Smokey, the Bridger, W.S. Hawken, Liver Eating Johnson, Pistol Grip and Carson all have inside diameter rod pipes about .480 to .535, by actual measurement. The entry pipes are .510, .5?, .480, .480, .490 (Carson) and .330 for the capbox Hawken, a .50 caliber, page 388 of Gordon's book. Nelson Museum of the West in Cheyenne, S. Hawken .500 inside and .475 entry pipe inside. Lincoln, NE ("Robidoux") Hawken .515 ID and entry pipe .485, my measurements.
The finish is probably a varnish with a dark brown color added.
Dan, I agree. There is very little damage to Bridger's stock, except the front of the left lock panel is worn off, probably saddle wear. I recently discovered that the toe had been broken off, accounting for the toe plate and butt plate being pinned together. The toe is set forward, giving less pitch down to the muzzle.