That evening, Dr. Sheppard goes to Poirot’s home for dinner. Poirot asks about Caroline, and Sheppard demands to know why Poirot visited while Sheppard was out; Poirot chuckles and says, “I always like to employ the expert.” He asks why Sheppard didn’t tell him the truth about Ralph, and Sheppard doesn't answer. Sheppard asks if Poirot is suspicious of Russell, considering what she asked about poisons.
Poirot doesn’t explain his remark about employing the expert. It could mean that he had a valuable meeting with Caroline, the “expert” in town gossip. But the remark also suggests that Poirot was trying to get Dr. Sheppard, the medical “expert,” out of the way by giving him something to do. With Sheppard gone, Poirot is able to learn information about Ralph that Sheppard has refused to tell him, and he appears to be becoming more suspicious of Sheppard.
Poirot, noticing that Sheppard is impatient, says that Sheppard is like “the little child who wants to know the way the engine works.” He proceeds to give Sheppard a lecture on his methods. Sheppard has told Poirot he left the house at 8:50; however, Sheppard’s clock could have been wrong. Yet Parker can confirm the time. Sheppard has also claimed he ran into a stranger. Poirot can confirm this because a maid ran into the stranger a few minutes earlier, and the stranger asked her the way to Roger Ackroyd’s house. The stranger was also seen at the Three Boars, where a barmaid reported he spoke with an American accent.
Poirot has to be careful not to rely too extensively on any single witness’s testimony, unless other witnesses can corroborate it. Poirot has clearly been conducting his own investigation, independent of Dr. Sheppard—for example, he spoke with people at the Three Boars in order to learn as much as he could about the mysterious stranger who Dr. Sheppard saw on the night of the murder.
Suddenly Poirot produces the quill that he found in the summerhouse. Dr. Sheppard remembers having heard about Canadians and Americans who consume heroin in such a way. Poirot points out that the use of the “scrap of starched cambric” should now be obvious to Sheppard. However, Sheppard claims that he can’t imagine what it was used for. He asks why the stranger went to the summerhouse, and Poirot points out that Mrs. Ackroyd said she’d brought Flora from Canada. Poirot next brings up the parlormaid’s dismissal, pointing out that it doesn’t take half an hour to fire someone.
Poirot has a few pieces of evidence to work with: the quill, which suggests drug use could be connected to Roger’s murder, the cambric, whose meaning Poirot teasingly refuses to divulge, and Ursula’s testimony. Poirot’s challenge is to distinguish between secrets that have some relevance to the murder of Roger Ackroyd and secrets that don’t (but might be interesting in their own right). The only way for Poirot to solve the crime is to learn everything about his suspects.
Poirot asks Dr. Sheppard for his thoughts. Dr. Sheppard produces a scrap of paper on which he’s jotted some thoughts. He notes that Roger Ackroyd was heard talking to someone around 9:30, that Ralph Paton probably came in through the window, as evidenced by his shoe prints, and that Ackroyd was nervous that evening. Finally, he suggests that the person in the study at 9:30 asked Roger for money. And yet, it couldn’t have been Ralph who killed Roger, since Roger was alive at 9:50 pm. The best hypothesis, Sheppard claims, is that Ralph left the window open, allowing a robber to enter.
Dr. Sheppard puts together a fairly obvious theory of how Roger Ackroyd was killed: Ralph came in through the window, left, and inadvertently allowed the killer to come in through the window afterward. However, Sheppard doesn’t believe that Ralph could be the killer, as Inspector Raglan seems to believe. This could be because Sheppard knows and trusts Ralph; furthermore, Ralph seemingly couldn’t have been the killer because Roger was still alive at 9:50.
Poirot notes that Sheppard’s theory doesn’t explain everything. It doesn’t explain the pushed-out chair, or the missing forty pounds—however, Sheppard points out, Roger may have given Ralph the forty pounds. Poirot agrees, but points out another thing—it’s unclear why Major Blunt was sure that Roger was talking with Raymond. Next, Poirot asks why Ralph has left the town if he’s innocent.
The problem with Sheppard’s theory, much like Raglan’s, is that he cherry-picks facts that support his theory and ignores everything else. Poirot’s theory will be much more thorough, explaining every aspect of the crime, including seemingly trivial details like the chair.
Poirot also wants to know what Dr. Sheppard thinks of the motive for murder. Sheppard points out that money could be a motive—Ralph stood to inherit Roger’s fortune. Poirot adds that there are other motives: the blackmailer could have been trying to conceal their name by stealing the envelope, or get out of a “financial scrape.” All of this, Sheppard points out, would suggest Ralph. Poirot, however, disagrees: he’s decided that Ralph Paton is innocent.
Poirot has entertained the idea that Ralph was the killer, but now he seems to be moving away from such a theory, partly because of the evidence and partly because of his own instincts. Nevertheless, it seems clear that money was an important motive for the killer: Roger was a rich man, and he was going to take action against Mrs. Ferrars’ blackmailer.