"I engaged her about three weeks ago when Mrs Emery, our former housekeeper, left. She came to me from Mrs Selbourne's Agency in Mount Street - a very well-known place. I get all my servants from there. They sent several women to see me, but this Mrs Middleton seemed much the nicest, and had splendid references. I engaged her on the spot, and notified the Agency of the fact. I can't believe that there was anything wrong with her. She was such a nice quiet woman." The thing was certainly a mystery. Whilst it was clear that the woman herself could not have committed the crime, since at the moment the shot was fired Mrs Havering was with her in the hall, nevertheless she must have some connection with the murder, or why should she suddenly take to her heels and bolt?

I wired the latest development to Poirot and suggested returning to London and making inquiries at Selbourne's Agency.

Poirot's reply was prompt:

"Useless to inquire at agency they will never have heard of her find out what vehicle took her up to hunters lodge when she first arrived there."

Though mystified, I was obedient. The means of transport in Elmer's Dale were limited. The local garage had two battered Ford cars, and there were two station flies.

None of these had been requisitioned on the date in question. Questioned, Mrs Havering explained that she had given the woman the money for her fare down to Derbyshire and sufficient to hire a car or fly to take her up to Hunter's Lodge. There was usually one of the Fords at the station on the chance of its being required. Taking into consideration the further fact that nobody at the station had noticed the arrival of a stranger, black-bearded or otherwise, on the fatal evening, everything seemed to point to the conclusion that the murderer had come to the spot in a car, which had been waiting near at hand to aid his escape, and that the same car had brought the mysterious housekeeper to her new post. I may mention that inquiries at the Agency in London bore out Poirot's prognostication. No such woman as "Mrs Middleton" had ever been on their books. They had received the Hon Mrs Havering's application for a housekeeper, and had sent her various applicants for the post. When she sent them the engagement fee, she omitted to mention which woman she had selected.

Somewhat crestfallen, I returned to London. I found Poirot established in an arm-chair by the fire in a garish silk dressing-gown. He greeted me with much affection.

"Mon ami Hastings! But how glad I am to see you. Veritably I have for you a great affection! And you have enjoyed yourself? You have run to and fro with the good Japp? You have interrogated and investigated to your heart's content?"

"Poirot," I cried, "the thing's a dark mystery! It will never be solved."

"It is true that we are not likely to cover ourselves with glory over it."