Again, Lycaon, when captured for the second time by Achilles, reminds that hero of what he had fetched or been worth to him on the former occasion[805]: ἑκατόμβοιον δέ τοι ἦλφον. Here we have a decisive proof of the figurative use of number. Had the young prince been ransomed by Priam, a great price, no doubt, would have been given. But Achilles sold him into Lemnos, ἄνευθεν ἄγων πατρός τε φίλων τε: and to the Lemnians he could hardly have value but as a labourer, although indeed it chanced that he was afterwards redeemed, by a ξεῖνος of Priam[806], at a high price. We cannot, then, suppose that he had brought any such return as would be represented by a full hundred of oxen. [805] Il. xxi. 79. [806] Il. xxi. 42. The evidence thus far, I think, tends powerfully to support the hypothesis, that there is an amount of vagueness in Homer’s general use of numbers, unless indeed as to very low ones, which cannot be explained otherwise than as metaphorical or purely poetical: and that his mind never had before it any of those processes, simple as they are to all who are familiar with them, of multiplication, subtraction, or division. I admit it to be possible, that his manner of treating number may have been owing to his determination to be intelligible, and to the state of the faculties of his hearers, as much as, or even more than, his own. But to me the supposition of the infant condition even of his faculties with respect to number, though at first sight startling, approves itself on reflection as one thoroughly in conformity with analogy and nature. Indeed the experience of life may convince us that to this hour we should be mistaken, if we supposed arithmetical conceptions to be uniform in different minds; that the relations of number are faintly and imperfectly apprehended, except by either practised or else peculiarly gifted persons; and that, in short, there is nothing more mysterious than arithmetic to those who do not understand it. As one illustration of this opinion, I will cite the difficulty which most educated persons, when studying history, certainly feel in mastering its chronology; while to those who are apt at figures it is not only acquired with ease, but it even serves as the _nexus_ and support of the whole chain of events. There were several occasions, upon which it would have been most natural and appropriate for Homer to use the faculty of multiplication; yet on no one of these has he used it. He constantly supplies us with the materials of a sum, but never once performs the process. ~_Silence as to the numbers of the armies._~