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‘But then why would it matter whether the books were up to date?’ I said, ignoring the sideswipe. ‘For a mortgage. And why do you suppose Tot insists that every guest has treatments?’

‘Isn’t that Dr Laidlaw?’ Alec said.

‘No, I’m sure it’s Tot. One of the bright young things that’s really here for the casino was moaning about it. They’ve even got Grant signed up for galvanic baths, whatever they are.’

‘That can’t be related,’ Alec said.

‘And what do you suppose he meant by that nasty vague threat about the mediums?’ I asked.

‘I’ve no idea, but I think we should get Grant safely away before it happens. Terrace or winter gardens?’ Alec said. ‘I need to speak to you.’

‘Depends if we need privacy,’ I said. ‘It’s such a lovely day the winter gardens will be deserted.’

‘Winter gardens it is,’ he agreed. ‘I’ve got the post-mortem report and I rather think privacy would be a good thing.’

I would have preferred fresh air, not to say a stiff breeze, if I was to be the audience for a report on livers and kidneys and suchlike, but the terrace was at capacity, muffled figures rolled in blankets on every deckchair, making the most of the brightness even though there was precious little warmth to the sunshine this late in the year. We settled ourselves under one of the open roof-vents, but since the gardeners had been misting the orchids very recently it was a stuffy spot nonetheless, not to mention the faint residue of alcohol and tobacco smoke which I could not miss, now that I had seen all the drinking and carousing which went on in here.

‘Well?’ I said. ‘Poison?’

‘Not a one,’ Alec replied. ‘Not a trace, not a wisp of anything in any of her organs. Nothing.’

‘And her heart was healthy.’

‘Her heart was fine.’

‘So what did she die of?’

‘Dieting?’ said Alec. ‘I’m only half joking. The doctor said again in the report what he said at the graveside. She had nothing in her stomach at all. Or anywhere. She was empty.’

‘Well, those bladders and adjacent systems you spoke about often… empty out at the last,’ I said. ‘It never happens in the beautiful death scenes in plays but I learned as much in the convalescent home.’

‘As did I in the trenches,’ Alec said. He sat forward and stared at the floor. ‘I feel wretched for the Addies, you know. I persuaded them to dig the poor old girl up and there’s nothing to show for it except a hint that her last few days were a misery for a woman who so much enjoyed her food. I can’t even lay hands on her jewellery and send it back to them.’

‘Jewellery?’

‘Well, the watch.’

‘Jewellery,’ I said again.

He looked up at me. ‘What is it, Dan?’

‘I’ve got it,’ I breathed.

‘Oh, at last,’ said Alec. ‘Go on then.’

‘It was something Regina said,’ I told him. ‘And I couldn’t remember what it was. I’ve been kicking myself that every time I talk to Regina I’m in a robe and turban without any of my things – my notebook and pencil – and I couldn’t write it down. But it’s not just that, you see. And then watching the librarian locking up yesterday made it even worse. I dreamed about it last night. And then I saw Grant sitting there this morning and she looked so out of place in her outdoor clothes.’

‘Well, what is it? Tell me,’ Alec said.

‘I know where Mrs Addie’s bag is,’ I said. ‘I never have my things when I speak to Regina because she takes away one’s clothes and folds them and she takes away one’s bag and jewellery and puts them in a sort of… it’s hard to describe but the clasp is very like the one I saw the librarian closing… then into a locked cupboard in return for a ribbon, with a key, which you wear round your wrist.’

‘And if Mrs Addie died – of untraceable poison? – in the mud room by the Turkish baths…’ Alec said.

‘Her clothes were folded in a neat bundle and could be produced a month later when someone thought of them,’ I said. ‘But her bag must have been locked away in a little pouch in a cupboard. Regina said guests sometimes leave things in there for weeks together, because it’s so secure. I’ll bet you anything you like it’s still there.’

‘But why didn’t they think of it?’ Alec said. ‘Whoever it was who killed her. Mrs Cronin, or Regina, or one of the Laidlaws.’

‘Definitely not Regina,’ I said.

‘Why not?’

‘Because,’ I said, ‘I think Regina probably noticed the clothes. She gave them to… Mrs Cronin, who gave them to Dr Laidlaw or Tot. But they couldn’t explain to the Addies why they weren’t with the rest of their mother’s things so they just hung on to them. Until we came along and they cut their losses. But if Regina had killed her she’d have remembered about the bag too.’

‘And why didn’t the real killer remember?’

‘Because no one else apart from Regina is as bound up with the question of keys and lockers and so it didn’t occur to them.’

‘But why didn’t anyone see the key? On the ribbon? On the corpse?’ Alec asked me, but even as he spoke the answer occurred to him and he groaned.

‘The ribbon came off the corpse when they heaved it out of the mud bath,’ I said. ‘If we really want Mrs Addie’s father’s watch back again we need to go to the apple house and start digging.’

Clearly, it was my turn for a task such as this one, after Alec’s graveside duty the day before, and so it is testament to his character as nothing else could be that he insisted we both go. We took stout waxed gloves and scarves to tie over our faces and we made a silent agreement to forget the emptiness of poor Mrs Addie’s various bodily systems, or not to discuss it anyway.

Besides, now that I knew that the smell was only more of the Moffat brimstone, along with a few traces of nothing worse than I had encountered during the war, it did not seem to smell quite as bad as it had before.

‘Shall we just shovel it out then?’ Alec said. As well as the opening in the top of the bath where one stepped in, there was a trapdoor in the back closed with a pin and sealed with some kind of putty and it looked as though most of the contents might run out quite readily if we got it open.

‘You shovel and I’ll go through the shovellings,’ I said, claiming the worst of the job for myself. Alec wrenched up the pin and removed it and immediately there was a cracking noise as the putty seal around the little door began to bulge.

‘I think you fit the pin in there to act as a handle,’ I said, pointing. Alec nodded and did so. Then he looked at me, pulled the scarf a little higher over his nose and yanked the door open.

I stepped back, but it was not the volcanic flow of reeking slime I was expecting. Instead, inside the trapdoor was a wall of dried grey clay which hardly moved except for a few flakes falling off and crumbling as they hit the floor. Alec raised his shovel to strike at the block of clay, but I stopped him.

‘Wait!’ He froze with his hands above his head. ‘Look!’ I said. I bent in close to the opening, pointing at a crack in the mud. I took my glove off for this was careful work. I picked away at the crack for a minute and then rubbed hard with the pads of my finger and thumb. Where I had rubbed one could see the faint pink colour of a scrap of fabric, less than a quarter-inch across. It was the needle in our particular haystack: the end of the ribbon. I took the scarf away from my face and grinned up at him.

‘I declare this key found,’ I said, and pinching the fraying end hard between my nails I pulled, it gave, I pulled some more, I had three inches of it out now and I took a better hold. A firm tug and it was six inches. I wrapped it around my hand.

‘Stop!’ Alec cried.

He was too late. I sat back with the whole length of unknotted ribbon in my hand and looked at the wall of mud somewhere inside of which the tiny key was still hiding.

‘Sorry,’ I said.

‘Don’t mention it,’ said Alec. ‘I always preferred knocking down sandcastles to building them.’ He raised the shovel high over his head again and brought it down cleanly into the middle of the clay.