"I don't know. Mademoiselle," said Poirot. "See, I admit it frankly. As a rule I know everything, but in this case, I-well, I do not. You, perhaps, know better than I do."

"Yes," said Lenox, "I know-but I am not going to tell you all the same."

She paused for a minute or two, her dark brows drawn together in a frown.

"You believe he did it?" she said abruptly.

Poirot shrugged his shoulders.

"The police say so."

"Ah," said Lenox, "hedging, are you? So lere is something to hedge about."

Again she was silent, frowning. Poirot said gently:

"You have known Derek Kettering a long time, have you not?"

"Off and on ever since I was a kid," said Lenox gruffly.

Poirot nodded his head several times without speaking.

With one of her brusque movements Lenox drew forward a chair and sat down on it, her elbows on the table and her face supported by her hands. Sitting thus, she looked directly across the table at Poirot.

"What have they got to go on?" she demanded.

"Motive, I suppose. Probably came into money at her death."

"He came into two million."

"And if she had not died he would have been ruined?"

"Yes."

"But there must have been more than that," persisted Lenox. "He travelled by the same train, I know, but-that would not be enough to go on by itself."

"A cigarette case with the letter 'K' on it which did not belong to Mrs. Kettering was found in her carriage, and he was seen by two people entering and leaving the compartment just before the train got into Lyons."

"What two people?"

"Your friend Miss Grey was one of them.

The other was Mademoiselle Mirelle, the dancer."

"And he, Derek, what has he got to say about it?" demanded Lenox sharply.

"He denies having entered his wife's compartment at all," said Poirot.

"Fool!" said Lenox crisply, frowning.

"Just before Lyons, you say? Does nobody know when-when she died?"

"The doctors' evidence necessarily cannot be very definite," said Poirot; "they are inclined to think that death was unlikely to have occurred after leaving Lyons. And we know this much, that a few moments after leaving Lyons Mrs. Kettering was dead."

"How do you know that?"

Poirot was smiling rather oddly to himself.

"Some one else went into her compartment and found her dead."

"And they did not rouse the train?"

"No."

"Why was that?"

"Doubtless they had their reasons."

Lenox looked at him sharply.

"Do you know the reason?"

"I think so-yes."

Lenox sat still turning things over in her mind. Poirot watched her in silence. At last he looked up. A soft colour had come into er cheeks and her eyes were shining.

"You think some one on the train must have killed her, but that need not be so at all. What is to stop any one swinging themelves on to the train when it stopped at Lyons? They could go straight to her compartment, strangle her, and take the rubies and drop off the train again without any one being the wiser. She may have been actually killed while the train was in Lyons station.

Then she would have been alive when Derek went in, and dead when the other person found her."

Poirot leant back in his chair. He drew a deep breath. He looked across at the girl and nodded his head three times, then he heaved a sigh.

"Mademoiselle," he said, "what you have said there is very just-very true. I was struggling in darkness, and you have shown me a light. There was a point that puzzled me and you have made it plain."

He got up.

run of good luck, and had soon won a few thousand francs.

"It would be as well," she observed drily to Poirot, "if I stopped now."

Poirot's eyes twinkled.

"Superb!" he exclaimed. "You are the daughter of your father, Mademoiselle Zia. To know when to stop. Ah! that is the art."

He looked round the rooms.

"I cannot see your father anywhere about," he remarked carelessly. "I will fetch your cloak for you. Mademoiselle, and we will go out in the gardens."

He did not, however, go straight to the cloak-room. His sharp eyes had seen but a little while before the departure of M. Papopolous.

He was anxious to know what had become of the wily Greek. He ran him to earth unexpectedly in the big entrance hall.

He was standing by one of the pillars, talking to a lady who had just arrived. The lady was Mirelle.

Poirot sidled unostentatiously round the room. He arrived at the other side of the pillar, and unnoticed by the two who were talking together in an animated fashion-or rather, that is to say, the dancer was talking, Papopolous contributing an occasional monosyllable and a good many expressive gestures.

"I tell you I must have time," the dancer was saying, "If you give me time I will get the money."

"To wait"-the Greek shrugged his shoulders-"it is awkward."

"Only a very little while," pleaded the other. "Ah! but you must! A week-ten days-that is all I ask. You can be sure of your affair. The money will be forthcoming."

Papopolous shifted a little and looked round him uneasily-to find Poirot almost at his elbow with a beaming innocent face.

"Ah! vous voilá, M. Papopolous. I have been looking for you. It is permitted that I take Mademoiselle Zia for a little turn in the gardens? Good evening. Mademoiselle." He bowed very low to Mirelle. "A thousand pardons that I did not see you immediately."

The dancer accepted his greetings rather impatiently. She was clearly annoyed at the interruption of her tete-d-tete. Poirot was quick to take the hint. Papopolous had already murmured: "Certainly-but certainly," and Poirot withdrew forthwith.

He fetched Zia's cloak, and together they strolled out into the gardens.

"This is where the suicides take place," said Zia.

Poirot shrugged his shoulders. "So it is said. Men are foolish, are they not. Mademoiselle?

To eat, to drink, to breathe the good air, it is a very pleasant thing. Mademoiselle.

One is foolish to leave all that simply because one has no money-or because the heart aches. L'amour, it causes many fatalities, does it not?"

Zia laughed.

"You should not laugh at love. Mademoiselle," said Poirot, shaking an energetic forefinger at her. "You who are young and beautiful."

"Hardly that," said Zia; "you forget that I am thirty-three, M. Poirot. I am frank with you, because it is no good being otherwise.

As you told my father, it is exactly seventeen years since you aided us in Paris that time."

"When I look at you, it seems much less," said Poirot gallantly. "You were then very much as you are now. Mademoiselle, a little thinner, a little paler, a little more serious.

Sixteen years old and fresh from your pension.

Not quite the petite pensionnaire, not quite a woman. You were very delicious, very charming. Mademoiselle Zia; others thought so too, without doubt."

"At sixteen," said Zia, "one is simple and a little fool."

"That may be," said Poirot, "yes, that well may be. At sixteen one is credulous, is one not? One believes what one is told."

If he saw the quick sideways glance that the girl shot at him, he pretended not to have done so. He continued dreamily: "It was a curious affair that, altogether. Your father, Mademoiselle, has never understood the true inwardness of it."

"No?"

"When he asked me for details, for explanations, I said to him thus: 'Without scandal, I have got back for you that which was lost. You must ask no questions.' Do you know. Mademoiselle, why I said these things?"

"I have no idea," said the girl coldly.

"It was because I had a soft spot in my heart for a little pensionnaire, so pale, so thin, so serious."

"I don't understand what you are talking about," cried Zia angrily.

"Do you not. Mademoiselle? Have you forgotten Antonio Pirezzio?"