He could not help her because he did not understand her, because it was not even possible for him to appreciate her. He had done his best for her, but what had that meant up to date? What had he done for her since that one moment of appeal?

And in his thoughts the answer came quickly. He had kept her safe. That at least.

If, indeed, she needed keeping safe. That was where the whole point lay. Did she need keeping safe? That preposterous confession! Really, not so much a confession as an announcement: "/ think I may have committed a murder." Hold on to that, because that was the crux of the whole thing. That was his metier. To deal with murder, to clear up murder, to prevent murder! To be the good dog who hunts down murder. Murder announced. Murder somewhere. He had looked for it and had not found it. The pattern of arsenic in the soup? A pattern of ^ung hooligans stabbing each other ^ ith knives? The ridiculous and sinister phrase, bloodstains in the courtyard. A shot fired from a revolver. At whom, and why?

It was not as it ought to be, a form of crime that would fit with the words she had said: "I may have committed a murder".

He had stumbled on in the dark, trying to see a pattern of crime, trying to see where the third girl fitted into that pattern, and coming back always to the same urgent need to know what this girl was really like.

And then with a casual phrase, Ariadne Oliver had, as he thought, shown him the light. The supposed suicide of a woman at Borodene Mansions. That would fit. It was where the third girl had her living quarters.

It must be the murder that she had meant.

Another murder committed about the same time would have been too much of a coincidence! Besides there was no sign or trace of any other murder that had been committed about then. No other death that could have sent her hot-foot to consult him, after listening at a party to the lavish admiration of his own achievements which his friend, Mrs. Oliver, had given to the world. And so, when Mrs. Oliver had informed him in a casual manner of the woman who had thrown herself out of the window, it had seemed to him that at last he had got what he had been looking for.

Here was the clue. The answer to his perplexity. Here he would find what he needed. The why, the when, the where.

"Quelle deception." said Hercule Poirot, out loud.

He stretched out his hand, and sorted out the neatly typed resume of a woman's life. The bald facts of Mrs. Charpentier's existence. A woman of forty-three of good social position, reported to have been a wild girl - two marriages - two divorces - a woman who liked men. A woman who of late years.had drunk more than was good for her. A woman who liked parties. A woman who was now reported to go about with men a good many years younger than herself. Living in a flat alone in Borodene Mansions, Poirot could understand and feel the sort of woman she was, and had been, and he could see why such a woman might wish to throw herself out of a high window one early morning when she awoke to despair.

Because she had cancer or thought she had cancer? But at the inquest, the medical evidence had said very definitely that that was not so.

What he wanted was some kind of a link with Norma Restarick. He could not find it.

He read through the dry facts again.

Identification had been supplied at the inquest by a solicitor. Louise Carpenter, though she had used a Frenchified form of her surname - Charpentier. Because it went better with her Christian name?

Louise? Why was the name Louise familiar? Some casual mention? - a phrase?

— his fingers rimed neatly through typewritten pages. Ah! there it was! Just that one reference. The girl for whom Andrew Restarick had left his wife had been a girl named Louise Birell. Someone who had proved to be of little significance in Restarick's later life. They had quarrelled and parted after about a year. The same pattern, Poirot thought. The same thing obtaining that had probably obtained all through this particular woman's life. To love a man violently, to break up his home, perhaps, to live with him, and then to quarrel with him and leave him. He felt sure, absolutely sure, that this Louise Charpentier was the same Louise.

Even so, how did it tie up with the girl Norma? Had Restarick and Louise Charpentier come together again when he returned to England? Poirot doubted it.

Their lives had parted years ago. That they had by any chance come together again seemed unlikely to the point of impossibility I It had been a brief and in reality unimportant infatuation. His present wife would hardly be jealous enough of her husband's past to wish to push his former mistress out of a window. Ridiculous! The only person so far as he could see who might have been the type to harbour a grudge over many long years, and wish to execute revenge upon the woman who had broken up her home, might have been the first Mrs. Restarick. And that sounded wildly impossible also, and anyway, the first Mrs. Restarick was dead!

The telephone rang. Poirot did not move.

At this particular moment he did not want to be disturbed. He had a feeling of being on a trail of some kind… He wanted to pursue it… The telephone stopped.

Good. Miss Lemon would be coping with it.

The door opened and Miss Lemon entered.

"Mrs. Oliver wants to speak to you," she said.

Poirot waved a hand. "Not now, not now, I pray you \ I cannot speak to her now." "She says there is something that she has just thought of - something she forget to tell you. About a piece of paper - an unfinished letter, which seems to have fallen out of a blotter in a desk in a furniture van. A rather incoherent story," added Miss Lemon, allowing a note of disapproval to enter her voice.

Poirot waved more frantically.

"Not now," he urged. "I beg of you, not «. now." "I will tell her you are busy." Miss Lemon retreated.

Peace descended once more upon the room. Poirot felt waves of fatigue creeping over him. Too much thinking. One must relax. Yes, one must relax. One must let tension go - in relaxation the pattern would come. He closed his eyes. There were all the components there. He was sure of that now, there was nothing more he could learn from outside. It must come from inside.

And quite suddenly - just as his eyelids were relaxing in sleep - it came.

It was all there - waiting for him! He would have to work it all out. But he knew now. All the bits were there, disconnected bits and pieces, all fitting in. A wig, a picture, 5 a.m., women and their hair dos, the Peacock Boy - all leading to the phrase with which it had begun: Third Girl.

"I may have committed a murder…" Of course!

A ridiculous nursery rhyme came into his mind. He repeated it aloud.

Rub a dub dub, three men in a tub And who do you think they be?

A butcher, a baker, a candlestick maker.

Too bad, he couldn't remember the last line.

A baker, yes, and in a far-fetched way, a butcher - He tried out a feminine parody: Pat a cake, pat, three girls in aflat And who do you think they be?

A Personal Aide and a girl from the Slade And the Third is a - Miss Lemon came in.

"Ah - I remember now - 'And they all came out of a weenie potato.' " Miss Lemon looked at him in anxiety.

"Dr. Stillingfleet insists on speaking to you at once. He says it is urgent.^ "Tell Dr. Stillingfleet he can-Dr.

Stillingfleet, did you say?" He pushed past her, caught up the receiver. "I am here. Poirot speaking!

Something has happened?" "She's walked out on me." "What?" "You heard me. She's walked out.

Walked out through the front gate." "You let her go?" "What else could I do?" "You could have stopped her." "No." "To let her go was madness." "No." "You don't understand." "That was the arrangement. Free to go at any time." "You don't understand what may be involved." "All right then, I don't. But I know what /'m doing. And if I don't let her go, all the work I've done on her would go for nothing.