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It's part of a shoe fitting device from a WW1 show fitting system- Great War Militaria - Great War Militaria
View attachment 688100
you see the little things on the rods at the bottom portion of the photo? Looks like one of those and the 13 1/2 would be appropriate for a shoe size.
Here is another one- WWI Personal : Lot 3519
It's the shoe fitting knob.