found, he could not presume death and would have been unable to enter into his inheritance.'

I saw a quick flash of green in Poiroes eyes as he rose to his feet.

'Then why bury it?' he asked very softly. 'Reflect, Giraud. Since it was to Jack Renauld's advantage that the body should be found without delay, why dig a grave at all?'

Giraud did not reply. The question found him unprepared. He shrugged his shoulders as though to intimate that it was of no importance.

Poirot moved towards the door. I followed him.

'There is one more thing that you have failed to take into account,' he said over his shoulder.

'What is that?'

'The piece of lead piping,' said Poirot, and left the room.

Jack Renauld still stood in the hall, with a white dumb face, but as we came out of the salon he looked up sharply.

At the same moment there was the sound of a footfall on the staircase. Mrs. Renauld was descending it. At the sight of her son, standing between the two myrmidons of the law, she stopped as though petrified.

'Jack,' she faltered. 'Jack, what is this?'

He looked up at her, his face set. 'They have arrested me, mother.'

'What?'

She uttered a piercing cry, and before anyone could get to her, swayed, and fell heavily. We both ran to her and lifted her up. In a minute Poirot stood up again.

'She has cut her head badly, on the corner of the stairs. I fancy there is slight concussion also. If Giraud wants a statement from her, he will have to wait. She will probably be unconscious for at least a week.'

Denise and Françoise had run to their mistress, and leaving her in their charge Poirot left the house. He walked with his head down, frowning thoughtfully. For some time I did not speak, but at last I ventured to put a question to him: 'Do you believe then, in spite of all appearances to the contrary, that Jack Renauld may not be guilty?'

Poirot did not answer at once, but after a long wait he said gravely: 'I do not know, Hastings. There is just a chance of it. Of course Giraud is all wrong-wrong from beginning to end. If Jack Renauld is guilty, it is in spite of Giraud's arguments, not because of them. And the gravest indictment against him is known only to me.'

'What is that?' I asked, impressed.

'If you would use your grey cells, and see the whole case clearly as I do, you too would perceive it, my friend.'

This was what I called one of Poirot's irritating answers.

He went on, without waiting for me to speak: 'Let us walk this way to the sea. We will sit on that little mound there, overlooking the beach, and review the case. You shall know all that I know, but I would prefer that you should come at the truth by your own efforts-not by my leading you by the hand.'

We established ourselves on the grassy knoll as Poirot had suggested, looking out to sea.

'That is all, my friend,' said Poirot's voice encouragingly. 'Arrange your ideas. Be methodical. Be orderly. There is the secret of success.'

I endeavoured to obey him, casting my mind back over all the details of the case. And suddenly I started as an idea of bewildering luminosity shot into my brain. Tremblingly I built up my hypothesis.

'You have a little idea, I see, mon ami. Capital. We proceed.'

I sat up, and lit a pipe. 'Poirot,' I said, 'it seems to me we have been strangely remiss. I say we-although I dare say I would be nearer the mark. But you must pay the penalty of your determined secrecy. So I say again we have been strangely remiss. There is someone we have forgotten.'

'And who is that?' inquired Poirot, with twinkling eyes.

'Georges Conneau!'

Chapter 20. An Amazing Statement

The next moment Poirot embraced me warmly on the cheek.

'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.'

'Exactement,' 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! 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 Cinema mon ami,' he remarked at last.

'You mean-'

'It would mean 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 farther-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?'

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