Poirot nodded.
"I had an interview with her the night that Monsieur Kettering was arrested. It was an interesting interview in more ways than one."
Again he fell silent, and Katherine did not interrupt his train of thought.
"Mademoiselle," he said at last, "I am now on delicate ground, yet I will say this to you. There is, I think, some one who loves Monsieur Kettering—correct me if I am wrong—and for her sake—well—for her sake I hope that I am right and the police are wrong. You know who that some one is?"
There was a pause, then Katherine said:
"Yes—I think I know."
Poirot leant across the table towards her.
"I am not satisfied, Mademoiselle; no, I am not satisfied. The facts, the main facts, led straight to Monsieur Kettering. But there is one thing that has been left out of account."
"And what is that?"
"The disfigured face of the victim. I have asked myself, Mademoiselle, a hundred times, 'Was Derek Kettering the kind of man who would deal that smashing blow after having committed the murder?' What end would it serve? What purpose would it accomplish? Was it a likely action for one of Monsieur Kettering's temperament? And, Mademoiselle, the answer to these questions is profoundly unsatisfactory. Again and again I go back to that one point—'why?' And the only things I have to help me to a solution of the problem are these."