Rick,
A swamped barrel tapers from both ends. From the muzzle, it tapers 10 to 12 inches where the size remains constant for several inches. From the breech, it tapers to the end of the non tapered section. The breech is larger than the muzzle.
The two primary benefits are reduce weght and enhanced balance. I have a DGW Tennessee Mountain Rifle in .50 caliber. It's one of the early ones, with the 7/8th inch barrel. This rifle weighs about 8.5 lbs. and is muzzle heavy. The barrel is 42 inches long.
My .50 caliber in the above photo weighs about 7.5 lbs. and balances a couple inches behind the ramrod entry pipe. The barrel is 44 inches long and just over an inch at the breech and just under an inch at the muzzle. I believe that Track of The Wolf lists the dimensions of the varoius weights of Colerain barrels in their catalog and on their web site.
And yes, the .36 makes a great squirrel rifle. Its not too bad on ground hogs either.