'You'd better look through these, Scilla,' I said.

'You look,' she said, glancing up from her letters with a smile. 'You can tell me what's what, and I'll look at them presently.'

Bill had had no secrets. The notebooks mainly contained his day-to-day expenses, jotted down to help his accountant at the annual reckoning. They went back some years. I found the latest, and leafed through it.

School fees, hay for the horses, a new garden hose, a repair to the Jaguar's head-lamp in Bristol, a present for Scilla, a bet on Admiral, a donation to charity. And that was the end. After that came the blank pages which were not going to be filled up.

I looked again at the last entries. A bet on Admiral. Ten pounds to win, Bill had written. And the date was the day of his death. Whatever had been said to Bill about Admiral's falling, he had taken it as a joke and had backed himself to win in spite of it. I would dearly have liked to know what the 'joke' had been. He had told Pete, whose mind was with the horses. He had not told Scilla, nor any of his friends as far as I could find out. Possibly he had thought it so unimportant that after he spoke to Pete it had wholly slipped his mind.

I stacked up the notebooks and began on that last pigeon-hole full of oddments. Among them were fifteen or twenty of the betting tickets issued by bookmakers at race meetings. As evidence of bets lost, they are usually torn up or thrown away by disappointed punters, not carefully preserved in a tidy desk.

'Why did Bill keep these betting tickets?' I asked Scilla.

'Henry had a craze for them not long ago, don't you remember?' she said. 'And after it wore off Bill still brought some home for him. I think he kept them in case William wanted to play bookmakers in his turn.'

I did remember. I had backed a lot of horses for halfpennies with Henry the bookmaker, the little shark. They never won.

The extra tickets Bill had saved for him were from several different bookmakers. It was part of Bill's pleasure at the races to walk among the bookmakers' stands in Tattersall's and put his actual cash on the best odds, instead of betting on credit with a bookmaker on the rails.

'Do you want to keep them for William still?' I asked.

'May as well,' said Scilla.

I put them back in the desk, and finished the job. It was late in the afternoon. We went into the drawing-room, stoked up the fire, and settled into armchairs.

She said, 'Alan, I want to give you something which belonged to Bill. Now, don't say anything until I've finished. I've been wondering what you'd like best, and I'm sure I've chosen right.'

She looked from me to the fire and held her hands out to warm them.

She said, 'You are to have Admiral.'

'No.' I was definite.

'Why not?' She looked up, sounding disappointed.

'Dearest Scilla, it's far too much,' I said. 'I thought you meant something like a cigarette case, a keepsake. You can't possibly give me Admiral. He's worth thousands. You must sell him, or run him in your name if you want to keep him, but you can't give him to me. It wouldn't be fair to you or the children for me to have him.'

'He might be worth thousands if I sold him – but I couldn't sell him, you know. I couldn't bear to do that. He meant so much to Bill. How could I sell him as soon as Bill's back was turned? And if I keep him and run him, I'll have to pay the bills, which might not be easy for a while with death duties hanging over me. If I give him to you, he's in hands Bill would approve of, and you can pay for his keep. I've thought it all out, so you're not to argue. Admiral is yours.'

She meant it.

'Then let me lease him from you,' I said.

'No, he's a gift. From Bill to you, if you like.'

And on those terms I gave in, and thanked her as best I could.

The following morning, early, I drove to Pete Gregory's stables in Sussex to jump my green young Forlorn Hope over the schooling hurdles. A drizzling rain was falling as I arrived, and only because I had come so far did we bother to take the horses out. It was not a very satisfactory session, with Forlorn Hope slipping on the wet grass as we approached the first hurdle and not taking on the others with any spirit after that.

We gave it up and went down to Pete's house. I told him Admiral was to be mine and that I would be riding him.

He said, 'He's in the Foxhunters' at Liverpool, did you know?'

'So he is!' I exclaimed delightedly. I had not yet ridden round the Grand National course, and the sudden prospect of doing it a fortnight later was exciting.

'You want to have a go?'

'Yes, indeed,' I said.

We talked over the plans for my other horses, Pete telling me Palindrome was in fine fettle after his Cheltenham race and a certainty for the following day at Bristol. We went out to look at him and the others, and I inspected the splint which Heavens Above was throwing out. His leg was tender, but it would right itself in time.

When I left Pete's I went back to Brighton, parking the Lotus and taking a train as before. I walked out of Brighton station with a brief glance at the three taxis standing there (no yellow shields) and walked briskly in the direction of the headquarters of the Marconicars as listed in the telephone directory.

I had no particular plan, but I was sure the core of the mystery was in Brighton, and if I wanted to discover it, I would have to dig around on the spot. My feelers on the racecourse had still brought me nothing but a husky warning on the telephone.

The Marconicars offices were on the ground floor of a converted Regency terrace house. I went straight into the narrow hall.

The stairs rose on the right, and on the left were two doors, with a third, marked Private, facing me at the far end of the passage. A neat board on the door nearest the entrance said 'Enquiries'. I went in.

It had once been an elegant room and even the office equipment could not entirely spoil its proportions. There were two girls sitting at desks with typewriters in front of them, and through the half-open folded dividing doors I could see into an inner office where a third sat in front of a switchboard. She was speaking into a microphone.

'Yes, madam, a taxi will call for you in three minutes,' she said. 'Thank you.' She had a pleasant high voice of excellent carrying quality.

The two girls in the outer office looked at me expectantly. They wore tight sweaters and large quantities of mascara. I spoke to the one nearest the door.

'Er- I'm enquiring about booking some taxis- for a wedding. My sister's,' I added, improvising and inventing the sister I never had. 'Is that possible?'

'Oh, yes, I think so,' she said. 'I'll ask the manager. He usually deals with big bookings.'

I said, 'I'm only asking for an estimate- on behalf of my sister. She has asked me to try all the firms, to find out which will be most – er – reasonable. I can't give you a definite booking until I've consulted her again.'

'I see,' she said. 'Well, I'll ask Mr Fielder to see you.' She went out, down the passage, and through the door marked Private.

While I waited I grinned at the other girl, who patted her hair, and I listened to the girl at the switchboard.

'Just a minute, sir. I'll see if there's a taxi in your area,' she was saying. She flipped a switch and said, 'Come in, any car in Hove two. Come in, any car in Hove two.'

There was a silence and then a man's voice said out of the radio receiving set, 'It looks as though there's no one in Hove two, Marigold. I could get there in five minutes. I've just dropped a fare in Langbury Place.'

'Right, Jim.' She gave him the address, flipped the switch again, and spoke into the telephone. 'A taxi will be with you in five minutes, sir. I am sorry for the delay, we have no cars available who can reach you faster than that. Thank you, sir.' As soon as she had finished speaking the telephone rang again. She said, 'Marconicars. Can I help you?'