“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 in 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: