I paused. ‘Well?’ I asked, for I felt that I had put my finger on all the vital facts.

Poirot looked at me pityingly, shaking his head very gently. ‘Mon pauvre ami! But it is that you have not the gift! The important detail, you appreciate him never! Also, your reasoning is false.’

‘How?’

‘Let me take your four points.’

‘One: Mr Lowen could not possibly know that he would have the chance to open the safe. He came for a business interview. He could not know beforehand that Mr Davenheim would be absent posting a letter, and that he would consequently be alone in the study!’

‘He might have seized the opportunity,’ I suggested.

‘And the tools? City gentlemen do not carry round housebreaker’s tools on the off chance! And one could not cut into that safe with penknife, bien entendu!’

‘Well, what about Number Two?’

‘You say Lowen had a grudge against Mr Davenheim. What you mean is that he had once or twice got the better of him. And presumably those transactions were entered into with the view of benefiting himself. In any case you do not as a rule bear a grudge against a man you have got the better of—it is more likely to be the other way about. Whatever grudge there might have been would have been on Mr Davenheim’s side.’

‘Well, you can’t deny that he lied about never having left the study?’

‘No. But he may have been frightened. Remember, the missing man’s clothes had just been discovered in the lake. Of course, as usual, he would have done better to speak the truth.’

‘And the fourth point?’

‘I grant you that. If Kellett’s story is true, Lowen is undeniably implicated. That is what makes the affair so very interesting.’

‘Then I did appreciate one vital fact?’

‘Perhaps—but you have entirely overlooked the two most important points, the ones which undoubtedly hold the clue to the whole matter.’

‘And pray, what are they?’

‘One, the passion which has grown upon Mr Davenheim in the last few years for buying jewellery. Two, his trip to Buenos Aires last autumn.’

‘Poirot, you are joking?’

‘I am serious. Ah, sacred thunder, but I hope Japp will not forget my little commission.’

But the detective, entering into the spirit of the joke, had remembered it so well that a telegram was handed to Poirot about eleven o’clock the next day. At his request I opened it and read it out:

‘“Husband and wife have occupied separate rooms since last winter.”’

‘Aha!’ cried Poirot. ‘And now we are in mid June! All is solved!’

I stared at him.

‘You have no moneys in the bank of Davenheim and Salmon, mon ami?’

‘No,’ I said wondering. ‘Why?’

‘Because I should advise you to withdraw it—before it is too late.’

‘Why, what do you expect?’