My grandfather promised to leave me this watch in his will the day the doctor told him he had three months to live.

I'd been saying how sorry I was when he raised his hand. "Don't be sad," he said. "Time is relative."

"It seems pretty damned real to me," I replied. "When you cross the road, you wait a few seconds for the car to go past or you die."

He smiled and shook his head. "Einstein said everything is relative except the speed of light. You can do deals." My grandfather had spent his early adult life managing minor variety acts; to him everything was a deal.

"But you've got to face facts, Granddad. You're only going to be around three months. Five or six with remission."

"Three months to you, maybe. But for me it will be a hundred years. You're already thinking of me as dead, but you're wrong. Like that man who jumped off the Empire State Building. As far as common sense goes, he was finished, but a gust of wind caught him and blew him in through someone's office window. He was completely unharmed."

"And you think he did some kind of deal?"

My grandfather smiled and shrugged his shoulders. "Who knows?" he replied. "I certainly shall."

I said good-bye to him, then, because I had to go to America on a four-month lecture tour. We kept in touch by E-mail (my grandfather liked to keep up-to-the-minute), and at his request I didn't return to England for the funeral or the reading of the will.

All I knew was that there was an envelope waiting for me at the solicitors', which, as I guessed, contained a beautiful, hand-engraved fob-watch, with Baxter and Simmonds, London, 1889 engraved on the back. The only other thing in the envelope was a slip of paper with the words "It's been an interesting century" written on it in my grandfather's handwriting. Of course, he had lived from 1903 to 1995, but I also remembered his boast that his last few months would seem like a hundred years.

The watch was perfect for me. It went with my slightly tweedy look. I dress like this because I like it, and because it commands a certain respect from students and senior academics, and at first I thought my grandfather had left me the watch just for the style of it.

For the first couple of weeks I wore my Longines (classic, with Roman numerals) as a back-up, but stopped when I realised the fob watch kept perfect time.

But a few weeks later it lost a couple of minutes. I was walking to the British Museum, cutting across Tottenham Court Road. I glanced at the watch, which said it was three minutes to one, then I noticed a bank of televisions in a shop window showing the opening sequence of the BBC One-o-Clock News. As I turned into Great Russell Street I saw a meter maid ticketing a car, and noticed two more illegally-parked cars ahead of me. I pulled out my watch as I walked and shifted the hands to one-o-clock, and as I did so I experienced the strangest sensation, a tightening round my forehead, a prickling on the back of my neck.

When I looked up, the whole street had changed.

I don't mean it was a different colour or anything, but all the people were different. A gaggle of foreign tourists had moved across the road, and a student of mine I hadn't noticed before was suddenly standing on the pavement in front of me, smiling shyly. I nodded, and went back to looking round. The meter maid had vanished altogether; then I caught sight of her with her back to me at the other end of the block, ticketing another car.

The car next to me had its ticket, but the intervening cars had been left alone.

A woman stepped out of one of the book shops, looked from the expired meter to the traffic warden, smiled delightedly, got into her car and drove away.

Later, sitting beneath the great jasper dome of the Reading Room, I tried moving the hands of my watch again. Nothing happened to the people working round me, and I didn't have that tight feeling in my temples. I set my watch to the right time, and forgot about the whole thing.

As soon as the vacation began, I went down to visit my grandmother. She quite understood my missing the funeral, and didn't mind my taking a late train, but she wanted to see me and I didn't like to disappoint her.

So it was with a feeling of anger and disappointment that I sat stuck on the Northern Line, listening to the muffled apologies of the driver over the Underground's loudspeaker system, waiting as the hands of my beautiful watch ticked up to and past the time of the last main line train.

That anger and disappointment seemed to centre in a ring of pressure round my forehead, and the hairs on the back of my neck started to prickle. I moved the hands of my watch again, back ten minutes, and the feeling eased. I found myself in a much more crowded tube train that was moving quickly. It pulled into London Bridge station with seven minutes to spare.

Sitting on the main line train, I moved the hands of the watch once more, but nothing unusual happened. I shrugged, and occupied my time watching the lights of South London turn into dark Surrey countryside, and daydreaming about what I could do if I, too, learned how to do deals with time.

My grandmother had a light meal ready for me when I arrived. As I ate it, I asked her about my grandfather's last three months. She said he'd been happy, but that he'd aged terribly as the disease had taken hold.

And he'd gone out a lot, she'd said, walking his old dog on the Downs when the doctor warned him to stay in bed, coming back exhausted, with a strange look in his eyes.

I shivered. If Grandpa had really done deals with time, what was to say he wasn't out on the hills at that very moment? Then I noticed the dog sleeping peacefully by the fire, which it wouldn't have done if the old man had been near. I went up to bed in the little attic room I'd used as a child, and slept like a log.

"It's a lovely day," my grandmother remarked over breakfast. "Would you mind taking Rufus out? My legs aren't what they used to be, and he hasn't had a decent walk since your grandfather passed away."

The old dog was delighted, tugging at his leash all the way along the road to the stile, where I could let him run free.

I was alarmed to see him race up the hill towards the old monument, a local beauty spot. Years spent in libraries and conferences meant I wasn't as fit as I should have been, and climbing the steep hillside had me out of breath in no time. But whether it was because he was following a familiar route he'd taken with my grandfather, or whether he caught a glimpse of a figure on the crest of the hill, the dog raced upwards and I had no choice but to follow.

I certainly saw someone.

It was an elderly man, visible for just a few seconds in the morning sunlight. I'd like to say I hurried towards it, but that would be an exaggeration. What I can say is that the glimpse of that familiar figure gave me the incentive to climb all the way to the top, where I collapsed on the base of the monument, looking down at the folded hills and the small triangle of sea I used to find so fascinating when I was a boy.

I lit a cigarette and enjoyed the view while Rufus ran round in aimless circles, sniffing the grass.

A gust of chill wind brought the sound of a train to my ears, and at first I was angry that something man-made was interfering with the sunlight and birdsong of that lovely morning.

Then I saw the train chugging between the hills towards London.
I was lighting another cigarette when I realised that though I'd seen the train to my left, the sound had come from the right.

I whirled round to see a second train winding South.

I should have explained that the line between my grandmother's station and the sea is a single track, and that there's been a lot of talk since the Cowden accident that the drivers should be supplied with two-way radios, as their telephones won't operate in these hills.

Logically speaking it makes no sense, because the distances are too great, but in that moment I could see people at the windows of both trains. Businessmen on their way to London reading papers, children looking out of the window, anxious for their first glimpse of the sea.

The crash, when it came, would happen out of sight behind a hill. The sheer horror of it brought a feeling of tightness to my forehead, and a prickling to the back of my neck.

I took my grandfather's watch out of my pocket, and adjusted the hands.