"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 me here if you hadn't wanted me to think about the ghost. This is where she appeared, isn't it?"

"Yes." Bill was distinctly short about it.

"How?"

"What?"

"I said, 'How?'"

"How? How do ghosts appear? I don't know. They just appear."

"Over four or five hundred yards of open park?"

"Well, but she had to appear here, because this is where the original one-Lady Anne, you know-was supposed to walk."

"Oh, never mind Lady Anne! A real ghost can do anything. But how did Miss Norris appear suddenly over five hundred yards of bare park?"

Bill looked at Antony with open mouth.

"I-I don't know," he stammered. "We never thought of that."

"You would have seen her long before, wouldn't you, if she had come the way we came?"

"Of course we should."

"And that would have spoilt it rather. You would have had time to recognize her walk."

Bill was interested now.

"That's rather funny, you know, Tony. We none of us thought of that."

"You're sure she didn't come across the park when none of you were looking?"

"Quite. Because, you see, Betty and I were expecting her, and we kept looking round in case we saw her, so that we should all be playing with our backs to her."

"You and Miss Calladine were playing together?"

"I say, however do you know that?"

"Brilliant deductive reasoning. Well, then you suddenly saw her?"

"Yes, she walked across that side of the lawn." He indicated the opposite side, nearer to the house.

"She couldn't have been hiding in the ditch? Do you call it the moat, by the way?"

"Mark does. We don't among ourselves. No, she couldn't. Betty and I were here before the others, and walked round a bit. We should have seen her."

"Then she must have been hiding in the shed. Or do you call it the summer-house?"

"We had to go there for the bowls, of course. She couldn't have been there."

"Oh!"

"It's dashed funny," said Bill, after an interval for thought. "But it doesn't matter, does it? It has nothing to do with Robert."

"Hasn't it?"

"I say, has it?" said Bill, getting excited again.

"I don't know. We don't know what has, or what hasn't. But it has got something to do with Miss Norris. And Miss Norris-" He broke off suddenly.

"What about her?"