εἴτ’ ἐπὶ δεξί’ ἴωσι πρὸς Ἠῶ τ’ Ἠέλιόν τε,
εἴτ’ ἐπ’ ἀριστερὰ τοίγε, ποτὶ ζόφον ἠερόεντα.
Apart from the question, whether the sense of right and left is suitable to this passage at all, and assuming it to be so, the meaning is from the left for ἐπὶ δεξιὰ and from the right for ἐπ’ ἀριστερὰ, on their way in each case to the opposite quarter.
Again, the portent which had drawn forth the observation of Hector was, (Il. xii. 219,)
αἰετὸς ὑψιπέτης, ἐπ’ ἀριστερὰ λαὸν ἐέργων,
namely, an eagle appearing on the right and then moving towards the left. Now ἐέργω is not properly a verb of motion; and yet we see that ἐέργειν ἐπ’ ἀριστερὰ means to close the army in from the right; that is to say, the eagle, which does the act ἐπ’ ἀριστερὰ, is itself on the right.
There were in fact three things, which originally might, and commonly would, be included in each of these phrases. For example, in ἐπ’ ἀριστερὰ,
1. Appearance at a particular point on the right;
2. Motion from that point towards the left;
3. Rest at another point on the left.
Of these the second named indicates the first and principal intention of the word; but when it passes to a second intention or derivative sense, it may include either the first point, or the third, or both. In the later Greek it appears rather to indicate the point of rest; but in the Homeric phrases of the corresponding word δεξιὸς, οἰνοχοεῖν ἐνδέξια, δεικνύναι ἐνδέξια, αἰτεῖν ἐνδέξια, ἀστραπτεῖν ἐπὶ δεξιὰ, ἐέργειν ἐπ’ ἀριστερὰ, the starting-point, and not the resting-point, is the one brought into view. It is the commencement of the motion, in every one of these cases, which is indicated by the phrase, and not its close.