Close enough, Dave wins.
It is an International Postal Supply "Flier" canceling machine type holder. The slots hold the pieces of steel type for hours, dates, months, and years. The center hold is for a screw which secures the type holder within a slide-out tray under the canceling machine. This round type holder is secured in the swing-out tray shown in the image below.
Many thanks to Frank R. Scheer, Curator Railway Mail Service Library