In the third passage the writer of the 24th Odyssey becomes a little more explicit:
Ἑρμῆς δὲ ψυχὰς Κυλλήνιος ἐξεκαλεῖτο
ἀνδρῶν μνηστήρων· ἔχε δὲ ῥάβδον μετὰ χερσί
καλὴν χρυσείην, τῇ τ᾽ ἀνδρῶν ὄμματα θέλγει
ὧν ἐθέλει, τοὺς δ᾽ αὖτε καὶ ὑπνώοντας ἐγείρει·
τῇ ῥ᾽ ἄγε κινήσας, ταὶ δὲ τρίζουσαι ἕποντο.
In Homer the word for herald's staff is σκῆπτρον, not ῥάβδος, and Homer, while representing Hermes as a messenger of the gods, nowhere calls him κῆρυξ.
Hesiod on the other hand describes Hermes as κήρυκ᾽ ἀθανάτων (Theog. 939) and as θεῶν κῆρυξ (Op. 80); and later it seems to have been universally held that Hermes was a herald and the patron of heralds. See, for example, Aeschylus (Ag. 498):
Ἑρμῆν, φίλον κήρυκα, κηρύκων σέβας.
It is obvious that, in these circumstances, the staff of Hermes must have come to be regarded as a herald's staff, and that in fact it was so regarded is proved by a fragment (Sophocles, Fr. 701) of Sophocles' Philoctetes Trojae preserved in the recently discovered beginning of Photius' Lexicon :
καὶ ῥάβδος ὡς κήρυκος Ἑρμαία διπλοῦ
δράκοντος ἀμφίκρανος.
Yet, although the Latin caduceum and caduceus (which are distortions, effected before Rome became literary, of the Tarentine Doric καρύκειον) are applied indifferently to a Greek herald's staff (the Romans did not use this implement) and to the staff borne by Mercury, in Greek proper I am unable to find the word κηρύκειον, in any of its forms, used of the staff of Hermes, except once in Hesychius, who writes (Sophocles, Fr. 700), referring to the play just mentioned, δράκοντα· τὸ κηρύκιον· Σοφοκλῆς Φιλοκτήτῃ, and once in an epigram by Nicarchus (Anth. Pal. XI. 124), who compares the staff of a certain physician, Zopyrus, to the staff of Hermes: