Next up are inspections of the body and of Ratchett's compartment with Dr. Constantine.
Poirot notes that the window is open. He checks it out, but finds no fingerprints.
As for the body, we learn it had twelve stab wounds. Two are very slight and three are severe.
Something strikes the doctor as odd: some of the wounds appear not to have bled. That means they must have been made much later than the others.
One of the wounds was made by a left-handed person, and some of the others by a right-handed person.
Poirot murmurs: two people? He checks the switches on the bed light and the overhead light. Both are off.
Poirot proposes a scenario: one murderer comes in, stabs, and turns off the light. The second comes in and does not see that Ratchett is dead. The second murderer stabs the body again.
That would also make sense, because then we could say that one person was a man (the strong stabs) and one was a woman (the weak stabs).
But why didn't Ratchett defend himself? He had a gun under his pillow, after all. Constantine picks up the victim's empty glass and confirms that the man was drugged.
Another clue: Poirot finds two matches in the ashtray and some burnt paper scraps. There are two different kinds of matches: one kind is Ratchett's, and one kind is from the train.
Two more clues: a piece of dainty fabric with an initial "H" on it, and a pipe cleaner. That means there's one clue for a woman and one for a man. Poirot is getting suspicious. The clues are a little too perfect, dropped "most conveniently" (1.7.85).
We discover the murder weapon has not been left behind. Also, the doctor pulls Ratchett's watch from his breast pocket. It's dented, and the hour reads 1:15 a.m.
The doctor thinks this clue cements the time of death, but, again, Poirot is not so sure. The clues are all too perfect.
How to proceed? Ah, yes, the paper scraps. But they're charred. Poirot, though, has an ingenious scientific way to read them.
The train match, he believes, is a clue the murderer didn't want us to see.
He has someone get some mesh hat wire from one of the woman passengers, and, along with a small stove and moustache curling tongs, he uses it to light up the paper and illuminate the letters.
The scraps read: "member little Daisy Armstrong" (1.7.123).
With that, Poirot knows who Ratchett really is – a man named Cassetti – and why he had to leave America.
Poirot finishes the investigation as the two men wonder how the murderer(s) escaped, since it clearly wasn't through the open window (which appears to be a red herring). How is the trick done?