Page:Frontinus - The stratagems, and, the aqueducts of Rome (Bennet et al 1925).djvu/421

in most parts of Italy; inches are the standard in…Now the digit, by common understanding, is 1/16 part of a foot;^[1] 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.^[2]

Later on, an ajutage called a quinaria^[3] came into use in the Citv, 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. But this is indefinite, because the plate, when made up into a round pipe, will be extended on the exterior surface and contracted on the interior surface. The most probable explanation is that the quinaria^[4] received its name from having a diameter of 5/4 of a digit, a standard which holds in

1. The Roman foot measured 11∙6 English inches, 0∙296 m
2. The difference between the areas of a square digit and a round digit whose diameter is equal to the side of the square digit is easily seen:
3. The quinaria was a measure not of volume but of capacity, i.e. as much water as would flow through a pipe one and a quarter digits in diameter, constantly discharging under pressure. "A quinaria was about 5,000 or 6,000 United States gallons per twenty-four hours, plus or minus 2,000 or 3,000 gallons, according to circumstances, favourable or unfavourable" (Herschel).
4. i.e. "a fiver."