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.
"Yes, I want to make phoenixes too, but somehow I think they may count as living things."
Hmm. What kinds of ingredients do they have?
Paint, crushed eggshells, a prism, salt, chicken feathers, an eyedropper, pine needles, an acorn, garlic cloves, sharp bits of wire, a knife...
...oooh, he has an idea, and he thinks he knows how to make it work. Probably. He wishes this idea would let him burn stuff. But it won't. He starts writing it down.
This time Slughorn calls on him first, when it's time to go over their ideas.
"I'm compleeeetely making it all up, here, but what I wanted was a prismatic egg, or something, so. I was thinking I'd do something like completely cover the egg in paint, and then use enough the same colour of paint to sorta glue the crushed eggshells on the prism? And also paint it. So there'd be a prism covered with crushed eggshells painted the same colour as the actual egg. And then, erm, something to indicate that I want to make the prism be inside the egg and shaped like an egg? What I thought was waiting until the paint dried, and then filling the eyedropper with something, maybe water, then holding the prism above the egg, and dropping whatever on the prism so that it'd fall from it to the egg. Erm, yeah, that's it." And he grins.
Miranda's decided to aim for the decorated wooden egg, but she wants a nested wooden egg, so she's incorporated a lot of repetitive steps and will be miming carving the shape of the egg with the knife around the shell. She is planning to roll the shell in various paint colors all mixed up for, hopefully, divinatory style results on her Matroyshka eggs. Slughorn approves her procedure and moves on.
So Sadde starts covering his prism and his eggshells in blue paint, using enough of it for the shells to get glued onto it and also completely covered by it.
"I dunno! Sorta like an egg-shaped... crystal thing? Maybe with lots of, like, inner facets or something to divide light. I dunno, really, I wanna see!"
Shrug. "This is the closest thing to science we've had yet, it's fun."
"Because we all know that science is about making weird art projects and seeing what unrelated objects they turn into?"
"And then writing that down and trying it again until you get it right, in order to generalise principles from that!"
The paint on the prism has dried, and now Sadde's waiting for the egg's to.
Miranda rolls her eggshell gently in paint droplets. "No control group, sample sizes of one..."
"Well, it's not a psychology experiment, I'm pretty sure—" Pause. Blink. He raises a hand.
"Are these processes deterministic? Like, if I try the same thing twice, do I always get the same result?"