It is a cap and ball that has been “converted” to cartridge use. Looks like a Colt dragoon.
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Actually, the pistol in the picture is a replica of an 1851 Colt .36 cap and ball revolver converted to .38 cal. I have one just like it. Very common in the Old West. I have read that the shot fired was a .45, so if it was a converted cap and ball revolver, it would likely be a .44 1860 Colt Army converted to take a .45 long Colt cartridge.