"Do you have any intentions of hurting anyone or anything while you're here?"

"No," says Miss Honey, with a questioning glance at Matilda. Matilda shrugs.

Terali is again fairly surreptitious about the chalk-smudging. She incorporates it into a polite bow. "There's a witch in the office down the hall."

"Let's go meet the witch, then," says Miss Honey, stepping forward to take Matilda's hand.

Kerah and Terali lead them down the hall. There is a large room that says Raha Torail-sa, Witch on the door and inside contains cauldrons and a whole lot of assorted plants and substances in various glass containers and baskets. The witch is about forty, also red-haired but with a scarf keeping her hair up and out of her face, and wearing a much simpler outfit than the wizards, with an apron covering most of it. "Hello! You must be Matilda and - Jennifer Honey? Am I pronouncing those right?"

"It sounds like it might be fun," says Matilda. "Oh, but we should probably do the clocks thing first." She digs a watch out of a pocket of her dress. "Can someone cast the spell that tells time, please?"

Terali does that.

"There are five splits to a tick, twenty-five ticks to a degree, twenty-five degrees to an angle, and twenty-five angles to a day," says Terali.

"Sixty seconds to a minute, sixty minutes to an hour, twenty-four hours to a day," says Matilda. "So your days are a smidge shorter than ours, they're, let me see, twenty-one hours forty-two minutes and five seconds. Okay. That's probably not too bad."

"You're very good at mental arithmetic," observes Raha.

"I like numbers."

"They come up a little in witchcraft - measuring things, mostly - but it's not very elaborate math," says Raha. "I'm trying to think of what the fastest way to see if you can do witchcraft would be. Maybe something like elixir base - it's not the first thing we usually learn, but that's because we try to start with good work habits and learning what all the ingredients are first, and if you can't do the magic that would only waste your time." Raha starts collecting various bottles of things.

Matilda peers interestedly at the bottles of things!

"This is just pure water," says Raha. "And this is pef tan, which is a flavor enhancer, because people do have to drink their elixirs. And this is lemon peel, and this is grass salt. It doesn't actually matter what kind of salt you use, but I use grass salt because of a religious dietary law. Four ingredients."

Matilda nods solemnly.

"A small batch of elixir base is one measure of water and one pinch of everything else," says Raha, and she gets a little bowl. "It doesn't even need to be heated. But if I don't do any magic to it -" She scoops some water into the bowl and takes a pinch of each of the other three things and stirs them around. Nothing happens. "They just float there. The salt dissolves, but not particularly fast." She sets that bowl aside and dips up a new measure of water. "Witchcraft means waking up the ingredients so that they'll behave. In the case of elixir base, we want them to behave two ways - we want the lemon peel and pef tan to dissolve along with the salt, and the whole thing to thicken. I don't cast any spells, so there's nothing much to look at, but -" She stirs, pinching salt into the water. It just about vanishes on contact; the viscosity goes up. She adds pef tan and lemon peel; they do the same thing. Now she has a bowl of something about the consistency of maple syrup, just barely yellow-green, nothing floating on it at all. "See?"

"Magic!" says Matilda. "But how do you do it?"

"That's the part that's hard to explain! Most of it is just paying attention. Here." She gets a third bowl. "Dip up a measure of water for yourself - it works best if you're doing all the moving around of the ingredients."

"Okay." She dips up a measure of water. "I wonder if it would be better or worse if I did any of my magic to it. I think probably it's simpler if I don't."

"Probably," agrees Raha. "I guess you could use it to stir, sorcerers can do that and it doesn't interfere, but we're trying to find out if you can make elixir base the usual way. Stir the water around and note how thin it is. You can taste a little if you think it might help -" She gets a spoon. "It needs to be thicker so you can add other things to it later and make elixirs. If you stir it a little slower, as though it were resisting you, you can imagine how it will be when it's all done, like I showed you - and then pinch in the salt and stir even slower..."

"There you go! Now, just the same with the lemon peel and pef tan."