In fact, this stretch of the A6 was one of the designated ‘hot routes’ – the most popular roads among bikers, especially on bank holiday weekends. There was another section between Buxton and Taddington, but it was the Cat and Fiddle road into Staffordshire that had received most attention, ever since a bikers’ magazine described it as more exciting to ride than the Manx TT. The latest figures showed motorcyclists accounting for a quarter of all fatalities and injuries on the roads in the county. No surprise, perhaps, when they seemed to be drawn to the most dangerous places.

Despite their appearance, some of these bikers would be riding circuits around the valley later in the day. And if it was a good day, no one would actually die.

‘So where are these people who think they saw the shooting victim on Saturday?’ said Murfin, yawning extravagantly.

‘Rose Shepherd was seen at the Riber Tea Rooms on South Parade, and the Aquarium on North Parade. Oh, and the Masson Mill shopping village. That’s a bit further down the road from here.’

‘We’ll have to split up, I suppose.’

‘It’ll be a lot quicker, Gavin.’

‘Hey, we’re not going in all these shops, are we?’

‘We ought to go into any that are close to where Miss Shepherd was seen. We’ve got to be thorough, while we’re here. The DCI wants a picture of what the victim was doing here, and who she met in the hours before she died.’

‘Shopkeepers, eh? I just hope they’re friendly.’

‘You’ll survive.’

Murfin wasn’t the only officer Cooper had heard expressing reluctance to enter shops on duty. Talking to shopkeepers had been part of the routine in his father’s time. But that was before they started measuring police performance against key indicators – which didn’t include retail crime. So shoplifting had become low priority. The larger businesses hired their own security guards and adjusted their budgets to account for ‘slippage’. Small businesses couldn’t do that. And an unsuspecting police officer made a handy target for a shopkeeper’s frustration.

He managed to park the Toyota on the roadside between Hodgkinson’s Hotel and a shop called The Biker’s Gearbox. Then he and Murfin took a parade each.

‘Tell the missus I died a hero’s death,’ said Murfin as he got reluctantly out of the car.

Cooper had drawn North Parade, and had to walk back the way he’d come. There must be a dozen cafés and fish restaurants in this length of road alone: Taste of the Waves, Frankie and Joe’s, the Promenade Fish Bar … And then there were all the pubs and restaurants, and the big hotels on the hillside.

Between them, they accounted for the most distinctive feature of Matlock Bath, a characteristic that Cooper remembered so well from previous visits and which was still present now, undiminished by the years. It was the smell of fish and chips, hot and vinegary, hanging permanently over the promenade like a haze.

Many of the shops, amusement arcades and restaurants were closed. Of course, it was a weekday and out of season, with the children back at school for the new term. But some had opened to cater for the bikers and a few other visitors.

He passed the photograph museum, Life in a Lens, and noticed that a Victorian tea room had been opened on the ground floor. He’d have to call and ask about the webcam later.

The aquarium had a window display of a deep-sea diver and a treasure chest, but the ground floor was taken up by an amusement arcade. He asked at the pay booth for the member of staff he wanted and was directed past the slot machines and up the stairs into the aquarium.

‘He’ll be with you in a minute.’

‘Thanks.’

At the top of the stairs, he waited by the original petrifying well. This was what the first visitors to Matlock Bath had come to see – ordinary items apparently turning to stone. Thermal water still ran down a channel through the building, pumped up into sprays and gurgling ominously somewhere beneath his feet. The objects he could make out under their layer of calcium included teapots, a bird’s cage, a telephone and a deer’s skull, complete with antlers. As usual, visitors had thrown coins into the water, forever hoping for a bit of good fortune. This was one belief that seemed to survive, no matter what – an enduring faith in the magical properties of water.

Cooper wondered if Rose Shepherd had tossed a coin in here on Saturday. She sounded like a woman who’d desperately needed a bit of good luck.

Suddenly, a man was standing beside him.

‘Is it me you’ve come to see?’

‘Yes, if you called the police in response to our appeals.’

Cooper fumbled for his ID, but the man didn’t even look at it.

‘I’m a bit busy, so you’ll have to keep up with me while I’m working. I have to check all the safety precautions and signs while it’s quiet.’

‘All right.’

‘Through this way, then.’

‘Before we go any further, is this the woman you remember seeing here on Saturday?’

The man glanced at the photograph. ‘Yes, that’s her. It’s the same photo that was in the papers, isn’t it?’

‘Yes, I’m just making sure. The reproduction is sometimes a bit poor.’

In the aquarium itself, red-eared terrapins basked on a concrete beach under halogen spot lamps. There were vegetarian piranhas and South American snakeheads that swam with their long bodies hanging in graceful curves, ready to travel across land to find more water if their habitat dried up. One glass tank contained only the hands of an unseen man scraping the silt off the bottom.

‘She came in on Saturday afternoon, about two fifteen. Didn’t stop here for long. She had a quick walk round, then spent a few minutes by the thermal pool.’

‘What made you notice her?’

‘Well, it’s not often we have people coming in on their own. A woman of sixty or so? She seemed harmless, but you never know.’

‘So you kept an eye on her?’

‘Discreetly. On my own initiative.’

‘What did she do?’

‘Pretty much what you did – stopped at the petrifying well, then came through here and looked at the fish. She liked the terrapins, as I recall.’

He opened a door, and they walked out of the heat of the aquarium on to a cool, tiled walkway beside an outdoor pool.

‘This was the original baths, you know. The Victorians thought the water cured rheumatism. The pool is still fed by the thermal spring. It’s a constant twenty degrees centigrade.’

Cooper looked over the side of the pool. It was full of colourful Japanese fish and fat mirror carp.

‘Twenty degrees centigrade? Lucky fish.’

‘The lady stood out here for a bit. There were some children feeding the fish. See? You can buy a carton of food from the machine for twenty pence.’

‘Did she speak to anyone?’

‘No, she was just watching.’

Despite the temperature of the water, it was much cooler out here, because the pool was open to the sky, with only a few rusty girders remaining of the roof. Looking up, Cooper noticed a camera mounted on the wall, focused on the feeding station.

‘Are you sure? No one standing near her? Or someone that she took a particular interest in?’

‘Only the children.’

Cooper waited on the red and black tiles while the man walked off to check a side door. There was a plop as one of the larger fish surfaced at the other end of the pool. And then he saw that people had thrown coins in here, too. Instead of buying food for the fish, visitors had tossed their twenty pence pieces into the water, so they lay glinting on the bottom.

‘We go out this way. Through the hologram gallery.’

A moment later, Cooper was back in darkness, standing in front of a pocket watch that seemed to float in mid-air. When he moved his head, the time on the watch face changed. The hands flicked from eight minutes before ten o’clock to six minutes past, and then to a quarter past. Disturbingly, the Roman numerals were in the wrong place, too. He wondered if it was symbolic. Look, it’s later than you think.