"We have here a hypothesis of the First and Second Murderer, as the great Shakespeare would put it. The First Murderer stabbed his victim and left the compartment, turning off the light. The Second Murderer came in in the dark, did not see that his or her work had been done and stabbed at least twice a dead body."
Immediately after examining Ratchett's body with Dr. Constantine, Poirot draws what seems like an outlandish, larger-than-life conclusion: that Ratchett was attacked by not one but two people independently of one another. This moment in the text is a masterful instance of writerly manipulation. In this line, Poirot implies that the two-murderers hypothesis is theatrical and unlikely-sounding, despite the fact that it may be the only explanation available. With this implication, Christie sets her readers' expectations regarding which theories of the case are sensible, which are crazy-sounding but possible, and which are unacceptably ridiculous. By framing a two-murderer scenario as weird but possible or even probable, Christie indicates, without saying it explicitly, that a scenario involving twelve murderers is impossibly intricate and unlikely. As a result, readers are consciously or unconsciously led astray from the even-more-outlandish but true scenario.
“And most conveniently she leaves her handkerchief behind! Exactly as it happens in the books and on the films—and to make things even easier for us it is marked with an initial.”
Here, Poirot starts to suspect that his criminals are actually familiar with the conventions of the very crime genre to which Murder on the Orient Express belongs. Starting here, and throughout the book, it's unclear whether the clues Poirot finds are reliable. This is because his crime-savvy suspects decide to actually shape a narrative of their own, dropping hints that they believe—based on their knowledge of book and movie detectives—will be irresistible to Poirot. Of course, Poirot himself doesn't fall for it, since he's suspicious of the clues precisely because they're so dramatic and fit so neatly into an intriguing narrative. Still, he's often unsure whether a given clue is real, planted, or—as they are in some cases—planted with the intention of being discovered as plants.
"All around us are people, of all classes, of all nationalities, of all ages. For three days these people, these strangers to one another, are brought together. They sleep and eat under one roof, they cannot get away from each other. At the end of three days they part, they go their several ways, never perhaps to see each other again.”
Bouc's observation, early in the novel, foreshadows later revelations and is at the same time ironically contradicted by them. On the one hand, it turns out not to be true that the train contains an unlikely, coincidental mix of strangers. The passengers all know each other, and are on the train together very much on purpose, after much careful planning. On the other hand, it's true that they remain an unlikely group, brought together by uncontrollable and unforeseen circumstances and now bonded to one another. Those circumstances, of course, are not their collective status as passengers on the Orient Express, but rather their shared relationship to the Armstrong family. Bouc's statement also might be understood as a nod to the book's highly contained setting. Poirot, while solving this mystery, does indeed sleep and eat under the same roof as his suspects. This inability to "get away from one another" is a major factor in the novel's tense, suspenseful mood.
"The impossible cannot have happened, therefore the impossible must be possible in spite of appearances."
This quote embodies one of Poirot's governing philosophies of mystery-solving: there's no point panicking, because there's an explanation for everything. One of the detective's greatest assets is his calm assuredness. Others, like Bouc, panic or marvel at a case's complexity, even labeling it impossible to solve. But Poirot is utterly faithful that an explanation can always be found. It's this faith that helps him so much. He doesn't feel the need to rush and he doesn't let his emotions get the better of him. Instead he slowly traces everything he knows to its ultimate conclusion, knowing that nothing is impossible, magical, or unexplainable.
"I know what you are going to say, and I’m telling you right now that I won’t do any such thing! Why, I’d rather sit up all night in the corridor.” She began to cry. “Oh, if my daughter could only know—if she could see me now, why—"
While every passenger on the train lies to Poirot to a certain degree, Mrs. Hubbard's lie is the most elaborate. She's actually Linda Arden, an actress—hence the convincing but false persona—and the grandmother to the murdered Daisy Armstrong. Mrs. Hubbard's most notable characteristic, other than her neuroticism and complaining, is an obsession with her daughter. She claims to have been visiting this daughter in Turkey, but at the novel's end, when her true identity is revealed, Mrs. Hubbard's attachment to her daughter appears much sadder and deeper. She is in fact motivated by grief for her daughter and granddaughter. If she is indeed neurotic, her neuroticism appears to be a manifestation of that grief.
"It is true,” she said. “I have no strength in these—none. I do not know whether I am sorry or glad.”
Here, the Princess admits that Poirot is correct about her on one count: no matter how strong-willed she is, her frail arms probably aren't capable of killing anyone. She expresses regret that this is the case, because she is a close friend of the Armstrong family and has every reason to want Ratchett dead. Her statement can be read in one of two ways. On the one hand, she may be trying to mislead Poirot. She makes herself sound very suspicious, and emphasizes her robust motive in wanting Ratchett dead, yet she knows that she won't ultimately be blamed because of her physical weakness. Thus, she may be trying to delay or confuse Poirot by presenting him with a tantalizing but impossible explanation for the murder.
But she also might be expressing a real emotion. After all, while Dragomiroff definitely stabbed Ratchett, readers are led to assume that the wound she left on him was one of the weak and non-fatal ones. As a result, the Princess may be expressing sincere regret that the strength of her feelings isn't matched by the strength in her arms.
“Not now. Not now. When it’s all over. When it’s behind us—then—”
This vague but urgent line of dialogue comes early in the book, long before any murder has taken place, and will end up hanging over the rest of the book. The line is carefully written to be as mysterious as possible, so that, while it could apply to murder, it seems just as likely that the "it" Debenham references could be something far more mundane. However, even if Debenham is referencing something irrelevant, the very tone of the conversation raises questions. As other micro-mysteries arise and get solved, another one remains: why, and how, do Mary Debenham and Colonel Arbuthnot know each other, and why are they so eager to hide this fact? It's this snatch of overheard conversation that ends up helping Poirot figure out his missing piece: namely, that every person on the train (and not only these two characters) is already well-acquainted with every other.
“She is cold. She has not emotions. She would not stab a man—she would sue him in the law courts.”
Constantine expresses doubts regarding Mary Debenham's ability to commit murder, simply because her composed attitude doesn't make her seem like a very violent or passionate person. Poirot finds this dismissal annoying, because he rightly believes that the crime is premeditated, which actually makes Debenham's personality seem suspicious. But the quote also hides another bit of insight. It is in fact likely that a character like Debenham would rather take her enemy to court than kill him. After all, her anxiety at various points in the novel reveals that she finds the whole murder business quite stressful. However, Ratchett/Cassetti has already been taken to court and found not guilty, in a verdict determined less by principles of justice than by fear of Ratchett's power. Therefore, it's possible that nobody in the train would voluntarily stab a man. Instead, they feel that they have been left with no other choice, since legal routes to punishing Ratchett have been compromised.
"Lie back and think—use (as I have heard you say so often) the little grey cells of the mind—and you will know!"
Later in the novel, Bouc will grow frustrated with his friend's reassurance that the mystery can be solved with nothing more than sheer brainpower. Here, though, he repeats one of Poirot's well-known mantras back to him, assuring the detective that he'll be able to find the murderer through the tried-and-true method of gathering evidence and then thinking that evidence over. The image of "little grey cells" is a revealing one, given its focus on the anatomical properties of the brain. It stresses that Poirot, for all his brilliance, is a normal person without extraordinary resources or superpowers. His primary tool in solving the case is simply his brain. As a result of this belief, Poirot displays a charming faith in Bouc and Constantine's ability to help him, despite the fact that these men clearly don't have his abilities—they have exactly the same tools he does. The book is structured, furthermore, so that the reader technically has the ability to solve the crime just as Poirot does, relying on their "grey cells." It's an egalitarian philosophy that just happens to make the story more engaging for its fans.
“In my opinion, M. Poirot,” he said, “the first theory you put forward was the correct one—decidedly so. I suggest that that is the solution we offer to the Jugo-Slavian police when they arrive. You agree, doctor?”
At the end of the novel, Poirot offers two possible theories explaining who has killed Ratchett. It's more than evident, given the number of holes in the first theory, and the reaction of Poirot's fellow passengers, that the second theory is the correct one. Yet that theory, if passed on to local police, would incriminate every passenger in the train. Instead, Bouc and Constantine quietly opt to ignore that explanation and support theory one, in which nobody is incriminated and the crime is blamed on a nonexistent stranger. With these lines, Bouc implicitly embraces the idea that Ratchett's murder was justified—that it was, in fact, an alternative form of justice superior to the corrupted, false justice meted out by law courts.