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The blushing Ormond accordingly made his way to the cottages, where, much to his relief, he found the men-folk absent and the women employed at the wash-tub. At first he was none too cordially received, but, after he had stripped off his uniform tunic and given young Mrs Pollock a hand with the mangle and carried two buckets of water from the well for Mrs Moggeridge, the atmosphere became less frigid, and he was able to put his questions.

But the results were disappointing. The women were able to give very good reasons for having seen nothing of any horse or rider on Thursday, 18th. The family dinners had been eaten as usual at twelve o’clock, and after dinner there was, the ironing to finish. There was a sight of washing, as Mr Ormond could see for himself, for Mrs Pollock and Mrs Moggeridge to deal with. There. was Granpa Pollock and Granma Pollock and Jem, what was that particular about his shirts and collars, and young Arthur and Polly and Rosie and Billy Moggeridge and Susie and Fanny and little David and the baby and jenny Moggeridge’s Baby Charles what was a accident what Mrs Moggeridge was looking after, jenny being out in service, all of which do make work and often the washing don’t get finished till Saturday and you couldn’t be surprised, what with the men’s jerseys and stockings and one thing and another and every drop of water having to be fetched. Nobody hadn’t been out of the house that afternoon, leastways, only at the back, not till after three o’clock for sure, when Susie took the potatoes out into the front garden to peel for supper. Susie see a gentleman then dressed in shorts and carrying a knapsack, come up the lane from the shore, but it wouldn’t be him as Mr Ormond wanted to know about, because he came in later on with a lady and told them about the body being found. Mr Ormond was quite pleased to hear about this gentleman, nevertheless. The gentleman was wearing horn-rimmed spectacles and he came; up the lane ‘somewhere between half-past three and four,’ and went straight off along the road towards Lesston Hoe. This must, of course, have been Perkins, and a brief calculation showed that this time fitted in reasonably well both with his own story and Harriet’s. Harriet had met him about half-a-mile further on at four o’clock. But that proved nothing, and the crucial period between 1.30 and three o’clock remained as obscure as before.

Puzzled and dissatisfied, Ormond chugged-slowly back to Darley, noticing as he went how little of the beach could actually be seen from the road. It was, in fact, only for about a mile on either side of the Flat-Iron that the road ran actually close to the edge of the cliffs, Here there was the breadth of a wide field between them and the height of the cliff hid the sands from view. It would not really have been so risky a business as one might suppose to ride in broad daylight to commit a murder at the Flat-Iron, and it was hardly surprising that no traveller on the road had seen the bay mare pass. But had she passed? There was the horseshoe to prove it and there was the ring-bolt on the rock to suggest it. It was the ring-bolt that was chiefly, bothering Constable Ormond, for if it was not there to hold the horse, what was it for? And Wimsey’s latest theory had made it necessary for the horse to be released and sent back before the Flat-Iron was reached.

And that was a very hit-or-miss theory, from the murderer’s point of view. How could he be sure that the animal would go back and would not hang about the place attracting attention? In fact, after being galloped violently for four and a half miles, it was far more likely to take matters easy. If one was to ignore the ring-bolt, was it not possible that the bay mare had been tethered somewhere, to be picked up later? There were weighty objections to that. There was no post or groyne along the shore to which she could have been tied, and if the murderer had brought her close in under the cliff, then he would have had to leave two lines of footprints — the mare’s in going and his own in returning. But he might have argued that this would not greatly matter if it was at some distance from the Flat-Iron. It might just be worth while to turn back and examine the shore from that point of view.

He did so, riding right up as far as the Flat-Iron itself, scrambling down by the same path that Harriet had used, and working his way along at the foot of the cliff in the direction of Darley: After about half-an-hour’s search, he found what he was looking for. There was a recess in the cliff where at some time there had been a fall of rock. Jammed in among the boulders was a large wooden post, which had apparently formed part of a fence — erected, no doubt, to keep men or animals from straying upon the dangerous part of the cliffs. If, the bay mare had been brought in there, she might easily have been tethered to the beam, while, owing to the overhang-of the cliff and the accumulation of fallen, stones, she would have been practically invisible, either from the sea or from the road above.

This discovery was gratifying, but it would have been more gratifying if Ormond could have found any positive indication that this had really, happened. The sand was so loose and dry that no recognisable marks-could be expected above high-water mark, nor, though he examined the wooden post very carefully with a lens, could he find any indications of its having been used as a horse-post. A strand of rope fibre, a horse-hair or two would have been better than a bank-note to Ormond at that moment, while a bunch of horse-droppings would have been worth its weight in rubies. But none of these simple, homely sights rewarded his anxious gaze. There was the piece-of timber and there was the recess in the cliff, and that was all.

Shaking his head, he walked to the edge of the water and set out at a brisk trot for the Flat-Iron. He found that by pelting along as fast as a heavyish, fully-clothed young constable could be expected to pelt on a hot summer’s day, he could reach the rock in twelve minutes exactly. It was too far. Five minutes’ walk was the most that Weldon could possibly have allowed himself by Wimsey’s calculation. Ormond again scrambled up the cliff, remounted his bicycle and began to do sums in his head.

By the time he arrived at the police — station, these sums had taken a definite form.

‘The way I look at it is this, sir,’ he said to Superintendent Glaisher. ‘We’ve been going along the line that it was Perkins that was providing the alibi for Weldon. Suppose it was the other way round. Suppose Weldon is providing the, alibi for Perkins. What do we know about Perkins? Only that he’s a school-teacher and that nobody seems to have kept tabs on him since last May. Now, he says he slept at Wilvercombe and didn’t start away that morning till one o’clock. That’s a bit thick to start with. The only proof he offers of that is that he bought some stuff at a chemist’s — he doesn’t remember the chemist and he isn’t clear about the time. Now we know that Weldon was in Wilvercombe that morning, and his time isn’t altogether accounted for, either. Supposing those two had met and fixed it all up there. Perkins comes along to Darley and gets the horse.’

‘We’ll have to find out whether anyone saw him pass through the village.’

‘That’s so, sir, We must check that up, naturally. But say he really got there at about 1.15 or so. Then he’d have plenty of time to get along with the mare, tie her up where that there post is, and buzz along on foot to the rock and commit his murder.’.

‘Wait a moment,’ said Glaisher. This place is fifteen minutes’ quick walk from the rock.’

‘More like fifteen minutes’ run, sir.’

‘Yes, but over wet sand; through water, actually. Shall we call it just over a mile? Right. Then that leaves three and a half miles for the mare. At eight miles an hour, that needs — eight miles in sixty minutes, one mile in sixty over eight’—Glaisher always had to work these rule-of-three problems out on the corners of blotting-pads; it had been the worst stumbling-block he had had to overcome on his way to promotion—‘thirty multiplied by seven over eight — oh, dear! divide by two — multiply — divide’