After about an hour and a half, she finally called a halt and tossed me a Thermos from her pack. While I fumbled the cup between my mittens, she rang Zodiac on the satellite phone.

‘Hagger still hasn’t called in.’

We went on. Now we were on the dome, an ice sheet hundreds of metres thick that covers two-thirds of Utgard. Strange to say, it felt like driving along a beach. On my left, a chain of mountains; to my right, a flat surface stretching down to the horizon. A few lonely rocks broke the surface, trivial in that vastness, until I realised they were the tops of mountains that had been buried in the sea of ice weighing down the island. The Inuit call them nunataks.

And it never got dark. The five-month-long polar day hadn’t quite dawned, but it was coming. Even when the sun got below the horizon, you knew it hadn’t gone far. We travelled in a protracted twilight, dim enough to see the tail light of the snowmobile in front, light enough that I could still make out the snow on the distant mountains. A few of the brighter stars peeked through the velvet sky. In that wide, wide space, so close to the top of the world, I could almost feel the planet spinning on its axis under me.

Eventually, where the ice dome funnelled into a glacier between mountains, Greta stopped and waved me to come up behind her.

‘The last place his GPS clocked in was near here,’ she shouted over the idling engines. She jumped down and disconnected the sleds, then tied two lengths of rope between the snowmobiles.

‘What’s that for?’

‘Crevasses.’

I surveyed the unbroken snow. ‘Are there many around?’

‘It only takes one.’ She made the rope fast in an intricate cradle of knots and carabiners. ‘Keep it tight. And don’t drive over the rope or you’ll rip it.’

We moved down the glacier in harness. The snowmobile didn’t want to go slowly: if I feathered the throttle, it would rev but not move; if I pressed harder, it suddenly popped into gear and lurched forward. It took all my concentration not to mow down the rope … let alone watch for crevasses … let alone spare any thought for Hagger. I wasn’t even sure the rope would do any good. If Greta went into a crevasse, the rope would more likely pull me in on top of her than save either of us.

Greta stopped. I let go the throttle so suddenly I almost fell off.

‘Is it a crevasse?’ I shouted. Then I saw it. A blue snowmobile, parked where the glacier rubbed up against the mountains. Pieces of equipment were scattered over the ground around it, hard to make out in the gloom.

I got down from the snowmobile.

‘Wait,’ Greta called. ‘Hold on to the rope. And check the snow.’

‘I’ll follow your track.’

‘Check it,’ she repeated. ‘The snowmobile has better weight distribution than you do.’

I edged over the snow, one hand on the safety line, the other holding the barrel of my rifle, using the butt to probe the ground in front. A hard crust had formed on top of the snow, but that was deceptive. It squeaked under my boots like polystyrene — and, like polystyrene, it snapped under my weight. Each time it broke, my heart froze while I waited for the drop. Each time, my feet landed softly in the powder snow underneath.

Greta was prowling around, examining the equipment he’d left.

‘Don’t you have to worry about crevasses too?’

‘Martin knew the drill.’ She pointed to four fuel cans that made a rough diamond around the abandoned snowmobile. ‘He marked out a safe area.’

‘So where’s he gone?’ I looked at the snowmobile. I looked at the boxes of equipment. No sign of Hagger. A shovel stood planted in the snow beside a square pit, about a metre deep. An open Thermos stood upright on one of the boxes, lid off, cup beside it, as if Hagger had been about to pour himself a cup of tea. The water inside the Thermos had frozen solid.

‘Here.’ Greta bent down and lifted a red climbing rope out of the wind-blown snow. It had been tied off on Hagger’s snowmobile. She followed it across the glacier.

Then she stopped. She leaned forward. The rope went taut behind her. I hurried over.

A dark cut opened in the ice, a snaking fissure going down — I couldn’t see how far. Narrow enough that you didn’t see it until you were nearly there; wide enough you could easily climb in. Or fall. The rope trailed down into the void.

‘Martin,’ I shouted. I stepped forward. My foot caught a lump of ice half buried in the snow and kicked it over the edge. Loose snow showered down after it.

‘Careful.’

Greta took a head torch from her pocket. Wrapping the strap around her wrist, she shone the beam down into the gloom.

‘Keep watching for bears,’ she said. ‘They come up quick.’

I glanced around anxiously. The sun, never far off, was circling back. The sky had started to blue. Even so, the shadows were deep enough to hide all manner of evils.

‘Look at this,’ said Greta, and even she couldn’t keep the emotion out of her voice. She pointed the torch down, wrist trembling slightly.

The crevasse was deep, maybe eight or nine metres. The walls bent and bowed, primitive shapes that seemed pregnant with meaning. The torch beam reflected brightly off them, all the way to the bottom.

A dark shadow lay flat against the ice.

It was Hagger. Neither of us doubted it. We called his name; Greta threw down the cup from the Thermos to see if he would stir. He didn’t move.

‘I’m going down,’ she announced.

You don’t just go down into a crevasse — not if you want to make it out again. Greta spent half an hour driving screws into the ice, fixing pulleys and carabiners, and running a network of ropes between them. When she’d finished, she was webbed in a harness clipped to one end of the rope; I held the other.

‘Slowly,’ she told me. ‘I tug once, it means you stop. Two tugs, I’m down.’

Standing well back, I paid out the rope. I didn’t like to think what would happen if she fell. I imagined the jerk of the rope, my feet slipping over the ice towards the edge of the hole. Would I hold on? Let go? I remembered Quam: the biggest danger in a situation like this is people trying to play the hero.

The rope went slack. Two tugs told me she’d got down safely. I crawled to the edge of the crevasse and peered in.

Hagger still hadn’t moved. Greta knelt beside him. She took off her mitten and wriggled her bare hand under the collar of his balaclava. It stayed there a long time.

‘Well?’ I called.

She shook her head.

Hagger was still wearing his climbing harness. Greta clipped him on to the rope, then added a loop around his chest so he wouldn’t spin. I lay on the ground and watched from above. Compact snow pressed hard against me; the cold seeped into my chest.

And something was digging into my ribs. I rolled over and scrabbled in the snow, expecting a pebble or a lump of ice. Instead, through my mitten, I felt something unmistakably man-made.

It was a key. A perfectly ordinary flat Yale key, attached to a teddy-bear key ring. The bear wore a T-shirt, grubby with fingerprints, that said I ♥ NY.

I stared at it and wondered how it had got there. Had it fallen out of Hagger’s pocket? There are no locks at Zodiac. Why did he need a key?

I zipped it into my pocket. Greta had finished with Hagger. She climbed the second rope, and together we pulled up the body. The hardest part was getting it over the cliff. Greta chopped a ramp in the crevasse lip with her ice axe, and I hauled him over. Like landing a fish.

‘He’s frozen stiff,’ I said. Not just the body — his coat and trousers were solid ice, as if they’d been soaked through and then frozen. How had he possibly contrived to get wet? The glaciers wouldn’t start melting for months, and we were a long way from the coast.