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“The doctor doesn’t think so,” Grimes said, reading my face. “Also, say it did fall out, it would have dropped close to the body. It’s a plain dark brown carpet in that room. Would the taxi-man, Mrs Ferris, and the other doctor have missed seeing it as they worked on the body? It’s a thousand to one against. There was no sign of it in the room then – no sign of it now. I’ve been over that room with a hand-brush. I’ll show you.”

He called out, and the local sergeant brought in a dust-pan with the sweepings of the sitting-room. There was little more than a litter of fluff and scraps, tiny bits of coal, fragments of paper, a couple of wireless screws, a thin, capped pencil, also the little red cylinder of indiarubber that belonged to it though it had been trodden out, one or two buttons, the half of what looked like the elastic button strap of a pair of braces… stuff like that, but no sign of anything like a dart.

“You’re going to say Gerald might have picked his dart up,” Grimes said. “Well, I don’t think he could have, not before it was seen. What’s more, I don’t think he’d risk his neck on anything so conspicuous… And then, there’s the pistol? What became of that? There’s no sign of it anywhere about or on Gerald… No, it won’t wash. You’re only making a case out o’ moonbeams, Toft.”

It seemed so. I stood dejected. Paul Toft said in his dreamy calm:

“There’s no getting over that.” He touched the tiny puncture on the skull. “That’s how he died… I feel that. And he was deliberately wounded under the hair so that we’d miss it.”

“Oh, heck!” wailed Grimes; “an’ I’ve just been telling you that all the facts say no!”

“Of course they would. The whole thing was carefully, brilliantly schemed to make facts say no,” the reedy man mused on. “From the careful employment of that taxi-driver as a witness, to the firing of an all but silent air-pistol from the pocket… a helpfully ragged pocket, remember… And you’ll probably find that Gerald Park is a first-rate marksman.”

“I probably will,” the Inspector said bitterly. “That won’t be so hard as to find how he managed to make a dart and a pistol vanish into thin air under the noses of witnesses. Just crank up a really good feeling to explain that, my lad.”

Toft only blinked and looked at me, and in trying to think of a way out I did remember something.

“Just precisely when did Gerald offer his empty coat to his uncle?” I asked.

“Didn’t you hear Mrs Ferris say it was after she came into the sitting-room,” Grimes said sourly.

“After he’d fetched the brandy,” Toft put in swiftly. “Yes, that’s the loophole, Doctor. He was out of sight of witnesses, at least while he was in the dining-room getting the brandy.”

“An’ a fat lot that’s going to help,” Grimes said as we went into the dining-room. It was, indeed, sparsely furnished; just a gate-table, six stiff chairs, and a side-board with two cupboards, one of which was the cellarette.

“I’ve even searched behind the pictures; there’s nothing here,” Grimes began, and added as Toft walked straight towards a French window in the rear, that opened on to the garden. “An’ that’s no good, either. It’s been locked all winter, an’ the key’s not in it.”

“That’s what makes it queer,” Paul Toft said. “The key’s usually left in this sort of window from year’s end to year’s end. Did someone want to create the impression that nobody could have got out through this window to-day?” He stood still, staring at the lock with his queer other – worldly gaze. Then he muttered:

“Hum! Someone locking this window, snatching out the key, moving on the run to the room across the hall… where would he hide the key?” His eyes twinkled at me. “How’s this for real pukka police deduction, Doctor? There’s a hall stand full of umbrellas on the way… Wouldn’t he toss the key into them in passing?”

I went to the hall stand. The third bulgy umbrella I upended and shook, shot a key to the hall floor. It fitted the French window.

We stepped through it on to a small redtiled veranda overlooking the garden. This was without railing, but it had an inclined glass roof supported by pillars to keep off the rain. We stood and looked at half an acre of neat garden.

“You think he might have nipped out here and chucked his pistol into one of them bushes, or hidden it in one of the flowerbeds?” Grimes asked in a voice not so assured as it had been. “A mug’s trick. He’d ha’ known bushes and flower-beds are the first things we think of.”

“And being a smart fellow he would think of a cleverer place,” Toft said. “Cleverer but handy… easy to use in a hurry, handy to get at when suspicious people like ourselves had gone.”

He stepped out into the garden and looked up at the roof of the veranda. A gutter ran along the edge of it, terminating in large, old-fashioned rain-water heads and down pipes at each end. With his left hand churning away at its indiarubber, Toft walked to the nearest down pipe, stretched his reedy arm up into the rain-water head, and, after a sharp tug, brought his hand away – with an air-pistol.

It was a short, but obviously powerful weapon with a rather full bore, and looked of foreign make. Toft broke it, charging its air chamber, and fired. It made very little sound, and was plainly in perfect working order.

“Job!” Grimes said in grudging admiration. “Your feelings do get you there, I fill… He’s a smart one, that Gerald, just fancy his thinking of locking the window after hiding this and then hiding the key to keep us from looking here… All the same, there’s the dart. He’s got everything so neatly alibi-ed that you’ll have to prove that dart before you can be sure of pinning it on him.”

That was a fact. Paul Toft stood, his great head brooding as he churned away at his indiarubber. Grimes and I examined the pistol, talking quietly not to disturb him. It was an interesting pistol, and I pointed out some oddnesses about it to Grimes – the size of the bore, for instance.

“Too big to carry any air-gun pellet I know,” I said. “Why, you could shoot a pencil from that.”

“Pencil!” Toft’s voice came suddenly, alight with eagerness. “That’s it, Doctor… I wonder why I felt?… But I remember reading about it now.”

“What?” both Grimes and I demanded in one voice, but his lank limbs were carrying him headlong into the house, and he was calling to the sergeant for the pan of sitting-room sweepings.

He was in the sitting-room when they were brought. Toft picked from the mess the little cylinder of rubber that had dropped out of the cap of the pencil.

“Clever,” he muttered. “Devilish clever… Dropping that pencil, too…”

“What’s the pencil got to do with it?” Grimes frowned.

Nothing,” Toft grinned, “but you’d never suspect that, would you? This bit of rubber looks as if it belonged to that pencil, doesn’t it? Just an ordinary eraser off the top of a pencil. But look-” Toft broke the pistol, exposing the breech hole, and into that he shoved the rubber cylinder. “It fits the pistol as perfectly as any lead slug, you see. Doctor, will you put that big book on top of that arm-chair. Good, now put a sheet of clean notepaper against it… and stand clear. I’m not such a good shot as Gerald Park.”

But he was good enough. He walked to the door, just where Gerald had stood, though instead of shooting from his pocket he took aim in the orthodox way, and fired.

Again the pistol made only a slight sound; a much sharper rap came from the paper where the rubber pellet struck. It struck with such force, in fact, that it bounded right across the room, and only Toft’s sharp eyes followed it to a corner under the book-case some twelve feet away.

“Your eyes show you the first advantage of such a bullet,” Paul Toft said. “Being rubber – having, in fact, a pneumatic tip – it bounces away with great violence from whatever it strikes. Bounces, you might say, right out of range of the victim, so that there is little chance of its being connected with him… and being innocent rubber, anyhow, it is likely to be over-looked. Only it’s not innocent rubber…”