First off, Welcome to the forum
This revolver dates back to the very late 1800's or early 1900's. It certainly wasn't carried by your grandpa during his time as a rent-a-cop.
I'm doing this without the catalog in front of me, so I may be off by a model or two. It's a Smith and Wesson 38 DA 2nd model . It's in what's known as a S&W 38 short. If you are considering shooting it you must be absolutly certain to buy ammo specifically made for this type of revolver, or you may very well ending up blowing up the revolver, and quite possibly your hands.
The revolver was not made with hardened steel parts and must only use a low powered round, or it's very dangerous.
The approximate value for your revolver would be somewhere around $200-250. Regional prices vary greatly all across the country.
There will be more members chiming in shortly I'm sure
I have the same revolver in Blued finish with a 3" barrel and I paid $150 for it about 2 months ago. Because your's is in nickel finish and looks pretty good, I'll value your's slightly above what mine is worth. If you're interested in selling it let me know. Maybe we can work something out.