As respects the first of these propositions, the numerical test, although a rude one, yet appears to be conclusive. We find that Homer uses the name Ἀργεῖοι in the plural two hundred and five times, of which twenty-eight are in the Odyssey; besides fifteen passages in which the singular is used. And the name Δαναοὶ about one hundred and sixty times, of which thirteen are in the Odyssey. But we find the name Ἀχαιοὶ, employed from seven to eight hundred times: that is to say, five hundred and ninety-seven times in the Iliad, and one hundred and seventeen times in the Odyssey; all these in the plural number, besides thirty-two places of the poems in which it is used in the singular, or in its derivatives Ἀχαίïς or Ἀχαιïκός. The particulars next to be stated will bear at once upon the first and upon the second proposition. Homer very rarely attaches any epithet to the name Ἀργεῖοι, more frequently by much to Δαναοὶ, and still oftener to Ἀχαιοί. To the first only six times in all: to the second twenty-four: and to the third near one hundred and forty times. It is not likely that metrical convenience is the cause of this diversity. We have already seen that Ἀργεῖοι is susceptible of a substantive force, which will carry one at least of the other names by way of epithet, as if it indicated an employment, and not properly the name of a race. A like inference may be drawn from the greater susceptibility of carrying descriptive epithets, which we now find the Danaan and Achæan names evince. For example, the name of the Scotts, Douglasses, or Grahams, four centuries ago, would have afforded larger scope for characteristic epithets than such a name as Farmers or Colonists, when used to point out a particular people, or than such a name as Lowlanders, while it still retained its descriptive character, and had not yet become purely titular or proper. We must probably look, then, to political significance for the basis of the use made by Homer of the Achæan name. When we examine the character of the epithets, this presumption is greatly corroborated. Homer uses with the word Ἀχαιοὶ, and with this word only, epithets indicating, firstly, high spirit, secondly, personal beauty, and thirdly, finished armour[693]. I take these to be of themselves sufficient signs, even were others wanting, to point to the Achæans as being properly the ruling class, or aristocracy, of the heroic age. The Achæan name, again, attains with Homer to a greater variety of use and inflexion than the Danaan or Argeian names. He has worked it into the female forms Ἀχαιΐδες, Ἀχαιïάδες, Ἀχαιαὶ, as on the other side he has done with the names Τρῶες into Τρωὲς, Τρωάδες, and Τρωαὶ, and Δάρδανοι into Δαρδανίδες: but he has not made any such use of the names Ἀργεῖοι and Δαναοί. The female use of the former appears indeed in the singular with the names of Juno and of Helen, but never as applicable to Greek women in general, or to a Greek woman simply as such.