This is a ‘loose coupler,’ or a ‘receiving transformer.’ It’s a modular component from the early ‘teens, whose function was to be the tuned circuit at the heart of a receiver. It worked by sliding a primary and secondary coil past each other; you could add variable condensers for more precision. A little telephone condenser filtered out RF noise. The larger Loose Couplers were sometimes called “Arlington” types, because they could tune to the very long wavelengths for time signal reception, broadcast from Virginia.
This picture, with a lot better informed commentary than mine, comes from Henry Rogers’ absolutely magnificent online Western Historic Radio Museum. If you’re serious about ham radio history, you should go start learning this site by heart.