Poirot leaned back in his chair, and brought the tips of his fingers together in familiar style. “The case was not quite satisfactory to me,” he observed judicially. “All along I was strongly under the impression that we were dealing with a cold-blooded and premeditated crime committed by some one who had been contented (very cleverly) with using M. Renauld’s own plans for throwing the police off the track. The great criminal (as you may remember my remarking to you once) is always supremely simple.” I nodded. “Now, to support this theory, the criminal must have been fully cognizant of Mr. Renauld’s plans. That leads us to Madame Renauld. But facts fail to support any theory of her guilt. Is there any one else who might have known of them? Yes. From Marthe Daubreuil’s own lips we have the admission that she overheard M. Renauld’s quarrel with the tramp. If she could overhear that, there is no reason why she should not have heard everything else, especially if M. and Madame Renauld were imprudent enough to discuss their plans sitting on the bench. Remember how easily you overheard Marthe’s conversation with Jack Renauld from that spot.” “But what possible motive could Marthe have for murdering Mr. Renauld?” I argued. “What motive? Money! M. Renauld was a millionaire several times over, and at his death (or so she and Jack believed) half that vast fortune would pass to his son. Let us reconstruct the scene from the standpoint of Marthe Daubreuil. “Marthe Daubreuil overhears what passes between Renauld and his wife. So far he has been a nice little source of income to the Daubreuil mother and daughter, but now he proposes to escape from their toils. At first, possibly, her idea is to prevent that escape. But a bolder idea takes its place, and one that fails to horrify the daughter of Jeanne Beroldy! At present M. Renauld stands inexorably in the way of her marriage with Jack. If the latter defies his father, he will be a pauper—which is not at all to the mind of Mademoiselle Marthe. In fact, I doubt if she has ever cared a straw for Jack Renauld. She can simulate emotion, but in reality she is of the same cold, calculating type as her mother. I doubt, too, whether she was really very sure of her hold over the boy’s affections. She had dazzled and captivated him, but separated from her, as his father could so easily manage to separate him, she might lose him. But with M. Renauld dead, and Jack the heir to half his millions, the marriage can take place at once, and at a stroke she will attain wealth—not the beggarly thousands that have been extracted from him so far. And her clever brain takes in the simplicity of the thing. It is all so easy. M. Renauld is planning all the circumstances of his death—she has only to step in at the right moment and turn the farce into a grim reality. And here comes in the second point which led me infallibly to Marthe Daubreuil—the dagger! Jack Renauld had _three___ souvenirs made. One he gave to his mother,