scriptstyle \pi \left({\frac {1}{2}}\right)^{2}=19\cdot 6$ (almost twenty) square digits.

[2] Trajan is meant.

[3] The water-men.

[1]

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