486 l^HILOSOPHICAL TRANSACTIONS. [aNNO f/GO. 



larly the invention of the pendulum) have introduced among the moderns. Add 

 to this, that the different state of Europe, which has for some ages been divided 

 into many considerable kingdoms and sovereign states, independent of each 

 other, equally civilized, and carrying on a more constant and regular n^ercantile 

 commerce with each other, than was known to the Romans, must necessarily in- 

 troduce more frequent inquiries into the weights and measures of the different 

 states, and a more careful examination of the respective standards of each, than 

 the Romans could have any occasion for : and use in these matters is the parent 

 of accuracy. We can arrive at no greater certainty from the marbles than from 

 the foot rules. These indeed do not differ so widely from each other as the 

 rules ; which seems to be the reason why most of the writers on this subject have 

 given them the preference: but of the 4 that are extant, no 2 agree in the same 

 measure ; nor is the age of any one of them known : and as they were intended 

 for representations only, and not for use, their accuracy may reasonably be 

 doubted. 



Festus, Frontinus, and Rhemnius Fannius say, the side of the quadrantal, 

 which contained 8 congii, was a Roman foot. A standard congius of Vespasian 

 is still in being, and has been measured by several learned men ; but the foot 

 derived from it exceeds those on the marbles, and the greatest number of the 

 foot-rules so much, that Mr. Greaves could find no better way of accounting 

 for so great a difference, than by supposing what Festus and Fannius say (for he 

 does not quote Frontinus) to be a vulgar error : whereas the name of this stan- 

 dard shows its figure to have been a cube ; which adds probability to their testi- 

 mony, that its side was intended for the measure of the foot. 



The measures of public roads in the itineraries can be of little use in this 

 inquiry ; for they omit fractions, and we do not know whether the distances of 

 the towns are reckoned from the market-places or from the gates ; but a difference 

 of half a mile in 6o is equivalent to the tenth part of an inch in the foot : there- 

 fore no exact measure is to be expected from thence, even though the modem 

 mensurations of Cassini, Riccioli, and others, were more unexceptionable than 

 they really are. The distances between the ancient mile-stones are not liable to 

 these objections; and if a sufficient number of such as stand nearest to Rome 

 were carefully measured, their authority would be considerable. But it is not 

 found that any are now standing within 30 miles of that city, nor that any of 

 these have been measured, or even any in Italy; and provincial measures are not 

 of equal authority. 



There is still another method by which may be discovered the measure of 

 the Roman foot; which is from the remains of the ancient buildings now stand- 

 ing at Rome: and though many have made use of some single parts of them for 

 this purpose, yet no one has hitherto compared the measures of the principal parts 



