A minute or two later the boat containing Patrick and Emily Brewster comes round the point.
Remember it is Patrick who bends down and examines the body, Patrick who is stunned - shocked - broken down by the death of his lady love!
His witness has been carefully chosen.
Miss Brewster has not got a good head, she will not attempt to go up the ladder. She will leave the cove by boat, Patrick naturally being the one to remain with the body - 'in case the murderer may still be about.'
Miss Brewster rows off to fetch the police.
Christine, as soon as the boat has disappeared, springs up, cuts the hat into pieces with the scissors Patrick has carefully brought, stuffs them into her bathing suit and swarms up the ladder in double-quick time, slips into her beach pyjamas and runs back to the hotel.
Just time to have a quick bath, washing off the brown suntan application, and into her tennis dress.
One other thing she does. She burns the pieces of the green cardboard hat and the hair in Linda's grate, adding a leaf of a calendar so that it may be associated with the cardboard.
Not a Hat but a Calendar has been burnt. As she suspected Linda has been experimenting in magic - the blob of wax and the pin show that.
"Then, down to the tennis court, arriving the last, but showing no sign of flurry or haste.
"And meanwhile Patrick has gone to the Cave.
Arlena has seen nothing and heard very little - a boat - voices - she has prudently remained hidden.
But now it is Patrick calling.
'All clear, darling,' and she comes out and his hands fasten round her neck - and that is the end of poor foolish beautiful Arlena Marshall..."
His voice died away.
For a moment there was silence, then Rosamund Darnley said with a little shiver:
"Yes, you make one see it all.
But that's the story from the other side.
You haven't told us how you came to get at the truth?"
Hercule Poirot said:
"I told you once that I had a very simple mind.
Always, from the beginning, it seemed to me that the most likely person had killed Arlena Marshall.
And the most likely person was Patrick Redfern.
He was the type, par excellence - the type of man who exploits women like her - and the type of the killer - the kind of man who will take a woman's savings and cut her throat into the bargain.
Who was Arlena going to meet that morning?
By the evidence of her face, her smile, her manner, her words to me - Patrick Redfern.
And therefore, in the very nature of things, it should be Patrick Redfern who killed her.
"But at once I came up, as I told you, against impossibility.
Patrick Redfern could not have killed her since he was on the beach and in Miss Brewster's company until the actual discovery of the body.
So I looked about for other solutions - and there were several.
She could have been killed by her husband - with Miss Darnley's connivance. (They too had both lied as to one point which looked suspicious.) She could have been killed as a result of her having stumbled on the secret of the dope smuggling.
She could have been killed, as I said, by a religious maniac, and she could have been killed by her stepdaughter.
The latter seemed to me at one time to be the real solution.
Linda's manner in her very first interview with the police was significant.
An interview that I had with her later assured me of one point. Linda considered herself guilty."
"You mean she imagined that she had actually killed Arlena?" Rosamund's voice was incredulous.
Hercule nodded. "Yes.
Remember - she is really little more than a child.
She read that book on witchcraft and she half believed it.
She hated Arlena.
She deliberately made the wax doll, cast her spell, pierced it to the heart, melted it away - and that very day Arlena dies.
Older and wiser people than Linda have believed fervently in magic.
Naturally she believed that it was all true - that by using magic she had killed her stepmother."
Rosamund cried: "Oh, poor child, poor child.
And I thought - I imagined - something quite different - that she knew something which would -" Rosamund stopped.
Poirot said: "I know what it was you thought.
Actually your manner frightened Linda still further.
She believed that her action had really brought about Arlena's death and that you knew it.
Christine Redfern worked on her too, introducing the idea of the sleeping tablets to her mind, showing her the way to a speedy and painless expiation of her crime.
You see, once Captain Marshall was proved to have an alibi, it was vital for a new suspect to be found.