not. The doors were all shut."

"Could anyone have been concealed in the room?"

"There is the big cupboard in the corner--but the idea is absurd." "_Pas tout à fait_, madame. One thing more: did M. Halliday make any mention of his plans for the evening?"

"He said nothing whatever, monsieur."

"I thank you, madame, and I apologize for disturbing you. Pray do not trouble--we can find our way out." We stepped out into the hall. A lady was just entering the front door as we did so. She ran quickly up the stairs, and I was left with an impression of the heavy mourning that denotes a French widow.

"A most unusual type of woman, that," remarked Poirot, as we walked away. "Madame Olivier? Yes, she--"

"_Mais non_, not Madame Olivier. _Cela va sans dire!_ There are not many geniuses of her stamp in the world. No, I referred to the other lady--the lady on the stairs."

"I didn't see her face," I said, staring. "And I hardly see how you could have done. 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 onto the sidewalk, 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.

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