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 here to look after a cantankerous old woman who has no earthly claim on her."

"I am silent," said Poirot, his eyes twinkling a little; "but all the same I say it is a pity. And now. Messieurs, let us come to business."

Both the other men looked at him in some surprise.

"You must not be shocked or alarmed at what I am about to say. Supposing, Monsieur Van Aldin, that, after all, Monsieur Derek Kettering did not murder his wife?"

"What?"

Both men stared at him in blank surprise.

"Supposing, I say, that Monsieur Kettering did not murder his wife?"

"Are you mad, Monsieur Poirot?"

It was Van Aldin who spoke.

"No," said Poirot, "I am not mad. I am eccentric, perhapsat least certain people say so; but as regards my profession, I am very much, as one says, 'all there.' I ask you. Monsieur Van Aldin, whether you would be glad or sorry if what I tell you should be the case?"

Van Aldin stared at him.

"Naturally I should be glad," he said at last. "Is this an exercise in suppositions, Monsieur Poirot, or are there any facts behind it?"

Poirot looked at the ceiling.

"There is an off-chance," he said quietly, "that it might be the Comte de la Roche after all. At least I have succeeded in upsetting his alibi."

"How did you manage that?"

Poirot shrugged his shoulders modestly.