'Hello!' he said as soon as I had finished, kissed Friday and put out the bedside light. 'I've got some information for you.'

'About?'

'Yorrick Kaine.'

I took the Cat downstairs, where he sat on the microwave as I made some tea.

'So what have you found out?'

'I've found out that an alligator isn't someone who makes allegations — it's a large reptile a bit like a crocodile.'

'I mean about Kaine.'

'Ah. Well, I've had a careful trawl and he doesn't appear anywhere in the character manifests either in the Great Library or the Well of Lost Plots. Wherever he's from, it isn't from published fiction, poetry, jokes, non-fiction or knitting patterns.'

'I don't believe you'd come out here to tell me you've failed, Chesh,' I said. 'What's the good news?'

The Cat's eyes flashed and he twitched his whiskers.

'Vanity publishing!' he announced with a flourish.

It was an inspired guess. I'd never even considered he might be from there. The realm of the self-published book was a bizarre mix of quaint local histories, collections of poetry, magna opera of the truly talentless — and the occasional gem. The thing was, if they became officially published they were welcomed into the Great Library with open arms — and that hadn't happened.

'You're sure?'

The Cat handed me an index card.

'I knew this was important to you so I called in a few favours.'

I read the card aloud.

'At Long Last Lust, 1931. Limited edition run of one hundred. Author: Daphne Farquitt.'

1 looked at the Cat. Daphne Farquitt. Writer of nearly five hundred romantic novels and darling of the Romance genre.

'Before she was famous writing truly awful books she used to write truly awful books that were self-published,' explained the Cat. 'In At Long Last Lust, Yorrick plays a local politician eager for self-advancement. He isn't a major part, either. He's only mentioned twice and doesn't even warrant a description.'

'Can you get me into the vanity publishing library?' I asked.

'There is no vanity library,' the Cat said with a shrug. 'We have figures and short reviews gleaned from vanity publishers' manifests and Earnest Scribbler Monthly, but little else. Still, we need only to find one copy and he's ours.'

He grinned again but I didn't join him.

'Not that easy, Cat. Take a look at this.'

I showed him the latest issue of The Toad. The Cat carefully put on his spectacles and read: 'Danish book-burning frenzy reaches new heights with Copenhagen-born Farquitt's novels due to be consigned to flames.'

'I don't get it,' said the Cat, placing a yearning paw on a Moggilicious Cat Food advert, 'what's he up to burning all her books?'

'Because,' I said, 'he obviously can't find all the original copies of At Long Last Lust and in desperation has whipped up anti-Danish feeling as a cover. With luck his book-burning idiots will do the job for him. I'm a fool not to have realised. After all, where would you hide a stick?'

There was a long pause.

'I give up,' said the Cat, 'where would you hide a stick?'

'In a forest.'

I stared out of the window thoughtfully. At Long Last Lust. I didn't know how many of the hundred copies still remained, but with Farquitt's books still being consigned to the furnaces I figured there had to be at least one. An unpublished Farquitt novel the key to destroying Kaine. I couldn't make this stuff up.

'Why would you hide a stick in a forest?' asked the Cat, who had been pondering this question for some moments in silence.

'It's an analogy,' I explained. 'Kaine needs to get rid of every copy of At Long Last Lust but doesn't want us to get suspicious, so he targets the Danes — the forest - rather than Farquitt — the stick. Get it?'

'Got it.'

'Good.'

'Well, I'd better be off, then,' announced the Cat, and he vanished.

I was not much surprised at this for the Cat usually left in this manner. I poured the tea, added some milk and then put some mugs on a tray. I was just pondering where I might find a copy of At Long Last Lust and, more importantly, thinking of calling Julie again to ask her how long her husband flicked on and off 'like a light bulb' when the Cat reappeared balanced precariously on the Kenwood mixer.

'By the by,' he said, 'the Gryphon tells me that the sentencing for your fiction infraction is due in two weeks' time. Do you want to be present?'

This related to the time I had changed the ending to Jane Eyre. They found me guilty at my trial but the law's delay in the BookWorld just dragged things on and on.

'No,' I said after a pause. 'No, tell him to come and find me and let me know what my sentence will be.'

'I'll tell him. Well, toodle-oo,' said the Cat, and vanished, this time for good.

I pushed open the door of Mycroft's workshop with my toe, held it open for Pickwick to follow me in, then closed it before Alan could join us and placed the tray on a worktop. Mycroft and Polly were staring intently at a small and oddly shaped geometric solid made of brass.

'Thank you, pet,' said Polly. 'How are things with you?'

'Fair to not very good at all, Auntie.'

Polly was Mycroft's wife of some forty-two years and although seemingly in the background was actually almost as brilliant as her husband. She was a bouncy seventy and managed Mycroft's often irascible and forgetful nature with a patience that I found inspiring. 'The trick,' she told me once, 'is to regard him like a five-year-old with an IQ of two hundred and sixty.' She picked up her tea and blew on it.

'Still thinking about whether to put Smudger on defence?'

'I was thinking of Biffo, actually.'

'Smudger and Biffo would both be wasted on defence,' muttered Mycroft, making a fine adjustment on one face of the brass polyhedron with a file. 'You ought to put Snake on defence. He's untried, I admit, but he plays well and has youth on his side.'

'Well, I'm really leaving team strategy to Aubrey.'

'I hope he's up to it. What do you make of this?'

He handed me the solid and I turned the grapefruit-sized object over in my hands. Some of the faces were odd sided and some even sided — and some, strangely enough, appeared to be both. My eyes had trouble making sense of it.

'Very . . . pretty,' I replied. 'What does it do?'

'Do?' Mycroft smiled. 'Put it on the worktop and you'll see what it does!'

I placed it on the surface but the oddly shaped solid, unstable on the face I had placed it upon, tipped on to another. Then, after a moment's pause, it wobbled again and fell on to a third. It carried on in this jerky fashion across the worktop until it fell against a screwdriver, where it stopped.

'I call it a Nextahedron,' announced Mycroft, picking up the solid and placing it on the floor, where it continued its random perambulations, watched by Pickwick, who thought it might be chasing her, and ran away to hide. 'Most irregular solids are only unstable on one or two faces. The Nextahedron is unstable on all its faces — it will continue to fall and tip until a solid object impedes its progress.'

'Fascinating!' I murmured, always surprised by the ingenuity of Mycroft's inventions. 'But what's the point?'

'Well,' explained Mycroft, warming to the subject, 'you know those inertia! generator things that self-wind a wristwatch?'

'Yes?'

'If we have a larger one of those inside a Nextahedron weighing six hundred tons, I calculate we could generate as much as a hundred watts of power.'

'But. . . but that's only enough for a light bulb!'

'Considering the input is nil, I think it's a remarkable achievement,' replied Mycroft somewhat sniffily. 'To generate significant quantities of power we'd have to carve something of considerable mass — Mars, say — into a huge Nextahedron with a flat plate falling around the exterior, held firm by gravity. The power could be transmitted to earth using Tesla beams and . . .'