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‘If he knew,’ said Alec.

‘Ah, but I think he did,’ I said. I was still feeling rather proud of this piece of deduction. ‘I think that at the very least he was in touch with Pip Balfour, that they had met and spoken. They were cousins, but not long-lost ones – or if they had been they’d found one another again.’

‘Because of the high esteem and all that,’ said Alec.

‘Well, that’s part of it,’ I said, trying not to look crestfallen, ‘but also – and this has only just occurred to me – because he left the fortune to George Pollard outright. Just to him. Not to his heirs and successors and there was no mention of what would happen if Pollard was no more.’ Alec was frowning at me. ‘I mean to say, darling, if you were to leave your last penny to someone you’d have to know that he was still alive to get it.’

‘That doesn’t make any sense at all,’ Alec said. ‘You’ve been misled by hindsight, Dan. You’re thinking about it in entirely the wrong way.’

Of course, it was at that moment that the waitress reappeared with her little notebook to take our order. I was vaguely aware of Alec listing our requirements but even though I left it to him and thought furiously I could still see no problem in my reasoning by the time she had gone.

‘Oh come on, Dandy, this isn’t worthy of you,’ he said when he turned back and saw my knitted brows. ‘Why didn’t Pip Balfour bother with survivorship and all that?’

‘Because he knew Pollard was alive and well,’ I said. ‘I told you.’ We stared at one another in silence for a minute until Alec gave in.

‘And knew that Pollard would still be alive and well when he himself died because he knew he’d be dying soon?’ I could feel the flush beginning and did not even bother trying to hide it. Besides, I was soon distracted from my embarrassment by the new puzzle Alec had unearthed out of the old one.

‘So… why would he have written it that way?’ I said. Alec shrugged his shoulders.

‘Makes no sense to me,’ he said. ‘Seems completely insane.’

‘And therefore completely in character,’ I said. ‘Another of Pip Balfour’s silly little teases? Did he mean for Lollie to find out about the will and spend her life worrying over it? If so, we’re back to the theory that George Pollard – not to mention Josephine Carson – doesn’t exist at all.’

‘But we just decided we didn’t believe in Pip’s teases, didn’t we?’

‘And I was sure that this George Pollard character must have got into the house and done the murder.’

We were sitting in blank stupefaction when our tea tray arrived and the little waitress looked delighted; she must have thought our tryst had descended into a quarrel.

‘Oh, heaven!’ I said, as Alec poured a thin stream of straw-coloured China tea into my cup. ‘Mrs Hepburn’s brews could be eaten with a knife and fork. And no milk, thanks. No, no sugar, nothing.’ I blew into my cup, took a long fragrant sip and smiled at him.

‘What about these two maids who witnessed it?’ Alec said at last. ‘Perhaps they’d be able to throw some light on matters?’

‘How?’ I said, remembering what Mr Faulds had thought about the unlikelihood of them seeing anything except the signature itself.

‘I don’t know,’ Alec said. ‘I’m casting around for anything, really. Odd that they should both have left, though. If they knew what was in the will and they knew George Pollard – from his coming to the house, perhaps – and one of them told Pollard for a cut of the money…’

‘But he didn’t come to the house,’ I said. ‘None of the servants remember ever hearing of him. And anyway, if Miss Abbott or Maggie had done that, they’d never have left. They’d have stayed. To let Pollard in. Because someone must have. No, I think the fact that the witnesses both left their jobs is far more suggestive of the will being a joke on Lollie. Pip wasn’t ready for her to find out and he made a concerted effort to get rid of the two people who could tell her that he’d written a new will in case she somehow persuaded the solicitor to let her see it.’

‘And he wrote it in March,’ Alec said. ‘Is that significant? Did anything happen in March?’ I shrugged. ‘And what was he waiting for, do you suppose? When was he going to tell Lollie about it? Was there some significant time to do that for any reason?’ I shrugged again.

‘Was there any significant timing in any of it?’ I said, and then I stopped chewing my mouthful of bread-and-butter.

‘Dandy?’

‘Yes,’ I said, through crumbs, ‘there was. Miss Abbott and Maggie witnessed the will. Miss Abbott left Lollie shortly afterwards. Maggie left on Saturday. Pip was killed sometime during Monday night, as soon as both witnesses were out of the house. I’ve no idea what it means but it can’t be a coincidence, surely.’

‘Well, they must be found,’ Alec said. ‘All three of them. Abbott, Maggie and Pollard.’

‘If there is such a person,’ I reminded him. ‘He’s popping in and out of existence like a jack-in-the-box.’ I put my elbows on the table and my head into my hands and groaned. ‘I thought you’d clear everything up for me! I thought if I got up into the air and talked it all through, things would be revealed in simple outline. And you’ve only made it madder and more confusing than ever and – worst of all – I know there’s something not right that I was closer to realising before today than I am now. I almost got it lying in bed last night, or was it this morning? It’s something to do with lying in bed anyway. Now it’s completely gone.’

‘What do you mean, “up into the air”?’ said Alec, which was very kind of him, for he might easily have taken offence at my sharing out of the blame in the way I had.

‘Hm?’ I said. ‘Oh, just life below stairs, you know. I hadn’t expected it to feel so literal, but to eat and work and sleep in a sub-basement with a whole house pressing down upon one is not conducive to leaps of reason. I just think if I could climb a high hill and look down I’d be able to see more.’

‘Well,’ said Alec, ‘I don’t think we can manage a hill, but we can certainly get you up into the air. Look, you wrap two cakes in your hanky and I’ll wrap two in mine.’

‘Four cakes?’ I said. ‘Didn’t you have any luncheon?’

‘One each,’ said Alec. ‘You – as befits the boss of this little outfit – have been marvellously focused but I’m far more easily distracted and I can’t stand it any more. Listen.’

When I did, I could hear the duet from the pavement: low, sustained howling and a series of percussive little yips.

‘She’s a very bad influence on Millie,’ said Alec, grinning. ‘Come on, let’s take them up the Scott Monument and tire them out for the evening.’

The Scott Monument – erected in honour of Sir Walter specifically and not, as I had long believed, to the general and misspelled glory of the Scots race – was a kind of airy turret in High Victorian Gothic style, not attached to anything but just rising up out of the grass as though some ecclesiastical architect had lavished all of his attention on the decorative touches but forgotten to build the cathedral itself. ‘Better than the Albert Memorial’ was the best one could say about it, and it was smaller, too – and sooty black, like everything in Edinburgh which cannot brush itself down or send itself to the laundry – so at least it did not draw the eye.

I had never climbed up it before, had in fact congratulated myself on not letting my sons find out that one could (for they would have badgered me to death on every shopping trip if they had known), and should have realised, from the fact that I had never noticed anyone else scaling its heights, that the staircases were hidden away at its core. As Alec, Bunty, Millie and I toiled up the darkest, narrowest, steepest spiral staircase imaginable, breathing in the sharp stink of damp, tarry stone, I could not help thinking that I could have reproduced the experience in the six floors of Number 31 in far greater comfort, and saved my sixpence.