Are you sure about the numbers on the grip?
If it is 6 numbers after the S, it's a postwar .38 Military & Police, which is now known as the Model 10, and was probably made in 1948.
The K that you note could indicate that it's a K-frame, but I've never seen one so marked. The number after the K is the floor assembly number.
If it is only 5 numbers, then it's one of the .38 Spl. chambered N-frame revolvers, which is larger and heavier and would have been made about 20 years later.
The patent dates, though, are a strong indication that this is a .38 Military & Police.
"The gift which I am sending you is called a dog, and is in fact the most precious and valuable possession of mankind" -Theodorus Gaza
Baby Jesus cries when the fat redneck doesn't have military-grade firepower.