Definitely a percussion rifle barrel.
I have seen some in .38 caliber (0.380"), but 0.360" is pretty standard. The forged iron barrels would perhaps start at .36 caliber, but in use the softer iron as compared to modern steels wears. Occasionally the rifling would be freshened up and the barrel smoothed. Then the gunsmith also made a new mold for the owner and he left the shop with a rifle that shot a slightly larger ball.
Calibers used to be measured in the number of lead balls per pound. "100 bore" would be about 0.350", which with a cloth patch is a sung fit in a 0.360" bore. 80 bore is about 0.38", 50 bore is about 0.50", 40 bore is about 0.50", "30 bore" was a 0.54" caliber, and "25 bore" became 0.58". Those became standard rifle diameters.