The wizards wisely hang back and wait before asking technical questions. Eventually Terali says, "Do you want a glass of water?"

"Yes, that would be good, thank you," sniffles Matilda.

There's a waterspout in the office, and paper cups. Terali gets Matilda some water.

The wizards look at the cup, and each other, and Terali just says, "You're welcome."

Slightly before the time when Matilda would be summoned for her next lesson, she appears in the room where she is usually summoned.

"It seems more convenient this way," says Matilda. "Miss Trunchbull taught my magic to do a lot of new things and I don't like most of them, but I like that I learned how to move between worlds."

"Do you have any idea how she taught the ialdae to do those things?"

"I think so," she says. "I think she caught magic like Lavender, but Lavender couldn't teach it anything new, and Miss Trunchbull couldn't teach it nearly as well as I can but she could still teach it some. I think whether or not someone catches ialdae, and whether or not they can teach it new things if they do, has to do with something about them. But I don't know what exactly."

"Maybe we could make an analysis to tell. Or you could teach your magic one. It wouldn't be especially useful with only Lavender and you to look at, but it might give us a clue."

"I've been trying to teach my magic one, but I can't tell very well whether it's worked or not, because of only being able to look at me and Lavender."

"Well - hm. How many people have you ever used magic on?"

"Lavender and Miss Trunchbull and most of the kids from my class last year and Miss Honey and I think that's it. I could try it on more people and see if they pick it up too."

"We can find you some people from here who'd like to have it, definitely. But why I asked was that your class in school probably isn't very unusual in how many people in it can catch ialdae. So if you looked at lots of people with an analysis - possibly only people from your world, depending on how it turns out to work - then you'd expect one or two people to be potential catchers per classful. How big are your classes?"

"There were twenty-six people in it, including me and Lavender."

"So out of a total of twenty-eight people three so far have ialdae, but you might be different because you were first, so about one in every thirteen or fourteen - maybe more, if some people are just slow catchers."

"That sounds about right," says Matilda. "We'd need to look at lots more people to be sure, though. Do you have lots of people to look at? And are the people who want ialdae all people it would be good to give ialdae to? I don't want to have to deal with another magic Trunchbull. One was enough."

"They'd all come very highly recommended," Terali assures her. "I don't think we'll have any trouble finding volunteers. Some people would really like to do magic but they don't have high enough channeling capacities to be wizards and they weren't born with any other kinds."

"Okay," she says. "If you find me lots of people to look at to see if they can catch ialdae, I'll look at them. And if you find me people who want to do magic and some of them can catch ialdae, I'll... see."

"We'll get word out and have them here in a lesson or two."