176. The term tmesis is sometimes applied generally to denote that a preposition is "separated" from the verb which it qualifies, thus including all adverbial uses, but is more properly restricted to a particular group of these uses, viz. those in which the meaning is the same as the preposition and verb have in composition.
οἳ κατὰ βοῦς Ὑπερίονος Ἠελίοιο ἤσθιον
who ate up (κατήσθιον) the oxen of the sun
οὕς ποτʼ ἀπʼ Αἰνείαν ἑλόμην
which I took from (ἀφειλόμην) Aeneas
ὑπὸ δʼ ἔσχετο μισθόν
and promised (ὑπέσχετο) hire
μετὰ νῶτα βαλών
turning his back
χεῖρας ἀπὸ ξίφεϊ τμήξας
cutting off his hands by a sword
This is the sense in which the wοrd τμῆσιs was employed by the Greek grammarians, who looked at the peculiarities of Homer as deviations from the later established usage, and accordingly regarded the independent place of the preposition as the result of a 'severance' of the compound verb. We may retain the term, provided that we understand it to mean no more than the fact that the two elements which formed a single wοrd in later Greek were still separable in the language of Homer.
The distinction between tmesis (in the strict sense) and other adverbial uses cannot be drawn with any certainty. The clearest cases are those in which the compound verb is necessary for the construction of other words in the sentence; e. g. in ἀπʼ Αἰνείαν ἑλόμην or ὑπὸ δʼ ἔσχετο μισθόν. On the other hand, the use is simply adverbial in
περὶ φρένας ἵμερος αἱρεῖ
desire seizes his heart all round
(because the compound περιαιρέω means tο strip off, to take away from around a thing).
and in the midst . . . the king Agamemnon
ὣς Τρῶες πρὸ μὲν ἄλλοι ἀρηρότες, αὐτὰρ ἐπ’ ἄλλοι
the Trojans, arrayed some in front, others behind