Thanks for all the replies.
Nickel is a "living" finish, like Silver. It will tarnish. I cleaned it with Wright's Silver Cream, which is very gentle. Mother's will polish the Nickel, not just clean it. If the Nickel is polished, it will get to the point where it will be completely shiny, and that is not what I was after.
The Wright's did an excellent job. It looks as good as the day I got it, if not better. The Double Nickel gets babied, so it was just a matter of getting the tarnish off.