bipolar wall wart wiring question

[ickystay]

I have an old wall wart that is +/- 12 volts dc. The old plug is gone so there are just 4 wires- red, white, black, and a shield. I get +12 between red and black. -12 between white and black. This thing plugs into the wall socket with a 3 prong plug. The shield is connected to the third (ground) prong but not to the center of the dc supply. I'm going to wire this to a 1/4" stereo plug and use a stereo jack on my project.

 

My question- should I connect the shield to the center of the +/- 12vdc?

 

Hope this makes sense. I figure I should, but kind of wonder why they are not internally connected in the first place.

 

Thanks.