The Collaborative International Dictionary of English v.0.48:

Megrim \Me"grim\, n. [OE. migrim, migrene, F. migraine, LL.
   hemigrania, L. hemicrania, hemicranium, Gr. ?; ?- half + ?
   skull. See Hemi- and Cranium, and cf. Hemicrania,
   Migraine.]
   1. A kind of sick or nervous headache, usually periodical and
      confined to one side of the head; now more commonly called
      migraine headache or migraine.
      [1913 Webster +PJC]

   2. A fancy; a whim; a freak; a humor; esp., in the plural,
      lowness of spirits.
      [1913 Webster]

            These are his megrims, firks, and melancholies.
                                                  --Ford.
      [1913 Webster]

   3. pl. (Far.) A sudden vertigo in a horse, succeeded
      sometimes by unconsciousness, produced by an excess of
      blood in the brain; a mild form of apoplexy. --Youatt.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

migraine \mi*graine"\, n. [F. migraine, LL. hemigrania, L.
   hemicrania, hemicranium, Gr. "hmikrani`a; "hmi- half +
   krani`on skull. See Hemi- and Cranium, and cf.
   Hemicrania, Migraine.]
   1. A kind of intense sick or nervous headache, usually
      periodical and confined to one side of the head; called
      also migraine headache. Same as megrim. --
      Mi*grain"ous, a.
      [1913 Webster]