Very few consecutive milestones have been found from which to deduce the foot. From one mile in the Appian way, and from two different ones between Nismes and Beaucairo, the foot has been deduced to be and 130.51 lines. From various recorded distances between towns, subject to the difficulty of knowing precisely from what parts of them the miles were measured, the foot has been found to be 132.34, 128.42, 130.99, 129-31, lines. D'Anville, from a collection of such measures, fixes it at 130'8 lines.
A specimen of the congius is yet remaining, which, by an inscription, is declared to have been placed in the Capitol by Vespasian as a standard. The congius is the eighth part of the amphora, or cubic foot. By ascertaining the weight of water which this contains, the foot was estimated by various observers at 131'15, and 132'41 lines. From the length of the foot drawn upon the congius itself have been obtained 132.8, 133.5 lines. From another congius preserved at Paris, Auzout found 134'18 lines for the Roman foot. ' There are two obelisks at Rome, which were brought by Augustus from Heliopolis. Pliny gives the height of these in feet, or rather, the height of the higher and the defect of the lower from it. Measure ment proves that, with respect to the higher, the number of Pliny must be corrupt ; but from his difference between the two, as com pared with the measured difference, the Roman foot is 137-19 lines.
The method of ascertaining the foot by buildings is as follows : Any remarkable length, such as that of the whole front of a building, being known nearly in lloman feet, is presumed to be exactly that number of feet which it must be nearly. This supposes that the Roman architects were in the habit of choosing exact numbers of feet when there was no particular reason for breaking a foot. Raper (' PhiL Trans.,' 1760) proceeds in the manner of which the following is an instance:-11e finds the distances between the columns in the temple of Fortuna tiring to be 91106 English feet. If this be an exact number of Roman feet, it must be 10; we know enough beforehand of the Roman foot to say it cannot be 9 or 11. Conse quently, if the distance between these columns be a whole number of feet, the foot must be. of the English foot. By processes of this sort, Or-eaves found 131'50 lines, La Hire 131.0 and 132-1, La Condamine 1309, Jacquier and 131'14. Raper, who went more into this subject than the others, found by different buildings 131-14, 13190, 131'10, 131.05, 131-16, 131.05, and 131-15 for the mean. Wurin, from the Verona amphitheatre, adds Raper thought he observed that the buildings subsequent to the time of Titus give a shorter foot than their predecessors : from instances he gets 13015, 130.33, with a moan of He refers the change to the destruction of the Capitol (where the standards were kept) in the time of Vitelliue.
From all these data Raper's average, adopted by \Verne is 131.15 French lines for the ancient foot, or English inches or '971 English feet. But Sir 0. Shuckburgh made a careful review of the three best modes of obtaining the required result, namely, rules, build ings, and tombs, and obtained -9672, -9631, 9696 of a foot English. (Young's ' Lectures,' ii. 153.) The mean of these is feet, or 11.6196 inches. Again, if we take a mean of the results given by others, namely, Bernard .970, Picard and Greaves Folkes 966, Raper -970, we have also 9683. We take then the Roman foot at 11'62 English inches, which is represented far within the probable limits of error by the following :-61 English feet make 63 Roman feet. We are well aware that eminent authorities of late years prefer 11.65 inches for the Roman foot, but we like to keep as near to the foot-rules as we can, consistently with giving due weight to other modes. Indeed, the question between 11'62 and 11.65 cannot be settled by authority, but must be decided by closer appreciation than has yet been made of the probabilities of the different methods.
The Roman measures of length may this be considered, we fully believe, to be as well known to us as they were to themselves. The
same cannot be said of the measures of weight. All writers agree that the amphora, or cubic foot, weighs 80 pounds of wine ; but it is also said that they considered wine to be of the same weight as water. We have no means of ascertaining the specific gravities of their wines ; those of our own vary from -99 to 194, water being taken as 1. But there is one very obvious consideration which, we believe, has escaped notice. No metrologist has given the Romans credit for seeing that water would do just as well to make comparisons and adjust standards by, as wine, believing, as they did, that both are of the saute weight. If wo suppose then that they preferred to spill water rather than wine, and assume inches for the foot, we have 1568984 cubic inches " English, in the amphora, or imperial gallons, or 56586 pounds averdupois of water. if the Roman pouud be the 80th part of this, it is '7073 pounds averdupois, or '8595 pounds troy. This is 4951 grains, or 60391 French grains. Now, according to Wurm, Bud sus made it 7200 French grains, Capellus and Rom6 do L'Isle 6048, Auseut 6220, Eieentielnnid 6210, Dupuis 6300, Leblanc and Do la Nauze 6144, Paucton 6312, Arbuthnot 6395. Of these, those of Itomd de L'Isle and La Nauze, which come the nearest to 60391, were determined from weighing coins : but the most modern valuations deduced from coins give 5040 grains. On coins however we do not much rely. The congius of Vespasian, already mentioned, gave to different experi menters 6094, 6336, and 6276 Paris grains ; but it is most probable that the capacity of this vessel has been somewhat increased by rust. There are also some ancient weights in stone or metal, preserved in different places, from which De L'Imlo brings out 6071 and 6042 grains. Bat others make different results, whether from the coins or the weights; and the result of the whole seems to be, that the Roman pound cannot he more accurately stated than in the following words : "something more than seven-tenths of a pound averdupois." The Attic TALENT is said by many writers to be 80 Roman pounds. Now this being taken, as in the article cited, at pounds averdupois, gives '7119 of a pound averdupoia. Between '707 and or very near to one of these extremes, we have little doubt the truth really lies. Accordingly, the Roman uncia is much nearer to our ounce aver dupois than to our ounce troy; and many metrologists have supposed that the former was originally the uncia.
We have never had any means of knowing whether the fundamental points of connection between the Greek and Roman measures are exact or only approximate. These are, that the foot is longer than the Roman by one twenty-fourth, and the Philetnrian foot by one-fifth ; that the ns-rpassr is an amphora and a half, and that the amphora of water or wine weighs an attic talent. Taking these relations for granted, we have for the Greek foot 1210 English inches or 1•008 feet, for the Philetxrian foot inches, for the metretes gallons, and for the attic talent pounds averdupois. There is one stadium left at Athens [STADIUM] which is 630 English feet, giving for the Greek foot 1•05 feet English ; but there is not much dependence to be placed on the measure. Such buildings as have been examined at Athens, in the manner already described, give as a mean 136 69 Paris lines, or 12 1 4 English inches. We may therefore say that the Greek foot was longer than the English one by the tenth part of an inch. The statements then as to the relations between the Greek and Roman measures appear to have been tolerably exact, and our know ledge of the relations between our measures and theirs, though not sufficient for scientific comparison, is abundantly exact for the purposes of the classical student, far more so than could have been expected to have been attainable by those who remember that for a long period all means of comparison were lost.'