Can we see the inside of the cap please? Honestly I would be guessing at straws here. I do feel based on it's very ornate design this wouldn't be food related (ie salt shaker etc); I'm leaning towards smell/perfume type of vessel as others have suggested. I would like to better understand if the cap is sealed or if the holes we see on the outside are allowing whatever is in the crystal to emit a smell or not. ALso I think the section @cxgirl circled looks like a rudamentary latch system to keep the lid on (ie turn the lid and lift straight up to remove the lid).
That definitely seems like a fragrance device to me. Like there should be a crystal stopper that should be under the cap when you don't want to use it...again just grabbing at straws here but that's my best guess.
An unusual piece, but personally, have a hard time seeing this as other than a caster/shaker, as already suggested, the lock fitting on the collar and lid would ensure its remaining in place when used to disperse whatever granulated, ground, or powdered substance it held. Find the silver mount at the bottom of the glass body odd - is there, for lack of a better term, a peg or protrusion of glass (typically inserted into a base) that the mount is covering? How are the feet attached to the base - soldered or with threaded posts and nuts? Suspect this piece has some decent age to it, bit surprised no marks at all, but that's certainly not unknown, and lots of very fancy silver pieces were produced for condiments, etc. Don't believe it's intended for fragrance, it's not a Lampe Berger or other catalytic perfume lamp, though I can see why it would be a thought, but I've used them for decades, and because they are alcohol burners (with a bit of essential oils added) and always have been, with or without a pierced cap, there will always be a solid metal cap covering the stone and opening that keeps the alcohol from evaporating when not in use. The small opening with a tall pierced top seems pointless if simply opened for scent to escape, and awkward for any type of potpourri, or for incense, as well as the glass revealing ash remains, without a way for the scent to diffuse up through that narrow neck and through the tall pierced top, just seems an unlikely use to me... Here is a French silver-mounted glass perfume burner, the silver collar stepped to accomodate both a stopper cap and pierced diffuser cap (though they also came with only a stepped stopper cap): https://www.rubylane.com/item/262281-SL-2528/Antique-French-Sterling-Silver-Cut-Crystal A French silver-mounted glass caster/shaker, the lid threaded to stay on and a pedestal base: https://theantiqueboutique.net/prod...ver-cut-crystal-sugar-shaker-caster-muffineer ~Cheryl