But I have a weakness for another eighteenth-century hat--the military cocked hat. I've seen it called a bicorne, though costume resources seem to indicate this term refers to the later, more Napoleonic-era hats--clearly, military nomenclature is not my forte. Colonial Willamsburg notes that no one quite knows where the term cocked hat came from--that it may be from the angle at which the hat was worn, to show off a gentleman's well-curled wig, or it may come from flattening of one side due to holding under the arm.
This piece is from the Met's Costume Institute--more info on provenance, etc. there. I can't tell for certain if it's a military style hat or not (my guess is yes, though it's rather beat-up and I'm unsure if the bit on the side is a military cockade or just decoration) but the shape is the same as the hats worn by many regiments of soldiers during the American Revolution.
The gentlemen with whom I reenact, however, have another explanation for "cocked hat" in the military sense. The hat (like the one above) was worn, not with the point right over the nose, but off to one side by soldiers. This was because the musket, when carried at the shoulder (as it was the majority of the time), would have bonked against the side of the hat were it worn straight on, so it was turned "cockeyed." You can sort of see that in this reprodocution recruiting poster, which shows a soldier going through the Manual of Arms, or standard drill.
Unfortunately, the dashing style of the hat was not terribly practical--with a pointed front, it did nothing to protect the wearer's face from sun or rain. So, many hats incorporated a brilliant mechanism for having your fancy pointed style and eating it too--one of the sides of the hat was tied rather than stitched into place. After all, these hats all started as round "blanks" and were then shaped into whatever suited the wearer's fashion--or regimental regulations.
The hat from the Met shows this perfectly--one of the sides unties and folds down (you can see the ties, probably leather strips) so that, on long marches or work detail, the soldier could turn his hat so that this part would shield his nose from sunburn or his eyes from raindrops. On parade, the hat would always have been worn with this bit folded up, in proper military decorum.
I'll leave you with a couple of pictures of cocked hats in action. You can see from photo #1 that the hats were "decorated" (ummm, can you use that word for military-ish trappings?) depending on rank and on regiment. The fellow in the back (full disclosure--my dad!) has white taping visible, per his regiment. The fellow in front (full disclosure--my husband!) has a green doo-hickey stuck on the front of his hat to show his rank--Lieutenant (this changed dependant on time period and region).