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I had in mind that form would suggest function and it might actually be some sort of standard for what ever it was. It's seems unlikely that semi-circular shape is purely decorative and it's not very practical for storing Ethiopics. It appears to have hinged flat sides and is stored in close proximity to an octant and telescope. I had considered plotting tools including maybe a large protractor, possibly a pelorus or theodolite. An officer's hat box seems less likely,

Robin Stuart