Source : Webster's Revised Unabridged Dictionary (1913)

Bye \Bye\ (b[imac]), n.
   1. A thing not directly aimed at; something which is a
      secondary object of regard; an object by the way, etc.; as
      in on or upon the bye, i. e., in passing; indirectly; by
      implication. [Obs. except in the phrase by the bye.]

            The Synod of Dort condemneth upon the bye even the
            discipline of the Church of England.  --Fuller.

   2. (Cricket) A run made upon a missed ball; as, to steal a
      bye. --T. Hughes.

   {By the bye}, in passing; by way of digression; apropos to
      the matter in hand. [Written also {by the by}.]