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The pathologist put on latex gloves and leaned over the chaise longue. We watched from across the room as he carefully checked Mrs Eagleton’s body, taking blood and skin samples, which he handed to one of his assistants. The photographer’s flash went off a couple of times above the lifeless face.

“Right,” said the pathologist, beckoning to us. “In exactly what position did you find her?”

“Her head was facing the back of the sofa,” said Seldom. “She was on her side…a little bit more…Her legs were straight, the right arm was bent. Yes, I think she was like that.” He glanced at me for confirmation.

“And that pillow was on the floor,” I added.

Petersen picked up the pillow and showed the forensic pathologist the bloodstain in the middle.

“Do you remember exactly where?”

“On the rug, about level with her head. It looked as if it fell while she was asleep.”

The photographer took another couple of photos.

“I believe,” the pathologist said to Petersen, “that whoever did this meant to smother her without leaving any trace, while she was sleeping. He took the pillow from under her head very carefully, without disarranging the hairnet, or perhaps he found the pillow already on the floor. But while he was pressing it over her face, she woke up and maybe put up a fight. And this is when our man got scared, pressed down with the back of his hand or possibly even pushed with his knee to get more pressure, and crushed her nose under the pillow without realising. That’s all it is: a little blood from the nose. At that age the blood vessels are very fragile. When he removed the pillow he found the face all covered in blood. He may have got scared again and dropped the pillow on the floor without trying to put things back as they were. Maybe he decided that it didn’t matter and just got out as quickly as he could. I think this is someone who’s killing for the first time. Probably right-handed.” He held his arms above Mrs Eagleton’s face to demonstrate. “Judging by where the pillow ended up on the carpet, I’d say he turned like this. That would be the most natural movement for a person holding it with their right hand.”

“Male or female?” asked Petersen.

“Now that’s interesting,” said the pathologist. “It could have been a strong man who damaged her by simply pressing down harder with the palm of his hand, or a woman who felt too weak and maintained the pressure by pushing down with the full weight of her body.”

“Time of death?”

“Between two and three in the afternoon.” The forensic pathologist then turned to us. “What time did you get here?”

“It was four-thirty,” Seldom said, looking at me quickly for confirmation. And then, addressing Petersen: “I think she was probably killed at three.”

The inspector looked at him with a spark of interest.

“Really? How do you know?”

“We didn’t arrive together,” said Seldom. “I came because of a note, a rather strange message I found in my pigeonhole at Merton. Unfortunately, I didn’t pay much attention to it at first. But I expect it would have been too late anyway.”

“What was the message?”

“‘The first of the series’,” said Seldom. “That’s all. In large, handwritten capitals. And underneath, Mrs Eagleton’s address and the time, as if it were an appointment: 3 PM.”

“Could I see it? Did you bring it with you?”

Seldom shook his head.

“When I collected it from my pigeonhole it was already gone three and I was late for my seminar. I read it on the way to my office and, frankly, I thought it must be yet another message from a madman. My book on logical series came out recently and I foolishly included a chapter on serial killers. Since then I’ve received all kinds of letters confessing to murders…Anyway, I threw the note in the wastepaper basket as soon as I got back to my office.”

“In that case, might it still be there?” asked Petersen.

“I’m afraid not,” said Seldom. “When I came out of my class I remembered the note. The Cunliffe Close address had left me a little anxious: during the class I remembered that that was where Mrs Eagleton lived, though I wasn’t sure of the house number. I thought I’d better reread the note, to confirm the address, but the porter had been in to clean my office and had emptied the wastepaper basket. That’s why I decided to come here.”

“We could try to find it anyway,” said Petersen, and he called over one of his men. “Wilkie, could you go to Merton College and have a word with the porter? What’s the man’s name?”

“Brent,” said Seldom. “But I don’t think it’ll be any use. The refuse lorry must have been by now.”

“If it doesn’t turn up we’ll call you so you can give our police artist a description of the handwriting. We’re going to keep this to ourselves for now, so I’d ask you both for your utmost discretion. Can you remember anything else about the note? The type of paper, ink colour, or anything that drew your attention.”

“It was in black ink, from a fountain pen, I think. The paper was ordinary white notepaper. The handwriting was large and clear. The note was carefully folded in four in my pigeonhole. And yes, there was something intriguing: under the words there was a neatly drawn circle. A small perfect circle, also in black.”

“A circle,” repeated Petersen thoughtfully. “Like a signature? A stamp? Or does it mean something else to you?”

“It may have something to do with the chapter on serial murders in my book,” said Seldom. “In it I maintain that, except in crime novels and films, the logic behind serial murders-at least those that have been documented historically-is generally very rudimentary, and relates to pathological mental states. The patterns are very crude, typified by monotony, repetition, and the overwhelming majority are based on some traumatic experience or childhood fixation. In other words, they’re cases that should be subjected to psychoanalysis rather than being true logical enigmas. In the chapter I conclude that crimes motivated by intellectual concerns, by intellectual vanity, like Raskolnikov’s or, in its artistic variant, Thomas de Quincey’s, would seem not to belong to the real world. Or else, as I suggest playfully in the book, the perpetrators were so clever that they were never found out.”

“I see,” said Petersen. “You think that someone who read your book took up the challenge. So in that case the circle would be…”

“Possibly the first symbol in a logical series,” said Seldom. “It would be a good choice: it’s a symbol that historically has probably had the greatest variety of interpretations, both in the world of mathematics and outside. It can mean almost anything. It’s a clever way to start a series: putting the symbol of maximum uncertainty at the beginning, so that we’re almost totally in the dark as to how it might continue.”

“Do you think this person is a mathematician?”

“No, not necessarily. My publishers were surprised at what a varied audience my book reached. And we still don’t even know whether we should interpret the symbol as a circle. I mean, the first thing I saw was a circle, possibly because of my mathematical training. But it could be a symbol from some esoteric cult, or ancient religion, or something else entirely. An astrologer might have seen a full moon, or your artist might have seen the outline of a face…”

“All right,” said Petersen, “let’s go back to Mrs Eagleton for a moment. Did you know her well?”

“Harry Eagleton was my tutor and they invited me to some of their parties and to dinner here after I graduated. And I was friends with their son, Johnny, and his wife, Sarah. They were both killed in an accident, when Beth was a child. She’s lived with Mrs Eagleton ever since. I haven’t seen much of them lately. I knew that Mrs Eagleton had been suffering from cancer for some time, and that she’d had to go into hospital on several occasions. I saw her at the Radcliffe a couple of times.”