\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.