OP, You will have to give us the correct serial number for the gun. None of the top-break guns has a prefix letter in the SN! Just guessing you mis-read a 5 as S? But that would make the gun a 5th change version, and your photos show an earlier model. The obvious difference is the barrel latch. If the SN is really 412xxx then it is a 4th change gun made between 1890 and 1909, toward the end of this range.

It does appear the gun is a .38 Safety though, but in photos the .32 and .38 caliber guns can be hard to tell the difference and you didn't say what caliber it is. These guns were catalogued by S&W from 1880 clear until 1940.

__________________
Gunsmithing since 1961