Mark, looks like your father's gun is from 1900 and F is the grade. According to Brophy's book the F Grade came in three different qualities, best, middle, and lowest. The best had Damascus barrels, the middle has English Stub Twist and the lowest has Royal Steel barrels. Only difference was in the F grade was the barrels.
Isn't it funny how back then they didn't trust change and preferred Damascus over forged steel.