At first I thought a cigar server, cigars in the opening, taper to light them, liveried servent carrying it from gentleman to gentleman around the table... however: why would a cigar server need what appear to be inkwells on either side so my next thought is a note dispencer. Paper in the center compartment, inkwells on the sides, possibly an opening on the upright element (in front of the taper) to hold a pen, taper used to heat a stick od sealing wax. But where is the holder for the sealing wax? And if it is for a desk, why the handle on the back?
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Your first instinct was correct. My reference calls it a "Smoker's Companion".
The two small containers on each side are for vestas and small tapers.
The hollow base held the cigars or cheroots.
The small device in the middle of everything ( see picture below ) is a guillotine cigar cutter.
Agree a lid would be necessary if cigars were stored here all the time.
However, the book does not mention a missing lid.
It may have just been used occasionally for short periods of time.
Here's a quote from my reference: "The angular handle makes the companion easy to carry from room to room or pass around the table".
I get the impression this was used when the owner had guests.
Probably brought this piece out to impress them.
Have never smoked a Russian cigar. Don't know what they were made of or how.
If they were dry-cured they would not need to be humidified. In a cold, dry climate, that is very possible.