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"But considering it was Mrs. Stratton," Roger added shrewdly, "I shouldn't be surprised if she wasn't in the sun parlour at all. It would have been far more typical for her to have been out on the cold, cold roof, pretending to commit suicide by pneumonia, and praying for someone to come up and catch her at it, for a little more glorification."

"Now you're at your guesswork again."

"Oh, admittedly. But if you're going to call every theory guesswork, even when I can argue it from observed facts and reasonable inferences, we're not going to get much further."

"No, no. I won't do that. But I would like to hear a little more evidence to support your theories. I don't deny that you've put up quite a possible case against Chalmers, but it all depends on one thing, doesn't it? And that is that he did it before he went out on that call."

Roger considered. "Yes, that's right. The time of death shows that she must have died within half an hour at most of leaving the ballroom, and Chalmers was away an hour. Yes, if he did it, it must have been before he went."

Colin heaved himself up in his chair, stretched and grinned. "Well, I didn't say anything before, because I didn't want to spoil your fun; but I'm afraid your case falls to the ground, Roger. I'm willing to bet you five pounds to a sixpence that Chalmers went out on that call before Mrs. Stratton ever left the ballroom at all. What do you say to that?"

Roger's face fell. "Oh! My goodness, yes, I believe you're right, Colin. You would be, of course. Yes, I remember distinctly. She only began saying she wanted to go home after Chalmers had gone out, and that was what led up to the scene. Dash you, Colin, that seems to have scuppered it."

"Ah!" said Colin complacently.

"Does it, though? Wait a minute. It was only because of the time of death that I said Chalmers must have done it before he went out. Supposing the presumed time of death isn't correct. It's Chalmers' own word we've got for that, you see, and if it suited him he could have pronounced a false time of death quite easily."

"No, you're wrong again, Roger. Mitchell supported him."

"He did?"

"Yes, they were talking about it up here, while you were downstairs with the inspector."

"Oh!" Roger considered.

"But that might have been a case of unconscious suasion, Colin," he went on eagerly. "I should think that a second doctor is always prejudiced in favour of the opinion of the one who made the examination first. Mitchell knows Chalmers is a sound man; he'd be perfectly ready to accept Chalmers' opinion, especially in a matter like this where there's a certain amount of latitude.

"Yes, the more I think of it, the more it fits in. The point may be a small one, but Chalmers has been gently rubbing his alibi into all of us, hasn't he? I remember, now, he took the very first opportunity of mentioning to me that the ballroom scene occurred after he'd been called out. It may have been quite a natural thing to say; but it may equally have been rather gratuitous.

"And look," Roger continued quite excitedly, "how quickly he got here after Ronald telephoned. He does live nearer than Mitchell, it's true. But why hadn't he gone to bed? He must have been home very nearly an hour - three quarters at any rate. Three quarters of an hour, at that time in the morning, and he hasn't even gone to bed. Or, apparently, undressed. Doesn't that look as if he might have been waiting for the telephone call which he knew very well would come? Obviously he wanted to get here first, before any other doctor or the police, to have a good look at the body in the light and remove any possibly suspicious or incriminating traces. Well? Isn't that all perfectly reasonable?"

"Ach, come now, Roger." Colin shook his head. "Your case against Chalmers won't hold water and you can't twist it into doing so."

"Perhaps you still believe I'm the man?" Roger asked unpleasantly.

"I wouldn't be surprised. Though if you say not, I'll help you look for another. But Chalmers won't do. He won't do at all."

"I still think he's got a lot to explain away," Roger said obstinately. "Yes, I'd very much like to ask friend Chalmers a few questions. No, it's no good shaking your head like a mantelpiece mandarin; there is a case against Chalmers. If he is the man, we can assume that he could cook the time of death to make it appear that Mrs. Stratton was dead half an hour before he got back to the house, can't we? Can't we, Colin?"

"Yes; but wait a minute, Roger. I ..."

"No, you wait a minute. Well, if we can assume that, there's a very big hole in his defence. In that case the theory is that he came back from his visit and, instead of coming into the ballroom to the rest of us, went straight up to the sun parlour to get his pipe. Then everything else as before. He knows he's pretty safe, because not a soul has seen him go up on the roof. Well, all he's got to do then is to wait till the coast is clear, run downstairs again, and then walk up, singing loudly, and announce himself. And he could know when the coast was clear, because the roof door can't be seen from the barroom or the landing. He'd only have to slip inside it and wait. How's that?"

"Oh, very neat, no doubt; but listen to me..."

"No, you listen to me. Therefore, the objection you made just now has no point, and the case against Chalmers remains as strong as ever it did. Stronger, if anything. And what's more, it may be quite easy to test it. All we've got to do is to find out where that call of his came from, and then very gently and subtly get to know at what exact time Chalmers left there to come back here. Of course they may not . . ."

"Will you listen to me, Roger!" Colin shouted. "I've just thought of something."

"Well done, Colin," Roger said kindly.

"It's your theory that whoever killed Mrs. Stratton held her up with one arm and pulled the noose round her neck with the other. That's right, isn't it?"

"Certainly. For a strong man . . ."

"Never mind about your strong man. That's how you say Chalmers did it, and he couldn't have done it any other way?"

"Yes. Well?"

"He couldn't, for instance, have done it without using both arms?"

"No. What about it? - Oh . . ." said Roger, in a dying kind of voice.

"Exactly," Colin cried, with tactless triumph. "Why, Roger, man, where were your eyes? You know as well as I do that Chalmers has a dud arm. He couldn't have held a fly with it that didn't want a noose round its neck, let alone a great strapping wench like Mrs. Stratton. Now perhaps you'll have the sense to admit that whoever did it, Chalmers couldn't? Will you?"

"Dash you, Colin," said Roger, annoyed, "must you rub it in?"

He tried to look on the bright side. At any rate the discussion had not been totally useless. Chalmers as well as David Stratton was now eliminated. But at this rate it looked like being a long job.

Colin was lighting a fresh cigarette. "Well, Roger," he said, "you've got to show me."

"Show you what?"

"That it wasn't you who strung up Mrs. Stratton," Colin said calmly.

CHAPTER X

THE CASE AGAINST DAVID STRATTON

IN SPITE of Roger's prophecy, he and Colin did get to bed that night, some time after five o'clock. When Roger got down the same morning, Colin had already breakfasted. The women and Williamson had not yet appeared. Roger was rather annoyed that he had got up so early.

Ronald Stratton found him in the dining room, toying in a somewhat disaffected way with a tired - looking egg and some bacon.