The round object is a lock/lock mechanism manufactured by Corbin Cabinet Lock Co, New Britan, Conn.
Edit: Possibly the lower half of something like this:
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Edit 2: Which by the way, is the lock for a trunk (e.g., steamer trunk)
Edit 3: I think there is a good chance that it is possible the broken bottom half of this one. All the materials, dowel/rivet (whatever) positions, rotation of the key hole and shape, location of the stamps, etc appear to match.
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Regardless, I think there is a strong possibility that you could pull either the exact patent number or exact model number off this piece with some careful cleaning and a magnifying glass. I was able to locate some evidence of stamps on the reverse side of it which you may not have been able to see.
I have circled the locations in the following picture:
View attachment 1350247
Some pareidolia may be at play, but letters and numbers in at least 3 of those are clear.