Novae erogationis ordinatio: Frontinus, Domitian, Nerva, and the Aqua Traiana

Appendix 1: The law and its limits

Frontinus’ De aquaeductu projects an alarming state of corruption tantamount to racketeering. But exactly who or what had suffered from the described abuses in a manner that would sway a judge, Frontinus doesn’t say, except in the vaguest terms.^[148] Most likely he was relying on the century-old Lex Quinctia and similar statutes as a quick reference to determine what practices violated the law. The problem is that all the most actionable violations seem to have happened at the hands of the state’s watermen; they designed and operated the grift. And, because they purportedly sold water illicitly to private customers on a fairly large scale (see Appendix 2), they may have assessed and collected the payments in a manner that emulated official transactions such as monthly bills, duly recorded in ledgers back at headquarters.^[149] The alternative prospect of bagmen going door to door in the dead of night to collect fees seems too thuggish and precarious for these sophisticated operations. In other words, it was safer to lead the customers to believe they were doing everything by the book—which may very well have been true if the procedure simulated the legal one and the customers were none the wiser (or, if they were smart, looked the other way). The legal fault line lay at the other end of the pipes, often out of sight (and, it was hoped, out of mind).

For example, Frontinus reports a widespread practice by which the aquarii sold water to local businesses using a secret network of pipes extending out from punctures in the mains, all concealed under the pavement (115). The ringleader was an official nicknamed a punctis, an evident parody of the titles of high-level imperial officials such as ab epistulis or a libellis.^[150] The handiwork of this “undersecretary of punctures” sounds dreadfully corrupt, but since the watermen were affiliated with the state, and since some businesses must always have been hooked up to the system legally and presumably paid a comparable fee for the privilege (see Appendix 2), conditions may well have challenged even an inspector to distinguish between the two arrangements without prying up the pavement to find the breaches. Could the paying customers, then, be blamed for this situation? Perhaps not; though such arrangements are usually perceived by all parties to be shady, the agents of corruption—who understand the system and its vulnerabilities best—develop creative ways to launder them, whether on the books or off. But once Frontinus caught on to these pipe networks he tore them out wholesale, leaving the businesses high and dry: “How much water was purloined by this method I estimate by the considerable amount of lead that has been recovered from the extracted branches” (115.4: quantum ex hoc modo aquae surreptum sit, aestimo ex eo quod aliquantum plumbi sublatis eiusmodi ramis redactum est).

The harder cases, though, were likely to reside along the free-flow conduits where dedicated castella had accumulated over decades or even centuries to distribute water to adjacent properties. How easy was it to distinguish illicit pipes connected to these tanks? Suppose Frontinus’ agents could not prove that a tap had been added in a certain way or at a certain time. Could they then make a successful claim that it was illicit, let alone that it had impaired the system downstream? If not, then how did its status differ from a legal water concession such as a grant or a public utility connection, other than by its lack of clear documentation? He implies that inscriptions on the pipes signal the difference between legal and illegal concessions (105.4–5), but the illusion that Rome’s aqueduct system maintained a consistent policy for control stamps—let alone marks designating pipe capacity, on which Frontinus is particularly insistent—has been thoroughly demolished.^[151]

Appendix 2: Water as a paid utility at Rome

If we are to nuance the astounding total of 10,000 quinariae of lost and “stolen” water, and the character of its availability to future private consumers, we need to establish the distinction between grants and concessions to paying customers. In places Frontinus’ text hints at the widespread presence of legal taps in the system for which its users paid a fee: in essence, a utility. Here is one:

I shall now lay out the things that the curator aquarum must observe along with the law and the senatorial decrees pertaining to drawing up his procedure. Regarding the right to conduct water to private properties, they [i. e., the law and decrees] should be observed, lest anyone without a letter from Caesar, that is, without a license for public water, should draw it—and lest anyone who draws it should receive more than was licensed. Accordingly, then, we shall ensure that the volume (modus) we said we were acquiring [i. e., the 10,000 quinariae] shall apply to new outlets (salientes) and new grants.

Nunc quae observare curator aquarum debeat et legem senatoresque consulta ad instruendum actum pertinentia subiungam. circa ius ducendae aquae in privatis observanda sunt, ne quis sine litteris Caesaris, id est ne quis aquam publicam non impetratam, et ne quis amplius quam impetravit ducat. ita enim efficiemus ut modus quem adquiri diximus possit ad novos salientes et ad nova beneficia principis pertinere (103.1–3).

The term grant, both as noun and verb, has been used far too promiscuously in Frontinus translations and scholarship. It should be confined to translating the term beneficium, which quite consistently throughout the De aquaeductu references an exclusive imperial gift of free water to a favored beneficiary’s property. The broader practice of licensing available water (aqua impetrata), whether to elite grantees or to paying customers, is called adtributio (108, 129.4). Both groups alike had to obtain a water license (107: ius impetratae aquae) and thereby acquired the right to conduct water^[152] from a public aqueduct (ius aquae ducendae). This right permitted a piped water connection to a private property, business, or bath; the pipe had to come from a castellum (nobody was allowed to puncture a conduit directly, 106) and required a letter of permission from the emperor. Such a letter may sound daunting, but it need not constitute anything more exalted than a generic triplicate form signed by a functionary of the cura aquarum in the emperor’s name. Any offtake of aqua impetrata belonged to the broader category of outlets generically called salientes.^[153] In contrast, a grant required a much higher level of official sanction, including the active intervention of the emperor himself, the curator aquarum, a procurator aquarum, and an imperial freedman, among others (105; see above).

As 107–108 specifies, this ius impetratae aquae was extended to an individual in lieu of the property supplied with water, much as a water bill today is often directed to, and paid by, the occupant. But it was the owner (dominus), not the occupant (possessor), to whom the initial right was given. For grants only, the right passed to any new occupant of the property, though notionally, at least, probably not beyond the death of the original grantee or the alienation of the property.^[154]

Information about paid utilities is elusive at Rome, but the demand from industries, baths, and other operations for piped water was acute—and potentially profitable for the city.^[155] Clearly the watermen appreciated this demand, as they took every opportunity to sell illicit water to waiting customers (109.1–2, 114–115—in the guise of ordinary utility bills?), and in the case of the epidemic of punctured pipes in the paved urban core, specifically to businesses (115.3: negotiationibus). Yet Frontinus mentions paid utilities only in reference to past practice when overflow water was distributed to baths and fulleries for a fee, overseen by magistrates with the “right to give or sell water” (94–95: ius dandae vendendaeve aquae)—a right that he indicates remained in place even while the administrative apparatus changed around it.

Though the private right to conduct water had been “observed differently” (94.2: aliter observata) than in his own time, user fees—whether in the form of taxes on properties near aqueducts or utility bills for those legally hooked up to them—must always have been widespread at Rome. In many cities such arrangements not only served private industry but even brought the utility to private homes for no commercial or industrial purpose (Vitr. 8.6.2; Dig. 7.1.27.3; 19.1.41; 30.39.5). At Pompeii, Herculaneum, and Ostia, the integration of businesses and industries into the public water network is more visible; similar arrangements are known from other Roman cities, too.^[156] De Kleijn cleverly suggests that water utilities serving businesses at Rome are not as invisible as they seem; we have simply been misinterpreting an entire class of names on existing stamped pipes, those of nonelites who are not specified as the pipemaker.^[157] We might even conjecture that such freedmen as Moschus, a commentariis aquarum, or Salvius, tabularius aquarum, or Titus Flavius Verus, tabularius rationis aquariorum, were engaged in managing affairs of this sort.^[158]

Unfortunately Frontinus’ statistics for distribution of water from each aqueduct to private properties draw no distinction between free and paid concessions. The water delivered to privati at the time of his audit amounted to 57.7 % of the total in the suburbs (extra urbem) and 38.6 % of that in the regionary city.^[159] Bearing in mind that neither of these geographic totals overlaps with the 10,000 lost quinariae, and that imperial properties were kept apart from the category designated privatis, the volumes seem too high to account for grants alone.

Appendix 3: Measuring the quinaria

Frontinus’ standard unit of volumetric flow rate (typically measured today in liters per second or m³/day), the quinaria, has been variously estimated by some, dismissed as unmeasurable by others. Even if measurable, whether it could be measured consistently to represent a single value also remains in dispute. A third point of contention is whether Frontinus’ quinaria value for each aqueduct, presented as a single total rather than a range, was meaningful, given that the volume of ancient aqueducts varied greatly across the seasons and the years. Fourth, scholars disagree pointedly on whether we can reconstruct the value of the quinaria on the basis of existing evidence.^[160] Yet into this maelstrom we must descend, because almost every aspect of Frontinus’ veracity depends on it.^[161]

Many have observed that Frontinus’ few references to his method for measuring water volume make no sense and are internally inconsistent. This in turn has led to suspicions that nobody understood how to measure flow rate in antiquity, and that any attempts to do so were incompetent, inaccurate, or both. My own view is that the quinaria was measurable—and habitually measured—in a reasonably consistent and rigorous way; and that the watermen not only knew perfectly well how to do it, but also (just as important) understood what conditions prevented it from being done competently. The fact that the record books digressed so sharply from Frontinus’ own findings may reflect badly on record-keeping habits at the cura aquarum, but they are probably not the mark of technical ineptitude. Frontinus, so skillful in all things administrative and political, was a rank amateur in technical matters and never took the time to master them; if there is anything to be learned from this article, it is that his time was divided and severely limited. Yet he would not have fashioned his own statistics from fallacious personal illusions of how water flow should be measured. After all, he published his commentary for posterity, which would have plenty of opportunity to check his work. He would simply have recruited a loyal and honest castellarius to oversee his inspection rounds, taken the professional’s measurements on trust, gotten briefings on a few key field methods to burnish his credentials, and—there is really no inconsistency here—botched the methodology inadvertently when trying to transmit it in writing. Again: he was a man in a hurry.

It was well understood that an essential factor in volumetric flow was time. It is hard to imagine that anybody with a daily timed water concession did not understand this. What’s more, Frontinus himself acknowledges, in separate passages, the importance of flowing water’s velocity and its area in cross-section. Yet flow was never understood as the modern formula Q = VA, because, for lack of precise short-term timing devices, velocity could not be practically modeled in terms of time.^[162] Nonetheless, quantifying water volume by other means was easy enough, at least in a controlled environment such as a tank. It could be done by installing a horizontal row of short, valve-fitted pipes or ajutages of known internal cross-section (that is, multiples of the quinaria) in the tank’s wall at a fixed distance below a predetermined and uniformly accepted level.^[163] By shutting the offtake and opening the pipes one by one until the desired water level was reached and equilibrium of flow was established, one simply added up the cross-sections of the open pipes to get the total in quinariae.

It was also easy to intuit that perfectly viable proxies for the full volumetric discharge of water issuing from that tank could then be measured, and thereby standardized, by inserting a gauge—i. e., some kind of flowmeter—into an open-flow offtake channel directly downstream from the tank after the measuring pipes had been shut off and the offtake reopened. The gauge could, for example, be a swinging door inside a frame with the hinges at the top and a protractor at the side to measure the angle of deflection by the current: a simple velocity proxy similar to a graduated windsock. Given that every tank with continuous flow was likely to have a unique quinaria total, in each case the area of the flowing water’s cross-section—calculated as depth by width—had to be established in the offtake channel, the velocity measured with the flowmeter at the same place, and a table of values established: angles of deflection (i. e., velocities) down one side, flow cross-section areas across the top, and quinaria total, measured at the tank just upstream, representing the intersection of each pair of values. No timing device—indeed, no awareness of time—was needed to conduct these operations. Once a full table of velocity and cross-section values had been assembled, with their equivalents in quinariae, it could be used forever thereafter, at any point in any aqueduct where one of the standard cross-sections could be found. All this work had surely been done long before Frontinus arrived on the scene (as a standard unit, the quinaria had been around since Augustan times: Aq. 25), and the reference tables were doubtless already widely available to engineers doing their rounds of the system.^[164]

The quinaria, then, was a precise and standardized unit easily measured in aggregate at tanks or reservoirs. The aggregate amounts could then be converted to proxies measured in the channel downstream; these proxies could be used anywhere with a smooth flow and a canonical cross-section. Two questions remain. a) How precisely could flow be measured outside these contexts? b) How valuable were any such measurements, given the vagaries of seasonal and interannual flow? The answer to the first, obviously, is that accuracy depended on conditions: that is, a measurable cross-section of flow. If the cross-section was off the charts in scale, or the flow too turbulent for a consistent reading, or too shallow to allow the instrument’s immersion, no good measurement could be made. If it was simply irregular in size (i. e., falling somewhere between canonical values on the table), volume could still be estimated, but less accurately. Finally, it should be noted that the shape of the cross-section mattered, in that it created variable degrees of frictional resistance to the water’s laminar flow.^[165] Frontinus shows some awareness of the effects of friction, though his engineers surely could not precisely model or compensate for them (Aq. 35; see note 105). Most likely these effects were simply disregarded or the quinaria total recalibrated using a fudge factor.

Frontinus probably resorted to fudge factors of various kinds when making his lighting rounds with his engineer. Yet he is perfectly prepared to admit that in various places along the aqueducts—and especially at certain sources—the instrumentation or method of measurement lacked precision or rigor or could not be applied at all (65.1, 69.2, 70.2, 71.1). At one point the volume reading is questionable because the swiftness of the current underrepresents it (73.6). At other points, “the measurement is more certain” (certior est mensura) or “the measurements are unquestionable” (indubitatae mensurae sunt, 69.2, 70.3, 72.3). These judgments bespeak the professional evaluation of his engineer, not his own understanding of the rationale.^[166] Yet he was keenly aware of seasonal fluctuation to the extent that he took care to measure flow in the summer—carefully and repeatedly, across the whole system (74.3). These remarks alone signal that a precise and consistent quinaria unit existed and that the limits of its measurement were well understood—by the experts, if not by their boss.

The standard unit could easily be applied to measure flow under controlled circumstances within an existing aqueduct. Can we then estimate Frontinus’ quinaria in modern terms? Perhaps, but any attempt must necessarily be an approximation founded on physical evidence of the aqueduct channels themselves. My own estimate established the quinaria at 32 m³/day (0.74 l/sec) by applying Blackman’s maximum volume estimates for the four best-preserved Roman aqueducts (Marcia, Anio Vetus, Anio Novus, Claudia) to Frontinus’ statistics for each, which yields 35 m³/day, then subtracting about a tenth of the total to approximate normal conditions.^[167] Kessener’s more recent estimage favors a single, meaningful value for the quinaria, placing it somewhere within Blackman’s range of 30–35 m³/day.^[168] Other estimates deviate further from this range, but I shall demonstrate below why I believe Kessener’s range (into which my own estimate comfortably fits) represents an approximation of the true quinaria.

Keenan-Jones, et al. raise a legitimate concern. By applying Frontinus’ quinaria volume to Blackman’s maximum volume, the suggested value range may exaggerate mean flow due to seasonal variability.^[169] This criticism reflects deep skepticism that Frontinus’ single set of volumes for the aqueducts accurately represents the system overall, which was prone to seasonal fluctuation. Frontinus himself is aware of the problem; it is why he took measurements in the summer, when sources flowed less abundantly. Yet, on the one hand, he recognized and augmented a viable remedy for low flow that the system already enjoyed in abundance: redundancy. It is this robust feature of Rome’s system that minimized variability. In fact, his summer measurements proved surprisingly consistent across those months: “I myself, having made the measurements in July, ascertained that the volume recorded above of each and every line remained uniform thereafter for the entire summer” (74.3: ipse actis mensuris Iulio mense hanc uniuscuiusque copiam quae supra scripta est tota deinceps aestate durantem exploravi).

That is precious information as, for among other things, it confirms that the total volumes he recorded (Aq. 64–73), and from which all his statistics are derived, were the July volumes, and that they remained unchanged in August and September. Perhaps he is dissembling, or maybe he simply got lucky and took his measurements during an unusually wet summer: as we saw, a flood was recorded for the year 97 (a bare fact that says nothing about total rainfall over the year, let alone in the summer).^[170] But consider the site of the Curtian and Caerulian sources of the Aqua Claudia: here alone, he measured 1,600 quinariae of water going to waste—all of it issuing from a supplementary branch of the Marcia which ran nearby (72.7–8). If Frontinus’ engineers could quantify that excess, then it was manifestly being discharged from a controlled, measurable environment—probably an overflow basin. In drier months, that excess water could have been recaptured as needed to supplement reduced levels in the Marcia, the Claudia, and other lines. Additional interchanges in the system are known, either from Frontinus or from physical remains. At Grotte Sconce, the abundant Anio Novus, soon to be sourced from a dammed reservoir that would likely have maintained high volumes even in drought conditions, could divert water into any or all of three other lines: the Claudia, the Marcia, and the Anio Vetus.^[171] Finally, I would note that the extension of the Anio Novus back to the dam at Subiaco created a virtually drought-proof remedy for that line—which being the highest of all the eastern lines, could easily supplement all the others.