Both pairs of barrels are marked with the Birmingham Black powder proof marks in use in part from 1813, modified in 1858, revised again in 1868 to form as seen on your barrels.The marks as seen remained in continuous use upto 1904. Barrels marked 13 were proof tested as 13,bore [.710 nominal diameter].Barrel set marked 14 was proof tested as a 14 bore [.693 nominal diameter].
The 14 bore barrels show an indistinct proof stamp that appears to be; A" Crown over an S",this may indicate that these barrels were subjected to a special test with exta heavy load but more likely they are a symbol to show that the barrels were serviceable.
The SJS seen on the barrels marked 13 could be the makers initials or those of the inspector at the proof house.