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.
[1913 Webster]
Little acquiesced, and Ransome disguised him in a
beard, and a loose set of clothes, and a billicock hat.
--Charles
Reade.
[Webster 1913 Suppl.]