amused at her mother’s manoeuvres, and yet with a sympathetic understanding of Katherine’s feelings. The situation was not helped by Chubby, whose naive delight was unquenchable, and who introduced Katherine to all and sundry as:

“This is Miss Grey. You know that Blue Train business? She was in it up to the ears! Had a long talk with Ruth Kettering a few hours before the murder! Bit of luck for her, eh?”

A few remarks of this kind had provoked Katherine that morning to an unusually tart rejoinder, and when they were alone together Lenox observed in her slow drawl:

“Not used to exploitation, are you? You have a lot to learn, Katherine.”

“I am sorry I lost my temper. I don’t, as a rule.”

“It is about time you learnt to blow off steam. Chubby is only an ass; there is no harm in him. Mother, of course, is trying, but you can lose your temper with her until Kingdom come, and it won’t make any impression. She will open large, sad blue eyes at you and not care a bit.”

Katherine made no reply to this filial observation, and Lenox presently went on:

“I am rather like Chubby. I delight in a good murder, and besides⁠—well, knowing Derek makes a difference.”

Katherine nodded.

“So you lunched with him yesterday,” pursued Lenox reflectively. “Do you like him, Katherine?”

Katherine considered for a minute or two.

“I don’t know,” she said very slowly.

“He is very attractive.”

“Yes, he is attractive.”

“What don’t you like about him?”

Katherine did not reply to the question, or at any rate not directly. “He spoke of his wife’s death,” she said. “He said he would not pretend that it had been anything but a bit of most marvellous luck for him.”

“And that shocked you, I suppose,” said Lenox. She paused, and then added in rather a queer tone of voice: “He likes you, Katherine.”

“He gave me a very good lunch,” said Katherine, smiling.

Lenox refused to be sidetracked.

“I saw it the night he came here,” she said thoughtfully. “The way he looked at you; and you are not his usual type⁠—just the opposite. Well, I suppose it is like religion⁠—you get it at a certain age.”

“Mademoiselle is wanted at the telephone,” said Marie, appearing at the window of the salon. “M. Hercule Poirot desires to speak with her.”

“More blood and thunder. Go on, Katherine; go and dally with your detective.”

M. Hercule Poirot’s voice came neat and precise in its intonation to Katherine’s ear.

“That is Mademoiselle Grey who speaks? Bon. Mademoiselle, I have a word for you from M. Van Aldin, the father of Madame Kettering. He wishes very much to speak with you, either at the Villa Marguerite or at his hotel, whichever you prefer.”

Katherine reflected for a moment, but she decided that for Van Aldin to come to the Villa Marguerite would be both painful and unnecessary. Lady Tamplin would have hailed his advent with far too much delight. She never lost a chance of cultivating millionaires. She told Poirot that she would much rather come to Nice.

“Excellent, Mademoiselle. I will call for you myself in an auto. Shall we say in about three-quarters of an hour?”

Punctually to the moment Poirot appeared. Katherine was waiting for him, and they drove off at once.

“Well, Mademoiselle, how goes it?”

She looked at his twinkling eyes, and was confirmed in her first impression that there was something very attractive about M. Hercule Poirot.

“This is our own roman policier, is it not?” said Poirot. “I made you the promise that we should study it together. And me, I always keep my promises.”

“You are too kind,” murmured Katherine.

“Ah, you mock yourself at me; but do you want to hear the developments of the case, or do you not?”

Katherine admitted that she did, and Poirot proceeded to sketch for her a thumbnail portrait of the Comte de la Roche.

“You think he killed her,” said Katherine thoughtfully.

“That is the theory,” said Poirot guardedly.

“Do you yourself believe that?”

“I did not say so. And you, Mademoiselle, what do you think?”

Katherine shook her head.

“How should I know? I don’t know anything about those things, but I should say that⁠—”

“Yes,” said Poirot encouragingly.

“Well⁠—from what you say the Count does not sound the kind of man who would actually kill anybody.”

“Ah! Very good,” cried Poirot. “You agree with me; that is just what I have said.” He looked at her sharply. “But tell me, you have met Mr. Derek Kettering?”

“I met him at Lady Tamplin’s, and I lunched with him yesterday.”

“A mauvais sujet,” said Poirot, shaking his head; “but les femmes⁠—they like that, eh?”

He twinkled at Katherine and she laughed.

“He is the kind of man one would notice anywhere,” continued Poirot. “Doubtless you observed him on the Blue Train?”

“Yes, I noticed him.”

“In the restaurant car?”

“No. I didn’t notice him at meals at all. I only saw him once⁠—going into his wife’s compartment.”

Poirot nodded. “A strange business,” he murmured. “I believe you said you were awake, Mademoiselle, and looked out of your window at Lyons? You saw no tall dark man such as the Comte de la Roche leave the train?”

Katherine shook her head. “I don’t think I saw anyone at all,” she said. “There was a youngish lad in a cap and overcoat who got out, but I don’t think he was leaving the train, only walking up and down the platform. There was a fat Frenchman with a beard, in pyjamas and an overcoat, who wanted a cup of coffee. Otherwise, I think there were only the train attendants.”

Poirot nodded his head several times. “It is like this, you see,” he confided, “the Comte de la Roche has an alibi. An alibi, it is a very pestilential thing, and always open to the gravest suspicion. But here we are!”

They went straight up to Van Aldin’s suite, where they found Knighton. Poirot introduced him to Katherine. After a few commonplaces had been exchanged, Knighton said: “I will tell Mr. Van Aldin that Miss Grey is here.”

He went through a second door into an adjoining room. There was

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