"And that is?"
"That in no possible way could Mrs. Inglethorp's death benefit Miss Howard. Now there is no murder without a motive."
I reflected.
"Could not Mrs. Inglethorp have made a will in her favour?" Poirot shook his head.
"But you yourself suggested that possibility to Mr. Wells?"
Poirot smiled.
"That was for a reason. I did not want to mention the name of the person who was actually in my mind. Miss Howard occupied very much the same position, so I used her name instead."
"Still, Mrs. Inglethorp might have done so. Why, that will, made on the afternoon of her death may----"
But Poirot's shake of the head was so energetic that I stopped.
"No, my friend. I have certain little ideas of my own about that will. But I can tell you this much--it was not in Miss Howard's favour."
I accepted his assurance, though I did not really see how he could be so positive about the matter.
"Well," I said, with a sigh, "we will acquit Miss Howard, then. It is partly your fault that I ever came to suspect her. It was what you said about her evidence at the inquest that set me off."
Poirot looked puzzled.
"What did I say about her evidence at the inquest?"
"Don't you remember? When I cited her and John Cavendish as being above suspicion?"
"Oh--ah--yes." He seemed a little confused, but recovered himself. "By the way, Hastings, there is something I want you to do for me."
"Certainly. What is it?"
"Next time you happen to be alone with Lawrence Cavendish, I want you to say this to him. 'I have a message for you, from Poirot. He says: "Find the extra coffee-cup, and you can rest in peace!" ' Nothing more. Nothing less."
" 'Find the extra coffee-cup, and you can rest in peace.' Is that right?" I asked, much mystified.
"Excellent."
"But what does it mean?"
"Ah, that I will leave you to find out. You have access to the facts. Just say that to him, and see what he says."
"Very well--but it's all extremely mysterious."
We were running into Tadminster now, and Poirot directed the car to the "Analytical Chemist."
Poirot hopped down briskly, and went inside. In a few minutes he was back again.
"There," he said. "That is all my business."