What is the cord or extension called to hold up the train of a long gown. It is used to hold up the train while dancing so that it will not drag on the floor.

I know of two techniques. The first is a "bustle button" that is sewn to the dress at the base of the spine. Then there is a loop (or a few loops for a very long train) on the skirt. When the loop is attached to the button the hem of the train is at floor level. The loops on the skirt are hidden in the decorations when the train is down. This is frequently used on wedding dresses.
The second is a little bit harder to manage when you're dancing. I've always heard it called a loop but I don't think that's the proper name. It's a cord -- or a covered embroidery hoop -- large enough to drape the train through and then go over your arm like a purse handle. That can look really pretty if it's draped right -- but it can also get very heavy after a while and the train may slip out.