Hawthorne uses a lot of symbolism and allegory in his written works and we can see both in this story. He uses mostly Romantic symbolism in this story. The rose which he brings back to life is a symbol for romance. Perhaps representing love or youth lost and then revived. Or even perhaps that youth is fleeting because the rose and the four guests are only young for a short time before Time steals away their youth once more. He also makes use of mirrors as a reflection of truth for example when Madam Wycherly is transfixed in front of the mirror watching her age melt away and her beauty and vitality return along with everyone else's old ways which allowed them each to age so terribly.
The story is also an allegory. An allegory is a type of extended metaphor or symbolism where the story itself, through the use of humor and sarcasm, represents some human vice or folly. In the case of this story the allegory highlight the vices of the woman's role in a male dominant society as well as a warning for the use of applied sciences. Madam Wycherly's beauty causes the men to fight stealing the show and trying to choke each other over her affections while she is concerned only with her new-found beauty. Dr. Heidegger's experiment is meant to teach a lesson through applied science, but rather these people learn nothing from the experiment and run off to find the fountain even though its effects are very fleeting.