The following morning, Hastings joins Poirot for breakfast in their London sitting room. Poirot is a small, impeccably neat man with an egg-shaped head and a trim military mustache. The detective reminds his friend of the importance of psychological reasoning to his investigative approach and laments that he hasn’t had any interesting cases lately.

Among his morning post, Poirot finds a letter from P. T. Renauld, who is writing from the Villa Geneviève in Merlinville-sur-Mer, France. Renauld explains he possesses a dangerous secret, fears imminent harm, and urgently requests Poirot’s presence. He adds that the matter may require travel to Santiago. A postscript beneath his signature begs Poirot, “For God’s sake, come!” (10). Poirot notes the postscript ink is paler than the rest of the text, proving it was added after the letter was reread rather than dashed off in panic. The detective explains that the carefully reasoned addition of the postscript makes the danger all the more credible. He decides to go immediately and invites Hastings to join him.

They take the 11 am train from Victoria, during which Poirot argues that psychological reasoning outstrips physical clue-hunting. At Calais, no car from Renauld awaits, so they hire one for the drive to Merlinville. On the approach to town, Hastings is struck by the beauty of a golden-haired young woman at a small villa’s gate, but Poirot says he saw “only a girl with anxious eyes” (16). At the Villa Geneviève, a police officer bars the gate and announces that Renauld was murdered that morning.

Poirot sends his card inside, and Lucien Bex, the Commissary of Police and a former acquaintance of the detective’s, brings them in and introduces Dr. Durand and the examining magistrate, Hautet. Learning that Poirot was summoned by the dead man himself, Hautet invites him to assist and notes that Giraud of the Paris Sûreté is expected shortly.

Bex outlines the morning’s findings: The housekeeper found the front door ajar, the maid Léonie found Mrs. Renauld gagged and bound in her bedroom, and Renauld’s body was discovered face down in a freshly dug pit just outside the villa grounds. He’d been stabbed in the back, and the time of death is placed between midnight and 2 am.

During questioning, the housekeeper, Françoise, reveals that a neighbor, Madame Daubreuil, had been visiting Renauld regularly. She implies that the two were having an affair and says that both Renauld and his wife had appeared visibly strained lately. The maid Denise contradicts Françoise and claims the previous night’s visitor was a different, younger woman who seemed English. Denise says she overheard Renauld urgently telling her to go at once. The household also reveals that Renauld had abruptly sent his chauffeur on holiday the previous day. This detail troubles Poirot, since Renauld had offered to send a car to Calais in his letter, yet he would have had no means to do so.

Hautet presents a letter found in Renauld’s overcoat pocket, a passionate, threatening note in English signed “Bella.” The writer professes obsessive love for Renauld and warns she would sooner kill him than lose him to another woman. Hautet attributes the murder to jealousy, claiming that a woman would be more likely to murder someone by stabbing them in the back. Poirot counters that digging the grave was heavy labor, which he believes indicates a male killer or accomplice. The officials resolve to cable Santiago for details of Renauld’s South American past. A search of his papers also produces a will drawn up two weeks earlier leaving the bulk of his estate to his wife, Eloise, with their son, Jack, left entirely dependent on her.

In the study, Poirot straightens a slightly crooked hearthrug and discovers a remnant of a destroyed check bearing the name Duveen in Renauld’s hand. He also retrieves a long black hair from one of the leather armchairs, confirming the room was where Renauld received his visitor the previous night.

Renauld’s body, which is being stored in a garden shed, shows a face frozen in shock and terror. The murder weapon, a narrow knife carrying no fingerprints, was left in the wound, indicating the killer wore gloves. Poirot notes that Renauld wore only underclothes beneath his overcoat and that the overcoat was very long.

Eloise, a tall, silver-haired woman, recounts the attack: Two masked men entered the bedroom. One was tall with a long black beard, and the other was short and stocky with a reddish beard. The shorter man gagged and bound her while the taller man took her dagger from her desk and held it to Renauld’s heart. The men forced Renauld to dress, demanded a secret in a South American variant of Spanish, and hustled him out. Before being taken, Renauld told his wife he would return by morning. She then fainted. She claims that the attack took place around 2 in the morning, but Bex discovers a watch that seems to have been damaged in the struggle and is now two hours fast. The watch says it’s 7 pm when the current time is 5 pm.

Mrs. Renauld says she first noticed her husband’s anxiety about 10 days prior but he deflected her questions, and she is surprised to learn he had contacted Poirot. She denies knowing anyone named Duveen or Bella and says she was unaware of the female visitor who came to see her husband the previous night. She identifies the murder weapon as a dagger made from airplane wire, which her son gave her as a memento of his service in the war. She also reveals that Renauld had telegraphed Jack in Paris the previous day, directing him to sail from Cherbourg for Buenos Aires and continue overland to Santiago. Jack’s destination startles everyone present because Renauld mentioned the city in his letter to Poirot.

Poirot examines the rope marks on the woman’s wrists and appears puzzled by what he observes. When she insists on identifying the body, she cries out her husband’s name and collapses. Poirot tells Hastings her grief is genuine, which overturns a theory he’d been forming.

Poirot, Hastings, and Bex walk out to inspect the crime scene. Poirot questions why the intruders would have tried the front door when a tree beside Mrs. Renauld’s window offered easier access. There are no footprints in the soft flower bed at the tree’s base. On the opposite side of the driveway, however, Poirot finds numerous footprints that Bex dismisses as the gardener’s. Poirot insists they are the most important clue so far.

Beyond the boundary hedge is an unfinished golf course where the grave was dug. There they encounter Mr. Giraud of the Paris Sûreté, a tall, arrogant man of about 30 with a low opinion of Poirot’s methods. Giraud has established that three sets of tracks come through the hedge, with the captors’ footprints deliberately obliterated on either side of Renauld’s. The spade and gloves used to dig the grave came from Renauld’s own property and carry no fingerprints.

Poirot takes a close interest in a short piece of lead piping near the grave, which Giraud dismisses as irrelevant. Noting that construction workers would soon have unearthed the body, Giraud takes this as proof the killers were strangers to the area. Poirot briefly wonders aloud whether the body was perhaps meant to be found and then sets the thought aside as absurd.