introduced as "a very strange old gentleman, whose eccentricity had become the nucleus for a thousand fantastic stories." In biological terms, a nucleus is the centre of a cell and controls all the activities of the cell. Thus, when Dr. Heidegger's "eccentricity" is described metaphorically as "the nucleus for a thousand fantastic stories," the implication is that his behavior is the force which controls the immediate world around him. In this sense, his eccentricity has a kind of power over others. What they talk about is determined by what he does, just as the behavior of a cell is determined by its nucleus.

A metaphor is comparison that does not use the words like or as. There are not many metaphors in Hawthorne's story, but two show up in the following sentence:

The fresh gloss of the soul, so early lost and without which the world's successive scenes had been but a gallery of faded pictures ...

In the first metaphor, as the old people drink the elixir of youth they begin to feel young again. This sense of youth and energy is likened to a "fresh gloss" painted on their souls. Gloss is a shiny varnish put on an object to refinish it, and fresh gloss would be varnish newly applied. This is an appropriate metaphor for the new feeling of youth they all are experiencing.

The second metaphor in the sentence compares the new events (scenes) going on the in the world to faded pictures for the old people. Nothing recent has seemed fresh or new until now, for being old, these folk have not taken much interest in current events. Comparing current events to faded pictures is a good way to convey how faint these happenings have seemed to the seniors.

Nathaniel Hawthorne constructs the story around a material reality that is also a metaphor: water. The magical potion that his companions drink, which restores their youth, is the water of the Fountain of Youth. They literally drink the liquid, which is so effective that they crave more of it. Not only do they get the positive benefits of youth, such as energy, but they also get some negative effects, such as rashness and poor judgment.

Hawthorne also makes "water" a metaphor for "youth." In the end, the doctor compares the wastefulness of youth going unappreciated by young people to water that is spilled on the ground.

[T]he Water of Youth is all lavished on the ground.

Heidegger goes on to claim he has learned his lesson, that he will never again wish for youth, using the metaphor of a fountain.

I bemoan it not; for if the fountain gushed at my very doorstep, I would not stoop to bathe my lips in it.

There is a good example of a metaphor right near the beginning of "Dr. Heidegger's Experiment"

 Colonel Killigrew had wasted his best years, and his health and substance, in the pursuit of sinful pleasures, which had given birth to a brood of pains, such as the gout, and divers other torments of soul and body.

Colonel Killigrew's sinful pleasure could not have literally "given birth" to his various pains.  Rather, Hawthorne means that the sinful life of overeating and loose morals had brought about the Colonel's ailments just like the process of birth brings about a new baby. 

This is a classic example of metaphor: it compares two things without using the words "like" or "as."

Nathaniel Hawthorne's "Dr. Heidegger's Experiment" is filled with similes, metaphors, symbolism, and allusions. Let's look at an example of each of these.

We see a combination of a simile and a metaphor when the "shadows of age" are described as flitting from the Widow Wycherly's face "like darkness from the crimson daybreak." "Shadows of age" is the metaphor, and the simile comparison is found in the second half. It is a beautiful and vivid combination of images that helps us clearly picture the change in the Widow.

Another metaphor appears when the narrator says of Mr. Gascoigne that "time had buried him from the knowledge of the present generation." The image suggests that this man is out-of-date, separated from the present. There is also a bit of personification here with regard to time. Dr. Heidegger is described with a metaphor, too, for his eccentricity is “the nucleus for a thousand fantastic stories.” This gives us a good idea of how others think of this man.

As for symbolism, we might look at the rose that the doctor has had tucked away in his book all these years. It is withered and faded like the people in the room, but it becomes beautiful and fresh again. This lasts only a little while, though, yet the doctor says that he loves the rose just as much in its wilted state. Here is the main message of the story.

Finally, there are many allusions in this tale that add depth and sometimes a sense of mystery. We hear of Hippocrates and Father Time, of the Fountain of Youth and the black letters in the book. That last allusion is somewhat obscure, but it tells us that whatever Dr. Heidegger's book is, it is not the Bible, which would probably have red letters to mark Jesus's words in the New Testament.