Found this today in an antique shop. It’s a pinback. The diameter is 1.5″ or 3.8cm. I see several of these around on the internet, all noted as being “vintage”. Southern went under the control of Norfolk-Western in 1982 and then was merged officially into the Norfolk Southern Railroad in 1990.
I could go out on a limb and say that this may date to before the railroads gave the old heave-ho to passenger service in this area, but I won’t. That’s definitely a diesel engine on the left, though. The caboose on the right fits the streamlined period, but that may just be to fit the design on this pin.
Basically, I just don’t know when these were handed out.
This one is in fair shape. Water damage, apparently, around the rim.
Blogging the Railroad Tunnels 
A while back, while walking the tracks in Big Stone Gap, I found a small plastic quarter-sized Norfolk & Western badge of sorts. It is basically the round N&W RY logo with a clear plastic face, so the design can be seen through. The back is flat, as if it were once stuck to something, and the front edges are smooth and slightly rounded. I’m not sure what it came off of, or how old it is. It is pretty scratched up. You can see the exact logo in the same style on the right at the top of the Norfolk and Western Railway Wikipedia page.
Good find! Check ebay and see if anyone’s got something like that listed. That’s how I scoped out the old Southern pinback.