The archæology of Rome, Part 8

by John Henry Parker

		SUPPLY.		SUMMARY OF DISTRIBUTION.
No.		As given in the Commentaries.	Measured at the head.	Outside City.	Inside the City.	Regiones served.	No. of Castella.
		quin.	quin.	quin.	quin.
I.	Appian	841	1825	5	699	II. VIII. IX. XI. XII. XIII. XIV.	20
II.	Anio Vet.	1541	4398	573	1508½	I. III. IV. V. VI. VII. VIII. IX. XII. XIV.	35
III.	Marcian	2162	4690	261½	1472	I. III. IV. V. VI. VII. VIII. IX. X. XII. XIV.	51
IV.	Tepulan	400	445	114	331	IV. V. VI. VII.	14
V.	Julian	649	1206	206	548	II. III. V. VI. VIII. X. XII.	17
VI.	Virgo	652	2504	200	2304	VII. IX. XIV.	18
VII.	Alsietine	——	——	392	——	Outside the city and the XIV. in the Naumachia.	—
VIII.	Claudian	2855	4607	685 }	3498	United within the city, and distributed throughout the XIV. Regiones.	92
IX.	Anio Nov.	3263	4738	728 }
		12,363	24,413	3164½	10,360½		247

	DETAILS OF DISTRIBUTION.			DETAILS OF THE PUBLIC SERVICE.
	Imperial.	Private.	Public.	Castra.		Public Works.		Munera.		Laous.
	quin.	quin.	quin.		quin.		quin.		quin.		quin.
I.	151	194	354	1	4	14	123	1	2	92	226
II.	66½	490	503	1	50	19	196	9	88	94	218
III.	116	543	439	4	41	15	41	12	104	113	253
IV.	42	237	50	1	12	3	7	—	—	13	32
V.	18	196	383	3	69	10	181	3	67	28	65
VI.	509	338	1167	—	—	16	1380	2	26	25	51
VII.	354	138	—	—	—	—	—	—	—	—	—
VIII.	} 1793	1506	1012	9	149	18	384	12	107	226	482
IX.
	3049½	3642	3908	19	325	95	2312	39	394	591	1327

Buecheler, in his edition of Frontinus, pp. xi., xii., xiii., explains the mathematical part of chap. 78 differently from Poleni and Dederich[153].

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.

The base measure chosen was the “quinary,” so called (according to the most natural derivation) because its diameter was five quarter-digits. And to this basis are reduced some twenty different moduli, to which the names were given of senary, septenary, octonary, denary, duodenary, and so on up to centenary. The reduction of these seems to be tolerably accurate according to the system which he pursues, and making allowance for transcribers’ errors. But either the relation of the circumference to the diameter of a circle had not been worked out to the same extent to which it has been in later times, or Frontinus considered the ratio adopted sufficient for his purpose. One of his calculations stands thus: he is measuring the Appian at a point where it is joined by a later branch; it had been assigned in the register as giving 841 quinaries: he says—

“I found the depth of the water five feet, and its breadth one foot and three quarters, which gives an area of eight feet and three quarters. This is equal to twenty-two centenaries and a quadragenary, which make 1,825 quinaries, or 984 quinaries more than is given in the Commentaries[157].”

Each centenary is shewn elsewhere to contain 81 quinaries and a fraction, and therefore 22 would give 1,792 in quinaries and a fraction. The quadragenary is marked to contain 32 quinaries and a fraction. Together, therefore, the 1,825. Now the area of each quinary, according to the system of Frontinus, would be the square of its diameter (i.e. 1¼ digit), multiplied by ¹¹⁄₁₄ (the ratio already ascertained). This equals ²⁷⁵⁄₂₂₄, which, multiplied by 1,825, produces 2,240½ digits (nearly). Finally, the area of 8¾ square feet, reduced to square digits, gives 2,240[158].