It will be observed that I can give no positive evidence for the length or breadth of the _as_. The pieces in the Museum are all fragments, and, even if there were any of them whole, they would not by any means decide the original _length_, although they would of course represent the _weight_. For as they are late, they would probably have been made at a time when the original rod was shrinking up into a more compact form, just as the Chinese bronze knives get shorter and thicker. But the fact remains that the _as_ was identified completely with the Roman _foot_ measure, the divisions being the same in each. We therefore may with great probability infer that the _as_ was originally a piece of copper a foot in length, and of a known thickness. We have seen that copper and iron are not weighed in the early stages of society, but are appraised by measurement. Why should not the same hold true for Rome? It may be asked, how came it that the _as_ was taken as the typical unit for weight and superficial measure, and to express even an inheritance? The answer is not far to seek. To express fractional parts has ever been a great difficulty with primitive people. As the Malays cannot conceive abstract numerals, but must append the concrete _padi_ to each of their numbers, so the old Italian found it necessary to employ some concrete object, the subdivisions of which were familiar, to express the fractional parts whether it be of an estate or anything else. The most common unit in use was the rod of copper divided into 12 thumbs. Accordingly, if a Roman wished to say that Balbus was heir to one-twelfth of an estate he expressed this by the homely formula that Balbus had come in for _one inch_, the denominator 12 being mentally supplied, as everyone knew that there were 12 inches in the copper bar. The same principle of taking some familiar object, the ordinary method of dividing which was known to all men, is seen in the method of expressing one-tenth. The Roman _denarius_ was divided into 10 _libellae_; accordingly, when Cicero wishes to say that a certain person had come in for a tenth part of an estate he says that he has come in for a _libella_ (_heres ex libella_). From this the reader will at once see that we might just as well declare that the word _denarius_ is an abstract word meaning _unity_ as make the same assertion about the _as_. Again, when the Roman land surveyors elaborated their system of mensuration, they found that the simplest method of expressing the fractional parts of the _jugerum_ was to employ the old duodecimal method of the _as_. Nor is this without a parallel elsewhere. As the yard was the common English unit of linear measure, it was applied to the most common unit of land, the quarter of the hide, which was accordingly termed a yard of land, or a virgate (_virga terrae_). The English analogy is even still more complete, for as the _as_ or foot-rod became the unit