"I hate projects," Mildred grumbled. "Ordinary schoolwork's bad enough, why give us extra when we've only just come back? Especially when it has a hundred different parts and takes weeks and weeks to do."

"There aren't a hundred parts to it," Maud said. She pushed her spectacles up on her nose with one finger. "There's only the essay, the illustrations and the model. That's three. And the illustrations will be easy for you because you can draw so beautifully. Mine will probably be stick figures."

"I'll help you with the drawing if you help me with the writing," Mildred said absently. It was late afternoon and the library was nearly empty, with only a few girls occupying the long tables. She and Maud had gone through nearly every shelf, looking for the books they needed, and now they were all the way at the back, where the setting sun shone through stained-glass windows and cast fragments of red and orange and yellow on the floor. Outside, she could see the leaves on the trees beginning to change their colours to match. It was probably the last sunny day they would get for months, and here she and Maud were, wasting away in this musty old place.

She tilted her head sideways and ran a finger along the spines of the books on the shelf nearest to her. "I think this is still the wrong section, Maud. These are all about invisibility spells-oh-here's a funny-looking one."

"What's it called?"

"Hang on, it's stuck." She worked the book loose from between its shelf mates-it was taller and thinner than either of them, and bound in a rough, rusty black leather that tended to catch on things-and turned it over so they were both looking at the cover.

"Ufeful Inftruction-" she began.

Maud giggled. "Those aren't F's, they're S's. People used to write them that way, a long time ago."

"Of course you'd know." Mildred prodded Maud playfully in the side, just above her uniform sash. "All right, then. Useful Instruction for Young Witches, by Dorcas Proudfoot. Being an attempt to set down the knowledge of ages in a form suited to the limited abilities of callow youth to comprehend." She rolled her eyes. "Thanks a lot, Dorcas."

"I don't think they thought much of children back then," Maud said. "Anyway, never mind that dusty old thing. We still need to find the books for our project, remember?"

"I know." Mildred opened the book and yelped as yellowed flakes of the flyleaf fell out and rained down onto the scuffed toes of her boots. "It's practically falling to bits, but it looks more interesting than anything else we've seen. Let's read a few pages. Just five minutes won't hurt. Here, you hold it-it'll probably disintegrate completely if I touch it any more."

Maud wavered and gave in. "Fine. Only five minutes though, Millie. We really do have work to do."

She took the book from Mildred, holding it by the sturdier edges of its cover, and paged through it until she landed on a double spread. The left-hand side was filled with a scratchy ink illustration done in the perspective of someone at the bottom of a well, looking up its dark, dripping walls to a tiny circle of light at the top. The artist had lovingly rendered the gelatinous slickness of the moss-covered stones, making it clear that there was no hope of ever climbing them. The right-hand page had a few lines of verse, which Maud read aloud in a whisper.

"Ding dong dell
A witch is in the well
Who put her there?
People of the town
Who will take her out?
No-one ever will
In the deep she'll drown
In the water chill and black
Unless she knows the spell
For their bones to crack
For their will to break
For their strength to take
Then shall she escape"

Mildred pulled a face. "And I thought ordinary nursery rhymes were awful sometimes. What's on the next page?"

Maud turned the leaf over, carefully, so as not to crumble the brittle paper any worse than it already was. "This one looks like a fairy tale, but it's in a foreign language, I can't read it."

Mildred looked over her shoulder. "Il était une fois… That's French, I was learning it at my old school before I came here. I can't really read it either, though. Try another page."

"The next one's a rhyme too," Maud said, and read out:

"Creeping and crawling
Rising and falling
Reaching and grasping
Catching and clasping
Stinking and rotting-"

"Ugh! Never mind that." Maud hurriedly flipped a few more pages.

"What did the rest say?"

"You don't want to know."

"Don't want to know what, Maud Spellbody?"

To their credit, neither Mildred nor Maud started at the sound of Miss Hardbroom's voice behind them. After a few terms at Cackle's, nearly everyone got used to it, and learnt to recognise the barely audible whooshing sound of manifestation that usually preceded it. The other skill most people acquired early was reading the emotional weather on the deputy head's face, and now both girls turned around and checked that ominous forecast with some trepidation. Independently, they concluded that HB was curious, but not angry. Yet.

"Nothing, Miss Hardbroom," Maud said. "It's only a book we found. Useful Instruction for Young Witches."

"It's horrible," Mildred blurted out before she could stop herself. She half expected to be told off for it, but all that happened was Miss Hardbroom's forehead crinkling up in mild consternation.

"Really, Mildred. It's a bit old-fashioned, but still very effective as a teaching tool, I'm sure. I owned a copy when I was a child. My grandmother gave it to me for my fifth birthday, to improve my character."

Which was stranger, Mildred wondered, that HB thought a four-hundred-year-old book was only a bit old-fashioned, or that Granny Hardbroom had believed witches being drowned and things creeping and grasping were good bedtime reading for a tiny kid? She imagined a dark-haired little girl in a cold, shadowy room, poring over horrifying illustrations by the light of a single candle, and felt a moment of pity for Miss Hardbroom.

"Didn't it scare you, though?" breathed Maud, apparently thinking the same thing.

"Well, yes, I was quite frightened of it at first." Miss Hardbroom said this with an air of rather grudging tolerance toward her younger self. "In fact, I used to lock it in the cupboard before I went to bed, in case the things in the illustrations came to life in the night. But soon enough I saw how silly that was and learnt to focus on the lessons instead." She tapped the book with one ebony fingernail, as if to punctuate her statement.

"What sorts of lessons?" Mildred asked.

"Lessons all young witches should be taught," Miss Hardbroom said severely. "I suppose they still are in most witching families, only with softer methods."

"My mum certainly never told me any of these stories," Maud said, glancing down at the open page. "This one's called The Witch Who Practised Necromancy and Was Consumed by Evil Spirits."

Miss Hardbroom looked at the page too and seemed to shudder faintly, as if recalling an unpleasant memory. "Yes, that is one of the...darker sections I remember. Look, girls, this is all very well, but it won't help you with your project, which, I hardly need remind you, counts for a large part of your final mark. Give me the book-"

She held out her hand, and Maud, trained to obey, automatically put the book into it.

"And now get on with finding what you came for, or you'll miss your evening meal. Mrs Tapioca has been boiling it in the kitchen for hours."

Yuck, Mildred mouthed to Maud, who stifled a smile.

Both of them expected Miss Hardbroom to put the book back on the shelf, but instead she tucked it under one arm, made an imperious magical gesture, and disappeared the way she had arrived, leaving them alone in the dimming light as afternoon faded into evening.

"That was weird," Maud said.

Mildred nodded. "But it explains a lot about HB, doesn't it? I mean, if you and I had had grandmothers who gave us creepy books to improve our characters, we'd probably have turned out a bit unusual too, wouldn't we?"

"My gran gave me underpants with the days of the week on them for my last birthday," Maud said.

"Mine gave me a top that didn't fit and a cake I was allergic to," Mildred said with a giggle. "How lucky are we?"

"Pretty lucky," Maud said. "Come on, let's go have our boiled slop. We can come back and finish later."

"Maybe tomorrow?"

"Maybe tonight," Maud said, with a touch of Hardbroom-esque severity, and looped her arm through Mildred's. "Don't think you're off the hook that easily, Mildred Hubble!"

"I still hate projects," Mildred said.

"I know you do."

Arms still linked, they left the library together.