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‘And we know that our bloke must have left the murder room somewhat bloodstained,’ Joe mused. ‘He could have cleaned up in the bathroom and then cleaned the bathroom but he’d have still been at his housework when Westhorpe arrived, surely?’

‘Or he’d have run straight into Constable Westhorpe in the corridor,’ said Cottingham finishing for him. ‘But he didn’t. So did he leave by the window, dropping the poker as he went?’

‘Having put his gloves back on again?’ objected Joe. ‘Doesn’t add up. We know he was wearing gloves when he got in through the window. Why in hell did he take them off to grasp a poker and take a whack at the Dame? Then, having conveniently left his dabs on the murder weapon, he gloves up again, exits, and leaves the thing where we were bound to find it on the roof?’

‘Someone’s playing games with us, sir.’

‘And don’t forget Sergeant Armitage was patrolling outside. He’d have to be blind and deaf to avoid seeing a bloke covered in blood clutching a jemmy and an emerald necklace shimmying down the drainpipes. Bill’s one of the most alert men I’ve ever served with. I honestly think no one would have got up the building, shattered a strong Ritz window and climbed down without him being aware. You know, Ralph, I incline to the suspicion that the killing wasn’t done at all by someone coming through that window. . Leaving nothing out for the moment, of course, but let’s just think about this. Could all that glass smashing have been a distraction? Have you got the plan you drew up at the scene?’

Joe noticed that Cottingham already had it in his hand. His inspector betrayed by a quick smile of satisfaction that he had got there before the boss.

‘The pane was smashed from the outside — no doubt of that — but it could have been done by opening the window and standing inside the room to do it. And you’d expect to find the shards of glass,’ he pointed with a pencil, ‘here, right below the window in this sort of pattern.’ He paused. ‘And we did. But I took the opportunity of returning to the scene yesterday before cleaning took place. I got the temporary boarding removed and with daylight streaming through the window — ’ his moustache bristled with triumph barely held in check — ‘I found quite another pattern, sir, which I have drawn up here.’

He produced a larger scale plan of the window area. ‘Shards, as I say, here right where you’d look for them but also marks, scrape marks across the nap of the Wilton carpet, here near the south wall. And also splinters of glass so small we didn’t see them on the night of the murder.’

‘So someone stood here at the window, swung it open and smashed it from inside. Someone bright enough and cool enough to sweep the shards into exactly the place you’d look for them.’

Cottingham nodded. ‘And there’s more. I took samples of the bigger pieces and sent them to the lab for microscope analysis. Well, you never know. . just in case. .’ He pushed another sheet across the desk. ‘One of them had tiny fibres of cotton attached, sir. Ivory, Egyptian. Matches exactly the Ritz bathroom towels. Our lad had muffled the sound of breaking glass.’

Joe smiled. ‘What a performance! But at least Bill will be pleased to hear there may be, after all, nothing wrong with his hearing. .. Oh, thanks, Charlie!’

They curled their fists around the china mugs and thoughtfully sipped the strong Assam brew.

‘Right, then. We’re looking for someone large, a man most probably, who was admitted to the Dame’s room — and therefore, we assume, was known to her — had a violent quarrel with her and killed her, apparently with some passion. Then he calmly and — does the word “professionally” intrude here, Ralph? — fakes up the burglar-through-the-window business and gets away, somehow managing to avoid being seen by Westhorpe on her way up.’

‘That’s about it, sir.’

‘And if a certain level of climbing ability is no longer required of our suspect, it looks as if Orlando could be joined in the gallery by a few more suspects. That Monty Mathurin, Cottingham — he’s moved up a few places. We’ll go and call on him.’

‘I’m not aware of an — Orlando, did you say, sir?’

‘Ah, yes. Beatrice’s brother. Interesting man. .’ And Joe reported his findings in Surrey to an intrigued Cottingham.

‘Orlando, though he has the strongest motive for bumping off his sister, would appear to have a watertight alibi. An alibi which Sergeant Armitage is checking this morning.’

Cottingham nodded his approval. Sandilands had a reputation for meticulous checking. He never took anyone or any statement at face value. Everything by the book. Steady police teamwork. He knew his boss would now spend an hour looking carefully through the reports delivered to his desk. But Sandilands was no plodding automaton. Cottingham had seen the man get to the heart of a problem in minutes but Joe’s flashes of inspiration were always backed up by days of evidence-collecting, interrogation and sound use of forensic science. Cottingham smiled. He wondered if Joe was aware of his nickname amongst the lower ranks. Padlock Holmes. It seemed to suit his style. And it was a style that suited Ralph Cottingham. He glanced about him at the opulence of the furniture, the good carpet, the personal telephone, the view over Horseguards, and was cheerfully envious. He sighed. One day, perhaps he might have a bit of luck?

Sandilands was talking again. ‘Ralph, when we’ve finished with this Irishman I’d like you to go straight back to the Ritz. Check the duty rosters. Any witnesses who were about in the corridors at the crucial time. If our bloke emerged from the murder room I’ll guarantee he didn’t use the lift. Check anyway! Again! But then, if he used the stairs, he would have encountered Westhorpe as you say. The third possibility. .’

‘He had a room of his own at the hotel? On the same floor, likely as not? He could have ducked through a doorway before Westhorpe surfaced. We did a preliminary check on Saturday night — there’s a list in the file — but now we know more I’ll be asking different questions.’

‘Draw up a short list of everyone who’d booked accommodation on the fourth floor or above on that night, will you?’ Joe grinned. ‘It’s all moving, Ralph!’

They met at one minute to nine before the door to one of the basement interview rooms. Peering through the small spyhole in the door they saw that their guest was already installed on the hard chair allocated to interviewees. A young detective constable was standing in the at-ease position opposite, avoiding eye contact with his charge.

Joe looked with interest at the Dame’s alleged lover. A tall, rangy man in his mid-thirties, he was sitting in a relaxed manner, one long leg thrown casually over the other and smoking a cigarette. Curly bronze-coloured hair, well-barbered and combed (nothing less than perfection would be accepted by the Ritz management), framed a lean brown face. An intelligent face, Joe decided, watching the grey eyes narrow against the smoke as he took another draw on his cigarette. Joe looked at his mouth. This neglected part of the human face, he always reckoned, could give away clues to character that the eyes were capable of disguising. Narrow lips but well-shaped. A mouth whose strength was outlined by deep lines running down on either side. Lines that could indicate humour and a readiness to laugh. Handsome? Yes, as reported. Attractive to women? He would expect so. Perhaps at some stage he would be lucky enough to be favoured with a judgement on the matter from Westhorpe. For a passing moment Joe wished that she were by his side.

‘Good-looking chap, sir,’ whispered Cottingham, echoing his thoughts. ‘No one’s idea of a villain, I’m sure.’

‘The best-looking bloke I’ve ever set eyes on stuck a knife in the throat of a young child and damn nearly shot me,’ said Joe wryly. ‘Shall we go in and get the measure of this Adonis?’