In order to regulate these several aqueducts, so that deflection in any part should be easily ascertained, means were provided for estimating the abundance of the water, and in this respect for its minuteness and clearness the treatise of Frontinus stands unrivalled, when compared with any work of ancient or even modern times. The mode of measurement is to take the area of a vertical section of the water flowing along the _specus_,—the object being to test each aqueduct by itself, and to see whether its proper supply was given or not. Had he been called upon to estimate the actual supply of the water, and not the relative, other points would have had to be taken into account, namely, the average fall of the aqueduct, from which to gather its velocity. On this, however, he does not touch. It must be borne in mind, also, that when Frontinus was appointed, the system had been long in force, and he had to follow the traditions and rules of his office. He made no revolution, he was simply a reformer. He tells us that in examining the books belonging to the office, he found certain measures given to certain aqueducts; these he had to verify, and a great part of his work is taken up in the account of his operations. To begin with, he is much troubled as to the measures employed. The _digitorum modulus_ (i.e. a pipe with a given measured orifice) is uncertain. There is the square digit and the round digit (in other words, a square pipe of which each side is one digit, and the round pipe of which the _diameter_ is one digit). As an instance of his accurate and clear expression, it may be worth while to quote his words on this point[154]:— “The measurement of the _Moduli_ is taken either by digits or inches. In Campania and in many places in Italy, the digit is used; in Apulia, the inch[155]. The digit, as all agree, is the sixteenth part of a foot; the inch, a twelfth part. But just as there is a different usage of inches and digits, so also there is no uniformity in the simple computation of the digit itself. There is one which is called the square digit, another the round digit. The square digit is _three-fourteenths greater_ than the round; the round is _three-elevenths smaller_ than the square, because the angles are taken off.” In this we obtain a key to most of his calculations[156], because they depend throughout upon the computation of the area of the circle.