The Collaborative International Dictionary of English v.0.48:

Methodic \Me*thod"ic\, Methodical \Me*thod"ic*al\, a. [L.
   methodicus, Gr. ?: cf. F. m['e]thodique.]
   1. Arranged with regard to method; disposed in a suitable
      manner, or in a manner to illustrate a subject, or to
      facilitate practical observation; well-ordered; as, the
      methodical arrangement of arguments; a methodical
      treatise. [WordNet sense 2] "Methodical regularity."
      --Addison.
      [1913 Webster]

   2. Proceeding with regard to method; characterized by method
      or orderliness; systematic; as, a methodical
      investigation. [WordNet sense 1] "Aristotle, strict,
      methodic, and orderly." --Harris.
      [1913 Webster]

   3. Of or pertaining to the ancient school of physicians
      called methodists. --Johnson.
      [1913 Webster] -- Me*thod"ic*al*ly, adv. --
      Me*thod"ic*al*ness, n.
      [1913 Webster]