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When I went back down to the entrance hall, Seldom was standing by the revolving door. He was staring at the piece of paper with the little drawing of the fish as if he couldn’t take his eyes off it.

“Are you thinking what I’m thinking?” he asked when he saw me. “I’m afraid to ring the hospital and enquire about Frank. Although the time doesn’t make sense,” he said, looking more hopeful. “When I went to the hospital yesterday at four, Frank was alive.”

“We could call Lorna from my office,” I said. “She’s on duty till midday; she must still be there. She can easily find put.”

Seldom agreed and we went upstairs. I let him make the call. After being passed from department to department, he was eventually put through to Lorna. He asked her cautiously if she’d mind going down to the second floor and seeing if Frank Kalman was all right. I realised that Lorna was asking questions; I couldn’t make out the words but I could hear her intrigued tone at the other end of the line. Seldom said only that a message had appeared at the Institute and that he was rather worried about it. And yes, it was likely that the message had something to do with Mrs Eagleton’s murder. They talked for a little longer. Seldom told her that he was in my office and that she could call him there once she’d been down to check on Frank.

He hung up and we waited in silence. Seldom rolled a cigarette and stood at the window to smoke. At one point he turned round, went to the blackboard and, deep in thought, slowly drew the two symbols: first the circle, then the fish in two short curved strokes. He stood motionless, chalk in hand, head bowed, every so often making small futile marks at the edge of the board.

It was almost half an hour before the phone rang. Seldom listened to Lorna in silence, his face inscrutable, occasionally answering monosyllabically. “Yes,” he said at last, “that’s exactly the time it says on the message.”

When he hung up and turned to me he looked relieved for a moment.

“It wasn’t Frank,” he said, “it was the patient in the next bed. Inspector Petersen has just been to the hospital morgue to check on the deaths that occurred on Sunday. The man who died was very elderly, over ninety. He was reported dead at two-fifteen yesterday, from natural causes. Apparently, neither the nurse nor the doctor in charge on that floor noticed a small dot on his arm, like the mark left by an injection. They’re going to do a postmortem on him now to find out what it is. But I think we were right. A murder that nobody considers a murder at first. A death that’s believed to be from natural causes and a dot on an arm, that’s all. An almost imperceptible dot. The murderer must have chosen a type of substance that doesn’t leave any trace. I’m sure they won’t find anything in the post-mortem. The dot is all that distinguishes this death from a death from natural causes. A dot,” repeated Seldom quietly, as if that were the starting point for a multitude of as yet invisible implications.

The phone rang again. It was Kim, from downstairs, telling me that a police inspector was on his way up to my office. I opened the door as Petersen’s tall, thin frame appeared at the top of the stairs. He was alone and was visibly annoyed. He came into the office and, as he was greeting us, caught sight of the two symbols Seldom had drawn on the blackboard. He sat down abruptly.

“There’s a crowd of mathematicians down there,” he said, almost accusingly, as if we were somehow to blame. “The press will be here any minute. We’ll have to tell them part of the story, but I’m going to ask them not to mention the first symbol of the series. Wherever possible we try to avoid publicising details of serial murders, particularly the recurring features. Anyway,” he said, shaking his head, “I’ve been to the Radcliffe. This time it was a very elderly man called Ernest Clarck. He’d been in a coma, connected to a respirator, for years. He didn’t have any family, apparently. The only link we can find so far with Mrs Eagleton is that Clarck, too, played a part in the war effort. But of course the same goes for any other man his age: that generation has the war years in common. The nurse found him dead during her rounds at two-fifteen and that was the hour she noted on his wristband, before moving him from the ward. Everything seemed perfectly normal-there were no signs of violence, nothing out of the ordinary. She took his pulse and wrote ‘death from natural causes’, because she thought it a routine case. She said she couldn’t understand how somebody could have got into the ward, because visiting hours were only just starting.

“The head doctor on the second floor admitted that he hadn’t checked the body thoroughly. He’d arrived at the hospital late, it was a Sunday and he wanted to get home as quickly as possible. But above all, they’d been expecting Mr Clarck to die for months, in fact they were surprised that he was still alive. So he trusted the nurse’s notes, copied the time and cause of death as they appeared on the label on to the death certificate and approved the transfer of the body to the morgue. I’m now awaiting the results of the post-mortem. I’ve just seen the note on the door downstairs. I suppose it was too much to expect that he’d use his own handwriting again, now that he knows we’re after him. But it definitely makes things more difficult. Judging by the typeface I’d say he cut the letters from the Oxford Times, possibly even from articles about Mrs Eagleton. But the fish has been drawn by hand.” Petersen turned towards Seldom. “What was your instinct when you saw the note? Do you think it’s from the same person?”

“Difficult to say,” answered Seldom. “It looks like the same type of paper, and the size of the symbol and its location on the page are similar. Black ink in both cases. Yes, in principle I’d say it was from the same person. I go to the Radcliffe almost every afternoon, to visit a patient on the second floor, Frank Kalman. Ernest Clarck was in the bed next to Frank’s. Also, I don’t come to the Institute that often but I did have to be here this morning. I think it’s someone who’s following my movements closely and knows quite a bit about me.”

“Actually,” said Petersen, taking out a small notebook, “we’re aware of your visits to the Radcliffe. You see,” he said apologetically, “we had to make enquiries about you both. Now, let’s see. You generally get to the Radcliffe around two in the afternoon, but this Sunday you got there after four. Why was that?”

“I was invited to lunch in Abingdon,” said Seldom. “I missed the one-thirty bus back. There are only two buses on Sunday afternoons and I had to wait at the station until three.” Seldom searched one of his pockets and coldly held out a bus ticket to Petersen.

“Oh no, that’s not necessary,” said the inspector, a little embarrassed. “I was just wondering if…”

“Yes, I had the same thought,” said Seldom. “I’m generally the first and only person to go into that ward during visiting hours. If I’d gone at my usual time, I’d have been sitting beside Mr Clarck’s corpse the entire time. I assume that’s what the murderer intended-that I’d be there when the nurse discovered that the man was dead during her round. But, again, things didn’t-turn out quite as he would have liked. In a way, he was too subtle: the nurse didn’t see the needle mark on Clarck’s arm, she thought he’d died of natural causes. And I arrived much later and didn’t even notice that there was a different patient in the next-door bed. For me, it was an absolutely normal visit.”

“But perhaps he wanted the murder to be taken for a natural death at first,” I said. “Maybe he prepared the scene so that the body would be removed before your eyes as if it were a routine death. In other words, that the murder should be imperceptible to you too. I think you should tell the inspector what you think,” I said to Seldom. “What you told me earlier.”