The width of the lead band on your 3"-caliber Hotchkiss Bolt (cylindrical solid-shot projectile) indicates it is has not been fired. Where you find one unfired artillery shell, there will often be more unfired ones at the same spot. You might want to borrow a metal detector, or at least do some "deep" probing in the dirt at that exact spot with a long steel rod. (The rod should be at least 24-inches long, and only about 1/4-inch thick.)
Regards,
Pete