They passed on to Tim Allerton's cabin, next door.
There were evidences here of an Anglo Catholic turn of mind - an exquisite little triptych, and a big rosary of intricately carved wood.
Besides personal clothing, there was a half completed manuscript, a good deal annotated and scribbled over, and a good collection of books, most of them recently published.
There were also a quantity of letters thrown carelessly into a drawer.
Poirot, never in the least scrupulous about reading other people's correspondence, glanced through them.
He noted that amongst them there were no letters from Joanna Southwood.
He picked up a tube of Seccotine, fingered it absently for a minute or two, then said,
"Let us pass on."
"No Woolworth handkerchiefs," reported Race, rapidly replacing the contents of a drawer.
Mrs Allerton's cabin was the next.
It was exquisitely neat, and a faint old-fashioned smell of lavender hung about it.
The two men's search was soon over.
Race remarked as they left it,
"Nice woman, that."
The next cabin was that which had been used as a dressing-room by Simon Doyle.
His immediate necessities - pyjamas, toilet things, etc., had been moved to Bessner's cabin, but the remainder of his possessions were still there - two good-sized leather suitcases and a kit bag.
There were also some clothes in the wardrobe.
"We will look carefully here, my friend," said Poirot, "for it is very possible that the thief hid the pearls here."
"You think it is likely?"
"But yes, indeed.
Consider!
The thief, whoever he or she may be, must know that sooner or later a search will be made, and therefore a hiding place in his or her own cabin would be injudicious in the extreme.
The public rooms present other difficulties.
But here is a cabin belonging to a man who cannot possibly visit it himself, so that, if the pearls are found here, it tells us nothing at all."
But the most meticulous search failed to reveal any trace of the missing necklace.
Poirot murmured
"Zut!" to himself and they emerged once more on the deck.
Linnet Doyle's cabin had been locked after the body was removed, but Race had the key with him.
He unlocked the door and the two men stepped inside.
Except for the removal of the girl's body, the cabin was exactly as it had been that morning.
"Poirot," said Race, "if there's anything to be found here, for God's sake go ahead and find it.
You can if anyone can - I know that."
"This time you do not mean the pearls, mon ami?"
"No.
The murder's the main thing.
There may be something I overlooked this morning -" Quietly, deftly, Poirot went about his search.
He went down on his knees and scrutinized the floor inch by inch.
He examined the bed.
He went rapidly through the wardrobe and chest of drawers.
He went through the wardrobe trunk and the two costly suitcases.
He looked through the expensive gold-fitted dressing-case.
Finally he turned his attention to the washstand.
There were various creams, powders, face lotions.
But the only thing that seemed to interest Poirot were two little bottles labelled Nailex.
He picked them up at last and brought them to the dressing-table.
One, which bore the inscription Nailex Rose, was empty but for a drop or two of dark red fluid at the bottom.
The other, the same size, but labelled Nailex Cardinal, was nearly full.
Poirot uncorked first the empty, then the full one, and sniffed them both delicately.
An odour of pear drops billowed into the room.
With a slight grimace he recorked them.