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He strode on to a narrow rear stairway, went swiftly down to the rear of the lower hall and found the back door opening onto the alley standing ajar. He stepped out and looked up and down the alley, but saw no one.

Back in the entrance hall, he put a coin in the wall telephone and called police headquarters. “This is Mike Shayne, and I’ve got a corpse for you.” He gave the address and hung up, turned and went to a door marked Janitor, opposite the stairway.

He opened the door and called, “Jake.”

A voice said, “Yassuh,” and in a moment a wrinkled Negro came to the door. “What yo’ want, Mist’ Shayne?”

“Do you know how a woman got in my apartment?”

“Yo’ sistuh? Yassah. Ah let her in, Mist’ Shayne. She said ’twas a s’prise like.”

“What time did you let her in?”

“’Bout a hour ago, Ah reckon.” Jake scratched his kinky head. “Jest after sundown. Ah was rakin’ the front yahd an’ she druv up in a taxi an’ asks me was yo’ heah an’ then could Ah unlock yo’ door so’s she could wait.”

“Have you seen any strangers around here since you let her in?”

“Strangers? Sho now—” He scratched his head again, then said, “Ah reckon yo’ mean that gentleman what come li’l while later. He asks has a gal come heah to see yo’ an’ Ah tells him ’bout yo’ sistuh waitin’. He jest snorts an’ goes up.”

“How long did he stay?” Shayne asked sharply.

“Ah don’ rightly know. Didn’ see ’im leave, Ah reckon. Ah got busy an’ didn’ take no notice. Is suthin’ wrong?”

“The girl is dead,” Shayne said curtly.

He heard car doors slam outside and hurried to the front door to admit Inspector Quinlan and members of the homicide squad.

The Inspector barked, “So it’s you, Shayne. The Sergeant did get the name right. Where’s the body?”

“Upstairs in my apartment.” Shayne led the way upstairs to his open apartment door. “In here,” he said. “I touched the outside knob opening the door, but didn’t go inside.”

Quinlan nodded to his men to get to work, stepped back beside Shayne, and asked, “Who is she?”

“Beatrice Meany, daughter of Mrs. Sarah Hawley. Lived out at the Hawley place with her husband and her mother.”

“Mixed up in the Groat case,” Quinlan said.

“She’s the girl who told me she’d asked Groat to come out last night, but denied seeing him arrive.”

“What was she doing here?”

“Your guess is as good as mine.” Shayne’s eyes brooded over the room. “She was too drunk to talk very straight when I was out at the Hawley house.”

“So you invited her here to finish the interview?”

“She invited herself.” Shayne told him about Beatrice’s phone call to his office to get the address of the apartment. “That’s all I know about it,” he ended bitterly. “She came here about an hour ago, evidently, and passed herself off as my sister in order to get in. A man came asking for me a little later. Jake told him I wasn’t in and only my sister was here, but he came up anyway. Jake didn’t see him leave.”

“Did Jake give a description of him?”

“He hadn’t got that far when you arrived. Here’s one thing more, Inspector.” Shayne showed him the light bulb at the head of the stairs. “That was unscrewed and the hall was dark when I came up. It was still warm when I screwed it in. I was careful not to touch it except right at the neck with two fingers.”

“All right,” Quinlan grunted. “I’ll have it checked. Let’s talk to the janitor.”

Jake was waiting for them at the foot of the stairs. He repeated the story he had told Shayne, for the Inspector’s benefit.

When asked for a description, the Negro said, “He was sorta fat, an’ sorta young. He had on a gray suit, Ah reckon, sorta dark.”

“Was he wearing a hat?” Shayne asked.

“A hat? Yassuh. Ah reckon so. Ah jest don’ recollec’k.”

“The description sounds like Mr. Meany,” Shayne told Quinlan. “The girl’s husband. He’s quite bald for so young a man, and you notice it if you see him bareheaded.”

Quinlan went to the telephone and talked to Headquarters. He dispatched men to the Hawley residence to pick up Gerald Meany and learn what they could about his movements that afternoon, hung up, and turned back to Shayne. “I suppose Jake saw you come in just now?”

“No one saw me come in,” he answered cheerfully.

“Can you prove she was dead when you got here?”

Shayne frowned and admitted, “Depends on how long she’s been dead. I can account for my actions to within about fifteen minutes of the time I called Headquarters.”

Quinlan got out his notebook. “Let’s have it.”

“I went to Room 319 at the St. Charles Hotel about an hour ago. Took about half an hour drinking a mint julep. Dropped in on the house dick for a chat on my way out, fooled around a few minutes, and drove straight back here.”

Quinlan went to the phone and called the St. Charles. He asked for the house detective, and after talking for a few minutes, hung up.

Shayne said, “Call Room 319 now, and see if there are still two people in the room where I left them. Mrs. Meredith will probably answer. You ask for Leslie Cunningham.”

When the connection was made, Inspector Quinlan said, “Mrs. Meredith? I’d like to speak to Mr. Cunningham.” When the sailor got on the line, the Inspector questioned him, jotting down the answers in his notebook. Presently he hung up and turned to Shayne.

“Davis and Cunningham check your story. Davis says you were there at seventeen minutes after six. Your report on the murder reached Headquarters at exactly six thirty-nine. That’s twenty-two minutes to account for from the time you left Davis, and it’s not more than a five-minute drive here. How much time did you waste after you got here before calling in?”

“Not more than five minutes,” Shayne told him.

“Don’t you know enough to report a murder as soon as you see it?”

“I thought I saw movement in my room when I got out of my car,” Shayne explained, “and watched the window for a while. When I found the dead woman, I thought the murderer might be just then getting out the back way, and I checked. Then I took time to turn on the hall light.”

“That puts you here at six thirty-four. It didn’t take you seventeen minutes to drive here from the St. Charles.”

“How does Kurt Davis place the time so exactly?”

“Claims he looked at his watch. It’s a habit of his.”

Shayne grinned wryly. “I suppose you wouldn’t believe me if I told you I went window shopping for twelve minutes.”

Quinlan’s face reddened. He barked, “Window shopping!”

“Let’s go up and see what the boys have got,” Shayne suggested. “Maybe I’ll think of something better than window shopping.”

Doctor Matson’s assistant met them in the doorway of Shayne’s apartment. He said, “Death by strangulation and possible fracture of the vertebrae. Not more than a half an hour ago, and probably within the past fifteen minutes. The doc will have to give it to you closer than that.”

Shayne asked, “Could she have been strangled by a woman?”

The young assistant considered for a moment then said, “It’s very doubtful. The contusions on her throat indicate a lot of strength in the hands that caused them.” He went on down the hall.

Shayne and Quinlan went inside the room where the photographer was putting away his equipment and the fingerprint men were finishing up their work.

Sergeant Donovan scowled at Quinlan. He said, “We haven’t got anything worth while. One set of prints everywhere, presumably yours, Mike. Her prints are on that brandy bottle on the table and on the arms of that chair behind her.”