349. οὖν in Homer does not properly express inference, or even consequence (like ἄρα). Its use is to affirm something with reference to other facts, already mentioned or known; hence it may generally be represented by a phrase such as after all, be this as it may, etc.
Il. 2.350 φημὶ γὰρ οὖν
for do declare that, etc.
Od. 11.350 ξεῖνος δὲ τλήτω, μάλα περ νόστοιο χατίζων,
ἔμπης οὖν ἐπιμεῖναι ἐς αὔριον
(nevertheless to wait)
Like ἄρα, it is used to emphasize correlative clauses, but only with the negative οὔτε . . . οὔτε and μήτε . . . μήτε.
Od. 6.192 οὔτʼ οὖν ἐσθῆτος δευήσεαι οὔτε τευ ἄλλου
Il. 16.97 αἲ γὰρ . . .
μήτε τις οὖν Τρώων . . .
μήτε τις Ἀργείων, κτλ.
So Il. 8.7, 17.20, 20.7; Od. 1.414, 2.200, 11.200, 16.302, 17.401.
The combination γʼ οὖν (not to be written γοῦν in Homer) occurs only twice, with the meaning in any case.
Il. 5.258 εἴ γʼ οὖν ἕτερός γε φύγῃσι
if one of these two dοes (after all) escape
Il. 16.30 μὴ ἐμέ γʼ οὖν οὗτός γε λάβοι χόλος
Cp. Il. 19.94 κατὰ δʼ οὖν ἕτερόν γε πέδησεν.
As an emphatic particle of transition οὖν is found in μὲν οὖν (Il. 9.550, and several times in the Odyssey), much more frequently in the combinations ἐπεὶ οὖν, ὡς οὖν. In these an approach to the illative force may perhaps be observed.
350. δὴ is properly a temporal particle, meaning now, at length (Latin iam): hence it implies arriving at a result, as ἐξ οὖ δὴ τὰ πρῶτα διαστήτην from the time that the pοint was reached when they quarreled; εἷ δή if it has come to this that, and so if finally, if really. With superlatives it expresses that the highest stage has been reached
Il. 1.266 κάρτιστοι δὴ κεῖνοι κτλ.
these were quote (finally) the mightiest
So in questions, πῶς δή how has it come to this that . . . ; and prohibitions, μὴ δή do not go so far as to . . .
δή may begin a sentence in Homer
ll. 15.437 Τεῦκρε πέπον, δὴ νῶϊν ἀπέκτατο πιστὸς ἑταῖρος
and often in the combinations δὴ τότε (tum νerο), and δὴ γάρ. The original meaning is best seen in these forms (where δή is emphatic), and in ἤδη (for ἦ δή), and ἐπεὶ δή.
As δὴ is one of the words which unite with a following vowel, so as to form one syllable, it is sometimes written δʼ, and so is liable to be confused with δέ. This occurs especially in the combinations δὴ αὖ, δὴ αὐτός, δὴ οὕτως.
Il. 1.131 μὴ δὴ οὕτως
Il. 1.340 εἴ ποτε δὴ αὖτε
Il. 10.385 πῆ δὴ οὕτως
Il. 20.220 ὅς δὴ ἀφνειότατος κτλ.
So in εἰ δʼ ἄγε the sense generally requires δή, see § 321.
Note that δῆτα, δῆθεν (cognate or derivative forms) are post-Homeric; as also are the combinations δήποu, καὶ δή.
351. νυ is obviously a shortened form of νῦν now. It is used as an affirmative particle (like δή, but somewhat less emphatic), especially in combinations such as ἦ ῥά νυ, καί νύ κε, οὔ νυ, μὴ νυ, ἐπεί νυ, and after interrogatives, as τίς νυν who now, τί νυ why now (see Od. 1.59-62).
The form νυ is exclusively epic: νυν (ῠ), which is used by Attic poets (Ellendt, Lex. Soph. ii. p. 183) appears in
Il. 10.105 ὅσα πού νυν ἐέλπεται
Il. 23.485 δεῦρό νυν, ἢ τρίποδος κτλ.
but it is probably not Homeric.
In Il. 10.105 the sense is distinctly temporal, and accordingly we should probably read νῦν ἔλπεται. The temporal sense also suits Il. 23.485, where moreover there is a variant δεῦρό γε νῦν τρίποδος, found in the Scholia on Aristophanes (Ach. 771, Eq.788).
352. θην is an affirmative enclitic, giving a mocking or ironical force, like the later δήπου and δὴθεν (which is perhaps originally δή θην).
Il. 2.276 οὔ θήν μιν πάλιν αὖτις ἀνήσει θυμὸς ἀγήνωρ
his bold spirit will not imagine impel him again
Il. 13.620 λείψετέ θην οὕτω γε
I think in this fashion you will leave, etc.
It is only Epic.