Slughorn explains, when everyone is assembled, that alchemy with an egg is actually where phoenixes are speculated to originate; but no one has the recipe any more and there haven't been new phoenixes for centuries. They will not be making living things today. But the eggshell is a good base from which to appear lots of possible objects; alchemy doesn't like to conjure things into existence in plain sight but is quite willing that new things appear inside eggshells, cocoons, geodes, and similar. Their eggs have been pre-drained of their interiors for this purpose, although some recipes use full eggs.
As last week, they are invited to come up with recipes on paper for review by the professor before trying anything. Known possible results available with this set of ingredients include wooden, decorated eggs nested inside the shell; a shellful of small sharp teeth (the commonest source of hens' teeth, as they have encountered once or twice in potions); successively smaller eggshells the smallest of which holds a blob of mercury; and a perfectly hardboiled egg which can be arbitrarily flavored by exact details of the process. But they are welcome to aim at another result as long as their procedure looks safe.
And Sadde drops water from the prism to the egg and tries cracking it to see what he got. "By the way, there's an implication there from what Slughorn said to our little project."
Upon cracking the egg, quite a lot of blue paint starts leaking from it, and Sadde tries to find a place he can deposit an eggful of paint without making a big(ger) mess. Upon doing so he finishes cracking it and a much tinier blue glass egg falls from it. The glass is itself tinted and not painted. "Huh. This is actually pretty neat." He looks up at Miranda again. "Anyway, apparently the metaphor thing is kinda personal so it's very possible that in addition to finding something meaningful you have to be the kind of person that would produce something?"
"Right. But there's no obvious way to find out, and there's different ways to make stuff, so it might be that anybody can make anything if they find the right set of steps."
"Yeah, no, I'm taking that as encouragement, it's another piece of the 'how come no one else ever managed to do it' puzzle that makes it easier to understand while simultaneously not making our attempt doomed from the start."
Professor Slughorn comes by, opens up her egg, finds that it does contain further wooden eggs but they aren't as pretty, and puts them all back together seamlessly for her.
And she shows Professor Slughorn his non-prismatic-but-still-pretty glass egg, beaming.
"Maybe white paint would have got it prismy?" asks Miranda.
"If Mr. Woods would care to retry with white paint another time he may come in whenever I'm in the lab and not overseeing a class to do so."
"So the first thing is, how exactly does this metaphor part work? Like, is it a personal metaphor or some sort of consensus amongst everyone or some combination?"
"Does learning new things affect it on the same level waiting a few decades does? Like, suppose someone wanted to use a plastic model of an atom for something, but then they learn that in fact that model resembles an atom no more than a chihuahua does, would that change anything?"
"Filed under things-to-test, then, somehow. Also what about wands? Can they be used as part of the metaphor? Can they be transformed?"
"What kinds of safety precautions should we take when actually experimenting with this, which will of course only happen after at least the full two years this course lasts and we're not about to go trying it every other weekend?"
"But then if we do end up being insane enough to try it before the two years are up, we won't actually know what to do and may end up exploding much more things than were strictly necessary."
He writes this all down, grinning. "Are there any other general precautions for alchemical experimentation? We really aren't gonna experiment anytime soon, but knowing things in advance tends to be useful."