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Mr. Ireton, at ease again, matched the other’s courtesy. “May I ask what these reasons were?”

“First, I wished to question the two maids. They have a room at the back, as Miss Ray has; and this afternoon, you may remember, they were still rather hysterical.”

“And that is all?”

“H’mf. Well, no.” Dr. Fell scowled. “Second, I wanted to detain all of you here for an hour or two. Third, I must make sure of the motive for this crime. And I am happy to say that I have made very sure.”

Joyce could not control herself. “Then you did overhear everything!”

“Eh?”

“Every word that man said!”

Despite Dan’s signals, Joyce nodded toward Mr. Ireton and poured out the words. “But I swear I hadn’t anything to do with Brenda’s death. What I told you today was perfectly true: I don’t want her money and I won’t touch it. As for my... my private affairs,” and Joyce’s face flamed, “everybody seems to know all about them except Dan and me. Please, please pay no attention to what that man has been saying.”

Dr. Fell blinked at her in an astonishment which changed to vast distress.

“But, my dear young lady!” he rumbled. “We never for a moment believed you did. No, no! Archons of Athens, no!” exclaimed Dr. Fell, as though at incredible absurdity. “As for what your friend Mr. Ireton may have been saying, I did not hear it. I suspect it was only what he told me today, and it did supply the motive. But it was not your motive.”

“Please, is this true? You’re not trying to trap me?”

“Do I really strike you,” Dr. Fell asked gently, “as being that sort of person? Nothing was more unlikely than that you killed your cousin, especially in the way she was killed.”

“Do you know how she was killed?”

“Oh, that,” grunted Dr. Fell, waving the point away too. “That was the simplest part of the whole business.”

He lumbered over, reflected in the mirrors and put down stick and shovel-hat on a table. Afterward he faced them with a mixture of distress and apology.

“It may surprise you,” he said, “that an old scatterbrain like myself can observe anything at all. But I have an unfair advantage over the police. I began life as a schoolmaster: I have had more experience with habitual liars. Hang it all, think!”

“Of what?”

“The facts!” said Dr. Fell, making a hideous face. “According to the maids, Sonia and Dolly, Miss Brenda Lestrange went down to swim at ten minutes to seven this morning. Both Dolly and Sonia were awake, but did not get up. Some eight or ten minutes later, Mr. Toby Curtis began practising with a target rifle some distance away behind the bungalow.”

“Don’t look at me!” exclaimed Toby. “That rifle has nothing to do with it. Brenda wasn’t shot.”

“Sir,” said Dr. Fell with much patience, “I am aware of that.”

“Then what are you hinting at?”

“Sir,” said Dr. Fell, “you will oblige me if you too don’t regard every question as a trap. I have a trap for the murderer, and the murderer alone. You fired a number of shots — the maids heard you and saw you.” He turned to Joyce. “I believe you heard too?”

“I heard one shot,” answered the bewildered Joyce, “as I told Dan. About seven o’clock, when I got up and dressed.”

“Did you look out of the windows?”

“No.”

“What happened to that rifle afterwards? Is it here now?”

“No,” Toby almost yelled. “I took it back to Ireton’s after we found Brenda. But if the rifle had nothing to do with it, and I had nothing to do with it, then what the hell’s the point?”

Dr. Fell did not reply for a moment. Then he made another hideous face. “We know,” he rumbled, “that Brenda Lestrange wore a beach robe, a bathing suit, and a heavy silk scarf knotted round her neck. Miss Ray?”

“Y-yes?”

“I am not precisely an authority on women’s clothes,” said Dr. Fell. “As a rule I should notice nothing odd unless I passed Madge Wildfire or Lady Godiva. I have seen men wear a scarf with a beach robe, but is it customary for women to wear a scarf as well?”

There was a pause.

“No, of course it isn’t,” said Joyce. “I can’t speak for everybody, but I never do. It was just one of Brenda’s fancies. She always did.”

“Aha!” said Dr. Fell. “The murderer was counting on that.”

“On what?”

“On her known conduct. Let me show you rather a grisly picture of a murder.”

Dr. Fell’s eyes were squeezed shut. From inside his cloak and pocket he fished out an immense meerschaum pipe. Firmly under the impression that he had filled and lighted the pipe, he put the stem in his mouth and drew at it.

“Miss Lestrange,” he said, “goes down to the beach. She takes off her robe. Remember that, it’s very important. She spreads out the robe in King Arthur’s Chair and sits down. She is still wearing the scarf, knotted tightly in a broad band round her neck. She is about the same height as you, Miss Ray. She is held there, at the height of her shoulders, by a curving rock formation deeply bedded in sand.”

Dr. Fell paused and opened his eyes.

“The murderer, we believe, catches her from the back. She sees and hears nothing until she is seized. Intense pressure on the carotid arteries, here at either side of the neck under the chin, will strike her unconscious within seconds and dead within minutes. When her body is released, it should fall straight forward. Instead, what happens?”

To Dan, full of relief ever since danger had seemed to leave Joyce, it was as if a shutter had flown open in his brain.

“She was lying on her back,” Dan said. “Joyce told me so. Brenda was lying flat on her back with her head towards the sea. And that means—”

“Yes?”

“It means she was twisted or spun round in some way when she fell. It has something to do with that infernal scarf — I’ve thought so from the first. Dr. Fell! Was Brenda killed with the scarf?”

“In one sense, yes. In another sense, no.”

“You can’t have it both ways! Either she was killed with the scarf, or she wasn’t.”

“Not necessarily,” said Dr. Fell,

“Then let’s all retire to a loony bin,” Dan suggested, “because nothing makes any sense at all. The murderer still couldn’t have walked out there without leaving tracks. Finally, I agree with Toby: what’s the point of the rifle? How does a .22 rifle figure in all this?”

“Because of its sound.”

Dr. Fell took the pipe out of his mouth. Dan wondered why he had ever thought the learned doctor’s eyes were vague. Magnified behind the glasses on the broad black ribbon, they were not vague at all.

“A .22 rifle,” he went on in his big voice, “has a distinctive noise. Fired in the open air or anywhere else, it sounds exactly like the noise made by the real instrument used in this crime.”

“Real instrument? What noise?”

“The crack of a blacksnake whip,” replied Dr. Fell.

Edmund Ireton, looking very tired and ten years older, went over and sat down in an easy chair. Toby Curtis took one step backward, then another.

“In South Africa,” said Dr. Fell, “I have never seen the very long whip which drivers of long ox spans use. But in America I have seen the blacksnake whip, and it can be twenty-four feet long. You yourselves must have watched it used in a variety turn on the stage.”

Dr. Fell pointed his pipe at them.

“Remember?” he asked. “The user of the whip stands some distance away facing his girl assistant. There is a vicious crack. The end of the whip coils two or three times round the girl’s neck. She is not hurt. But she would be in difficulties if he pulled the whip towards him. She would be in grave danger if she were held back and could not move.