Trial by Jury
This theme is problematic in Murder on the Orient Express. While Poirot solves a complicated crime, which implicates everyone on board the train, he also finds that those guilty of the crime acted in order to punish a man for another heinous crime. Those guilty on the train consist of 12 people, the same number which makes up a jury.
It is as if Christie quite deliberately disturbed our ideas of the letter and the spirit of the law. While the people guilty of killing Ratchett are guilty of murder according to the letter of the law, they are also a jury who impose a death sentence on a man who had previously gotten away with killing a child. This is not the only area which Christie blurs our ideas of the letter and the spirit of the Law.
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Moral Law vs. Written Law
Poirot is not only a sleuth, he is also a retired police officer. He has the deductive reasoning skills of someone like Sherlock Holmes, but he also carries with him the duty of a law enforcement officer. In the end of the book, Poirot leaves the guilty people to their own conscience as to how to proceed with his findings. Poirot makes it clear that he knows exactly what happened and he has the evidence to prove it. Yet, in the final analysis, he chooses to not pursue the matter beyond the confines of the action.
Poirot understands that there is a moral law, one which demands justice for the murder of an innocent child. And there is a written enforceable law which demand that those who take revenge outside of the law are guilty of a crime. Poirot seems to come down on the side of moral law. Again, Agatha Christie leaves it to us to decide what is truly right and just.
Reason and Logic
Poirot is in many ways the perfect hero for the time that he novel was written. There was a prevailing belief that the human mind, if properly focused and trained, is capable of what would appear to be super-human capacity. Poirot can observe more than the common person. In the train station, for example, even amid the noise and confusion of people and trains, Poirot is able to focus his Reason on the pieces of information which are truly important.
Not only that, he is capable of retaining this information and applying it to later circumstances. Poirot is a man of superior intellect because he is a man of superior discipline. Because of this, his powers of reason and logic are beyond even the most clever people. He can sort through all of the smokescreens and lies of other characters and find out exactly what is the matter. This is how he is able to solve the crime.