my pc has been revitalized - fingers crossed it stays that way.
We are accustomed to seeing epergnes (from epargner, to economize - apparently) in the form/shape of Chris's example - designed for flowers, and produced, as such, commonly during the second half of the C19 - but.......................... early epergnes from c. 1730 and for the remainder of the C18 and into the early C19 were used to 'present pickles and condiments on the crowded dinner table', in affluent Georgian homes. Later during this period these condiments were replaced by sweetmeats etc.
The shape of the (usually) quite smallish containers for these edibles was dish-like, and these hung from branches of the main epergne often on silver wires, or glass loops that formed part of the dish itself.
The culinary connection for epergnes looks to have morphed into bonbon dishes around the mid C19 - possibly around the time that they also appear as flower holders - but I'm not sure of the dates lines for these changes.
Purely as a personal opinion and bearing in mind the size of these examples, it may well be that they formed part of a silver epergne, for example, as bonbon dishes - I don't see them being small enough to be used in the context of Georgian condiment epergnes. The later mid Victorian examples were often cut like these and were quite ornate - earlier examples tended not to be so decorative.
I have a problem in going with the museum's suggestion of finger bowl - although they may well be correct. I have twenty plus finger bowls and rinsers, and only one has any kind of cut rim (and that's a piece from well into the C20 and the cutting is very subdued). For obvious reasons I doubt that a cut rim, with projections like these, would have been practicable in use on a piece into which you had to dip your digits - especially if the candle light was a bit dodgy.
However, think I'd go with the museum's thoughts on date.
Ref. (and quote from) - 'SWEETMEAT and JELLY GLASSES' - Therle Hughes - 1982.