Not military then, unless someone rifled a volley gun
Probably a sporting gun. Curiously scales often work better than calipers because balls were sold by how many you got to the pound.
Lots of shotguns but very few sporting rifle shooters before the Victorian fad for deer stalking in Scotland and they didn't shoot ball. English deer were taken by horse and hound. I'd guess pioneer gentleman rifle shooter with a German Jaeger rifle import, the Germans liked to shoot patched ball from a .50
Or, maybe, as it was in a stream... Napoleonic refugee militia out shooting English frogs in practice for the real thing