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‘In an arithmetical progression…’ began Mrs. Bradley, knitting her black brows. She paused.

‘And I wish we could see into the future—say into 1957,’ continued Laura, taking advantage of the pause.

‘Do you? I do not. We have enough here to help us, I think. I expect the police will check the disappearances, under dates, of people in the adjoining counties, and— ’

‘And we could buy all the Ordnance Maps of England and Wales and mark them off,’ said Laura, with enthusiasm. ‘Isn’t it a tallish order, though?’ she added, as the magnitude of the otherwise delightful task came home to her.

‘That remains to be seen,’ Mrs. Bradley replied. ‘Jot down the details of these four disappearances we have already…’

‘That means counting this last one, and, somehow, I feel, it’s different from the rest. Still… oh, I don’t know…’

Mrs. Bradley left her at work and sent for George, the chauffeur.

‘George,’ she said, giving him a slip of paper, ‘I want you to drive to these three places and report to me upon the lie of the land.’

‘Very good, madam,’ replied the sober, stocky, smart and respectable man. ‘What particular aspect of the lie of the land would you be requiring?’

‘I don’t know, George. And I don’t want to put ideas into your head. Just the general lie of the land, let us say, and please don’t question the inhabitants. I want you to let me have your views in a completely unbiassed form.’

‘Very good, madam.’ He glanced at the list he was holding. ‘It will take me all of half a day, madam, to get round these three places. They’re all inside the County boundary, but some of the roads are narrow and all are winding.’

‘Time is of no particular object, George, at present.’

‘Very good, madam. I shall do my very best.’

He returned that evening to present his findings and a written report.

‘The 1939 address, madam, is a small Tudor cottage about two miles beyond the village of Easey. It is situated behind a small copse, is occupied but is up for sale. It is in a remote spot, in spite of being only two miles out of the village. There is one road leading to it. The subsoil seems to be gravel, and there is a small river—a branch of the Frome—nearby. The village boasts an ancient church of Norman origin with fourteenth-century additions, some good Queen Anne and early Georgian houses, another Elizabethan (or earlier) Tudor cottage now used as a blacksmith’s forge which is reputed to be haunted, a small general shop-cum-post-office, and two public houses, a small one called the Kicking Wether and a larger and more modern one called the Storbright Arms. Beyond the cottage, which is on a by-road, is the main road to Salisbury.’

‘Splendid, George.’

‘I have a more detailed report, madam.’ He handed it over. ‘Of the other two addresses, the 1930 one is about a mile and a half to two miles out of the village of Newcombe Soulbury on the road to Yeovil, and the 1921 address is just on this side of Slepe Rock, eight miles south-west (roughly speaking, madam) of Hopham. At Newcombe Soulbury the house consists of two adjoining cottages converted into one and embodying what looks to me like an artist’s studio. I didn’t attempt to examine the building closely, madam, as it appeared to be occupied, but one noticed the conversion of the upper floor with a very large north window. The garden was untended and the curtains were drawn across the downstair windows. The subsoil, as one would expect to find in that locality, is mostly chalk. The house is half-way up a very steep hill, and is situated at least a mile and a half from the railway station at Newcombe Soulbury.’

‘This is marvellous, George! Exactly what I wanted.’

‘The 1921 address, madam, I was unable to locate with exact certainty, failing enquiry of the local inhabitants. My guess is that it has been pulled down and a refreshment shack put up on or near the site. It is very near the sea. At Slepe Rock itself a mushroom sort of hotel has been built with a pull-in for motor coaches and a small car park on the opposite side of the road. The refreshment shack would be incorporated in this enterprise. Slepe Rock, I believe, madam, has only been exploited to any extent since about the year 1935. It was just getting into its stride, as it were, when the war broke out. Before 1935 I should say that the house stood in one of the loneliest places in England, madam. It is in a dip among four or five very large turf-covered hills of the Downs type, and the road which leads down past it to the cove is still not much more than a track. It looks a real old smugglers’ hole to me, madam.’

‘You’ve done wonders, George. Thank you very much. The common factor stands out in almost militant fashion, does it not?’

‘The lonely situations of the respective addresses, madam?’

‘Exactly, George. It is what I hoped for and partly expected. The plot thickens. And now I wonder whether you would like the day off to-morrow? I am going to London and shan’t need you.’

‘Thank you, madam, but, if quite convenient, I should be obliged if you would permit me to drive you to London, for the reason that I would then be able to take my mother to a music hall.’

‘I didn’t know music halls were your cup of tea, George, but I’m delighted to hear that they are!’

‘They are not, as a matter of fact, in the ordinary way, madam, although I enjoy them occasionally. The fact is, madam, that my mother, I have recently discovered, is nourishing a passion for Mr. Max Miller, and chooses to believe that he picks her out as the special recipient of his shafts of wit. Mr. Miller, although you may not be aware of the fact, madam, has a good-natured way of appearing to address himself to the more hysterical female portion of his audience in order to rally and admonish them. This my mother greatly appreciates.’

‘Why does she want you with her?’

‘Well, madam, she does not follow all the more modern references, but she keeps them in mind and I am in request to explain them to her as soon as the performance is over.’

‘Isn’t that rather difficult?’

‘I should select the adjective “embarrassing,” madam. It is not always an enviable task to explain Mr. Miller’s more Athenian epigrams in a crowded Underground train.’

In London Mrs. Bradley made a lightning round of visits and an important telephone call. Her visits, in chronological order, were to her son in his chambers, to the British Museum, to the London Library, to the geological section of the Victoria and Albert Museum, and to a famous archaeologist of her acquaintance. She then rang up O’Hara.

‘I am exceedingly grateful to you for introducing me to a most fascinating affair,’ she said. ‘I have interviewed my son, and also the Chief Constable, and you need have no fear of being arrested as an accessory after the fact of murder. It is not certain yet, in fact, that a murder has been committed. However, the affair is now in the hands of the Chief Constable and the County Police. From time to time I will let you know what progress, if any at all, is made in the enquiry… You would like to help if help is required?… and your cousin, too? Excellent!’

‘Are they still interested?’ asked Laura, who was in the room during the conversation over the telephone.

‘Oh, yes, I think so. And now I must set to work, child.’

‘Golly! What on earth have you been doing all day, then?’

Mrs. Bradley grinned.

‘I think I must study George’s reports with relation to the Ordnance Survey, child. Then, to-morrow I think I shall visit the scenes of these disappearances. It will be very interesting to compare them.’

‘May I come with you?’

‘1 should not think of going without you.’

‘You do think these people have been murdered, don’t you? We ought to try to trace what connection they have with one another, oughtn’t we?’