Page:Frontinus - The stratagems, and, the aqueducts of Rome (Bennet et al 1925).djvu/423

 the following ajutages also up to the 20-pipe, the diameter of each pipe increasing by the addition of $1⁄4$ 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.

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 readilv 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 $1 1⁄3$ digits. Its capacity is [slightly] more than $1 1⁄3$ quinariae, i.e. $1 1⁄2$ twelfths of a quinaria plus $3⁄288$ plus $2⁄3$ of $1⁄288$ more. The square digit, reduced to the circle is 1 digit plus $1 1⁄2$ 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 $1⁄2$ twelfth plus $1⁄72$ of a quinaria.

 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 