"You see," he said, "we make progress."

"In fact you are quite certain of her guilt."

When the Count and Countess had departed, Poirot looked across at the other two.

"My dear friend, surely there is no doubt of it? I thought your reassuring manner was only to smooth things over till we are dug out of the snow and the police take charge."

"You do not believe the Count's positive assertion -- on his word of honour -- that his wife is innocent?"

"Excellent work," said M. Bouc cordially. "For my part, I should never have dreamed of suspecting Count and Countess Andrenyi. I will admit I thought them quite hors de combat. I suppose there is no doubt that she committed the crime? It is rather sad. Still, they will not guillotine her. There are extenuating circumstances. A few years' imprisonment -- that will be all."

"Mon cher -- naturally -- what else could he say? He adores his wife. He wants to save her! He tells his lie very well -- quite in the grand Seigneur manner, but what else than a lie could it be?"

M. Bouc broke off. The door at the end had opened, and Princess Dragomiroff entered the dining car. She came straight to them and all three men rose to their feet.

"Oh, I am not so sure about the handkerchief. You remember, I always told you that there were two possibilities as to the ownership of the handkerchief."

Poirot shot a glance of triumph at the other two.

"Well, you know, I had the preposterous idea that it might be the truth."

"All the same --"

She spoke to Poirot, ignoring the others. "I believe, Monsieur," she said, "that you have a handkerchief of mine."

He produced the little square of fine cambric.

"Is this it, Madame?"

"No, no. The handkerchief, remember. The handkerchief clinches the matter."

"That is it. It has my initial in the corner."

She gave him a cold stare.

"That is correct, Monsieur. My handkerchiefs are always initialled in the Russian characters. H is N in Russian."

"But, Madame la Princesse, that is the letter H," said M. Bouc. "Your Christian name -- pardon me -- is Natalia."

"Pray be seated, Madame," said Poirot.

"In fact you deliberately lied to us in the matter."

"Certainly. I would do the same again. Her mother was my friend. I believe, Messieurs, in loyalty -- to one's friends and one's family and one's caste."

She sighed. "I may as well, I suppose."

"None whatever."

"You did not tell us that this handkerchief was yours at the inquiry this morning."

"You have really no idea."

M. Bouc was somewhat taken aback. There was something about this indomitable old lady which made him feel flustered and uncomfortable.

She sat down.

Princess Dragomiroff answered contemptuously. "I suppose you mean because I did not tell you that Helena Andrenyi was Mrs. Armstrong's sister?"

"You did not ask me," said the Princess dryly.

"You need not make a long business of this, Messieurs. Your next question will be -- how did my handkerchief come to be lying by a murdered man's body? My reply to that is that I have no idea."

"You will excuse me, Madame, but how much can we rely upon the truthfulness of your replies?" Poirot said the words very softly.

"So that was it," murmured Poirot softly. "I noticed just a trifling hesitation when I asked the maid if she knew to whom the handkerchief belonged. She was uncertain whether or not to admit that it was her mistress's. But how does that fit in with that strange central idea of mine? Yes, it might well be."

"You see my difficulty, Madame. In this matter of the handkerchief, even, am I to believe you? Or are you shielding your friend's daughter?"

"In this case I consider that justice -- strict justice -- has been done."

"Have you anything further you wish to ask me?"

With a slight inclination of her head she passed out of the dining car.

"She must have done so. She saw it and said nothing? Ah, well, that shows that she too can be loyal."

"You do not believe in doing your utmost to further the ends of justice?"

"Oh! I see what you mean." Her face broke into a grim smile. "Well, Messieurs, this statement of mine can be easily proved. I will give you the address of the people in Paris who make my handkerchiefs. You have only to show them the one in question and they will inform you that it was made to my order over a year ago. The handkerchief is mine, Messieurs."

Poirot leaned forward.

She rose.

"Your maid, Madame, did she recognize this handkerchief when we showed it to her this morning?"

"But the feebler ones?"

"Could she have murdered Ratchett?" asked Poirot of the doctor.

He shook his head.

"Ah!" said M. Bouc with a characteristic gesture --"she is a terrible old lady, that!"

"Those blows -- the ones delivered with great force penetrating the muscle -- never, never could anyone with so frail a physique inflict them."

"I am thinking," said Poirot, "of the incident this morning when I said to her that the strength was in her will rather than in her arm. It was in the nature of a trap, that remark. I wanted to see if she would look down at her right or her left arm. She did neither. She looked at them both. But she made a strange reply. She said, 'No, I have no strength in these. I do not know whether to be sorry or glad.' A curious remark that. It confirms me in my belief about the crime."

"The feebler ones, yes."

"No. By the way, did you notice that Count Andrenyi keeps his handkerchief in his right-hand breast pocket?"

"It did not settle the point about the left-handedness."

M. Bouc shook his head. His mind reverted to the astonishing revelations of the last half hour. He murmured: "Lies -- and again lies -- it amazes me, the amount of lies we had told to us this morning."

"It has this advantage," said Poirot. "If you confront anyone who has lied with the truth, they usually admit it -- often out of sheer surprise. It is only necessary to guess right to produce your effect.

"I shall be very disappointed if it is not so."

"There are more still to discover," said Poirot cheerfully.

"And who do we tackle next?"

"Such duplicity is terrible," said M. Bouc. "But it seems to please you," he added reproachfully.

"You think so?"

"Ah! A process of elimination."

"We are going to tackle that pukka sahib, Colonel Arbuthnot."

"Then one person, at any rate, will be completely freed from suspicion."

"And supposing, my friend, that your guess happens to be wrong?"

"That is the only way to conduct this case. I select each passenger in turn, consider their evidence and say to myself, 'If so and so is lying, on what point are they lying and what is the reason for the lie?' And I answer if they are lying -- if, you mark -- it could only be for such a reason and on such a point. We have done that once very successfully with Countess Andrenyi. We shall now proceed to try the same method on several other persons."

"Exactly."