I finally got permission from a landowner to metal detect in a sugarcane field used briefly as an encampment by the US 19th Army Corps (according to a hand-drawn Federal map from the period). Besides a couple small unidentifiable metal pieces, and a shell from a .38 Special, I did find the below ball, which measures .56 caliber . . . a common enough Civil War caliber. But this thing is made of iron, not lead. So I'm thinking it's actually a ball bearing. But what do you all think?