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The next moment Poirot embraced me warmly. “Enfin! You have arrived. And all by yourself. It is superb! Continue your reasoning. You are right. Decidedly we have done wrong to forget Georges Conneau.”

I was so flattered by the little man’s approval that I could hardly continue. But at last I collected my thoughts and went on.

“Georges Conneau disappeared twenty years ago, but we have no reason to believe that he is dead.”

“Aucunement,” agreed Poirot. “Proceed.”

“Therefore we will assume that he is alive.”

“Exactly.”

“Or that he was alive until recently.”

“De mieux en mieux!”

“We will presume,” I continued, my enthusiasm rising, “that he has fallen on evil days. He has become a criminal, an apache, a tramp—a what you will. He chances to come to Merlinville. There he finds the woman he has never ceased to love.”

“Eh eh! The sentimentality,” warned Poirot.

“Where one hates one also loves,” I quoted or misquoted. “At any rate he finds her there, living under an assumed name. But she has a new lover, the Englishman, Renauld. Georges Conneau, the memory of old wrongs rising in him, quarrels with this Renauld. He lies in wait for him as he comes to visit his mistress, and stabs him in the back. Then, terrified at what he has done, he starts to dig a grave. I imagine it likely that Madame Daubreuil comes out to look for her lover. She and Conneau have a terrible scene. He drags her into the shed, and there suddenly falls down in an epileptic fit. Now supposing Jack Renauld to appear. Madame Daubreuil tells him all, points out to him the dreadful consequences to her daughter if this scandal of the past is revived. His father’s murderer is dead—let them do their best to hush it up. Jack Renauld consents—goes to the house and has an interview with his mother, winning her over to his point of view. Primed with the story that Madame Daubreuil has suggested to him, she permits herself to be gagged and bound. There, Poirot, what do you think of that?” I leaned back, flushed with the pride of successful reconstruction.

Poirot looked at me thoughtfully.

“I think that you should write for the Kinema, mon ami,” he remarked at last.

“You mean—?”

“It would make a good film, the story that you have recounted to me there—but it bears no sort of resemblance to everyday life.”

“I admit that I haven’t gone into all the details, but—”

“You have gone further—you have ignored them magnificently. What about the way the two men were dressed? Do you suggest that after stabbing his victim, Conneau removed his suit of clothes, donned it himself, and replaced the dagger?”

“I don’t see that that matters,” I objected rather huffily. “He may have obtained clothes and money from Madame Daubreuil by threats earlier in the day.”

“By threats—eh? You seriously advance that supposition?”

“Certainly. He could have threatened to reveal her identity to the Renaulds, which would probably have put an end to all hopes of her daughter’s marriage.”

“You are wrong, Hastings. He could not blackmail her, for she had the whip hand. Georges Conneau, remember, is still wanted for murder. A word from her and he is in danger of the guillotine.”

I was forced, rather reluctantly, to admit the truth of this.

“Your theory,” I remarked acidly, “is doubtless correct as to all the details?”

“My theory is the truth,” said Poirot quietly. “And the truth is necessarily correct. In your theory you made a fundamental error. You permitted your imagination to lead you astray with midnight assignations and passionate love scenes. But in investigating crime we must take our stand upon the commonplace. Shall I demonstrate my methods to you?”

“Oh, by all means let us have a demonstration!”

Poirot sat very upright and began, wagging his forefinger emphatically to emphasize his points.

“I will start as you started from the basic fact of Georges Conneau. Now the story told by Madame Beroldy in court as to the ‘Russians’ was admittedly a fabrication. If she was innocent of connivance in the crime, it was concocted by her, and by her only as she stated. If, on the other hand, she was not innocent, it might have been invented by either her or Georges Conneau.

“Now is this case we are investigating, we meet the same tale. As I pointed out to you, the facts render it very unlikely that Madame Daubreuil inspired it. So we turn to the hypothesis that the story had its origin in the brain of Georges Conneau. Very good. Georges Conneau, therefore, planned the crime with Madame Renauld as his accomplice. She is in the limelight, and behind her is a shadowy figure whose alias is unknown to us.

“Now let us go carefully over the Renauld Case from the beginning, setting down each significant point in its chronological order. You have a notebook and pencil? Good. Now what is the earliest point to note down?”

“The letter to you?”

“That was the first we knew of it, but it is not the proper beginning of the case. The first point of any significance, I should say, is the change that came over M. Renauld shortly after arriving in Merlinville, and which is attested to by several witnesses. We have also to consider his friendship with Madame Daubreuil, and the large sums of money paid over to her. From thence we can come directly to the 23rd May.”

Poirot paused, cleared his throat, and signed to me to write.

“23rd May. M. Renauld quarrels with his son over latter’s wish to marry Marthe Daubreuil. Son leaves for Paris.

“24th May. M. Renauld alters his will, leaving entire control of his fortune in his wife’s hands.

“7th June. Quarrel with tramp in garden, witnessed by Marthe Daubreuil.

“Letter written to M. Hercule Poirot, imploring assistance.

“Telegram sent to Jack Renauld, bidding him proceed by the Anzora to Buenos Ayres.

“Chauffeur, Masters, sent off on a holiday.

“Visit of a lady, that evening. As he is seeing her out, his words are ‘Yes, yes—but for God’s sake go now. …’ ”

Poirot paused.

“There, Hastings, take each of those facts one by one, consider them carefully by themselves and in relation to the whole, and see if you do not get new light on the matter.”

I endeavoured conscientiously to do as he had said. After a moment or two, I said rather doubtfully:

“As to the first points, the question seems to be whether we adopt the theory of blackmail, or of an infatuation for this woman.”

“Blackmail, decidedly. You heard what Stonor said as to his character and habits.”

“Mrs. Renauld did not confirm his view,” I argued.

“We have already seen that Madame Renauld’s testimony cannot be relied upon in any way. We must trust to Stonor on that point.”

“Still, if Renauld had an affair with a woman called Bella, there seems no inherent improbability in his having another with Madame Daubreuil.”

“None whatever, I grant you, Hastings. But did he?”

“The letter, Poirot. You forget the letter.”

“No, I do not forget. But what makes you think that letter was written to M. Renauld?”

“Why it was found in his pocket and—and—”

“And that is all!” cut in Poirot. “There was no mention of any name to show to whom the letter was addressed. We assumed it was to the dead man because it was in the pocket of his overcoat. Now, mon ami, something about that overcoat struck me as unusual. I measured it, and made the remark that he wore his overcoat very long. That remark should have given you to think.”

“I thought you were just saying it for the sake of saying something,” I confessed.

“Ah, quelle idée! Later you observed me measuring the overcoat of M. Jack Renauld. Eh bien, M. Jack Renauld wears his overcoat very short. Put those two facts together with a third, namely that M. Jack Renauld flung out of the house in a hurry on his departure for Paris, and tell me what you make of it!”

“I see,” I said slowly, as the meaning of Poirot’s remarks bore in upon me. “That letter was written to Jack Renauld—not to his father. He caught up the wrong overcoat in his haste and agitation.”

Poirot nodded.

“Précisement! We can return to this point later. For the moment let us content ourselves with accepting the letter as having nothing to do with M. Renauld père, and pass to the next chronological event.”

“May 23rd,” I read, “M. Renauld quarrels with his son over latter’s wish to marry Marthe Daubreuil. Son leaves for Paris. I don’t see anything much to remark upon there, and the altering of the will the following day seems straightforward enough. It was the direct result of the quarrel.”

“We agree, mon ami—at least as to the cause. But what exact motive underlay this procedure of M. Renauld’s?”

I opened my eyes in surprise.

“Anger against his son of course.”

“Yet he wrote him affectionate letters to Paris?”

“So Jack Renauld says, but he cannot produce them.”

“Well, let us pass from that.”

“Now we come to the day of the tragedy. You have placed the events of the morning in a certain order. Have you any justification for that?”

“I have ascertained that the letter to me was posted at the same time as the telegram was despatched. Masters was informed he could take a holiday shortly afterwards. In my opinion the quarrel with the tramp took place anterior to these happenings.”

“I do not see that you can fix that definitely—unless you question Mademoiselle Dabreuil again.”

“There is no need. I am sure of it. And if you do not see that, you see nothing, Hastings!”

I looked at him for a moment.

“Of course! I am an idiot. If the tramp was Georges Conneau, it was after the stormy interview with him that Mr. Renauld apprehended danger. He sent away the chauffeur, Masters, whom he suspected of being in the other’s pay, he wired to his son, and sent for you.”

A faint smile crossed Poirot’s lips.

“You do not think it strange that he should use exactly the same expressions in his letter as Madame Renauld used later in her story? If the mention of Santiago was a blind, why should Renauld speak of it, and—what is more—send his son there?”

“It is puzzling, I admit, but perhaps we shall find some explanation later. We come now to the evening, and the visit of the mysterious lady. I confess that that fairly baffles me, unless it was Madame Daubreuil, as Françoise all along maintained.”

Poirot shook his head.

“My friend, my friend, where are your wits wandering? Remember the fragment of cheque, and the fact that the name Bella Duveen was faintly familiar to Stonor, and I think we may take it for granted that Bella Duveen is the full name of Jack’s unknown correspondent, and that it was she who came to the Villa Geneviève that night. Whether she intended to see Jack, or whether she meant all along to appeal to his father we cannot be certain, but I think we may assume that this is what occurred. She produced her claim upon Jack, probably showed letters that he had written her, and the older man tried to buy her off by writing a cheque. This she indignantly tore up. The terms of her letter are those of a woman genuinely in love, and she would probably deeply resent being offered money. In the end he got rid of her, and here the words that he used are significant.”

“ ‘Yes, yes, but for God’s sake go now,’ ” I repeated. “They seem to me a little vehement, perhaps, that is all.”

“That is enough. He was desperately anxious for the girl to go. Why? Not only because the interview was unpleasant. No, it was the time that was slipping by, and for some reason time was precious.”

“Why should it be?” I asked, bewildered.

“That is what we ask ourselves. Why should it be? But later we have the incident of the wrist watch—which again shows us that time plays a very important part in the crime. We are now fast approaching the actual drama. It is half-past ten when Bella Duveen leaves, and by the evidence of the wrist watch we know that the crime was committed, or at any rate that it was staged, before twelve o’clock. We have reviewed all the events anterior to the murder, there remains only one unplaced. By the doctor’s evidence, the tramp, when found, had been dead at least forty-eight hours—with a possible margin of twenty-four hours more. Now, with no other facts to help me than those we have discussed, I place the death as having occurred on the morning of June 7th.”

I stared at him, stupefied.

“But how? Why? How can you possibly know?”

“Because only in that way can the sequence of events be logically explained. Mon ami, I have taken you step by step along the way. Do you not now see what is so glaringly plain?”

“My dear Poirot, I can’t see anything glaring about it. I did think I was beginning to see my way before, but I’m now hopelessly fogged.”

Poirot looked at me sadly, and shook his head. “Mon Dieu! But it is triste! A good intelligence—and so deplorably lacking in method. There is an exercise most excellent for the development of the little grey cells. I will impart it to you—”

“For Heaven’s sake, not now! You really are the most irritating of fellows, Poirot. For goodness’ sake, get on and tell me who killed M. Renauld.”

“That is just what I am not sure of as yet.”

“But you said it was glaringly clear?”

“We talk at cross-purposes, my friend. Remember, it is two crimes we are investigating—for which, as I pointed out to you, we have the necessary two bodies. There, there, ne vous impatientez pas! I explain all. To begin with, we apply our psychology. We find three points at which M. Renauld displays a distinct change of view and action—three psychological points therefore. The occurs immediately after arriving in Merlinville, the second after quarrelling with his son on a certain subject, the third on the morning of June 7th. Now for the three causes. We can attribute No. 1 to meeting Madame Daubreuil. No. 2 is indirectly connected with her since it concerns a marriage between M. Renauld’s son and her daughter. But the cause of No. 3 is hidden from us. We have to deduce it. Now, mon ami, let me ask you a question; who do we believe to have planned this crime?”

“Georges Conneau,” I said doubtfully, eyeing Poirot warily.

“Exactly. Now Giraud laid it down as an axiom that a woman lies to save herself, the man she loves, and her child. Since we are satisfied that was Georges Conneau who dictated the lie to her, and as Georges Conneau is not Jack Renauld, follows that the third case is put out of court. And, still attributing the crime to Georges Conneau, the first is equally so. So we are forced to the second—that Madame Renauld lied for the sake of the man she loved—or in other words, for the sake of Georges Conneau. You agree to that.”

“Yes,” I admitted. “It seems logical enough.”

“Bien! Madame Renauld loves Georges Conneau. Who, then, is Georges Conneau?”

“The tramp.”

“Have we any evidence to show that Madame Renauld loved the tramp?”

“No, but—”

“Very well then. Do not cling to theories where facts no longer support them. Ask yourself instead who Madame Renauld did love.”

I shook my head perplexed.

“Mais, oui, you know perfectly. Who did Madame Renauld love so dearly that when she saw his dead body, she fell down in a swoon?”

I stared dumbfounded.

“Her husband?” I gasped.

Poirot nodded.

“Her husband—or Georges Conneau, whichever you like to call him.”

I rallied myself.

“But it’s impossible.”

“How ‘impossible?’ Did we not agree just now that Madame Daubreuil was in a position to blackmail Georges Conneau?”

“Yes, but—”

“And did she not very effectively blackmail M. Renauld?”

“That may be true enough, but—”

“And is it not a fact that we know nothing of M. Renauld’s youth and upbringing? That he springs suddenly into existence as a French Canadian exactly twenty-two years ago?”

“All that is so,” I said more firmly, “but you seem to me to be overlooking one salient point.”

“What is it, my friend?”

“Why, we have admitted Georges Conneau planned the crime. That brings us to the ridiculous statement that he planned his own murder!”

“Eh bien, mon ami,” said Poirot placidly, “that is just what he did do!”