"It certainly explains that point," agreed Poirot.
Inspector Colgate went on: "And think of the place chosen.
The very spot for the purpose.
The lady goes off on her float.
That's natural enough. It's what she does every day.
She goes round to Pixy Cove where no one ever goes in the morning and which will be a nice quiet place for an interview."
Poirot said: "But yes, I too was struck by that point.
It is, as you say, an ideal spot for a rendezvous.
It is deserted, it is only accessible from the land side by descending a vertical steel ladder which is not everybody's money, bien entendu.
Moreover, most of the beach is invisible from above because of the overhanging cliff.
And it has another advantage. Mr Redfern told me of that one day. There is a cave on it, the entrance to which is not easy to find but where any one could wait unseen."
Weston said: "Of course, the Pixy's Cave - remember hearing about it."
Inspector Colgate said: "Haven't heard it spoken of for years, though.
We'd better have a look inside it.
Never know, we might find a pointer of some kind."
Weston said: "Yes, you're right, Colgate, we've got the solution to part one of the puzzle. Why did Mrs Marshall go to Pixy's Cove?
We want the other half of that solution, though. Who did she go there to meet?
Presumably someone staying in this hotel. None of them fitted as a lover - but a blackmailer's a different proposition."
He drew the register towards him.
"Excluding the waiters, boots, etc., whom I don't think likely, we've got the following.
The American - Gardener, Major Barry, Mr Horace Blatt, and the Reverend Stephen Lane."
Inspector Colgate said: "We can narrow it down a bit, sir.
We might almost rule out the American, I think. He was on the beach all the morning. That's so, isn't it, M. Poirot?"
Poirot replied: "He was absent for a short time when he fetched a skein of wool for his wife." Colgate said: "Oh, well, we needn't count that."
Weston said: "And what about the other three?"
"Major Barry went out at ten o'clock this morning. He returned at one-thirty.
Mr Lane was earlier still. He breakfasted at eight. Said he was going for a tramp.
Mr Blatt went off for a sail at nine-thirty same as he does most days.
Neither of them is back yet?"
"A sail, eh?" Colonel Weston's voice was thoughtful.
Inspector Colgate's voice was responsive. He said: "Might fit in rather well, sir."
Weston said: "Well, we'll have a word with this Major bloke - and let me see, who else is there?
Rosamund Darnley.
And there's the Brewster woman who found the body with Redfern. What's she like, Colgate?"
"Oh, a sensible party, sir.
No nonsense about her."
"She didn't express any opinions on the death?"
The inspector shook his head.
"I don't think she'll have anything more to tell us, sir, but we'll have to make sure. Then there are the Americans."
Colonel Weston nodded.
He said: "Let's have 'em all in and get it over as soon as possible.
Never know, might learn something. About the blackmailing stunt if about nothing else."
Mr and Mrs Gardener came into the presence of authority together.
Mrs Gardener explained immediately.
"I hope you'll understand how it is, Colonel Weston (that is the name, I think?)."
Reassured on this point she went on:
"But this has been a very bad shock to me and Mr Gardener is always very, very careful of my health -"
Mr Gardener here interpolated. "Mrs Gardener," he said, "is very sensitive."
"- and he said to me,
'Why, Carrie,' he said, 'naturally I'm coming right along with you.'