What is “Hope's” ?
Copper with solder seams showing suggests it is functional rather than laboratory equipment which would be polished brass. Maybe an outer case and some insulation has been removed.
It looks like a “one off” or prototype item, the solder spread suggests an apprentice.
The spout seems to have been used for a hose attachment, probably to partially drain it.
Do you have the lid upside down. Does the chimney align / mate with the inner tube?
The rolled bead on the upper edges of the main body and chimney suggest removal of sharp edges which implies human contact when being used. It could be part of high voltage or VHF cavity resonator. But I would have expected a greater radius of curvature than the simple bead shown.
Part of a water heater or a “Bain Marie” for some process carried out in the central tube, like calibrating thermometers ?
Without some idea of the inner tube attachment geometry I can make no more deductions, only guess.
Are there any wires attached ?
Is the central vertical line at the very top of the picture in the background ?
It looks like scrap copper, or an interesting puzzle, depending on the space you have available to store it.