Kathrine,
As FlyFish suggested, it's a .38 Military & Police 4th Change.
Serial numbers ran from 241704 in 1915 to 1000000 in 1942.
Although there is no way to be exact without a factory letter, S&W started heat treating the cylinders around 1920 at SN 316XXX. So, your serial number of 397272 would likely be 1920's.
Jim
As FlyFish suggested, it's a .38 Military & Police 4th Change.
Serial numbers ran from 241704 in 1915 to 1000000 in 1942.
Although there is no way to be exact without a factory letter, S&W started heat treating the cylinders around 1920 at SN 316XXX. So, your serial number of 397272 would likely be 1920's.
Jim