Guys,
I agree with Rich, the change in barrel diameter at the transition from octagon the round at the "wedding ring" is very slight on original barrels, only a few thousandths of an inch. Also, on many original barrels the swamp, or taper and flare, is not very pronounced. I just bought an original barrel from Ebay marked with the date 1851. it is 44 inches long, 0.890 breech, 0.820 waist, 0.860 muzzle. Just looking at the barrel it appears to be a straight sided barrel, but it is swamped. Also, rifled bore of 0.335 diameter, muzzle coned to a maximum 0.370 diameter, rather rough so I will re-bore it to about a 0.360 bore.
Jim