Among all the numbers found in Homer, the highest which he appears to use with a clearly determinate meaning, is that of the three hundred and sixty fat hogs under the care of Eumæus in Ithaca[799]; [799] Od. xiv. 20. οἱ δὲ τριηκόσιοί τε καὶ ἑξήκοντα πέλοντο. The reason for considering this number as having a pretty definite sense in the Poet’s mind (quite a different matter, let it be borne in mind, from the question whether the circumstance is meant to be taken as historical) is, that it stands in evident association with the number of days, as it was probably then reckoned, in the year. It seems plain that he meant to describe the whole circle of the year, where he says, that for each of the days and nights which Jupiter has given, or, in his own words[800], [800] Od. xiv. 93. ὅσσαι γὰρ νύκτες τε καὶ ἡμέραι ἐκ Διός εἰσιν, the greedy Suitors are not contented with the slaughter of one animal, or even of two. Eumæus then gives an account of the wealth of Ulysses in live stock, both within the isle and on the mainland, from whence the animals were supplied: and adds, that from the Ithacan store a goatherd took down daily a fat goat, while he himself as often sent down a fat hog. I have dwelt thus particularly on the detail of this case, because it may fairly be inferred from the correspondence between the number of the hogs and the days of the year, that for once, at all events, the Poet intended to speak, though somewhat at random, yet in a degree arithmetically, and that of so high a number as 360. There are other cases of lower numbers in different parts of the poems, where it may be argued, with varying measures of probability, that Homer had a similar intention. ~_The ἑκατομβὴ and numerals of value._~ The word ἑκατομβὴ, without doubt, affords a striking proof of vagueness in the ideas of the heroic age with respect to number: and this vagueness extends, yet apparently in varying degrees, to the adjective ἑκατομβοῖος. I have elsewhere[801] referred to adjectives of this formation as indicative of the fact, that for those generations of mankind oxen may be said to have constituted a measure of value; and this fact certainly involves an aim at numerical exactitude. It seems, indeed, on general grounds far from improbable, that the business of exchange may have been the original guide of our race into the art, and thus into the science, of arithmetic. [801] Agorè, p. 82.