I still have a few of these unissued badge holders left. The leather is 1 13/16" in diameter and the holes are spaced 13/16" apart. The two patent numbers are from 1938 and 1940.
I had some of these by a different manufacturer, still on the original store display card, and clearly marked as for war workers. I live just a few blocks from the Rock Island Arsenal, and there are several other factories in the area that were doing war work.