Source : Webster's Revised Unabridged Dictionary (1913)

Billycock \Bil"ly*cock\, n., or Billycock hat \Bil"ly*cock hat`\
   [Perh. from bully + cock; that is, cocked like the hats of
   the bullies.]
   A round, low-crowned felt hat; a wideawake. ``The undignified
   billycocks and pantaloons of the West.'' --B. H. Chamberlain.

         Little acquiesced, and Ransome disguised him in a
         beard, and a loose set of clothes, and a billicock hat.
                                                  --Charles
                                                  Reade.