"I am staying down at Eastbourne — no, I can't be, I'm not dressed for the part — we've both come down for the afternoon, then. I am going to get into conversation with two women who know me already in my professional capacity. When the talk turns on hat brooches I want you to produce this from your bag, and say that you have just bought it for your sister. Your name, by the way, is Eleanor Raymond, and your sister's is Mary. That is all. Just leave the brooch lying round until I arrange my tie. That will be the signal that I have had all I want."

"All right. What is your first name, by the way?"

"Alan."

"All right, Alan. I nearly forgot to ask you that. It would have been a joke if I had not known my cousin's name!…It's a queer world, isn't it? Look at those primroses in the sun and think of all the people in terrible trouble this minute."

"No, don't. That way madness lies. Think of the pleasantly deserted beach we're going to see in a few minutes."

"Do you ever go to the Old Vic?" she asked, and they were still tolling each other how wonderful Miss Baylis was when they ran into the station; and Grant said, "Come on, Eleanor," and, grabbing her by the arm, picked her from the carriage like a small boy, impatient to try a spade on the sands.

The beach, as Grant had prophesied, was in that pleasantly deserted condition that makes the south-coast resorts so attractive out of the season. It was sunny and very warm, and a few groups lay about on the shingle, basking in the sun in an aristocratic isolation unknown to summer visitors.

"We'll go along the front and come back along the beach," Grant said. "They are bound to be out on a day like this."

"Heaven send they aren't on the downs," she said. "I don't mind walking, but it would take till tomorrow to quarter these."

"I think the downs are ruled out. The lady I am interested in isn't much of a walker, I should say."

"What is her name?"

"No, I won't tell you that until I introduce you. You are supposed not to have heard of her, and it will be better if you really haven't."

They walked in silence along the trim front towards Holywell. Everything was trim, with that well-ordered trimness that is so typically Eastbourne. Even the sea was trim — and slightly exclusive. And Beachy Head had the air of having been set down there as a good finish off to the front, and of being perfectly conscious of the fact. They had not been walking for more than ten minutes when Grant said, "We'll go down to the beach now. I'm almost certain we passed the couple I want some time ago. They are down on the shingle."

They left the pavement and began a slow foot-slipping stroll back to the piers again. Presently they approached two women who were reclining in deck-chairs facing the sea. One, the slighter one, was curled up with her back to Miss Dinmont and the inspector, and was apparently reading. The other was snowed round with magazines, writing-pad, sunshade, and all the other recognized paraphernalia of an afternoon on the beach, but she was doing nothing and appeared to be half asleep. As they came abreast of the chairs the inspector let his glance fall casually on them and then stopped.

"Why, Mrs. Ratcliffe!" he said. "Are you down here recuperating? What glorious weather!"

Mrs. Ratcliffe, after one startled glance, welcomed him. "You remember my sister, Miss Lethbridge?"

Grant shook hands and said, "I don't think you know my cousin —"

But the gods were good to Grant that day. Before he could commit himself, Miss Lethbridge said in her pleasant drawl:

"Good heavens, if it isn't Dandie Dinmont! How are you, my dear woman?"

"Do you know each other, then?" asked Grant, feeling like a man who has opened his eyes to find that one more step would have taken him over a precipice.

"Rather!" said Miss Lethbridge. "I had my appendicitis in a room at St. Michael's, and Dandie Dinmont held my head and my hand alternately. And she held them very well, I will say that for her. Shake hands with Miss Dinmont, Meg. My sister, Mrs. Ratcliffe. Who'd have thought you had cousins in the force!"

"I suppose you are recuperating too, Inspector?" Mrs. Ratcliffe said.

"You could call it that, I suppose," the inspector said. "My cousin is on holiday from Mike's, and I have finished my case, so we are making a day of it."

"Well, it isn't teatime yet," said Miss Lethbridge. "Sit down and talk to us for a little. I haven't seen Dandie for ages."

"You'll be glad to have that awful case off your hands, Inspector," her sister said as they subsided on the shingle. She spoke as though the murder had been just as much of an event in Grant's life as it had been in hers, but the inspector let it pass, and presently the talk veered away from the murder and went via health, restaurants, hotels, and food to dress, or the lack of it.

"I love your hat brooch," said Miss Dinmont idly to her friend. "I can think of nothing but hat brooches this afternoon, be-cause we've just been buying one for a mutual cousin who is getting married. You know — like getting a new coat and seeing people's coats as you never saw them before. I have it here somewhere." She reached for her bag without altering her reclining position, and rummaged in it until she produced the blue velvet box. "What do you think of it?" She opened it and extended it to them.

"Oh, lovely!" said Miss Lethbridge, but Mrs. Ratcliffe said nothing for a little.

"M. R.," she said at last. "Why, the initials are the same as mine. What is your cousin's name?"

"Mary Raymond."

"Sounds like a goody-goody heroine out of a book," remarked Miss Lethbridge. "Is she goody?"

"No, not particularly, though she's marrying an awful stodge. You like it, then?"

"Rather!" said Miss Lethbridge.

"Beautiful!" said her sister. "May I have a look at it?" She took the case in her hands, examined the brooch back and front, and handed it back. "Beautiful!" she said again. "And most uncommon. Can you get them ready-made, so to speak?"

Grant's infinitesimal shake of the head answered Miss Dinmont's cry for help. "No, we had it made," she said.

"Well, she's a lucky devil, Mary Raymond, and if she doesn't like it, she has very poor taste."

"Oh, if she doesn't like it," said Grant, "she can just fib and say she does, and we'll never be a bit the wiser. All women are expert fibbers."

"'Ark at 'im!" said Miss Lethbridge. "Poor disillusioned creature!"

"Well, isn't it true? Your social-life is one long series of fibs. You are very sorry — You are not at home — You would have come, but — You wish some one would stay longer. If you aren't fibbing to your friends, you are fibbing to your maids."

"I may fib to my friends," said Mrs. Ratcliffe, "but I most certainly do not fib to my maids!"

"Don't you?" said Grant, turning idly to look at her. No one, to see him there, with his hat tilted over his eyes and his body lounging, would have said that Inspector Grant was on duty. "You were going to the United States the day after the murder, weren't you?" She nodded calmly. "Well, why did you tell your maid that you were going to Yorkshire?"

Mrs. Ratcliffe made a movement to sit erect and then sank back again. "I don't know what you're talking about. I most certainly never told my maid I was going to Yorkshire. I said New York."

That was so patently possible that Grant hastened to get in first with, "Well, she thinks you said Yorkshire," before Mrs. Ratcliffe inevitably said, "How do you know?"

"There isn't anything a police inspector doesn't know," he said.

"There isn't anything he won't do, you mean," she said angrily. "Have you been walking out with Annie? I shouldn't be surprised if you suspected me of having done the murder myself."

"I shouldn't wonder," said Grant. "Inspectors suspect all the world."