‘My dear Alleyn,’ he said. ‘I can’t tell you how relieved I am to see you. If anything could lessen the appalling nature of this calamity it would be the assurance that we are in your hands.’ There followed, inevitably, the news that Mr Period was acquainted with Alleyn’s brother and was also an ardent admirer of Alleyn’s wife’s paintings. ‘She won’t remember an old backwater buster like me,’ he said, wanly arch, ‘but I have had the pleasure of meeting her.’

All this was said hurriedly and with an air of great anxiety. Alleyn wondered if Mr Period’s hand was normally as tremulous as it was this morning or his speech as breathless and uneven. As soon as Alleyn decently could do so, he got the conversation on a more formal basis.

He asked Mr Period how long Mr Cartell had been sharing the house and learned that it was seven weeks. Before that Mr Cartell had lived in London where he had been the senior partner of an extremely grand and vintage firm of solicitors, from which position he had retired upon his withdrawal into the country. The family, Mr Period said, came originally from Gloucestershire – Bloodstone Parva, in the Cotswolds. Having got as far as this he pulled himself up short and, unaccountably, showed great uneasiness.

Alleyn asked him when he had last seen Mr Cartell.

‘Ah – yesterday evening. I dined out. At Baynesholme. Before the party.’

‘The treasure hunt?’

‘You’ve heard about it? Yes. I saw them start and then I came home. He was in his room, then, walking about and talking to that – his dog. Great heavens!’ Mr Period suddenly exclaimed.

‘What is it?’

‘Desirée – his – Lady Bantling, you know! And Andrew! They must be told, I suppose. I wonder if Connie has thought of it – but no! No, she would hardly – My dear Alleyn, I beg your pardon, but it has only just struck me.’ He explained confusedly, the connection between Baynesholme and Mr Cartell, and looked distractedly at his watch. ‘They will be here at any moment. My secretary – a delightful gel – and Andrew who is to drive her. I suggested an eleven o’clock start as it was to be such a very late party.’

By dint of patient questioning, Alleyn got this sorted out. He noticed that Mr Period kept feeling in his pockets. Then, apparently recollecting himself, he would look about the room. He opened a cigarette-box and when he found it empty, ejaculated pettishly.

Alleyn said: ‘I wonder if you’ll let me give you a cigarette and smoke one myself: it’s all wrong of course, for a policeman on duty –’ He produced his case.

‘My dear Alleyn! Thank you. Do. Do. So will I. But I should have offered you one long ago, only with all this upset Alfred hasn’t filled the boxes and – it’s too tiresome – I’ve mislaid my case.’

‘Really? Not lost, I hope.’