IMHO as the doublegun makers were transitioning to the creatively names fluid steel tubes, they were likely using up their pattern welded stock without regard to grade of the gun

Hammer 1901 F grade with Birmingham Provisional Proof 4 Iron SN 89971

[Linked Image from photos.smugmug.com]

A 1902 Smith F grade hammergun with Rubans Royal

[Linked Image from photos.smugmug.com]

1896 Smith No. 1 hammerless with Birmingham Proof 4 Iron Turkish

[Linked Image from photos.smugmug.com]