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.'

'And you want me to go to the police and admit I wiped the prints off the chair, Roger?'

'Yes.'

'Nothing doing,' said Colin firmly.

'But you must, man!'

'Must nothing. I wiped your prints off that chair to save you from getting into a nasty jam, Roger, through your own silly carelessness. I'm not going to put myself in a jam over it instead.'

'But don't you see . . .'

'What I see is that you ought to have wiped the prints off yourself. So go and tell the police you did, you old rascal.'

'But I can't!' wailed Roger. 'I'm too well -  trained to destroy evidence. They'd smell a rat at once if I told them I'd done such a thing.'

'Ach, rubbish!' said Colin rudely. 'You're afraid to take the blame, that's all. You think it would put you in bad with the police for the future.'

'And so it would.'

'Well, I can't help that. You should have thought of that before you interfered. No, no; this is your pigeon, Roger. Nothing to do with me at all. Nothing at all.'

'Look here, Colin,' Roger said desperately, 'if you won't own up like a man, I'll tell the police myself that you did wipe that chair.'

'Right you are. And I'll tell them that you moved it.'

'But you can't! That would give David away, and we've got him absolutely covered.'

'Then you tell them you wiped off the prints yourself.'

Roger groaned. Colin was being excessively Scottish. But Roger could not but admit to himself that Colin had reason. He had performed an action which Roger ought to have performed for himself, and he did not see why he, and not Roger, should have the blame.

Nevertheless, Colin must not be allowed to have reason. It looked like finishing Roger with the police for ever if he were. 'Look here, Colin, if I can think up some excellent reason for you to have done it, won't you . . ,

'No, I won't, Roger, and that's flat.'

'Oh, blast,' said Roger.

There was a knock at the door. 'Come in,' called Roger morosely.

Mrs. Lefroy's head appeared round the lintel. 'Oh, Mr. Sheringham, Ronald asked me to let you know that the police are here again. He's upstairs with them, in the ballroom.'

'Thank you. No, don't run away, Mrs. Lefroy. Come in and see if you can persuade Colin to be noble. I can't.'

'Oh, Colin, you will be noble, surely.'

'Don't you try your wiles on me, Agatha. I'm proof against all that sort of thing.'

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