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“Aren’t illegal broadcasts tracked down?”

“Yeah. There are regular listening posts, with directional equipment. But if a set broadcast only a couple of sentences like that, they’d probably be overlooked. So that’s no help.”

We were slowing down already for the apartment building when I remembered. “How’s about what your radio ghost friend said just now? Are you chummy with Randall’s wife?”

He took time to word his answer. I could have counted to ten before he said, “You’d find out anyway, I suppose. Yes, I like her a lot and she likes me. Her husband…”

“Didn’t understand her?” I prompted.

He glared at me, and started to say something that would probably have led to trouble if I’d let him finish.

“Hold it, pal,” I cut in. “Here’s the big thing to think about. Whoever put on that broadcast just now knew about you and Mrs. Randall. How many people know that. Pete Burd, maybe?” He calmed down. “I don’t know. Anyone might have guessed, I suppose. Uh—Charlie Randall didn’t mind, so we weren’t too secretive about being seen.”

“Randall knew you were making love to his wife!”

“I think so. He wouldn’t have cared, if he had known. You know that little blonde who used to sell cigarettes at the Green Dragon?”

“I think I know which one you mean,” I told him. “The one with the nice—”

“That one,” he said. “She doesn’t work there any more.” The car stopped in front of the Deauville Arms, and I got out, carrying the gimmicked radio. I waited until Barranya came around the car to join me.

When we got into the elevator I said, “We’re going to Randall’s flat first, both of us. You’ll have to bear up a while yet before you go to sleep.”

“Why can’t I go on up, while you—”

“Nix,” I said. “I’m going to report to Holding, and you’re not going in that flat before I go with you. Listen, Barranya, the only thing I don’t like about your alibi is that it’s too damn good. Maybe you got something upstairs I’d like to see before you dismantle it. Such like a phonograph with your—”

I broke off, because as soon as I mentioned it I knew it wasn’t a phonograph record that had made that call. Because I’d done part of the talking, and he’d answered what I said. I remembered that lousy gag about not shooting at random but at Randall. But I took Barranya with me just the same. Holding would want to see him.

The Randall flat was full of photographers and fingerprint men. I parked Barranya in the hallway, and told the man on duty at the door to keep an eye on him. I went in to give Holding my report and the radio set.

The coroner was working on the body; they’d moved it into the bedroom after taking photos. Captain Holding showed me the position of the chair and the ropes; everything checked with what I’d heard over the telephone.

Holding said, “Maybe Barranya could have called you from the phone booth in the hall at your precinct station, and then gone on into the waiting room while—”

“No, dammit,” I said. “I traced the call. It came from here. It must be some kind of a frame, but it’s the goofiest thing I ever heard of. If anybody wanted to frame Barranya, why’d they give him that message about me that sent him to my office only two minutes after the murder?”

Holding shrugged. “Do you know anybody connected with the case who’s a good voice imitator?”

“Not unless it’s Barranya, and he wouldn’t imitate his own voice. Nuts! I’m going in circles, and this toothache is driving me batty. Say, how’s Mrs. Randall doing on alibis?”

“Excellent. We called the hotel in Miami she was supposed to be at. She’s there all right. I talked to her myself.”

“Just now?”

“What do you mean, just now? Think we could have notified her yesterday, Sergeant?”

I shook my head. “Don’t mind me, Cap. My mind just isn’t working any more. But one thing. I take it you’re going to send men up to search Barranya’s place. Maybe while he’s here and you’re talking to him? Well, I’d like to go up with them.”

“You should go home, Bill. This is our job, now that you’ve reported,” Holding pointed out.

“Got to stay awake till I can see a dentist at nine. Having something to do will keep my mind off this damn toothache. Anyway, this is my big day, Cap. If Barranya’s spirit controls are in working order, I’m due to be bumped off.”

“I’ll question Barranya now. I’ll hold him a while, and give you plenty of time, though.”

“Swell. I’m even going to take the kitchen sink apart up there. Say, know who lives above and below this flat—on the third and fifth?”

“Third’s vacant. Guy named Shultz has the fifth, in between here and Barranya.”

“What’s he do?” I asked.

“Manufacturer. Pinball games and carnival novelties.” Holding saw the sudden look of interest I gave him, and went on. “Yes, he did a little business with Randall. But he’s clear on this. He’s out of town, he and his wife. We’ve checked and it’s on the up and up.”

“How about Burd?”

“Murphy’s on the way over there now. I’m going to have that cigarette girl angle looked into, too. We can trace her easy enough if Randall set her up somewhere. Might be an angle there.”

“More curves than angles,” I said. “Sure you don’t want me to—”

“I do not. Send in Barranya, and take Clem and Harry up to his flat.”

Clem and Harry and I spent two hours searching, but there wasn’t anything in Barranya’s flat worthy of interest except a bottle of Scotch in the cupboard. The homicide boys didn’t touch it because they were on duty, but I wasn’t.

When they left, I sat down at the table in the living room to wait. Holding kept Barranya down there another half hour. He looked mad when he came in. By that time my tooth had stopped jumping up and down and settled into a slow steady ache that wasn’t quite so bad.

I waved my hand toward the Scotch on the table, and the extra glass I’d put there. “Have a drink.”

“Thanks, Sergeant, I shall. After that, if you don’t mind, I’d like to turn in.”

“Don’t mind me,” I told him. “Go right ahead and turn in. It’s your flat.”

“But—” He looked puzzled.

“Don’t mind me, I’m just sitting here thinking.”

He poured himself a drink from the bottle and refilled my glass. He said, “And how long do you expect to sit there and think?”

“Until I’ve figured out how you killed Charlie Randall.”

He smiled, and sat down on a corner of the table. He said, “What makes you think I killed Randall?”

“The fact that you couldn’t have,” I told him, very earnestly. “It’s all too damn pat, Barranya. It’s like a stage illusion. It’s a show. It doesn’t ring true. It’s just the kind of murder and kind of alibi that an illusionist would arrange. The kind of thing that wouldn’t occur to an ordinary guy.”

“You’re logical, Sergeant, up to a point.”

“And I’m going to get past that point. Go on to bed if you’re tired.”

He chuckled and stared down into the amber liquid in his glass. “Is that all that makes you think I did it?”

“Not quite,” I said. “We found something very suspicious in this flat. That’s what makes me sure.”

He looked up quickly.

“We found nothing, Barranya. Absolutely nothing of interest.”

His smile came back; mockingly, I thought. “And you find that suspicious?”

“Absolutely. I have a strong hunch that before you left here this evening you took away and hid any papers, any notations, you wouldn’t have wanted the police to find. And the gimmicks connected with the seances you hold here.”