For comparison, Springfield 1903 Rifle Barrel Steel
https://books.google.com/books?id=KdARAAAAIAAJ&pg=PA1073&lpgMining and Metallurgy: Published Monthly by the American Institute of Mining and Metallurgical Engineers, 1919
The Government specifications for barrel steel for model 1903 rifle (Springfield) call for carbon 0.50 to 0.60 per cent., manganese 1.00 to 1.29 per cent., silicon under 0.25 per cent., sulfur under 0.06 per cent., phosphorus under 0.08 per cent. The minimum physical requirements are: Tensile strength, 110,000 lb. per sq. in.; yield point 75,000 lb. per sq. in.
Three barrels were analyzed with an average of:
Carbon .48%
Manganese .98%
Sulfur .05%
Phosphorus .06%
This would be similar to AISI 1551 with slightly higher sulfur and phosphorus.
Winchester Nickel Steel, introduced for the Model 1894 rifle about 1896: 100,000 - 107,000 psi with an elastic limit of 81,000 psi
Marlin “Special Smokeless Steel” introduced for the Model 1893 rifle in 1897 and Model 21 Grade C Pump in 1907: 100,000 psi
Remington Ordnance Steel, introduced in 1897 for the 1894 Hammerless Double: 110,000 psi with an elastic limit of 60,000 psi
I've not been able to find a composition analysis of the Marlin or Remington steels
