You have a .32 Hand Ejector Third Model. You can narrow the shipping date a bit to 1917-1920.
These revovers are fairly common, but condition helps. Do the grips have the S&W medallions? If so, those would probably be factory fitted and may the serial number written in pencil on the inside. Are the hammer and trigger nickel plated as well or are they color case hardened? Nickel would indicate an aftermarket finish.
I read your other post about your grandfather's .38 special. Iffn' I was you, I would do some research on his law enforcement career, such as newspaper clippings from the area that he worked. All of this would add to the guns when you pass them on.