She never looked at us."
"That is why I said she was an unusual type," said Poirot placidly. "A woman who enters her home - for I presume that it is her home since she enters with a key - and runs straight upstairs without even looking at two strange visitors in the hall to see who they are, is a very unusual type of woman - quite unnatural, in fact.
Mille tonnerres! what is that?"
He dragged me back - just in time.
A tree had crashed down on to the side walk, just missing us.
Poirot stared at it, pale and upset.
"It was a near thing that!
But clumsy, all the same - for I had no suspicion - at least hardly any suspicion.
Yes, but for my quick eyes, the eyes of a cat, Hercule Poirot might now be crushed out of existence - a terrible calamity for the world.
And you, too, mon ami - though that would not be such a national catastrophe."
"Thank you," I said coldly. "And what are we going to do now?"
"Do?" cried Poirot. "We are going to think.
Yes, here and now, we are going to exercise our little gray cells.
This M. Halliday now, was he really in Paris?
Yes, for Professor Bourgoneau, who knows him, saw and spoke to him."
"What on earth are you driving at?" I cried.
"That was Friday morning.
He was last seen at eleven Friday night - but was he seen then?"
"The porter -"
"A night porter - who had not previously seen Halliday.
A man comes in, sufficiently like Halliday - we may trust Number Four for that - asks for letters, goes upstairs, packs a small suit-case, and slips out the next morning.
Nobody saw Halliday all that evening - no, because he was already in the hands of his enemies.
Was it Halliday whom Madame Olivier received?
Yes, for though she did not know him by sight, an impostor could hardly deceive her on her own special subject.
He came here, he had his interview, he left.
What happened next?"
Seizing me by the arm, Poirot was fairly dragging me back to the villa.
"Now, mon ami, imagine that it is the day after the disappearance, and that we are tracking footprints.
You love footprints, do you not?
See - here they go, a man's, Mr. Halliday's... He turns to the right as we did, he walks briskly - ah! other footsteps following behind - very quickly - small footsteps, a woman's. See, she catches him up - a slim young woman, in a widow's veil.
'Pardon, monsieur, Madame Olivier desires that I recall you.' He stops, he turns.
Now where would the young woman take him?
She does not wish to be seen walking with him.
Is it coincidence that she catches up with him just where a narrow alleyway opens, dividing two gardens.
She leads him down it. 'It is shorter this way, monsieur.'
On the right is the garden of Madame Olivier's villa, on the left the garden of another villa - and from that garden, mark you, the tree fell - so nearly on us.
Garden doors from both open on the alley.
The ambush is there.
Men pour out, overpower him, and carry him into the strange villa."
"Good gracious, Poirot," I cried, "are you pretending to see all this?"
"I see it with the eyes of the mind, mon ami.
So, and only so, could it have happened.
Come, let us go back to the house."
"You want to see Madame Olivier again?"
Poirot gave a curious smile.
"No, Hastings, I want to see the face of the lady on the stairs."
"Who do you think she is, a relation of Madame Olivier's?"
"More probably a secretary - and a secretary engaged not very long ago."
The same gentle acolyte opened the door to us.
"Can you tell me," said Poirot, "the name of the lady, the widow lady, who came in just now?"