¹ De architectura VIII, 6Google Scholar.

² De aquis urbis Romae. I have used the text and facsimile of Herschel, , The two books on the water supply of Rome, Boston, 1899Google Scholar, and a microfilm copy of Poleni, , Frontini de aquaeductibus urbis Romae, Padua, 1722Google Scholar. The new Teubner edition by Kunderewicz (1973) I did not see until my work was substantially complete.

³ Ashby, T., The Aqueducts of Ancient Rome, Oxford, 1935Google Scholar.

⁴ Reina, V., Corbellini, G. and Ducci, G., Livellazione degli antichi acquedotti romani, Memorie della società italiana della scienza detta dei XL, Serie 3, vol xx (1917)Google Scholar (hereafter Livellazione).

⁵ van Deman, E., The building of the Roman Aqueducts, Washington, 1934Google Scholar.

⁶ I have, in preparing this paper, examined Ashby's papers on the aqueducts held by the British School at Rome. The major portion of this part of the papers consists of photographs; the item most pertinent to the present work is an annotated copy of Livellazione, but this contains little which has not been incorporated into his book. I am grateful to the British School for the opportunity to examine this collection.

⁷ E.g. Lanciani, R., Topografia de Roma antica, Rome, 1880Google Scholar; or de Montauzan, C. GermainLes aqueducs antiques de Lyon, Leroux, Paris, 1909, 335Google Scholar; the techniques used reflect not only their shortage of quantitative data but a more primitive state of development of the theory of flow in open channels. A more modern attempt is Jones, G. B. D., Blakey, I. J. and Macpherson, E. C. F. ‘Dolaucothi, The Roman Aqueduct’, Bulletin of the Board of Celtic Studies xix (1962), 78Google Scholar.

⁸ The carrying capacity of the Marcia, on my calculations, was modest enough. Marcia was, furthermore, spring-fed unlike Novus which was river-fed; the peak flows would almost certainly not occur together, even if the full output of the springs were enough to run Marcia full, which we do not know.

⁹ These are sections with a slope something below ‘average’ for Marcia. The effect of roughness tends to be less pronounced in sections of small slope; I used it here because this is a well-defined piece of aqueduct. (A roughness of 0,025 m represents a channel very heavily obstructed, e.g. by extensive weed, and is certainly too large for masonry or rock channels.)

¹⁰ I cannot agree with Jones (cited in n. 7) 79: ‘… Roman aqueducts, which were not, of course, channels of the open flow variety’. The presence of a roof is of no significance for the flow unless the water level increases so that the surface of the water reaches it.

¹¹ ‘Aquam quae Marcia appellatur duplicavi fonte novo in rivum eius inmisso’ boasts Augustus (Res Gestae 20). Frontinus' gauging technique, so frequently abused for being inaccurate, is incomprehensible if no variation in water depth were admitted.

¹² E.g. Ashby, , Aqueducts, 103–4Google Scholar. Surprisingly, to judge from the footnote on 104, Ashby appears here to contemplate that the specus was intended to operate as a pipe in spite of the opening, though the deposit shows that it did not do so usually.

¹³ de Montauzan, , Aqueducs de Lyon, 283Google Scholar.

¹⁴ Ashby, , Aqueducts, 221Google Scholar; Livellazione 27.

¹⁵ Ibid., 272.

¹⁶ There are some interpolations and omissions in the sequence of labels, so 167 points are plotted in Livellazione and not 165 as might be supposed.

¹⁷ Blackman, D. R., ‘On Measurements of Aqueducts’, MMEL 27Google Scholar, and ‘The Hydraulics of the Aqueducts at Rome’, MMEL 35, Department of Mechanical Engineering, Monash University, 1973Google Scholar. Not all of my speculations on the length of sections have been incorporated in the calculations here. Vetus is too short by 16 km, and Marcia by 12 km. Sections 154–58 of Marcia are certainly too short. In error, section 68 [147] was omitted from the calculations on Novus; these omissions do not alter the conclusions.

¹⁸ Of the extreme widths (i.e. greater than 1,5 m) note Vetus: nr 33 may be my misreading of Ashby—the rock-cut channel was perhaps lined which would reduce its width. Marcia: the extreme widths are all upstream of the serenae. Claudia: nr 59 has been scaled up from fig. 51 of Livellazione—a dubious procedure; nr 130, I cannot now find the source of this; nr 145, the value is an estimate from the stated width of the foundation; nr 85 is an error, as the value 1,68 is the height; nr 182 is from Livellazione, but it is not clear to which aqueduct it applies.

¹⁹ The great variability should be a warning against using the width of the specus in an isolated fragment for ascribing the fragment to any particular named aqueduct. See e.g. Panimolle, , Gli acquedotti di Roma antica, Rome, 1963, 53Google Scholar, who does this.

²⁰ Esperandieu, , Le Pont du Gard, Paris, 1968Google Scholar.

²¹ Ashby, , Aqueducts, 320Google Scholar.

²² Ibid. p. 319.

²³ Ibid. p. 318.

²⁴ de Montauzan, , Aqueducs de Lyon, 10Google Scholar; the widths are taken from pp. 56, 67, 69, 82, 87, 131, 296, 296 and 197 respectively.

²⁵ Foster, P., ‘The Roman Aqueduct at Dorchester’. Proc. of the Dorset Archaelogical Soc., 78 (1956) 79Google Scholar, which contains references also to earlier work of Coates, Richardson etc. on this aqueduct.

²⁶ Vitruvius VIII, 6, 1. Rose's reading of the text, which is accepted by Granger in the Loeb edition, is challenged by Montauzan, loc. cit., 167, who would preserve the reading in the MS ‘sicilicus’; this would make the Vitruvian minimum 0,2‰ instead of 0,5‰. An attractive feature of Montauzan's reading of Vitruvius is that there would remain only three cases on my reckoning for which the slope fell below Vitruvius' minimum. Fensterbusch, by interpolating ‹silicio ne plus› would have Vitruvius set upper and lower limits of 0,5 and 0,2‰; if this is the correct reading then Vitruvius fares still worse than presently as an hydraulic commentator. ‘‰’ is used to mean ‘parts per thousand’.

²⁷ M. Cetus Faventinus, De diversibus fabricis architectonicae. A text and a translation are given by Plommer, W. H., Vitruvius and later Roman building manuals. Cambridge, 1973Google Scholar. Slopes are discussed at §7.

²⁸ Palladius De re rustica. The text is not readily available, and the only editions I have seen are one edited by Merula and Colucia, published by Jensen in 1472, one of Gesnerus of 1734, and the old Teubner edition of 1898 by Schmitt; I have not seen the new Teubner version edited by R. H. Rogers. The pertinent part in Merula and in Schmitt reads ‘Si per planum veniet, inter centenos vel [sic] sexagenos pedes sensim reclinetur structura sesquipedem, ut vim possit habere currendi’ (IX, 11)Google Scholar; Gesnerus reads ‘sexagenos vel centenos’. This would give slopes of 15‰ or 25‰; de Montauzan's (loc. cit. 167, where the place quoted in Palladius is surely in error) unstated authority evidently has ‘centenos et sexagenos pedes’, which gives the figure he quotes of 9,4‰; there are no technical grounds for favouring either reading. The whole matter is absurdly sensitive to the vagaries of scribes.

²⁹ Anio Novus has an elevation of 250 m at Tivoli and of 68 m at its end. The direct route is about 20 millia passus = 2960 m, whence 6‰. The actual mean slope will be less as the route becomes more tortuous.

³⁰ I quote these mean values partly for form's sake. It must be clear that the overall slope depends on the total fall and the nature of the route chosen or forced. Thus, to compare these with recommended slopes in the literature, or even with values such as de Montauzan (loc. cit. in n. 7) quotes at 171 or Matthews (cited in n. 33) for the Gallic aqueducts is to miss the point; the topography around Lyon is quite different from that around Rome.

³¹ By ‘Frontinus' discharge’ I mean the value found by using Frontinus' discharge in quinariae and di Fenizio's estimate of the quinaria of 0,48 litres/s. (Di Fenizio, , ‘Sulla portata degli antichi acquedotti romani e determinazione della quinaria’, Giornale del genio civile, liv (1916) 277–331Google Scholar). No approbation for Frontinus or di Fenizio is thereby intended; this was a convenient method of choosing a trial discharge.

³² The observations are given by Ashby, , Aqueducts, 113Google Scholar. There is no hydraulic impediment to a limited stretch of channel with an uphill slope, but I would have been unwilling to suppose that such stretches would occur in surveyed channels. There appears, however, to be a well attested case, quoted by Matthews (cited in n. 33), so the possibility of its occurring in Marcia cannot be discounted; it remains, however, implausible, which is the view I have taken here. The adverse slopes and levels at Rottenburg (Samesreuther, E. ‘Romanische Wasserleitungen in der Rheinlander’, Berichte über die Romanische-Germanische Kommission, 1936, 98–101Google Scholar) pose problems even for a pipe flow, and are inadmissible for an open channel.

³³ Matthews, K. D., ‘Roman Aqueducts’ Expedition xiii (1970) 2–16Google Scholar. At 15 he quoted the depth, as determined by the deposit left at the water surface, to be 0,60 m. The dimensions of the specus given are 1,7 m wide by 2,5 m high. The width is unusual for Marcia (see Fig. 2) and not remarked on elsewhere; it is not included in my tabulations. On the assumption, presumably, of uniform flow a discharge of 1,6 m³/s is calculated; this is closer to my prediction of 1,4 m³/s than to Frontinus' value of 2,25 m³/s, but as a method of estimation suffers from the limitations discussed earlier. Note that the calculations suggest depths as small as 0,6 m only where the flow is rapid.

³⁴ See n. 31.