ON ROMAN AQUEDUCTS. 343 



loped of four different systems ; that of Vitruvius is a fifth ; and 

 there are certain exceptional cases mentioned by Frontinus in 

 speaking of the frauds of the aquarii, which it is not very easy 

 to connect with any of the five. In the midst of all this com- 

 plexity it is well to have one point fixed, namely, the historical 

 significance of the name quinaria applied to what appears in 

 Frontinus as the fundamental modulus to which in practice 

 all others were referred. This I think has been effected by 

 the considerations just suggested, and it is curious to remark 

 that neither Frontinus nor**any one else was likely to have 

 fallen on them. He was probably aware of the real state of 

 the case, but if the difficulty suggested by Dureau de la Malle 

 had occurred to him, he could only have got rid of it by actual 

 measurement, and not by a calculation founded on the specific 

 gravity of the material employed. In conclusion, it may be 

 well to observe that there are many cases in which the un- 

 certainty arising from the experimental comparison of ancient 

 and modern standards may be avoided: for instance, if it is 

 stated that a modius of a particular kind of grain weighed 26lbs. 

 (I refer of course to what Pliny says of the far of Clusium), 

 we may determine at once what an imperial bushel of it would 

 weigh by very simple considerations. The congius of water 

 like the gallon weighed lOlbs., and therefore i a congius 

 and a gallon are filled with the same substance, the former 

 will weigh, whatever the substance may be, as many Roman 

 pounds as the latter weighs pounds avoirdupois. Now the 

 modius is 3 congii, and the bushel 8 gallons, and consequently 

 the grain of which Pliny speaks would weigh 69 Ibs. and a 

 third the bushel. This is more than our best English wheat, 

 but some specimens of Australian wheat have been known to 

 weigh as much as 70 Ibs., and it is said that in Spain this 

 weight is not unusual. Another point of interest suggested 

 by the statement of Vitruvius is the comparative thickness 

 of Roman and English sheet lead. By the process of milling, 

 that is, of rolling a plate of lead between heavy rollers whose 

 distance is gradually diminished as the sheet becomes thinner, 

 the weight corresponding to a given surface may be reduced 

 much below the minimum possible in the old process of casting. 

 Thus milled lead sometimes weighs only 4 Ibs. in the square 

 foot. But it is more natural to compare the Roman lead which 



