VOL. LI.] PHILOSOPHICAL TRANSACTIONS. 4S() 



Greaves. Auzout. Diff. Diff. per foot. 



The Statilian foot 972 969. 9(y ~ 2.04 2.1 



'1 he braccio of Florence ... 1913 1908.84 — 4. i6 2.18 



The braccio of Siena 1974 1973.2 1 — • 0.79 0-4 



Paetus's palm 732 12>\.^b — 0.65 0.89 



All these differences fall the same way, and show that Greaves's London foot 

 bore a less proportion to Auzout's Paris foot than that of 1000 to 1065.4. 



After thus examining many other measures of different things, as taken by 

 the modern philosophers, Mr. R. thence concludes : All that can be determined 

 from such uncertain and discordant data, as here collected, is a measure that 

 shall probably be neither the greatest nor the least magnitude of the Roman 

 foot. And for this he takes a mean from all the measures above recited, which 

 is nearly 968 thousandth parts of the London foot. 



Before entering on the examination of the ancient buildings it may be proper 

 to say something concerning the nature of the evidence to be expected from 

 them. All buildings are planned and executed by some measure of the country 

 where they are built. At Rome this measure was the foot, which was divided 

 by the workmen into 4 palms, and each palm into 4 digits.* 



If the Roman buildings were correctly executed, and we had the true dimen- 

 sions of their several parts in any known measure, some divisors consisting of 

 Roman feet, and parts of those feet, applied to these measures, must, in the 

 same building, give the same quotient to all ; and this quotient will be the mea- 

 sure of the foot, by which that building was constructed, in parts of the known 

 measure. Therefore, where a range of simple divisors, applied to the principal 

 parts of any building, give as nearly the same quotient as can be expected from 

 the common inaccuracies of workmanship, we may reasonably conclude that 

 these divisors were the architects' numbers ; and the foot derived from them, 

 that by which the building was constructed. 



As an architect cannot be supposed to be limited to a few digits in the extent 

 of the front, or of the depth of large buildings, it is probable such measures 

 consisted of whole feet. These and the diameters of circular buildings Mr. R. 

 calls prime measures. In all large prime measures, the preference is to be given 

 to a round number for the divisor ; as it is more probable a building should be 

 designed for 100 feet in front than for 99 to 101 : and because the passus was 

 5 feet, Mr. R. reckons any multiple of 5 a round number. 



■" Vitruvius, lib. 3, c. 1. Frontinus de Agrorum Qualit. Both these authors are technical writers, 

 and give this as the division used by workmen 5 and the ancient foot-rules are so divided. They both 

 mention the duodecimal division, which seems to have been used by the vulgar ; for the Romans 

 divided every integer into i2 unicae. — Orig. 



VOL. XI. 3 R 



