Ian, I'm sorry to have to tell you that iron balls which are 1-inch in diamrter or less are extremely difficult to correctly identify. Although there are several sizes of civil war case-shot (antipersonnel balls from inside an explosive shell) and Canister-ammo balls, there are also a great many Civilian-usage balls which ae the same size. Ball-bearings are just one example of Civil-usage small metal balls.
There is one civil war artillery ball which was exactly 1-inch in diameter... the case-shot balls inside a 6.4"-caliber ("100-pounder") yankee Parrott case-shot shell. But there are also a lot of 1.0"-diameter ball bearings, and etc.
I must mention, you seem to have measured that ball with the rust/dirt-encrustation still on it. The ball's actual original metal diameter underneath the encrustation is what you need to measure. Because case-shot balls and under-1-inch Canister-ammo balls are only worth a dollar or so, I put the encrusted ball on a concrete sidewalk and use a hammer to bash off the rust-encrustation, and then I measure the "naked metal" diameter. You don't have to bash off every bit of the rust-crust... just do two spots on exactly-opposite sides of the ball, then use a Digital Caliper to get a precise measurement of the ball's diameter.
