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“Her husband saw to it that she was on the train with that friend of hers. He took her to the station.”

Hive looked angrily incredulous. Booker’s offence against professional ethics plainly was something new in his experience.

“Ah,” said Purbright, “I see you’ve reached the correct inference already. You were employed by Booker for no other purpose than to learn in advance of a specific arrangement by Palgrove and Doreen Booker to spend a night together. Booker knew that he had only to prevent his wife at the last minute from keeping the appointment for Palgrove to be stranded for the night, or for the relevant part of it, with no means of proving that he had not been at home murdering his wife. Better still, from Booker’s point of view, was the strong likelihood that Palgrove would actually try and provide himself with an alibi for the sake of his respectability—an alibi that was bound to be disproved once a murder investigation got under way.

“Now we can see, Mr Hive, why your perseverance beyond the point at which Booker wanted you to quit was so embarrassing to him.”

Hive had been listening with a look of judicious agreement. At the last, however, it was succeeded by a frown.

“You know, what’s rather puzzled me right from the beginning,” he said, “is why Booker picked on Mrs P. I’ve thought a lot about this, but I can’t quite see the logic.”

“Now, Mortimer,” said Miss Teatime, “you must stop hiding your light under a bushel. False modesty does not deceive a shrewd young police inspector as it might me. Admit that you know perfectly well why Mr Booker behaved as he did. Or am I to guess and will you say if I am right?”

Mr Hive accepted one of Purbright’s cigarettes. “All right, Lucy. You guess.”

“I have mentioned already,” began Miss Teatime, “that Mr Booker impresses me as an uncharitable man. That means that he is insensitive and therefore likely to lack consideration for others. I have also said that he is arrogant. With arrogance goes jealousy and a tendency to be vengeful. Someone has stolen his wife—very well, that man must lose his. But as he obviously does not much value her, the account must be balanced by extra payment. What more fitting than conviction for murder—and what more convenient to arrange? The life of some perfectly innocent, if not particularly endearing woman is an irrelevancy in the reckoning of a gentleman such as Mr Booker.”

Hive glanced at the inspector, who nodded thoughtfully (he was thinking of a certain confiscated radio set).

“Full marks, Lucy,” said Hive.

The inspector added his congratulations, which Miss Teatime hastened to say were undeserved as she had merely tried to echo what was in the mind of her good friend Mortimer.

“I wonder,” said Purbright, “if you’d care to try another piece of mental divination—you do seem rather good at it—and tell me what you suppose was in Mrs Palgrove’s mind when she wrote this.”

He passed to her one of the ‘Dear Friend’ letters.

“Before you read it, I should mention that we are quite satisfied as to its authenticity in spite of its not being signed. So long as it was Palgrove who was assumed to have killed his wife, the letter made perfect sense, even if some of the phrasing is a bit queer. But what now? How on earth was she induced to write such a thing?”

Miss Teatime put on a pair of spectacles. They made her look more benign than ever, until one noticed behind the lenses a certain gleam of eager alertness. Purbright was reminded of a village librarian scanning a passage of Henry Miller.

When she had finished, Miss Teatime removed her glasses and looked straight at Purbright. She was smiling.

“Why, Inspector, this is a standard piece of modern public relations technique. In the charity field, of course. I remember that the Canine Rescue League used an almost identical device not very long ago.

“It is a whimsical method of soliciting donations, you see.” She tapped the paper with her spectacles. “The letter purports to have been penned by a dog—representative, as it were, of all dogs everywhere that are in danger of being put to sleep to satisfy human convenience. A picture of the beast is appended, as a rule, in order to sharpen the appeal to the emotions. Sometimes there is a paw-print at the bottom—very heart-tugging, you must agree.”

Purbright tried not to look deflated. “Then that letter had nothing to do with Mrs Palgrove’s death? It was just coincidence that a number of people received it on the same day as she was killed?”

“It is for you to decide that, inspector. For my own part, I should be inclined to be wary of coincidences.”

Purbright thought a while. Then he said: “We shall probably never know for certain, but it is quite conceivable that it was Booker who devised the letter and prevailed upon Mrs Palgrove to type out copies. These he undertook to post for her. He could have kept them until the right moment arrived, removed the attached photographs—you’ll notice the pin holes, by the way—and then sent them, or some of them, to the people he thought would best serve his purpose. I think it was originally his intention to substitute for the animal photograph a print of a picture of Mrs Palgrove herself. We know that he ordered three such copies from a Nottingham firm, but something went wrong and they were not delivered in time.”

Miss Teatime was looking at him wonderingly.

“You are being remarkably frank with us, Inspector.” The observation was really a question.

“What you mean,” said Purbright, “is that I am being remarkably indiscreet. You may be right, but in saying these things to Mr Hive I prefer to think of myself as confiding in a professional colleague.”

Hive smiled at his finger ends and forthwith gave them the treat of a wander over his moustache.

“The point is,” the inspector went on, “that I am faced with a considerable difficulty. It is from Mr Booker that an indiscretion is required, not from me. But how is he going to be persuaded to commit one? What evidence we have against him is in solution, so to speak: it needs one admission from him round which to crystallize.”

For several moments, nobody said anything.

Then Mr Hive cleared his throat. “Suppose...”

The others looked at him. His mouth shut again. He shook his head, frowned regretfully.

A little later, a fresh thought animated Hive’s face. He sat straighter in his chair. “You know, the last time I was talking to that fellow, he practically threatened me. No, damn it, he did threaten me. I didn’t like it.”

Miss Teatime looked anxious. Purbright asked: “What kind of threat did he make?”

“Well, perhaps not a threat in so many words. But his attitude was extremely unpleasant. Guilty conscience, obviously. I wonder if I were to upset him a bit more...”

“Now, do be careful, Mortimer.”

Hive waved away Miss Teatime’s caution. He reached for the telephone that stood in the middle of the tea things.

“Just a minute.” Half rising, Purbright laid a hand on his arm. “Is there an extension?”

“That is the extension,” said Miss Teatime. “The switchboard is in the next room but one as you go away from the staircase. There will be no one there at the moment.”