Billycock
Billycock , noun
[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.
Little acquiesced, and Ransome disguised him in a beard, and a loose set of clothes, and a billicock hat.
Also: Billycock hat