Prolongation from rhoomai (to dart; probably akin to rhoumai); to strengthen, i.e. (impersonal passive) have health (as a parting exclamation, good-bye) -- farewell.
see GREEK rhoumai
STRONGS NT 4517a: σ [σ ,Sigma: the practice (adopted by Griesbach, Knapp, others, after H. Stephanus, et al.) of employing the character sigma σ in the middle of a compound word has been abandoned by the recent critical editors; cf. Winers Grammar, § 5, the passage cited; Lipsius, Gram. Untersuch., p. 122; Matthiae, § 1 Anm. 5; Alexander Buttmann (1873) Ausf. Sprchl. § 2 Anm. 3; Kühner, § 1 Anm. 1. Tdf. edition 8 writes sigma ς' also even at the end of a word, after the older manuscripts. On movable final sigma ς' see ἀχρἱσ', μεχρἱσ', ὁυτὡσ'. The (Ionic) combinations ῥς for ῥρ, and σς for ττ (cf. Fischer, Animadvers. ad Veller. etc. i., pp. 193f, 203; Kühner, § 31, pp. 124, 127), have become predominant (cf. ἄρσην, θαρσέω, θάρσος, ἀπαλλάσσω etc., γλῶσσα, ἥσσων (which see), θάλασσα, κηρύσσω, περισσός, πράσσω (which see), τάσσω, τέσσαρες, φυλάσσω, etc.), except in a few words, as κρείττων (which see), the derivatives of ἐλαττῶν (of which word both forms are used indiscriminately), ἥττημα, ἡττάω (yet see 2 Corinthians 12:13), etc.; cf. Buttmann, 7. Some proper names are spelled indifferently with one sigma ς' or with two; as, Ἐλισ῾σ᾿αιος. Zeta ζ' is occasionally substituted for sigma ς', especially before mu μ', see σβέννυμι, Σμύρνα (σμύρνα, cf. Sophocles Glossary, § 58, 3, and Lexicon, under the word; Tdf. Proleg., p. 80; WHs Appendix, p. 148; Buttmann, 5; Alexander Buttmann (1873) Ausf. Sprchl. § 3 Anm. 6; Bezae manuscript, Scrivener edition, p. xlviii.; Liddell and Scott, under the word Zeta ζ', I. 3, and Sigma ς', II. 14 c.); so also xi Ξ, as ξυμβαίνω 1 Peter 4:12 Rbez cf. Kühner, § 325, 5; Alexander Buttmann (1873) Ausf. Spr. as above; see ξύν.]