Unfortunately, because of copyright I can't show you a photo. But this Monmouth Cap fascinates me. This is a welsh pattern and the example shown is from the sixteenth century. That's the 1500's!! These hats were so common that people never bothered to describe them, so researchers can only guess that this one is typical.

Doesn't it remind you a modern bucket hat? I especially love the brim. I imagine the loop was for hanging the hat up indoors. It looks like it's a turned under hem, doesn't it? If you look at the closeup you can see that this was some seriously chunky yarn too.