the following ajutages also up to the 20-pipe, the diameter of each pipe increasing by the addition of 14 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 113 digits.[1] Its capacity is [slightly] more than 113 quinariae, i.e. 112 twelfths of a quinaria plus 3288 plus 23 of 1288 more. The square digit, reduced to the circle is 1 digit plus 112 twelfths of a digit plus 172 in diameter; its capacity is 1012 of a quinaria. The circular digit is 1 digit in diameter; its capacity is 712 plus 12 twelfth plus 172 of a quinaria.[2]
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
- ↑ Cf. 38 ff.
- ↑ Frontinus's fractions and the symbols which represent them are as follows. The total value in each case is the sum of the various members.
Uncia 112 𐆑 or · Sextans 16 𐆐 or Z Quadrans 14 𐆐𐆑 or :· Triens 13 𐆐𐆐 or :: Quincunx 512 𐆐𐆐𐆑 Semissis 12 S Septunx 712 S𐆑 Bes 23 S𐆐 Dodrans 34 S𐆐𐆑 Dextans 1012 S𐆐𐆐 Deunx 1112 S𐆐𐆐𐆑 Semuncia 12 · 112 (124) S̲ or 𐆒 Scripulus 1288 ℈ He also uses Sescuncia, 112×112, (or18); Duella, 136; Sicilicus, 148; and Sextula, 172; and depends on combinations of these to express exact terms. Owing to corruptions in text, Frontinus's figures are often at variance with obvious facts.
