Source : Webster's Revised Unabridged Dictionary (1913)

Fine \Fine\ (f[imac]n), v. i.
   To become fine (in any one of various senses); as, the ale
   will fine; the weather fined.

   {To fine} {away, down, off}, gradually to become fine; to
      diminish; to dwindle.

            I watched her [the ship] . . . gradually fining down
            in the westward until I lost of her hull. --W. C.
                                                  Russel.