Inspector Raglan turns over the new information: the murder could have happened as early as 9:30, and Charles Kent might have been the man Raymond heard asking Roger Ackroyd for money. However, he couldn’t have placed the phone call from the station, since the station is on the other side of town from the saloon.
Flora’s confession clears something up at least, in that it’s now possible that Roger may have been dead even before 9:50, and as early as 9:30 (at which time Roger was heard talking to someone in the study).
Dr. Sheppard returns to his office and later goes home. There, Caroline tells him that Poirot is waiting for him. Poirot informs Sheppard that he’s arranged for Miss Russell to come to Sheppard’s offices, telling her that Sheppard needs to meet with her for medical reasons. Poirot smiles and says that everything is becoming clearer—but this annoys Sheppard. Poirot shows Sheppard an article that he’s arranged to have placed in tomorrow’s paper, stating that Ralph Paton has been apprehended just as he was about to sail to America. The article is false, but Poirot hopes to use it to his advantage. Poirot also notices a homemade radio in Sheppard’s home, and Sheppard admits that he’s always loved machines.
Poirot reveals that he’s often willing to take matters into his own hands, even if it means behaving somewhat unethically. He places a false story in the newspaper, with the goal of tricking some of the suspects (who might be lying on Ralph’s behalf) into coming forward. Lying to the hundreds or even thousands of people who read the paper could certainly be considered an unethical act, but for Poirot it’s justified by the fact that it might lead to solving the crime. Notice, also, that Sheppard loves machines—something that will be revealed as important.
Poirot and Dr. Sheppard leave for Sheppard’s office, where they find Miss Russell. Poirot informs Russell that Charles Kent was arrested. In that instant, Sheppard realizes that Kent reminded him of Russell. When Poirot tells Russell that Kent must have been the killer, Russell becomes distressed. She admits that Charles came to see her in the summerhouse. She says she left a note there, letting him know that he’d have to wait, and then rushed back to the house (leaving her out of breath). Russell then met with Kent around 8:50. Poirot guesses that Charles is Miss Russell’s son, and Russell nods—many years ago, while she was living in Kent, she had an illegitimate child. As he grew up, Charles began taking drugs, and begged his mother for money. On Friday, around 9:25, Miss Russell gave him money. She insists that he couldn’t have killed Roger Ackroyd, though, since Ackroyd was speaking to someone around 9:30.
Poirot senses that Miss Russell is loyal to Charles Kent in some way, and when he lies and tells Russell that Charles is guilty of the crime, he confirms his suspicions. Poirot doesn’t always know everything, but he knows how to deal with suspects and convince them to divulge hidden information that might be useful to the case (he also learns why Charles’s last is “Kent”—Russell named him after the town where he was born). Notice that, as the novel goes on, the secrets the characters give up become increasingly painful (in the 1920s, having an illegitimate child would have been perceived as a shameful thing by most of Christie’s readers). Poirot himself doesn’t seem to judge Russell’s behavior in any way: his goal is to reach the truth about one specific crime.
Miss Russell leaves the room, and Dr. Sheppard tells Poirot that her testimony suggests that Ralph Paton is the murderer. Poirot reveals that he’d already suspected some connection between Russell and Charles Kent, since 1) Russell mentioned drugs and 2) the goose quill suggested drugs, too. Russell had asked Sheppard about cocaine, and then pivoted to talking about poisons because she didn’t want to draw attention to herself. Sheppard realizes that “there was not much which escaped Hercule Poirot.”