much deeper, except in the spring thaw. There are other lakes out there. Litla-Brunnavatn, Reydarvatn, Uxavatn.’

‘Sure.’

‘What were their names? The couple?’

‘David and Gudrun. Or Duna.’

Thorbergur looked out at the workshop floor. A new customer had arrived and was looking in their direction. He was a regular and Thorbergur nodded to him.

‘Would you be prepared to do this for me?’ Erlendur asked, standing up. ‘I’m rather up against it, timewise. There’s an old man lying at death’s door who’s been waiting for an answer ever since his boy disappeared. It would be good to be able to bring him news of his son before he goes. I know the chances are pretty slim but it’s the only thing I’ve got to go on and I want to give it a stab.’

Thorbergur stared at him.

‘Hang on – are you expecting me to drop everything and go this minute?’

‘Well, maybe not before lunch.’

‘Today?’

‘I… just whenever you can. Do you think you could do this for me?’

‘Do I have any choice?’

‘Thank you,’ Erlendur said. ‘Call me.’

Erlendur had some difficulty locating the holiday cottage and drove past the turning twice before finally catching sight of the sign, which had almost been obscured by low-growing scrub: ‘Solvangur’. He took the turning, drove down to the lake and parked by the cottage.

This time he knew what he was looking for. He was alone and had told nobody what he was doing. He wouldn’t do so until the case was solved, if it ever was. It was still too vague; he still lacked evidence; he himself was still unsure whether he was doing the right thing.

He had talked to the police pathologist who’d performed the post-mortem on Maria and had asked if she had taken any sleeping pills shortly before the time of her death. The pathologist said he had found a small amount of a sleeping drug but nowhere near enough to explain her death. Erlendur asked if it was possible to calculate how long before her death Maria had taken the drug but the answer he received was inconclusive. Possibly the same day.

‘Do you think a crime’s been committed?’ the pathologist asked.

‘Not really,’ Erlendur said.

‘Not really?’

‘Did you find any burn marks on her chest?’ Erlendur asked tentatively.

The pathologist had the post-mortem report open in front of him. They were sitting in his office. He looked up from the document.

‘Burn marks?’

‘Or bruises of any kind,’ Erlendur added hurriedly.

‘What are you looking for?’

‘I hardly know.’

‘You’d have been informed if we’d found burn marks,’ the pathologist said dismissively.

Erlendur did not have the keys to the holiday cottage but that didn’t matter; his interest was in the veranda, more specifically in the hot tub and its distance from the water’s edge. The lake was covered by a thin film of ice and the waves clinked against the frosted rocks of the shore. A short distance away a small sandbank extended into the water, intersected by a rivulet that was now frozen. Erlendur took out a sample jar that Valgerdur had lent him and filled it with water from the lake. He paced out the distance from the lakeside to the veranda, five paces, then from the end of the veranda to the hot tub; six paces. The tub had a cover made of aluminium and plexiglas, which was locked with a small, simple padlock. He fetched a tyre iron from the Ford and bashed the padlock until it opened, then lifted the lid, which turned out to be extraordinarily heavy. It was held open by a hook fixed to the wall of the house. Erlendur didn’t know much about hot tubs; he had never sat inside one, nor did he feel the slightest urge to do so. He assumed the tub would not have been used since Maria killed herself.

Before leaving town he had gone to a builders’ supplier and spoken to an employee who presented himself as something of an expert. Erlendur’s interest was directed at the waste pipe and the technology used to fill hot tubs. Empty and fill, he said. The employee was keen initially, but when he realised that Erlendur was not intending to buy he quickly abandoned his sales patter and became more bearable. He showed Erlendur a model with computer-controlled draining and filling, assuring him that it was very popular these days. Erlendur hemmed and hawed.

‘Is it the best system?’ he asked.

The employee frowned.

‘Lots of people just prefer to control it manually,’ he said. ‘They want to be able to turn on the taps themselves and then turn them off when the tub’s full. Like filling a bath. You control the heat with regular hot and cold taps.’

‘And if it’s not manual?’

‘Then there’s zero-crossing technology.’

‘Zero-crossing technology?’

Erlendur looked the employee up and down. He was barely out of adolescence, with a fine down on his chin.

‘Yes, an electronic remote-control system, usually located in the toilet. You press a button and the tub begins to fill with hot water at the required temperature. Then you press another button and it empties.’

‘Are the inlet and outlet separate?’

‘No, it’s the same pipe. The water is sucked out through a filter in the bottom, and when you want to fill it the water flows up the same way.’

‘Hardly the same water, surely?’

‘No, of course not. Fresh water is piped up through the filter but some people see this as a bit of a fault in the system. I wouldn’t buy one like that.’

‘Why not? What’s the problem?’

‘The pipe is supposed to be self-cleaning but sometimes small particles of grit get left behind from the last time it was emptied. You know, something that’s been lying in the pipe. That’s why people prefer to do it manually. Though it may be nonsense, of course. Some people swear by this system.’

After talking to the salesman, Erlendur had a short conversation with a forensic technician with the CID who had been in charge of the operation at the holiday cottage. He thought he remembered seeing a little control panel in the lavatory for filling and emptying the hot tub.

‘So the tub is electronically controlled?’ Erlendur asked.

‘From what I could tell,’ the forensic technician answered. ‘But I’d probably have to take another look.’

‘What’s the advantage of an electronically controlled system?’

‘Well, it employs zero-crossing technology,’ the technician explained and was a little startled when Erlendur hung up on him with a heavy sigh.

Erlendur stared into the tub for a long time, then peered round in search of the taps but couldn’t spot any. The sales employee had told him that they might be anywhere near the tub but were usually located under the veranda. Erlendur couldn’t find any trapdoor in the veranda that could conceal the taps, so he assumed that the technician had been right about its being electronically controlled. Clambering down into the tub, he bent over the filter in the bottom and managed to prise it loose. Dusk was falling but he had a torch and shone it down the drain. A little water had frozen in the waste pipe. Erlendur took out another sample jar, snapped off a piece of ice from inside the pipe, and placed it in the jar.

He closed the tub again with the heavy plexiglas cover and replaced the broken padlock.

After that he walked round the cottage until he encountered a shed behind it which he assumed was the boathouse. Pressing his face against a small window he made out a boat inside. He wondered if it was the same boat that Magnus and Leonora had been in on that fateful day long ago. There were low piles of logs stacked against the shed.

The boathouse was locked with a small padlock that Erlendur smashed with the same ease as he had the

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