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On this Friday afternoon, very much aware of the murderer lurking somewhere in the building, she peeked out into the hall before hurrying across to the incinerator door. Then she quickly dumped the rubbish, but someone had thrown something greasy away recently, and a piece of paper stuck to the ramp. Wrinkling her nose in distaste, she reached in and freed it.

That’s when it happened again. This time, it was an upper arm, elbow to shoulder, and it didn’t pause at the sixth floor. It sailed right on by, elbow foremost, and left Mrs. Kelly staring at the blank brick walls of the shaft.

She was back in her own living room, the door locked and the chain attached, before she had time to think. And when she recovered sufficiently, she decided at once to call that smarty Detective Sean Ryan, because now she knew why there had only been the forearm disposed of yesterday.

Of course. The murderer was afraid to drop all of the body at once. It would take him half an hour or more, and someone on a lower floor would be bound to see something in that time. Besides, he might be afraid the whole body wouldn’t burn in just one day.

That’s why he dropped just one piece, each afternoon at four. The incinerator had been burning for an hour by that time, and so would be nice and hot. And it would have two more hours to burn before it was turned off.

Ah-hah, Detective Ryan, she thought, and reached for the phone. But then she stopped, her hand an inch from the phone, suddenly knowing exactly what Detective Ryan would have to say. “More arms, Mrs. Kelly? And this one didn’t even stop, just whizzed right by? Do you know how fast a falling arm would go, Mrs. Kelly?”

No. Mrs. Kelly wasn’t going to go through another humiliating interview like the one yesterday.

But what could she do? A murder had been committed, and what could she do if she couldn’t even call the police?

She fretted and fumed, half-afraid and half-annoyed, and then she remembered something Detective Ryan had said yesterday. Corroboration, that’s what he had said. Proof of murder, proof someone was missing from this building.

Very well, corroboration he would get. And then he’d have to swallow those smart-alecky remarks of his. How fast does a falling arm go indeed!

All she had to do was find proof.

Almost a full week went by, and no proof. Every afternoon at four, Mrs. Kelly stood by the incinerator door and in growing frustration watched another part sail by. Saturday, the left forearm. Sunday, the left upper arm. Monday, right foot, knee to toes. Tuesday, right leg, hip to knee. Lower half of the torso on Wednesday. Left foot, knee to toes on Thursday.

And Mrs. Kelly knew she had only three days left. The upper half of the torso, the left leg, and the head.

For the first time in her life, Mrs. Kelly disliked the automatic privacy that was a part of living in a New York City apartment. Twenty-seven years she had lived in this building, and she didn’t know a soul here, except for the superintendent on the first floor. But the people in the sixteen apartments on the four floors above her were total strangers. She could watch the front door forever, and never know who was missing.

On Tuesday (right leg), it occurred to her to watch the mailboxes. It seemed to her that this murderer, whoever he was, would be staying in his apartment as much as possible until the body had been completely eliminated. There was a possibility he wouldn’t even leave to pick up his mail. If there were a stuffed mailbox, it might be the clue she needed.

There wasn’t a stuffed mailbox.

On Wednesday (lower half of the torso), she thought to go back to the mailboxes again, this time to get the names of the occupants of the sixteen apartments up above. That afternoon, clutching her list, she watched the piece go by, and repaired furiously to her apartment.

It was all that Detective Sean Ryan’s fault, that rumpled man. He must be a widower, or a bachelor. No woman would let her man out of the house as rumpled as all that. Nor wearing a necktie as horrible as that wide orange thing Detective Ryan had had around his neck.

Not that it made any difference. Mrs. Kelly had had trouble enough for one lifetime with Bertram, rest his soul. Housebreaking a man was a life’s work, and a woman would be a fool to try to do the job on two men, one right after the other. And Mrs. Aileen Kelly was certainly no fool.

Though she was beginning to feel very much like a fool, as day after day the pieces of that poor murdered woman fell down the incinerator shaft, and Mrs. Kelly still without a shred of proof.

Thursday, she considered the possibility of hiding in a hallway, where she could watch the incinerator door. According to the way the pieces were falling, there were four parts left. If Mrs. Kelly were to spend each of the four days hidden in the hallway on each of the four floors above, sooner or later she would catch the murderer red-handed.

But, how to hide in the hallways? They were all bare and empty, without a single hiding place.

Except, perhaps, the elevator.

Of course, of course, the elevator. She rushed out of her apartment, got into the elevator, and peered through the round porthole in the elevator door. By pressing her nose against the metal of the door and peeking far to the left, she could just barely catch a glimpse of the incinerator door. It would work.

Accordingly, she was in the elevator at five of four, and pushing the button marked 7. The elevator rose one flight and stopped. Mrs. Kelly took up her position, peering out at the incinerator door, and so she stood for three minutes.

Then the elevator started with a jerk, cracking Mrs. Kelly smartly across the nose, and purred down its shaft, stopping at the fourth floor. Someone else had called it.

Furious, Mrs. Kelly glared at the overcoat-bundled man who stepped aboard at the fourth floor and pushed the button marked 1.

On the first floor, the overcoated man left the building, while Mrs. Kelly dashed to the incinerator door, opened it, opened the ramp, and watched the left foot go falling by, to land in the midst of the flames below.

That did it for fair. There were only three days left now, and four floors to check. And if she didn’t find out who the murderer was before Sunday, he would have disposed of the body completely, and there wouldn’t be a shred of proof. Mrs. Kelly stormed back to the elevator, thinking, “Three days and four floors. Three days and four floors.”

And the roof.

She stopped in her tracks. The roof. The top of the incinerator shaft was up there, covered only by a wire grating. It wouldn’t be hard to bend that grating back, and drop something down the shaft.

Which meant it didn’t have to be somebody in this building at all. It could be someone from almost anywhere on the block, coming across the roofs to drop the evidence as far from home as possible.

Well, there was a way to find out about that. It had snowed all day yesterday and last night, but it hadn’t snowed today. The flat roof would have a nice thick layer of snow on it. If anyone had come across it to the incinerator shaft, he would have had to leave tracks.

Getting into the elevator, she pushed the button for the tenth floor, and waited impatiently as the elevator rose to the top of the building. Then she mounted the flight of stairs to the roof door, unbent the wire twisted around the catch, and stepped out.

She had been in too much of a hurry to stop and dress properly for the outdoors. It was cold and windy up on the roof, and the snow was ankle-deep. Mrs. Kelly turned the collar of her housecoat up and held the lapels closed against her throat. Her old scuffy slippers were no protection against the snow.

She hurried off to the right, to the incinerator chimney, circled it, and found no footprints beyond her own.