The Collaborative International Dictionary of English v.0.48:

Magic \Mag"ic\, Magical \Mag"ic*al\, a. [L. magicus, Gr. ?, fr.
   ?: cf. F. magique. See Magi.]
   1. Pertaining to the hidden wisdom supposed to be possessed
      by the Magi; relating to the occult powers of nature, and
      the producing of effects by their agency.
      [1913 Webster]

   2. Performed by, or proceeding from, occult and superhuman
      agencies; done by, or seemingly done by, enchantment or
      sorcery; as, a magical spell. Hence: Seemingly requiring
      more than human power; imposing or startling in
      performance; producing effects which seem supernatural or
      very extraordinary; having extraordinary properties; as, a
      magic lantern; a magic square or circle.
      [1913 Webster]

            The painter's magic skill.            --Cowper.
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   Note: Although with certain words magic is used more than
         magical, -- as, magic circle, magic square, magic wand,
         -- we may in general say magic or magical; as, a magic
         or magical effect; a magic or magical influence, etc.
         But when the adjective is predicative, magical, and not
         magic, is used; as, the effect was magical.
         [1913 Webster]

   Magic circle, a series of concentric circles containing the
      numbers 12 to 75 in eight radii, and having somewhat
      similar properties to the magic square.

   Magic humming bird (Zool.), a Mexican humming bird (Iache
      magica), having white downy thing tufts.

   Magic lantern. See Lantern.

   Magic square, numbers so disposed in parallel and equal
      rows in the form of a square, that each row, taken
      vertically, horizontally, or diagonally, shall give the
      same sum, the same product, or an harmonical series,
      according as the numbers taken are in arithmetical,
      geometrical, or harmonical progression.

   Magic wand, a wand used by a magician in performing feats
      of magic.
      [1913 Webster]