“Oh! not necessarily the very remote past. I look at it like this. Arlena Marshall was attractive, fatally attractive, to men. It’s possible, I think, that she also tired of them rather quickly. Amongst her—followers, shall we say—was one who resented that. Oh, don’t misunderstand me, it won’t be someone who sticks out a mile. Probably some tepid little man, vain and sensitive—the kind of man who broods. I think he followed her down here, waited his opportunity and killed her.”

“You mean that he was an outsider, that he came from the mainland?”

“Yes. He probably hid in that cave until he got his chance.”

Poirot shook his head. He said:

“Would she go there to meet such a man as you describe? No, she would laugh and not go.”

Rosamund said:

“She mayn’t have known she was going to meet him. He may have sent her a message in some other person’s name.”

Poirot murmured:

“That is possible.”

Then he said:

“But you forget one thing, Mademoiselle. A man bent on murder could not risk coming in broad daylight across the causeway and past the hotel. Someone might have seen him.”

“They might have—but I don’t think that it’s certain. I think it’s quite possible that he could have come without anyone noticing him at all.”

“It would be possible, yes, that I grant you. 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. Anyone could come on to 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 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.”