'Billycock hat' definitions:

Definition of 'Billycock hat'

From: GCIDE

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.]