I think you have your title right, it being a half mold for bullets or musket ball. It would be one of two "inserts" that would fit into a clamp to let you pour, say a 50 cal. ball and change inserts for other calibers. Inserts now are available for pouring fishing jigs in different styles and weights. Great find, Sage!
what is the material it is made of?
is it brass? or ceramic? or maybe soapstone?
The first picture made me think of the bone cupels used in the testing of gold ore, but they are not segmented.
Looks somewhat imprecise for a bullet mold to me, usually they are just two part molds, and this would have to be at least a three part mold if not having four segments held together to make a sphere. I think the jury is still out on this one.
I don't think it's part of a bullet mold either. All the ones I have ever seen are two vertical pieces instead of horizontal. Can't see how it would work that way. Monty