Here comes number 2

I believe that this is a holder for a hollow steel tube with cutting points around the upper edge. A brass or gold balance screw was placed with the threaded section in the center hole in the tube. the screw was then rotated with downward pressure to remove a small amount of material under the screw head. This allowed poising of the balance (by removing weight) without the modification being visible after the screw was put back into the balance.
The set screw on the left side of your photo should allow the tube to be removed and inserted into the center hole. I think that these originally came with two different size tubes, for different sized balance screws.

Ed
Thanks alot. That one had me stumped. I did come across the extra cutter, in a tube type holder.

Frank