χρύσεα χαλκείων, ἑκατόμβοι’ ἐννεαβοίων.
Here there seems to be a mixture of the metaphorical and the arithmetical use. For, on the one hand, it is singular that he should have chosen numbers which require the aid of a fraction to express their relation to one another. He could certainly not have meant to say that the values of the two suits were precisely as 100:9, or as 11⅑:1. And yet, on the one hand, he could scarcely use the term ἐννεαβοῖα, except with reference to the known and usual value of a suit of armour, while the ἑκατομβοῖα, from its use in other places, must be suspected of having no more than a merely indeterminate force.
With this fractional relation of 100:9, may be compared the arrangement at the feast in Pylos, where each division of five hundred persons was supplied with nine oxen. These numbers, however, are probably less vague than in some other cases: for the provision stated, though large, is not beyond what a rude plenty might suggest on a great public occasion.
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.
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.
The first example in the Iliad is supplied by that passage of the unhappy speech of Agamemnon to the Assembly in the Second Book, which causes the fever-fit of home-sickness. He compares the strength of the Greek army with that of the Trojans; and he only effects the purpose by this feeble but elaborate contrivance. ‘Should the Greeks and Trojans agree to be numbered respectively, and should the Trojans properly so called be placed one by one, but the Greeks in tens, and every Trojan made cupbearer to a Greek ten, many of our tens would be without a cupbearer[807].’ In the first place, the fact that he calls this ascertaining of comparative force numbering ἀριθμηθημέναι is remarkable; for it would not have shown the numbers of either army; nor even the difference, by which the Greeks exceeded a tenfold ratio to the Trojans; but simply, by leaving an unexhausted residue, the fact that they were more, whether by much or by little, than ten times as many as the besieged. Secondly, it seems plain that, if Homer had known what was meant by multiplication, he would have used the process in this instance, in lieu of the elaborate (yet poetical) circumlocution which he has adopted; and would have said the Greeks were ten times, or fifteen times, or twenty times, as many as the inhabitants of Troy.
After this, Ulysses reminds the Assembly of the apparition of the dragon they had seen at Aulis. The phrase χθιζά τε καὶ πρώιζα, which he employs, may grammatically either belong to the epoch of the gathering at Aulis, or to the time of the plague, which had carried off a part of the force a fortnight or three weeks before. In whichever connection of the two we place it, it affords an instance of extreme indefiniteness in the use of two adverbs which are at once expressive of time and of number; for on one supposition he must use them to express whole years, and on the other they must mean near a fortnight, and therefore a certain number of days.