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‘At any rate,’ said Wimsey, ‘I think we’ve got the actual time of the death pretty well fixed by now. That ought to help.’

“Yes,” admitted Inspector Umpelty, ‘if what you and the lady tell me is correct, that does seem to settle it. Now but what I’d like a doctor’s opinion on it, no offence to you. But I think you’re right, all the same. It’s a great pity you happened — to fall, asleep when you did, miss.’ He looked reproachfully at Harriet.

But wasn’t it lucky I was there at all?

The Inspector agreed that it was.

‘’And taking this question of the time as settled,’ he went on, ‘we’ve got some information to hand now that may clear matters up, a bit. At least, from all I can see, it just goes to show that this murder-stuff is clean impossible, as I’ve said it was all along. But if we prove that, then we’re all right, aren’t we?’

The conference was taking place in the Inspector’s cosy little villa in the suburbs of the town. Rising, Mr Umpelty went to a cupboard and extracted a large sheaf of official reports.

‘You see, my lord, we haven’t been idle, even though suicide looks more probable than anything else on the face of things. We had to take all the possibilities into account, and we’ve gone over the district with, as you might say, a magnifying glass.’

After an inspection of the reports, Wimsey was obliged to admit that this boast seemed justified. Chance had helped the police very considerably. An application had recently been made by the local authorities to the County Council to have the coast-road between Lesston Hoe and Wilvercombe put into better repair. The County Council, conscious that times were bad and that money was tight; had courteously replied that it did not think there was sufficient traffic along the said coast-road to justify the proposed expenditure. As a result of these negotiations, persons had been appointed (at a modest wage) by the County Council to take a census of the vehicular traffic passing along the said road, and one of these watchers had been stationed, during the whole of, Thursday, 18 June, at the junction formed by the coast-road and the high road from Lesston Hoe to Heathbury. At the other end of of the twelve miles or so which interested the detectives: was Darley Halt, where, as Harriet had already discovered for herself, the gates were always shut, unless particularly summoned to be opened for a passing vehicle. On either side of the railway gates was a wicket for foot passengers, but this was of the kind that does not admit anything so large even as a push-cycle. It was clear, therefore, that unless the hypothetical murderer had come on foot, he must have been seen at one end or other of the road, or else have come from some intermediate farm. During the past four days, the police had carefully investigated the bona fides of every traveller over this section of the road, Every car, motor-cycle, push-cycle, van, lorry, wagon and beast had been laboriously checked up and accounted for. Nothing had been unearthed to suggest suspicion of any kind. Indeed, all the persons using the road were local inhabitants, well known to all the police officers, and each one of them had been able to give an exact account of his or her movements during. the day. This was not so surprising as it may appear, since nearly all of them were either tradesmen, accomplishing a given — round; in a given time, or farmers with business on their land or in the adjacent towns, who had witnesses to prove their departure and arrival. The only persons whose times could not very well be checked were those who loitered attendance, upon cows and sheep in transit; but, apart from the extreme improbability of these rustics having gone out of their way, to cut a gentleman’s throat with an Endicott razor, Inspector Umpelty was quite ready to vouch personally for all of them.

‘In fact, my lord,’ he said, ‘you may take it from me that all these people we have checked up are all right. You can put them right, out of your mind. The only possibility left now for your murderer is that he came by sea, or else on foot along the shore from either Wilvercombe or Lesston Hoe, and, as this young lady says, Wilvercombe is the more probable direction of the two, because, anybody coming — from Lesston Hoe would have seen her and put his crime off’ to a more convenient season, as Shakespeare says.’

‘Very well,’ said Wimsey. ‘All right. We’ll admit that. The murderer didn’t take any sort of wheeled conveyance for any part of the journey. Still, that leaves a lot of possibilities open. We’ll wash out the Lesston Hoe side altogether and only take the Wilvercombe direction. We now have at least three suggestions. One: the murderer walked by the road from Wilvercombe or Darley, came down on to the beach at some point out of view from the Flat-Iron, — and thence proceeded by the shore. Two: he came from one of those two cottages where the, fishermen live (Pollock and Moggeridge, I thing you said the names were). You don’t mean to say you’ll answer personally for those men, do you, Inspector?’

‘No, I don’t — only they weren’t there,’ retorted the Inspector, with spirit. ‘Moggeridge and his two sons were over in Wilvercombe, buying some stuff there — I’ve got witnesses to that. Old Pollock was out in his boat, because Freddy Bares, saw him, and his eldest boy was probably with him. We’re going to pull those two in, and that’s why I said the murderer might have come by sea. The only other Pollock is a boy of about fourteen, and you can’t suppose it was him that did it, nor yet any of the women and children.’

‘I see. Well then. Three: the murderer walked the whole way along the coast from Darley or Wilvercombe. By the way, didn’t you say there was somebody camping out along there, just beyond Darley Halt.’

‘Yes,’ said Harriet, ‘a square-built sort of man, who spoke — well, not quite like a countryman — like a gentleman of the country sort.’

‘If anybody had passed that way, he might have seen him.’

‘So he might,’ replied the Inspector, ‘but unfortunately we haven’t laid hands on that particular gentleman, though we’ve got inquiries out after him. He packed: up and departed early on Friday morning, taking his belongings in a Morgan. He’d been camping at the bottom of Hinks’s Lane since Tuesday, and gave the name of Martin.’

‘Is that so? And he disappeared immediately after the crime. Isn’t that a trifle suspicious?’

‘Not a bit.’ Inspector Umpelty was quite triumphant. ‘He was having his lunch at the Three Feathers in Darley at one o’clock and he didn’t leave till 1.30. If you’ll tell me how a man could walk four and a half miles in half-an-hour, I’ll get a warrant made out for Mr Martin’s arrest.’

‘Your trick, Inspector. Well — let’s see. Murder at two o’clock — four and a half miles to go. That means that the murderer can’t have passed through Darley later than 12.50 at the very outside. That’s allowing him to do four miles an hour, and since he would have to do at least part of the distance along the sand it’s probably an over-estimate. On the other hand, he wouldn’t be likely to do less than three miles an hour. That gives 12.30 as his earliest time — unless, of course, he sat and talked to Alexis for some time before he cut his throat.’

‘That’s just it, my lord. It’s all so vague. In any case, Mr Martin isn’t much good to us, because he spent Thursday morning in Wilvercombe — or so he mentioned to the landlord of the Feathers.’

‘What a pity! He might have been a valuable witness. I suppose you’ll go on looking for him, though it doesn’t seem as if he’d be very much good to us. Did anybody notice the number of his Morgan?’