Weston said: "We're coming down - now."
The first person they saw was Colgate.
His face was gloomy.
"Just a minute, sir." Weston and Poirot followed him into Mrs Castle's office.
Colgate said: "I've been checking up with Heald on this typewriting business.
Not a doubt of it, it couldn't be done under an hour.
Longer, if you had to stop and think here and there.
That seems to me pretty well to settle it.
And look at this letter."
He held it out.
"My dear Marshall,
"Sorry to worry you on your holiday but an entirely unforeseen situation has arisen over the Burley and Tender contracts..." "Etcetera, etcetera," said Colgate.
"Dated the 24th - that's yesterday. Envelope postmarked yesterday evening E.C.I and Leathercombe Bay this morning.
Same typewriter used on envelope and in letter. And by the contents it was clearly impossible for Marshall to prepare his answer beforehand.
The figures arise out of the ones in the letter - the whole thing is quite intricate."
"H'm," said Weston gloomily.
"That seems to let Marshall out.
We'll have to look elsewhere."
He added: "I've got to see Miss Darnley again. She's waiting now."
Rosamund came in crisply.
Her smile held an apologetic nuance.
She said: "I'm frightfully sorry.
Probably it isn't worth bothering about. But one does forget things so."
"Yes, Miss Darnley?" The Chief Constable indicated a chair.
She shook her shapely black head.
"Oh, it isn't worth sitting down.
It's simply this.
I told you that I spent the morning lying out on Sunny Ledge.
That isn't quite accurate.
I forgot that once during the morning I went back to the hotel and out again."
"What time was that, Miss Darnley?"
"It must have been about a quarter past eleven."
"You went back to the hotel, you said?"
"Yes, I'd forgotten my glare glasses.
At first I thought I wouldn't bother and then my eyes got tired and I decided to go in and get them."
"You went straight to your room and out again."
"Yes.
At least, as a matter of fact, I just looked in on Ken - Captain Marshall.
I heard his machine going and I thought it was so stupid of him to stay indoors typing on such a lovely day.
I thought I'd tell him to come out."
"And what did Captain Marshall say?"
Rosamund smiled rather shamefacedly.
"Well, when I opened the door he was typing so vigorously, and frowning and looking so concentrated that I just went away quietly.
I don't think he even saw me come in."
"And that was - at what time, Miss Darnley?"
"Just about twenty past eleven.
I noticed the clock in the hall as I went out again."
"And that puts the lid on it finally," said Inspector Colgate.
"The chambermaid heard him typing up till five minutes to eleven. Miss Darnley saw him at twenty minutes past, and the woman was dead at a quarter to twelve.
He says he spent that hour typing in his room and it seems quite clear that he was typing in his room.