I think the mirror idea makes sense too, but in pewter or silver. I have seen lead disk used as lids. I think a lead pig is another name for a thick lead container, in the shape of a cylinder. The lids generally just sat on top of the container instead of screwing down. I don't know if 'lead pig' is an official word or not for a cylindrical container, but when I was a child, I heard my Daddy use the term. It could very well be a pocket mirror as Johnny has stated. Either way, I think the 'pattern' is typical of the Federal period. Both Hepplewhite & Sheraton used lots of circles and ovals in their furniture do-dads, whereas their legs were straight and tapered.
Going back to the lead pig, the container or pig could have been to hold some type of poison, thus putting the bullseye lid on it. Think about the old black/white cartoon days, and some Bubba would wander in a bull pen . . .the bull would snort, paw, then his eyes would be pulsating circles, hense bullseyes. In actuality, the bullseye dartboard came from the rings of a tree when cut diagonally, which also made the lines for the first dart boards. I'm rambling, so I'll shut up, but the mirror idea is a good one, but was just throwing out the possibility of it being a lid with the inside ring being where it flat locked on the container. Breezie
