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'Mon ami,' said Poirot, 'you make one error. You do not allow for the fact that a man who had decided to make away with another man or with himself in a figurative sense - might be that rare machine, a man of method. He might bring intelligence, talent, a careful calculation of detail to the task; and then I do not see why he should not be successful in baffling the police force.'

'But not you , I suppose?' said Japp good-humouredly, winking at me. 'He couldn't baffle you, eh, Monsieur Poirot?'

Poirot endeavoured, with a marked lack of success, to look modest.

'Me, also! Why not? It is true that I approach such problems with as exact science, a mathematical precision, which seems, alas, only too rare in the new generation of detectives!'

Japp grinned more widely.

'I don't know,' he said. 'Miller, the man who's on this case, is a smart chap. You may be very sure he won't overlook a footprint, or a cigar-ash, or a crumb even. He's got eyes that see everything.'

'So, mon ami,' said Poirot, 'has the London sparrow. But all the same, I should not ask the little brown bird to solve the problem of Mr Davenheim.'

'Come now, monsieur, you're not going to run down the value of details as clues?'

'By no means. These things are all good in their way. The danger is they may assume undue importance. Most details are insignificant; one or two are vital. It is the brain, the little grey cells' - he tapped his forehead - 'on which one must rely. The senses mislead. One must seek the truth within - not without.'

'You don't mean to say, Monsieur Poirot, that you would undertake to solve a case without moving from your chair, do you?'

'That is exactly what I do mean - granted the facts were placed before me. I regard myself as a consulting specialist.'

Japp slapped his knee. 'Hanged if I don't take you at your word. Bet you a fiver that you can't lay your hand - or rather tell me where to lay my hand - on Mr Davenheim, dead or alive, before a week is out.'

Poirot considered. 'Eh bien, mon ami, I accept. Le sport, it is the passion of you English. Now - the facts.'

'On Saturday last, as is his usual custom, Mr Davenheim took the 12.40 train from Victoria to Chingside, where his palatial country place, The Cedars, is situated. After lunch, he strolled round the grounds, and gave various directions to the gardeners. Everybody agrees that his manner was absolutely normal and as usual. After tea he put his head into his wife's boudoir; saying that he was going to stroll down to the village and post some letters. He added that he was expecting a Mr Lowen, on business. If he should come before he himself returned, he was to be shown into the study and asked to wait. Mr Davenheim then left the house by the front door, passed leisurely down the drive, and out at the gate, and - was never seen again. From that hour, he vanished completely.'

'Pretty - very pretty - altogether a charming little problem,' murmured Poirot. 'Proceed, my good friend.'

'About a quarter of an hour later a tall, dark man with a thick black moustache rang the front-door bell, and explained that he had an appointment with Mr Davenheim. He gave the name of Lowen, and in accordance with the banker's instructions was shown into the study. Nearly an hour passed. Mr Davenheim did not return. Finally Mr Lowen rang the bell, and explained that he was unable to wait any longer, as he must catch his train back to town.

'Mrs Davenheim apologized for her husband's absence, which seemed unaccountable, as she knew him to have been expecting the visitor. Mr Lowen reiterated his regrets and took his departure.

'Well, as everyone knows, Mr Davenheim did not return. Early on Sunday morning the police were communicated with, but could make neither head nor tail of the matter. Mr Davenheim seemed literally to have vanished into thin air. He had not been to the post office; nor had he been seen passing through the village. At the station they were positive he had not departed by any train. His own motor had not left the garage. If he had hired a car to meet him in some lonely spot, it seems almost certain that by this time, in view of the large reward offered for information, the driver of it would have come forward to tell what he knew. True, there was a small race-meeting at Entfield, five miles away, and if he had walked to that station he might have passed unnoticed in the crowd. But since then his photograph and a full description of him have been circulated in every newspaper, and nobody has been able to give any news of him. We have, of course, received many letters from all over England, but each clue, so far, has ended in disappointment.

'On Monday morning a further sensational discovery came to light.

Behind a portière in Mr Davenheim's study stands a safe, and that safe had been broken into and rifled. The windows were fastened securely on the inside, which seems to put an ordinary burglary out of court, unless, of course, an accomplice within the house fastened them again afterwards. On the other hand, Sunday having intervened, and the household being in a state of chaos, it is likely that the burglary was committed on the Saturday, and remained undetected until Monday.'

'Précisément,' said Poirot dryly. 'Well, is he arrested, ce pauvre M.

Lowen?'

Japp grinned. 'Not yet. But he's under pretty close supervision.'

Poirot nodded. 'What was taken from the safe? Have you any idea?'

'We've been going into that with the junior partner of the firm and Mrs Davenheim. Apparently there was a considerable amount in bearer bonds, and a very large sum in notes, owing to some large transaction having been just carried through. There was also a small fortune in jewellery. All Mrs Davenheim's jewels were kept in the safe. The purchasing of them had become a passion with her husband of late years, and hardly a month passed that he did not make her a present of some rare and costly gem.'

'Altogether a good haul,' said Poirot thoughtfully. 'Now, what about Lowen? Is it known what his business was with Davenheim that evening? '

'Well, the two men were apparently not on very good terms. Lowen is a speculator in quite small way. Nevertheless, he has been able once or twice to score a coup off Davenheim in the market, though it seems they seldom or never actually met. It was a matter concerning some South American shares which led the banker to make his appointment.'

'Had Davenheim interests in South America, then?'

'I believe so. Mrs Davenheim happened to mention that he spent all last autumn in Buenos Aires.'

'Any trouble in his home life? Were the husband and wife on good terms?'

'I should say his domestic life was quite peaceful and uneventful.

Mrs Davenheim is a pleasant, rather unintelligent woman. Quite a nonentity, I think.'

'Then we must not look for the solution of the mystery there. Had he any enemies?'

'He had plenty of financial rivals, and no doubt there are many people whom he has got the better of who bear him no particular goodwill. But there was no one likely to make away with him - and, if they had, where is the body?'

'Exactly. As Hastings says, bodies have a habit of coming to light with fatal persistency.'

'By the way, one of the gardeners says he saw a figure going round to the side of the house towards the rose-garden. The long french window of the study opens on to the rose-garden, and Mr Davenheim frequently entered and left the house that way. But the man was a good way off, at work on some cucumber frames, and cannot even say whether it was the figure of his master or not. Also, he cannot fix the time with any accuracy. It must have been before six, as the gardeners cease work at that time.'