But the point is that he could not count on that possibility."
Rosamund said: "Aren't you forgetting something? The weather."
"The weather?"
"Yes.
The day of the murder was a glorious day but the day before, remember, there was rain and thick mist.
Any one could come onto the island then without being seen.
He had only to go down to the beach and spend the night in the cave. That mist, M. Poirot, is important."
Poirot looked at her thoughtfully for a minute or two.
He said: "You know, there is a good deal in what you have just said."
Rosamund flushed.
She said: "That's my theory, for what it is worth.
Now tell me yours."
"Ah," said Hercule Poirot. He stared down at the sea.
"Eh bien, Mademoiselle.
I am a very simple person. I always incline to the belief that the most likely person committed the crime.
At the very beginning it seemed to me that only one person was very clearly indicated."
Rosamund's voice hardened a little. She said: "Go on."
Hercule Poirot went on. "But you see, there is what you call a snag in the way! It seems that it was impossible for that person to have committed the crime."
He heard the quick expulsion of her breath.
She said rather breathlessly: "Well?"
Hercule Poirot shrugged his shoulders.
"Well, what do we do about it?
That is my problem."
He paused and then went on.
"May I ask you a question?"
"Certainly."
She faced him, alert and vigilant.
But the question that came was an unexpected one.
"When you came in to change for tennis that morning, did you have a bath?"
Rosamund stared at him. "A bath?
What do you mean?"
"That is what I mean.
A bath!
The receptacle of porcelain, one turns the taps and fills it, one gets in, one gets out and ghoosh - ghoosh - ghoosh, the water goes down the waste pipe!"
"M. Poirot, are you quite mad?"
"No, I am extremely sane."
"Well, anyway, I didn't take a bath."
"Ha!" said Poirot.
"So nobody took a bath.
That is extremely interesting."
"But why should any one take a bath?"
Hercule Poirot said: "Why, indeed?"
Rosamund said with some exasperation:
"I suppose this is the Sherlock Holmes touch!"
Hercule Poirot smiled. Then he sniffed the air delicately.
"Will you permit me to be impertinent. Mademoiselle?"
"I'm sure you couldn't be impertinent, M. Poirot."
"That is very kind of you.
Then may I venture to say that the scent you use is delicious - it has a nuance - a delicate elusive charm."
He waved his hands, and then added in a practical voice,