Hercule Poirot's observation had not been at fault.
There were no pearls on the table by Linnet Doyle's bed.
Louise Bourget was bidden to make a search among Linnet's belongings.
According to her, all was in order.
Only the pearls had disappeared.
As they emerged from the cabin a steward was waiting to tell them that breakfast had been served in the smoking-room.
As they passed along the deck, Race paused to look over the rail.
"Ah! I see you have had an idea, my friend."
"Yes.
It suddenly came to me, when Fanthorp mentioned thinking he had heard a splash, that I too had been awakened sometime last night by a splash.
It's perfectly possible that, after the murder, the murderer threw the pistol overboard."
Poirot said slowly, "You really think that is possible, my friend?"
Race shrugged his shoulders.
"It's a suggestion.
After all, the pistol wasn't anywhere in the cabin.
First thing I looked for."
"All the same," said Poirot, "it is incredible that it should have been thrown overboard."
Race asked, "Where is it then?"
Poirot replied thoughtfully,
"If it is not in Madame Doyle's cabin, there is, logically, only one other place where it could be."
"Where's that?"
"In Mademoiselle de Bellefort's cabin."
Race said thoughtfully:
"Yes. I see -" He stopped suddenly. "She's out of her cabin.
Shall we go and have a look now?"
Poirot shook his head.
"No, my friend, that would be precipitate.
It may not yet have been put there."
"What about an immediate search of the whole boat?"
"That way we should show our hand.
We must work with great care.
It is very delicate, our position, at the moment.
Let us discuss the situation as we eat."
Race agreed.
They went into the smoking-room.
"Well," said Race as he poured himself out a cup of coffee, "we've got two definite leads.
There's the disappearance of the pearls. And there's the man Fleetwood.
As regards the pearls, robbery seems indicated, but - I don't know whether you'll agree with me -" Poirot said quickly,
"But it was an odd moment to choose?"
"Exactly.
To steal the pearls at such a moment invites a close search of everybody on board.
How then could the thief hope to get away with his booty?"
"He might have gone ashore and dumped it."
"The company always has a watchman on the bank."
"Then that is not feasible.
Was the murder committed to divert attention from the robbery?
No, that does not make sense; it is profoundly unsatisfactory.
But supposing that Madame Doyle woke up and caught the thief in the act?"
"And therefore the thief shot her?
But she was shot whilst she slept."