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"I see what you mean," said Dr. Mitchell slowly. "Yes, perhaps an hour was rather an overstatement on my part After all, Chalmers has been practising longer than I have. He may quite probably be right in cutting it down to half an hour."

"As an outside limit. It may quite well have happened immediately?"

"Oh, yes; quite well."

"Good again. Now, another point: You made your report to the inspector last night. Have you made one to the superintendent yet?"

"Yes. I was intending to go down to see him this afternoon, but he came to me instead, directly after lunch. He told me about the post - mortem at the same time."

"Yes? And what did you report to him?"

"There was nothing to add, really, to what Pd said to the inspector. He asked a good many questions . . ."

"He did, did he?"

"Yes, but I had to keep telling him I couldn't give him any more information till after the p.m."

"Of course. Now I understand this afternoon you found a good deal of bruising on the body, and particularly one place on the back of the head?"

"Yes, we did. Not a very bad one, and it was hidden under the hair, just at the back of the scalp; though I don't think we'd have missed it last night if we hadn't both been so whacked."

"Yes."

Roger paused. Now that he had come to the really crucial part of the interview, he was not quite sure how to proceed. Somehow Dr. Mitchell had got to help him to explain that bruise away, and yet he could not even hint to the doctor why. But Roger was sure that the police would draw precisely the same deduction from it as his own; and while the body bruises were damning enough, the stunning bruise might be fatal. Somehow a convincing explanation of that bruise had got to be found - must be found - before there could be any hope of achieving anything else at all.

"Yes," he said at last, taking the bull by the horns "and how do you account for the presence of that bruise on the head, Mitchell?"

"Well," said Dr. Mitchell bluntly, "I suppose someone must have given her a knock on it."

Roger looked at him in distress. This was about as bad as it could be. "Is that the only possible explanation? I mean, it looks so much like that quarrel which we know didn't take place," he added feebly.

"She must have had a bang on the head to cause a bruise like that," Dr. Mitchell pointed out, with reason.

"Yes, but couldn't she have banged it herself?"

"Oh, she could have, undoubtedly. But do people bang themselves on the back of the scalp?"

"I mean, on a low doorway, or something like that?"

"Not unless she was going through it backwards, surely." Roger felt he was losing grip. He was handicapped by not being able to come out into the open. It was impossible to explain that the police, suspecting not just a more complicated suicide but something far more serious, would almost certainly have been wondering if there might be just such a sign of violence on the back of the head to explain the absence of any indication of a scuffle on the asphalt surface; for asphalt marks very easily, and if a scuffle had taken place traces of it would undoubtedly remain. And here just such a sign was.

"Well, isn't there any way she could have got it without having it inflicted on her by another person?" he asked desperately. "And, for that matter, the body bruises too?"

Dr. Mitchell looked serious. "I quite see what you mean, Sheringham, but there's no getting away from it: she does look as if she'd been knocked about a bit. Bryce himself said so, and he's sure to put it in his report. He actually said: 'Hullo, who's been knocking Ena about?'"

"Hell," said Roger despondently.

Then suddenly he turned on the other a face full of excitement. "Mitchell! Were the knees of her stockings torn?"

"The knees of her stockings? I don't believe they were. No, I'm sure they weren't, because one was stuck to her kneecap with a spot of dried blood, and there had been no sign before we turned it down. Why?"

"Because that explains everything," said Roger happily. "All the bruises. Shall I tell you where she got that mark on the back of her head? From the grand piano."

"The grand piano?"

"Yes. in the ballroom. Good lord, what an idiot I am. Of course her knees couldn't have been bruised on the roof, because the asphalt would have torn her stockings. But what will break the skin underneath thin silk, and yet not injure the silk? Moderate friction against a polished wood surface. In other words, we both saw Mrs. Stratton bruising her knees, and all the rest of her - if we happened to be watching. Now have you got me?"

"That Apache dance she did with Ronald!"

"Of course." Roger beamed at his pupil. It is so much better for the pupil himself to voice the obvious conclusion. That means that he will take it for granted afterwards that he thought of it for himself, without any prompting; and consequently he will stick to it like glue.

"By Jove," Roger followed this up, "and I remember now seeing her get up off the floor once by the piano, rubbing her head. Did you see that?"

"No, I can't say I did."

"Oh, yes," said Roger with enthusiasm, who had not seen it either, but was determined that Mrs. Lefroy should have, and Ronald himself, and Colin. "She rubbed her head and said, 'Oo - er, that was a nasty bump; do it again, Ronald,' or something like that, you know."

"Well, that's the explanation, undoubtedly," agreed Dr. Mitchell, equally relieved.

"Yes. And I suppose," added Roger, with a passing qualm of anxiety, "that all the bruises are accounted for in the same way?"

"Oh, certainly. She came down once or twice very heavily. I thought at the time that she must be getting hurt, but she seemed to like it."

"Precisely. And that's another point for the coroner's jury. They'll be quite ready to believe that a person who liked getting hurt would enjoy the idea of suicide. And so, for that matter, she did. Well, that's most satisfactory. Did you say something just now, by the way, about a cup of tea?"

Dr. Mitchell rose with alacrity.

Roger almost danced in again through the front door of the Stratton house. Everything was going splendidly. Only one snag now remained, and that depended not on the police but Colin. But before even breaking the good news to Ronald, Roger hurried straight upstairs to the empty ballroom. And there he did a very regrettable thing.

Closing the door carefully behind him, he chose a nice nubbly piece of moulding on the lower edge of the grand piano and, going down on his hands and knees, rubbed his head carefully against it. There is a certain amount of grease on every head of hair, and Roger contemplated with pleasure the faintly dull patch he had caused on the brilliant shine of the varnish; he would have liked a nice black hair to add to it, but unfortunately such a thing was not available.

It would have been unkind, Roger felt, seeing that the police would probably look for it, not to gratify them with a nice bit of evidence.

Then he went down to look for Ronald and Mrs. Lefroy and tell them what they remembered seeing. The questionable ethics of all this simply did not occur to him - any more than did the notion that Ena Stratton might really and truly have banged her head on that grand piano.

CHAPTER XIII

WIPING THE SLATE

AT TWENTY minutes to six Roger, no longer losing grip, was closeted with Colin Nicolson in Ronald's study, with what looked like an uphill job in front of him.

"Every other point is cleared up," he pleaded. "Every single one. There's only that chair left. If we can clear that up, too, there's not only no case left, there isn't even any more room for suspicion."