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Except for a couple of battles near the Texas-Mexico border where the Mexican artillery fired some copper/brass balls, none were ever used in North America (the US and Canada).
Based on the size (1.4") of copper or brass ball you found, and the fact that it is a perfectly spherical ball manufactured with a super-smooth surface, I believe it is most likely to be a waterpump check-valve ball. To prevent water from leaking around them, they need to be perfectly spherical with a super-smooth surface. Copper and brass are preferred because those metals do not rust or corrode in the wet environment. Also, copper and copperbrass are toxic to algae, which could otherwise "gum up the works." Copper/brass check-valve balls have been discussed previously here in the What-Is-It? forum. Here's a scan I saved from that discussion, posted by BigCypressHunter.