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 mercantile commerce with each other, than was known to the Romans, must necessarily introduce 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 standard shows its figure to have been a cube; which adds probability to their testimony, 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 60 is equivalent to the tenth part of an inch in the foot: therefore no exact measure is to be expected from thence, even though the modern 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 standing 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

of any one of them with each other, which is the only way to discover the measure by which a building was constructed.

With this view therefore Mr. R. carefully examined the measures of the buildings contained in that treasury of ancient Roman architecture, entitled Les Edifices antiques de Rome, and published at Paris by Mons. Desgodetz in the year 1682. In order to this, it was first necessary to ascertain the proportion of the Paris foot (the measure used by this author) to some known English standard. The Paris foot is one 6th part of the toise in the Chatelet; which was renewed in the year 1668, and the new standard has continued in use ever since.

In the year 1742 the R. A. S. at Paris, at the request of the R. S. of London, sent over a measure of half the toise of the Chatelet; from which Mr. Graham determined the proportion of the Paris foot to that of London, to be as 1065.41 to 1000. Mons. le Monnier, of the R. A. S., from the same originals, found their proportion as 864 to 811, or as 1065.351 to 1000. The difference · is inconsiderable, and we may, without injustice to Mr. Graham's known skill and accuracy in these matters, suppose their true proportion to be as 1065.4 to 1000. Mr. Graham's measure of the London yard, together with that of half the toise of the Chatelet, are deposited in the archives of the R. S. at London; and of the R.A.S. at Paris; and whenever Mr. R. mentions the London foot, without specifying any particular standard of it, he would be understood to mean this measure. In this inquiry we are to seek a common measure to the several parts of each building, that shall not differ very widely from some assumed magnitude of the Roman foot: and though we might take this assumption from any of the ancient foot-rules now remaining, yet the nearer it is taken to the truth, the better guide it will be to us, and the more it will facilitate our inquiry. Now as a mean measure derived from these rules will probably be nearer the truth than either the greatest or the least of them, so one that shall include such other remains of antiquity, as have hitherto been made use of to discover the measure of the Roman foot, will be still more unexceptionable, as the writers on this subject are not agreed, which of the different authorities is to be preferred. The representations of this foot in sculpture are 4 in uumber; one on the sepulchral inonument of Cossutius, formerly in the Colotian gardens at Rome; another on that of Statilius, in the Belvedere; a 3d on that of M. Ebutius in the Villa Mattei; and the 4th on a marble, without incription, dug up of late years in the Via Aurelia, which being in the possession of the Marquis Capponi, is called by P. Revillas the Capponian foot. Most of the early writers on this subject have expressed their measure of the Roman foot by a diagram; and Snellius observing that the paper contracted in drying, after the impression was taken off, endeavoured to make a proper allowance for it. But Greaves, finding the measures of these figures to differ in different copies of the same impression, took another method;

and seems to have been the first that compared the original figures on the monuments of Cossutius and Statilius with a modern standard. This he did with such care and diligence, that his measures deserve a particular examination.

The London foot, which he used on this occasion, was taken from the iron standard of 3 feet in the Guild-hall, London; which having been long since lost or destroyed, we have nothing left to discover its true magnitude but the measures others have taken of it, and those which have since been taken of such magnitudes as Greaves had compared with his copy of it.

Snellius, from a measure sent him of this iron standard, determined the proportion of the Rhynland to the London foot, as 1000 to 968. The Rhynland foot, according to Picard, contains 696 such parts as the Paris foot contains 720: whence the proportion of the latter to this measure from the iron standard, is as 1065.4 to 997 nearly. Eisenschmid found the Rhynland foot to contain 1391.3 such parts as the Paris foot contains 1440; which gives 1065.4, to less than 9964, for the proportion of the Paris foot to that of the iron standard. Huyghens makes the Paris to the Rhynland foot as 144 to 139; whence the proportion of the former to Snellius's London foot, will be nearly as 1065.4 to 995. But there is reason to believe that Huyghen's measure of the Rhynland foot was too small. By these comparisons it appears that Snellius's measure of the London foot, from this iron standard, was at least 3 parts in 1000 shorter than Graham's London foot.

Our countryman Norwood, in 1635, measured the distance between London and York, in order to determine the length of a degree on the meridian; which he found to contain 367196 London feet of this iron standard. The French found the measure of a degree in the latitude 66° 20′, to be 57438 toises, and at the equator 56783. Hence the measure of a degree in 52° 44′ (the middle latitude between London and York) will be found to be 57276 toises, or 343656 Paris feet. These numbers give the proportion of the Paris foot to that of the iron standard, as 1065.4 to 997.1-, wanting somewhat less than 3 parts in 1000 of Graham's London foot.

Picard's paper De Mensuris, and another on the same subject by Auzout, printed with it, contain some measures which Greaves had before compared with his London foot. Both these papers were written after the renewal of the standard of the Chatelet in 1668. The former is so full of inacuracies and mistakes, that little use can be made of it; but Auzout's measures appear to be accurate; and as he seems to have taken his Paris foot from the toise in the Chatelet for this purpose, it was probably a correct measure of that standard.

Such of his measures as answer to Greaves's, are here reduced to thousandth parts of the London foot, reckoning his Paris foot to contain 1065.4 such parts.

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 dimensions 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 measure 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; 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 12 unica.-Orig.

The diameters of columns are of less authority than any other horizonta measures; not only on account of the difficulty of measuring them correctly, but because errors of workmanship, to which they are more liable than square measures, more sensibly affect the magnitude of the foot in small measures than in large ones.

Uprights, of any considerable height, are of less authority than horizontal measures, from the difficulty of taking them correctly; and being designed by modules, few of them answer well to the foot measure. But here we must except such shafts of columns as are of one block of marble; which seem to be as good authority as any part of a building: for the necessity of making them all exactly of the same length, must produce accuracy; and the doing this was no difficult piece of workmanship. Being likewise commonly (if not always) wrought at the quarry, to save expence in the carriage, they were probably bespoke to some simple measure; and we shall find all such shafts answer to some number of whole palms.

In this ingenious way then Mr. R. took the measures of the principal parts of a great number of the ancient Roman buildings, and divided them by the most -probable divisors, for the near length of the foot. These quotients fall mostly between the numbers 963 and 972, that is, of such parts as the London foot contains 1000. And at length Mr. R. concludes thus:

It appears from the measures of these buildings, that the Roman foot before the reign of Titus exceeded 970 parts in 1000 of the London foot, and in the reigns of Severus and Dioclesian fell short of 965. Whether this difference proceeded from any alteration in the standard, or from a false measure of it being got into common use, either before the reign of Titus or after, is uncertain. We have no account of any alteration made by law in the Roman standards after the Plebiscitum Silianum, quoted by Festus; but as great a difference as this might arise from their having been lost or destroyed.

They were kept in the capitol; and Rigaltius, from a passage in Hyginus, observes that the standard of the foot was deposited in the temple of Juno Moneta. Now the capitol was burnt no less than 3 times; first in the civil war of Sylla, then again when Sabinus was besieged in it by the troops of Vitellius; and the 3d time in that dreadful conflagration which happened in the reign of Titus. Whether the standards were destroyed in the first of these fires is uncertain; but they could hardly escape the fury and confusion of the 2d, when, according to Pliny, the temple of Juno Moneta seems to have been burnt to the ground. And if we may credit Xiphilin (whose account of the 3d is in some measure confirmed by Spartian), not only the temple of Jupiter Capitolinus, but those adjoining to it, were burnt down in the last.....

Vespasian rebuilt the capitol after the 2d conflagration, and restored the