“Well, seeing as Jeffrey has gone to the trouble of specifying the time, place, and date for each of the ghost’s appearances, we’re going to plot them against the building plans.”

Cheryl’s expression said that wasn’t much of an answer. “Because I need to know what exactly it is that she’s haunting,” I explained. “I thought it was the Russian artifacts, but it isn’t. So it’s something else.”

“Does it have to be that specific?”

“No, but it usually is. Most ghosts have a physical anchor. It can be a place or it can be an object—from time to time it can even be another person. But there’s nearly always something. Some specific thing that they’re clinging to.”

Neither of them looked convinced. “This archive of yours counts as a place, doesn’t it?” Pen demanded. “Can’t she just be haunting the whole building?”

“I’m talking more specific than that, Pen. Within the building, or maybe close by, there should be an area that’s uniquely hers. An area that she associates herself with and that she hangs around in most of the time. Or a particular thing that she owned in life, maybe, and still has strong feelings for.”

“How is that gonna help you?” asked Cheryl.

“Because once I know what it is, I may have a better idea who she was and how she died.”

Cheryl nodded. She got it. So now I could tell her the bad news.

“And you’re going to have to put the crosses in, because you’re the resident expert.”

I handed her a magic marker. It took two tries, because she didn’t want to take it. She was looking at the plans with a deeply pained expression. “I suck at this stuff,” she wailed. “This is almost maths. I’m a humanities graduate, yeah?”

“We’ll work it out together,” I promised. “Pen, you read aloud from the book. Not all the entries—just the ones that mention the ghost.”

“Should I add voices?” Pen asked hopefully.

“There’s just the one voice. Think of Sourdust from Titus Groan, and you’ll be on the right lines.”

That seemed to appeal to her. “I can do that,” she said approvingly.

“Then let’s go.”

We made a start, but Cheryl was right—it wasn’t easy. The building had changed so damn much over the years, and the plans—even the recent ones—looked so different from the baroque, three-dimensional maze that the archive had become. But on the other hand, Peele’s notes were meticulous, and he always gave chapter and verse. I felt a grudging respect for the man. After two dozen ghost sightings, a lot of people would have started using ditto marks, but not Jeffrey. Every damn time, he recorded the when and the where and the who in the same amount of rich, unnecessary detail.

And one by one, we plotted them out on the plans.

As we worked, I thought about that missing page—a blank space surrounded by information—information that up to now I hadn’t even tried to use. But there was a pattern hidden in the random flux of things going bump in the tail end of the afternoon. There had to be. And the incident book was still the key.

Every sighting became a cross, and the plans slowly took on a fly-specked appearance as Cheryl marked each one down. Basement. First floor. Second floor. Basement. First floor. Third. Fourth. She’d almost never shown up on the fourth floor—only twice in eighty or so appearances—and never in the attic. Visits to the third floor were rare, too, and they were always in strong room K or the corridor outside. On the second floor, she’d turned up in half a dozen rooms and in the corridor, and on the first floor and in the basement, she was even more ubiquitous.

We sat back, staring at the fruits of our labors. The silence was the silence of revelations not arriving. In droves.

“She’s all over the place,” said Cheryl.

“Yeah,” I agreed in a slightly dead tone. “She is.”

“No, she’s not.” Pen’s voice was a little slurred, but there was a weight of certainty in it. We both looked at her.

She shrugged. “She’s on a running rope.”

“Explain,” I said.

Pen bent over the plans. “Okay,” she said, “suppose this cross here was a bit farther over—I mean, suppose she was in the corner of this room, not out in the middle. And this one—she could easily have been ten yards or so farther down the corridor.”

She rubbed out two of the crosses as she spoke; drew in two more. A third she moved only half an inch or so, to place it closer to a cluster that was already there. She looked at me expectantly.

“Straight lines,” I said. “She works in straight lines.”

Pen tutted. “They’re not straight, Fix. They’re curved!”

I started to feel a tingling in the back of my neck as my hairs rose—not from a ghostly visitation but from the gathering, inescapable sense of something opaque becoming obvious.

“Fuck me sideways,” I murmured.

Cheryl was looking from one of us to the other and back again. “Is someone gonna tell me the news?”

My eyes flicked backward and forward, from basement, to first floor, to second floor, third, fourth.

“Okay,” I said, “so I’m an idiot. I don’t have a good visual imagination. It’s like—the Milky Way.”

“It’s like what?” Cheryl demanded. But Pen was nodding excitedly.

“The Milky Way. We see it as a line in the sky because we’re looking at it from the wrong angle. But it’s not a line, it’s a disc. And these aren’t lines, either. Put the vertical dimension back in, and it’s right there. It’s—”

“—a running rope,” Pen finished.

“I’m gonna sulk,” Cheryl warned.

I put the plans one on top of another and held them up to show her. She squinted at them doubtfully. Now that I’d seen what Pen was driving at, I couldn’t believe that Cheryl was still missing it.

“Look—on each floor, she turns up in a whole lot of different places, but they make a rough circle. A really big circle in the basement, then a slightly smaller one on the first floor. Smaller still on the second, but still with more or less the same center. On the third floor, you’ve just got a scattering of points, all very close together. But suppose you mapped all of this in three dimensions. What would you get?”

“A headache,” said Cheryl bitterly.

“You’d get a hollow hemisphere.”

“The higher she gets in the building,” I said, pointing, “the less room she’s got to move in horizontally. Don’t you get it? Think of a dog on a leash. If its owner beats it with a stick, what’s it going to do?”

“Run away,” said Cheryl. “I think I’m being patronized now.”

“No, you’re not. Just see it in your mind. The dog will run away as far as the leash will let it. And then it will keep running, but it will only be able to go in a circle, right? A circle with the owner—and the stick—right in the middle.”

“Okay.”

“But suppose it was a space dog. With a jet pack. It would still go out to the full extent of the leash, but it wouldn’t be a circle anymore—because the dog would be free to move up and down and all around . . .”

“So it’d be a sphere.”

“Exactly!”

Cheryl looked again at the overlaid plans. The black crosses showed clearly through: concentric circles, narrowing as they went up through the building.

“There is a fixed place,” I said. “A tether of some kind—but she’s not haunting it. She’s getting as far away from it as she can. She’s running on the end of a leash.”

“And the man with the stick—”

“Is at the center. The place where she doesn’t want to go. The place where she’s never been seen.”

Cheryl took the plans from me and laid them down on the table again. “It’s got to be on the first floor,” she murmured. Then she glanced at Pen and me to double-check her logic. “The first floor or the basement. I mean, she’ll have the widest circle where she’s on the same level as . . . the thing. The place. Whatever.”

Pen nodded emphatically. “So where is it?” I asked. “What’s at the center of the sphere?”

Cheryl traced the line of the main corridor, muttering to herself. “That’s the front desk. These are the first-

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