342 ON ROMAN AQUEDUCTS. 



in the case of a centenaria to 60 in that of a quinaria. It will 

 be observed that these weights and the intermediate ones men- 

 tioned in the same passage are proportioned to the corresponding 

 widths, which indicates that the lead employed was always of 

 the same thickness. We see from these statements that a strip 

 of lead 10 feet long and 16 digits wide would weigh 192 Ibs. ; 

 192 being to 16 as 12 to 1. Now it is not necessary to convert 

 this number of Roman pounds into English pounds, and simi- 

 larly the digits into inches, in order to obtain the result we 

 seek. We may make use of a method which, if not perfectly 

 accurate, has at least the advantage of not depending on any 

 experimental comparison of ancient and modern standards. For 

 we know that the Eomans reckoned 80 Ibs, as the weight of a 

 cubic foot of water. The specific gravity of lead is about 11*4; 

 but as lead is seldom pure, and when alloyed is alloyed with 

 substances lighter than itself, we will take that of the pipes 

 at 11. A cubic foot of lead will therefore weigh 880 Ibs., and 

 Iby what we have just seen the weight of a prism whose base 

 is a square foot and height the thickness sought will be (16 

 digits being of course equal to a foot) 19*2 Ibs. Dividing the 

 latter number by the former, and multiplying the quotient by 16, 

 we obtain the .thickness of the lead in digits : it is approximately 

 0'35. Subtracting this from the diameter corresponding to a 

 circumference of 5 (that is, from 1*59, the ratio of the circum- 

 ference of the diameter being taken at 3*14), there remains for 

 the diameter of the bore l*24 r or within a 100th of a digit of 

 the 5 quarter digits assigned by Frontinus to the diameter 

 of the quinaria r which is a nearer coincidence than we were 

 entitled to expect. So far therefore from the statement of 

 Yitruvius being contradicted by that of Frontinus, they appear 

 to be in perfect harmony, the quinaria being at once the pipe 

 made of a strip of lead 5 digits in width, and that whose bore 

 was f of a digit. Not so, however, the other moduli of the 

 system. The vicenaria of Frontinus is not that made of a strip 

 of lead 20 digits in width, but that whose bore is equal to 20 

 quarter digits. The discrepancy between the two things is 

 not inconsiderable, as may be seen by a little calculation. The 

 truth is, that the nomenclature used with reference to the 

 water supply of Rome, appears to have been very unsettled. 

 We find in the treatise of Frontinus traces more or less deve- 



