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your shirt-front that you had strawberries for dessert. Holmes, you astonish me. Tut, tut, you know my methods. Where is the tobacco? The tobacco is in the Persian slipper. Can I leave my practice for a week? I can.”

Antony smiled and went on smoking. After waiting hopefully for a minute or two, Bill said in a firm voice:

“Well then, Holmes, I feel bound to ask you if you have deduced anything. Also whom do you suspect?”

Antony began to talk.

“Do you remember,” he said, “one of Holmes’s little scores over Watson about the number of steps up to the Baker Street lodging? Poor old Watson had been up and down them a thousand times, but he had never thought of counting them, whereas Holmes had counted them as a matter of course, and knew that there were seventeen. And that was supposed to be the difference between observation and non-observation. Watson was crushed again, and Holmes appeared to him more amazing than ever. Now, it always seemed to me that in that matter Holmes was the ass, and Watson the sensible person. What on earth is the point of keeping in your head an unnecessary fact like that? If you really want to know at any time the number of steps to your lodging, you can ring up your landlady and ask her. I’ve been up and down the steps of the club a thousand times, but if you asked me to tell you at this moment how many steps there are I couldn’t do it. Could you?”

“I certainly couldn’t,” said Bill.

“But if you really wanted to know,” said Antony casually, with a sudden change of voice, “I could find out for you without even bothering to ring up the hall-porter.”

Bill was puzzled as to why they were talking about the club steps, but he felt it his duty to say that he did want to know how many they were.

“Right,” said Antony. “I’ll find out.”

He closed his eyes.

“I’m walking up St James’ Street,” he said slowly. “Now I’ve come to the club and I’m going past the smoking-room —windows-one-two three four. Now I’m at the steps. I turn in and begin going up them. One-two-three-four-five-six, then a broad step; six-seven-eight-nine, another broad step; nine-ten-eleven. Eleven I’m inside. Good morning, Rogers. Fine day again.” With a little start he opened his eyes and came back again to his present surroundings. He turned to Bill with a smile. “Eleven,” he said. “Count them the next time you’re there. Eleven and now I hope I shall forget it again.”

Bill was distinctly interested.

“That’s rather hot,” he said. “Expound.”

“Well, I can’t explain it, whether it’s something in the actual eye, or something in the brain, or what, but I have got rather an uncanny habit of recording things unconsciously. You know that game where you look at a tray full of small objects for three minutes, and then turn away and try to make a list of them. It means a devil of a lot of concentration for the ordinary person, if he wants to get his list complete, but in some odd way I manage to do it without concentration at all. I mean that my eyes seem to do it without the brain consciously taking any part. I could look at the tray, for instance, and talk to you about golf at the same time, and still get my list right.”

“I should think that’s rather a useful gift for an amateur detective. You ought to have gone into the profession before.”

“Well, it is rather useful. It’s rather surprising, you know, to a stranger. Let’s surprise Cayley with it, shall we?”

“How?”

“Well, let’s ask him—” Antony stopped and looked at Bill comically, “let’s ask him what he’s going to do with the key of the office.”

For a moment Bill did not understand.

“Key of the office?” he said vaguely. “You don’t mean—Tony! What do you mean? Good God! do you mean that Cayley— But what about Mark?”

“I don’t know where Mark is—that’s another thing I want to know —but I’m quite certain that he hasn’t got the key of the office with him. Because Cayley’s got it.”

“Are you sure?”

“Quite.”

Bill looked at him wonderingly.

“I say,” he said, almost pleadingly, “don’t tell me that you can see into people’s pockets and all that sort of thing as well.”

Antony laughed and denied it cheerfully.

“Then how do you know?”

“You’re the perfect Watson, Bill. You take to it quite naturally. Properly speaking, I oughtn’t to explain till the last chapter, but I always think that that’s so unfair. So here goes. Of course, I don’t really know that he’s got it, but I do know that he had it. I know that when I came on him this afternoon, he had just locked the door and put the key in his pocket.”

“You mean you saw him at the time, but that you’ve only just remembered it—reconstructed it in the way you were explaining just now?”

“No. I didn’t see him. But I did see something. I saw the key of the billiard-room.”

“Where?

“Outside the billiard-room door.”

“Outside? But it was inside when we looked just now.”

“Exactly.”

“Who put it there?”

“Obviously Cayley.”

“But—”

“Let’s go back to this afternoon. I don’t remember noticing the billiard-room key at the time; I must have done so without knowing. Probably when I saw Cayley banging at the door I may have wondered subconsciously whether the key of the room next to it would fit. Something like that, I daresay. Well, when I was sitting out by myself on that seat just before you came along, I went over the whole scene in my mind, and I suddenly saw the billiard-room key there outside. And I began to wonder if the office-key had been outside too. When Cayley came up, I told you my idea and you were both interested. But Cayley was just a shade too interested. I daresay you didn’t notice it, but he was.

“By Jove!”

“Well, of course that proved nothing; and the key business didn’t really prove anything, because whatever side of the door the other keys were, Mark might have locked his own private room from the inside sometimes. But I piled it on, and pretended that it was enormously important, and quite altered the case altogether, and having got Cayley thoroughly anxious about it, I told him that we should be well out of the way for the next hour or so, and that he would be alone in the house to do what he liked about it. And, as I expected, he couldn’t resist it. He altered the keys and gave himself away entirely.”

“But the library key was still outside. Why didn’t he alter that?”

“Because he’s a clever devil. For one thing, the inspector had been in the library, and might possibly have noticed it already. And for another—” Antony hesitated.

“What?” said Bill, after waiting for him to go on.

“It’s only guesswork. But I fancy that Cayley was thoroughly upset about the key business. He suddenly realized that he had been careless, and he hadn’t got time to think it all over. So he didn’t want to commit himself definitely to the statement that the key was either outside or inside. He wanted to leave it vague. It was safest that way.”

“I see,” said Bill slowly.

But his mind was elsewhere. He was wondering suddenly about Cayley. Cayley was just an ordinary man—like himself. Bill had had little jokes with him sometimes; not that Cayley was much of a hand at joking. Bill had helped him to sausages, played tennis with him, borrowed his tobacco, lent him a putter …. and here was Antony saying that he was what? Well, not an ordinary man, anyway. A man with a secret. Perhaps a murderer. No, not a murderer; not Cayley. That was rot, anyway. Why, they had played tennis together.

“Now then, Watson,” said Antony suddenly. “It’s time you said something.”

“I say, Tony, do you really mean it?”

“Mean what?”

“About Cayley.”

“I mean what I said, Bill. No more.

“Well, what does it amount to?”

“Simply that Robert Ablett died in the office this afternoon, and that Cayley knows exactly how he died. That’s all. It doesn’t follow that Cayley killed him.”

“No. No, of course it doesn’t.” Bill gave a sigh of relief. “He’s just shielding Mark, what?”

“I wonder.”

“Well, isn’t that the simplest explanation?”

“It’s the simplest if you’re a friend of Cayley and want to let him down lightly. But then I’m not, you see.

“Why isn’t it simple, anyhow?”

“Well, let’s have the explanation then, and I’ll undertake to give you a simpler one afterwards. Go on. Only remember the key is on the outside of the door to start with.”

“Yes; well, I don’t mind that. Mark goes in to see his brother, and they quarrel and all the rest of it, just as Cayley was saying. Cayley hears the shot, and in order to give Mark time to get away, locks the door, puts the key in his pocket and pretends that Mark has locked the door, and that he can’t get in. How’s that?”

“Hopeless, Watson, hopeless.”

“Why?”

“How does Cayley know that it is Mark who has shot Robert, and not the other way round?”

“Oh!” said Bill, rather upset. “Yes.” He thought for a moment, “All right. Say that Cayley has gone into the room first, and seen Robert on the ground.”

“Well?”

“Well, there you are.”

“And what does he say to Mark? That it’s a fine afternoon; and could he lend him a pocket-handkerchief? Or does he ask him what’s happened?”

“Well, of course, I suppose he asks what happened,” said Bill reluctantly.

“And what does Mark say?”

“Explains that the revolver went off accidentally during a struggle.”

“Whereupon Cayley shields him by doing what, Bill? Encouraging him to do the damn silliest thing that any man could possibly do confess his guilt by running away!”

“No, that’s rather hopeless, isn’t it?” Bill thought again. “Well,” he said reluctantly, “suppose Mark confessed that he’d murdered his brother?”

“That’s better, Bill. Don’t be afraid of getting away from the accident idea. Well then, your new theory is this. Mark confesses to Cayley that he shot Robert on purpose, and Cayley decides, even at the risk of committing perjury, and getting into trouble himself, to help Mark to escape. Is that right?”

Bill nodded.

“Well then, I want to ask you two questions. First, is it possible, as I said before dinner, that any man would commit such an idiotic murder—a murder that puts the rope so very tightly round his neck? Secondly, if Cayley is prepared to perjure himself for Mark (as he has to, anyway, now), wouldn’t it be simpler for him to say that he was in the office all the time, and that Robert’s death was accidental?”

Bill considered this carefully, and then nodded slowly again.

“Yes, my simple explanation is a wash-out,” he said. “Now let’s have yours.”

Antony did not answer him. He had begun to think about something quite different.

CHAPTER IX Possibilities of a Croquet Set

“What’s the matter?” said Bill sharply.

Antony looked round at him with raised eyebrows.

“You’ve thought of something suddenly,” said Bill. “What is it?”

Antony laughed.

“My dear Watson,” he said, “you aren’t supposed to be as clever as this.”

“Oh, you can’t take me in!”

“No …. Well, I was wondering about this ghost of yours, Bill. It seems to me—”

“Oh, that!” Bill was profoundly disappointed. “What on earth has the ghost got to do with it?”

“I don’t know,” said Antony apologetically. “I don’t know what anything has got to do with it. I was just wondering. You shouldn’t have brought

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