Interesting question and timing Bill. I dropped 2 "Armory Steel" barrels at METL today (Crescent and Meriden Fire Arms) for composition analysis by Optical Emission Spectroscopy (OES). Crescent advertised the barrels as "Decarbonized Steel" into the 20s.
Dave Suponski published an analysis of Parker Steel, Titanic Steel, Vulcan Steel, and Trojan Steel in the Summer 2014
Parker Pages, and Walt Snyder has shared the results of an Ithaca barrel tested in 1919. I also have the published composition of a number of early Fluid Steels including Winchester Nickel Steel, Halcomb Steel Co. Nickel Steel, and several Krupp variants.
Most early Fluid Steels are AISI low carbon steels, 10XX variants. Krupp Fluss steel and Krupp Spezial are AISI 1060 and 1045.
Turns out Parker Steel is Resulphurized Decarbonized Steel, likely "rolled" for added strength like Winchester Standard Ordnance Rolled Steel.
Anyway - until we actually OES a bunch of vintage barrel segments, we won't really know what they are. What we could have done, and known, with all the chopped off barrel ends!!
For the record, I'm still collecting fluid steel segments IF we know the name on the barrel. 
