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“On the hatch. She put it there when she got her cable and evidently forgot to take it indoors. It was just above the spot where we found it, which was about three feet away from the place where Merryman threw down the hyacinth; everything was nice and handy.” He turned to Tim. “You and Miss Carmichael were the first to leave the general group. I think you walked over to the starboard side, didn’t you?”

Tim, pink in the face, nodded.

“Er — yes.”

“Do you mind telling me exactly where?”

“Er — no. No. Naturally not. It was — where was it? Well, it was sort of a bit further along than the doorway into the passengers’ quarters. There’s a seat.”

“And you were there, would you say — for how long?”

“Well — er—”

“Until after the group of passengers on deck had dispersed?”

“O, Lord, yes! Yes.”

“Did you notice whether any of them went in or, more importantly, came out again, by that doorway?”

“Er — no. No.”

“Gentlemen of your vintage,” Alleyn said mildly, “from the point of view of evidence are no damn good until you fall in love and then you’re no damn good.”

“Well, I must say!”

“Never mind. I think I know how they dispersed. Mr. Merryman, whose cabin is the first on the left of the passage on the starboard side and has windows looking aft and to that side, went in at the passengers’ doorway near you. He was followed by Mr. McAngus, who has the cabin opposite his across the passage. The others all moved away in the opposite direction and presumably went in by the equivalent passengers’ entrance on the port side, with the exception of Mrs. Dillington-Blick and Aubyn Dale, who used the glass doors into the lounge. Captain Bannerman and I had a short conversation and he returned to the bridge. Father Jourdain and I then walked to the after end or back or rear or whatever you call it of the deck, where there’s a verandah and where we could see nothing. It must have been at that moment somebody returned and garrotted Esmeralda.”

“How d’you remember all that?” Captain Bannerman demanded.

“God bless my soul, I’m on duty.” Alleyn turned to Father Jourdain. “The job must have been finished before we walked back along the starboard side.”

“Must it?”

“Don’t you remember? We heard someone singing ‘A Broken Doll.’ ”

Father Jourdain passed his hand across his eyes. “This is, it really is, quite beastly.”

“It appears that he always sings when he’s finished.”

Tim said suddenly. “We heard it. Brigid and I. It wasn’t far off. On the other side. We thought it was a sailor but actually it sounded rather like a choirboy.”

“Oh, please!” Father Jourdain ejaculated and at once added, “Sorry. Silly remark.”

“Here!” the captain interposed, jabbing a square finger at the newspaper-covered form on the table. “Can’t you do any of this funny business with fingerprints? What about them?”

Alleyn said he’d try, of course, but he didn’t expect there’d be any that mattered as their man was believed to wear gloves. He very gingerly removed the newspaper and there, shockingly large, smirking, with her detached head looking over her shoulder, was Esmeralda. In any case, Alleyn pointed out, the mantilla had been wound so tightly round the neck that any fingerprints would be obliterated. “It’s a right-handed job, I think,” he said. “But as we’ve no left-hand passengers that doesn’t cast a blinding light on anything.” He eased away the back lace, exposing part of the pink plastic neck. “He tried the necklace first but he never has any luck with beads. They break. You can see the dents in the paint.”

He dropped the newspaper over the doll and looked at Tim Makepiece.

“This sort of thing’s up your street, isn’t it?”

Tim said, “If it wasn’t for the immediacy of the problem it’d be damned interesting. It still is. It looks like a classic. The repetition, the time factor — by the way, the doll’s out of step in that respect, isn’t it?”

“Yes,” Alleyn said. “Dead out. It’s six days too soon. Would you say that made the time theory look pretty sick?”

“On the face of it — no, I don’t think I would; although one shouldn’t make those sorts of pronouncements. But I’d think the doll being inanimate might be — well, a kind of extra.”

“A Jeu d’esprit?”

“Yes. Like a Malcolm Campbell amusing himself with a toy speedboat. It wouldn’t interfere with the normal programme. That’d be my guess. But if one could only get him to talk.”

“You can try and get all of ’em to talk,” said Captain Bannerman sardonically. “No harm in trying.”

“It’s a question, isn’t it,” Alleyn said, “of what we are going to do about it. It seems to me there are three courses open to us. (A) We can make the whole situation known to everybody in the ship and hold a routine enquiry, but I’m afraid that won’t get us much further. I could ask if there were alibis for the other occasions, of course, but our man would certainly produce one and there would be no immediate means of checking it. We know, by the way, that Cuddy hasn’t got one for the other occasion.”

“Do we?” said the captain woodenly.

“Yes. He went for a walk after leaving his silver-wedding bouquet at a hospital.”

“My God!” Tim said softly.

“On the other hand an enquiry would mean that my man is fully warned and at the cost of whatever anguish to himself goes to earth until the end of the voyage. So I don’t make an arrest and at the other side of the world more girls are killed by strangulation. (B) We can warn the women privately and I give you two guesses as to what sort of privacy we might hope to preserve after warning Mrs. Cuddy. (C) We can take such of your senior officers as you think fit into our confidence, form ourselves into a sort of vigilance committee, and try by observation and undercover enquiry to get more information before taking action.”

“Which is the only course I’m prepared to sanction,” said Captain Bannerman. “And that’s flat.”

Alleyn looked thoughtfully at him. “Then it’s just as well,” he said, “that at the moment it appears to be the only one that’s at all practicable.”

“That makes four suspects to watch,” Tim said after a pause.

“Four?” Alleyn said. “Everybody says four. You may all be right, of course. I’m almost inclined to reduce the field, tentatively, you know, very tentatively. It seems to me that at least one of your four is in the clear.”

They stared at him. “Are we to know which?” Father Jourdain asked.

Alleyn told him.

“Dear me!” he said. “How excessively stupid of me. But of course.”

“And then, for two of the others,” Alleyn said apologetically, “there are certain indications; nothing like certainties, you might object, and yet I’m inclined to accept them as working hypotheses.”

“But look here!” Tim said. “That would mean—”

He was interrupted by Captain Bannennan. “Do you mean to sit there,” he roared out, “and tell us you think you know who done — damnation! Who did it?”

“I’m not sure. Not nearly sure enough, but I fancy so.”

After a long pause Father Jourdain said, “Well — again, are we to know which? And why?”

Alleyn waited for a moment. He glanced at the captain’s face, scarlet with incredulity, and then at the other two; dubious, perhaps a little resentful.

“I think perhaps better not,” he said.

When at last he went to bed, Alleyn was unable to sleep. He listened to the comfortable pulse of the ship’s progress and seemed to hear beyond it a thin whistle of a voice lamenting a broken doll. If he closed his eyes it was to find Captain Bannerman’s face, blown with obstinacy, stupid and intractable, and Esmeralda, smirking over her shoulder. And even as he told himself that this must be the beginning of a dream, he was awake again. He searched for some exercise to discipline his thoughts and remembered Miss Abbott’s plainsong chant. Suppose Mr. Merryman had ordered him to put it into English verse?