And when it has been a week since she last looked at her water-cooling spell, she pulls it out again. The textbook said to check how it would kill you; does it give any details on how to do that? The obvious first thing is to redo the calculations and see how much of what meanings remain after all the cancellations are done, but there might be some other way to find flaws in a diagram and she should do all of them before starting the second draft.

It suggests checking for flaws in your lines, your rune placement, your math, whether you've placed the runes you meant to place and didn't absentmindedly put in a different one somewhere, your math again, and whether the size of the diagram is right for what you want to do.

The runes are all the ones she wanted. These lines are imperfect and this rune should be a bit to the left. Her math comes out the same as the last time she did it but she's not satisfied with how much light and stone she has left over; she redoes the last three sections and gets it down to something closer to the size of the residuals from the boiling diagram. The size matches the water-boiling diagram, so that's fine--or is it? The effect size goes as the size of the largest rune, and similar effects like two different temperature changes should need similar sizes, right?

The textbook doesn't say how to make your own cooling spell!

Well of course not, but it could stand to say anything about sizing at all. She'll leave it sized like the heating one and leave it alone for a while and rework the cancellations again and again until her largest residual meaning is smaller than the largest residual meaning on the heating one or it's been six weeks, whichever comes first. 

She can get it that way if she tries hard enough and does enough magical stoichiometery.

Magical stoichiometry is fun! She does as much of it as necessary and then some. Checking the precision of her lines and the placement of her runes is less fun, but she does it just as diligently. On the days when she's not looking at it to let it fade from her head so she can catch any mistakes, she comes up with French for "Remove heat from this water; cool it to five degrees Celsius."

She revises her letter to her parents to include information about the war that they ought to know before either of them tries touching her medallion, though she doubts either of them would go for it even without that.

She gets a pot of warm water, and a thermometer, and the diagram, and the letter, all set up neatly on her desk.

She casts a spell of her own design.

The water chills; condensation appears on the cup.

Seeing condensation on a cup does not usually make her feel like the coolest person ever, but this time it does. She starts in on turning the new diagram into a clay stamp like the previous one.

She has the textbook practically memorized by now, and photocopies of all the diagrams in it; she returns it to the library, complete with the slip of paper bearing her name and phone number, before the next DnD night.

D&D proceeds; they get to the edge of the desert, where some cultists decide they're at risk of fulfilling a prophecy they don't want fulfilled and start harrying them.

That's a really interesting situation, because they get to investigate all of: how plausible the prophecy seems, how well they actually fit it, and whether it's the sort of prophecy they want fulfilled regardless of what the cultists think. Margaret gets into a lively debate/speculation session with Brenda about it.

"I think if the cultists are trying to avert it, it can't be the kind of prophecy that's really worth much, and except for fighting cultists who started it anyway we can just ignore it, Xavier isn't railroading us," says Brenda.

"Why would people trying to avert it make it less likely to be true? Or do you just mean that it's probably a prophecy that something bad will happen?"

"I mean if they're trying to avert it they think they can."

"Oh, I see. And if it was important enough to matter then it would happen whatever they or we did about it. I'm trying not to think about it in terms of whether Xavier finds this plot interesting or just wanted to give these guys an excuse to attack us . . ."

"I've played with him before, if we're not out to troll him he'll roll with anything we do."

"It's nice that he's willing to improvise like that. I think we should try to find out what the prophecy says instead of just chasing the cultists off."

"I guess that makes sense, then we'll know what they might try besides just trying to kill us."

"Yeah, definitely." They try to convince the rest of the party to track the cultists back to their hideout and investigate.

Xavier ends the session before they get there.

Then they'll have to wait a week to find out.

"I'm pretty excited to find out what it is," she says to Brenda on the way out. "I bet it has something to do with those emblems they were wearing."

"You don't think those are just their culty holy symbols?"

"Oh, I bet they are their culty holy symbols. But if you're founding a cult and you're picking your new holy symbol, why not base it on the prophecy you're building the cult around? I guess it depends how important this prophecy is to them whether that follows or not."

"It might not be that important. Although I guess they did jump on us pretty quick..."

"If it's not that important, they're probably up to something else nefarious too, so it's just as well we're investigating."