Welcome to the forum. Any .38 M&P with a serial number between roughly 420000 and 580000 is likely to have hardened parts and a mushroom ejector rod knob. Basically you are looking for 1922-1928 production.

You'll get an argument about the purpose of heat treated steel. It definitely wears better because it is harder, but it is also a little stronger for metallurgical reasons that I don't really understand. My own suspicion is that the factory did it in the early '20s so they could get away from the process of putting those finicky little hardened shims in the cylinder notches to keep them from wearing loose too fast. Easier (and presumably cheaper) to harden the entire piece than to decorate it with little slivers.

You're in luck on the square butt, if that's what you want. In the 1920s most of them were made that way, with round butt guns far less common. Good luck in the hunt.

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David Wilson