Leyland hurried back after luncheon to catch the three-twelve. It was essential for him, he said, to see the solicitors; possible that he would have to break his journey at Wallingford on the way back. Mr. Quirk unexpectedly asked him for a lift into Oxford; it was his idea that something might be done towards tracing the movements of the man in the punt before he reached the river at all. His purchases, probably made at Oxford, of provisions for a river tour might yet be remembered by the shop people. Leyland agreed that such investigations would be best carried out by private effort; he was not anxious to start false alarms, still less true alarms, as to the suspicions entertained by the Force. Bredon also applauded the expedition; he himself had a commission for Mr. Quirk to execute in Oxford; as to its precise nature, Angela was pertinaciously inquisitive, her husband obstinately dumb.

Once they were left to themselves, he insisted that they must take a holiday. He was bored, he said, with the very name of Burtell; he had long since ceased to feel the smallest interest as to the whereabouts of either cousin, in this or in a future existence; they would forget their solicitudes, and spend an afternoon mud-larking on the Windrush. Angela had the gift, rare in her sex, of falling in with masculine moods without affectation; and their day was all the more pleasant for being totally unworthy of record. If Thames banishes care by his easefulness, the tributary Windrush is an even more certain remedy; that tempestuous rush over the shallows, those sudden windings, those perils of overhanging trees, demand entire concentration if you are to make headway against the unruly stream. An afternoon spent on the Thames is spent with an old, tried, mature companion, who refreshes you even by his silence; an afternoon on the Windrush is like an afternoon spent with a restless, inquisitive child; you find in perpetual distraction the source of repose. Both Miles and Angela had been stung with nettles, scratched with brambles, tormented by thistles underfoot, lashed with willow-branches, wetted by sudden inundations, tired out by ceaseless paddling, punting, and towing, before they returned to the Gudgeon; the Burtell mystery seemed, by that time, a remote memory of the past, so much of mimic struggle and of miniature history had been fought through in the interval.

Mr. Quirk met them on their return, at about a quarter-past six, cool, polite, and inexhaustibly loquacious. His success with the shops had been only partial; at one large store there had been distinct memories, fortified by “the books,” of a stranger who had made considerable purchases with a view to camping on the river; the date tallied, but unfortunately no mental picture survived of “Mr. Wallace,” still less any legend as to his previous movements. At the same time, in answer to a raised eyebrow, Mr. Quirk was happy to assure Mr. Bredon that his commission had been carried out. Nor was Angela left long in suspense. Dinner was no sooner over than four packs of cards appeared from nowhere, and her husband sat down to his interminable and intolerable game of patience.

“Miles,” she said reprovingly, “you know you aren’t allowed to play patience when you’re on a job! Does this mean you’ve given it up altogether?”

“No, it means that I want to smooth out the creases in my mind. Too much accumulation of evidence always means tangle and brain-fag. I must take my mind off the thing if I’m to see it at arm’s length, and that may mean seeing it from a new angle. Remember Mottram, remember the Load of Mischief, and try not to edge those cards off the table by leaning against it. I shall retire to bed punctually at eleven; have no fears. But meanwhile, leave me to my pasteboard. Go and tell Quirk what a handsome fellow I was when you first knew me.”

The Ingle-room was still a welter of unintelligibly disposed cards, Miles was still wandering to and fro, ruffling his hair as he controlled their destinies, when Leyland looked in next morning. His errand was an urgent one. Ever since Nigel Burtell’s disappearance, the police had naturally intercepted all the correspondence which reached his Oxford lodgings, but hitherto their curiosity had gone unrewarded. There was a healthy crop of bills, but never anything in the nature of a private missive. By that morning’s post⁠—it was Tuesday morning⁠—a single post card had arrived, the address printed in block capitals, the postmark Paddington, the back covered with a series of apparently unrelated figures, which clearly indicated a cipher. “I don’t deny that I had a try at it myself,” confessed Leyland, “though I never was much use at ciphers. It beats me, anyhow, and I thought your husband might make a better job of it. Of course, if he’s taken to patience⁠—”

“I’ll take it in to him,” said Angela. “He can’t do worse than kick me out. You’ve got a copy, I suppose? Very well, I’ll give him the original, and you and I and Mr. Quirk will put our heads together over the copy.”

Bredon hardly looked up when she came into the room. “What? A cipher? Oh Lord! Never mind, prop it up against that inkstand on the table there; I’ll look at it from time to time when I want a rest. Better give me a pencil and a clean sheet of paper, in case it happens to arouse my interest. But it’s probably one of these insoluble ones. Good. And don’t forget to shut the door gently.”

“We mustn’t hope for much from him,” admitted Angela as she returned to the parlour⁠—“the refectory” Bredon always called it. “Do they use ciphers much in the States, Mr. Quirk? Now, let’s have a look at it.”

The cipher, in case the reader cares to try his hand at it, was not at first sight very illuminating. It consisted of a row of figures, with no other mark, no spacing even, to guide in their interpretation. They ran thus:

“9123468537332006448121021817841607954824103712559441029152917904.”

“Sixty-four in all,” commented Leyland. “It’s obviously impossible that one cipher should stand for one letter, because that means your alphabet is reduced to ten letters. They must be groups of figures, then, that represent letters; and they can’t be groups of three, five, six, or seven, supposing the groups to be uniform, because that wouldn’t divide out right. I take it, then, that they are groups of two, four, or eight. The trouble is, you see, there are no repetitions. That’s to say, if you make the groups eights or fours there are no repetitions at all, and, even if you make the groups twos, the only repetitions you get are 91 and 37, each with a single repetition.”

“And that’s nonsense, isn’t it?” agreed Angela. “Because it would have to mean that the message used all the letters of the alphabet and four nonexistent letters, and only repeated itself twice.”

“I recollect,” said Mr. Quirk, “one of the leading cryptographers in the States telling me that letter-ciphers had been practically abandoned nowadays, and word-ciphers were used instead. Say, isn’t it likely a message of sixteen words, instead of sixteen letters?”

“And if it is, we can take our boots off and go to bed,” replied Leyland. “You can’t solve a word-cipher on a single message, unless you’ve got the key beforehand. Stands to reason they wouldn’t be using any of the recognized codes. Well, here’s for it.”

Their brows were knitted over it three-quarters of an hour later, when Bredon suddenly shouted from the door of the Ingle-room:

“The groups are threes.”

“Go back and count again,” retorted Angela indignantly. “You can’t have even looked at the thing. Three won’t go into 64.”

“You will go the wrong way about these things. You sit over the cipher and try to worry it out, and of course it won’t come out. But if you do as I do, keep taking a look at it and then going away and forgetting about it, you come to it fresh every time. And then, with luck, you see the arrangement of groups which makes the whole thing look natural. It’s the eye does it, not the brain.”

“Well, how do you work out the threes, anyhow?”

“Don’t count up to nine; count up to twelve. You can count tens, elevens, or twelves as if they were single units.”

“Have you read it yet?”

“No, but you ought to be able to do it now. I’m busy.”

They rewrote the cipher accordingly, and it certainly did look more promising. “912/346/853/733/200/644/812/1021/817/841/607/954/824/1037/1255/944/1029/152/917/904.”

Bredon came down to luncheon rubbing his hands, with the intimation that he had “got it out.”

“The cipher?”

“No, the patience. It was a long sight more difficult. Leyland gone back to Oxford?”

“No, he’s scouring round the country investigating another of Mr. Quirk’s great ideas. You do give us all plenty of exercise, I must say. Come on, Mr. Quirk, spill it.”

With some hesitation, Mr. Quirk unfolded his great idea. He argued, in the first place, that it must be a book-cipher of some description; that was the only possible method for a couple of amateur cryptographers. If it was a book, it must be a book which was in the possession of both parties. “Now, we know Nigel Burtell was one of the two parties who’s the other? I put it to you⁠—Derek Burtell!”

“Derek! But you’ve spent a week trying to convince us that they’re both in a watery grave.”

“I must admit that I have been led to revise my conclusions very considerably. One of our greatest American thinkers has said that it’s only a fool who doesn’t acknowledge his mistakes. Now, according to my latest view both those two cousins are alive, and what’s more, they’re in correspondence with one another.”

“This all opens up very wide possibilities. But let us have the great idea.”

Stripped of some circumlocution, the great idea was as follows. The cipher must have been prearranged between the two cousins, possibly just before they parted, but more probably in the course of their tour. It appeared that, for whatever reason, they had separated on the Sunday night, Nigel sleeping at Millington Bridge, as we have seen, and Derek presumably finding a bed somewhere else. It looked, therefore, as if the cousins had meant to part for good on the Sunday night, keeping the cipher as a means of correspondence. Each, then, had already access to the book from which the cipher was taken; Nigel at Millington Bridge, and Derek⁠—where? Derek could not have been far off; they had been on the river till late, and there were no last trains to be caught. Derek, therefore, was somewhere close at hand; Mr. Quirk had been looking at the map, and he suggested White Bracton, a village inland, it was true, but only a mile and a half by road from the bridge. Assuming that Derek spent the night there, the book which gave the clue to the cipher had been, and probably still was, at the White Bracton Inn.

“Isn’t it a brainwave?” said Angela. “Wasn’t it a very remarkable idea?”

“It was,” Bredon admitted, “a very remarkable idea. But it’s rough luck on Leyland to be sent scouting across to White Bracton for the book, when of course, equally, it’s here.”

“What’s that?” asked Mr. Quirk.

“Of course it’s here. Any country hotel keeps a railway timetable. Most country hotels don’t keep Bradshaw, which fortunately narrows the area of our search.”

“Oh, oh, oh, how perfectly beastly of you!” moaned Angela. “You mean the groups were the names of trains?”

“Of course they were. That’s the advantage of playing patience. You come fresh to the puzzle every time; and about the sixteenth time those figures suddenly stand out in your mind as train times⁠—8:24, 10:37, 12:55, and so on. Of course the extra noughts in 200 and 607 are only to make the cipher look uniform. Once you’ve got the idea, you see that it must be so. The cipher runs up to 12 because the clock runs up to twelve. There are a lot of eights and nines about, because most morning trains start at eight something or nine something. Oh, it’s as clear as daylight.”

“Except what the thing means,” Angela pointed out.

“Well, obviously the time of a train can only suggest a word or a letter if you connect it with the name of the station it starts from. I assume you have to take a page of the timetable, and find a station from which the first train or the last train⁠—the first train, I suppose, from the nature of the figures⁠—starts at nine-twelve, then one from which the first train starts at three forty-six, and so on. It must be Great Western, because it’s the only railway in these parts. It must be a main line, or you wouldn’t get a train starting as early as three forty-six. Oh, have you got a timetable there, Mr. Quirk?”

Mr. Quirk had produced a local guide from somewhere, and was scanning its pages. “Here, you’d better do this,” he said. “I never was much good with Bradshaw.”

“Well, we’ll try, anyhow. Take down, please, Mrs. Bredon. London, Reading, Chippenham, Weymouth and Taunton; that sounds good enough. Dash, it’s not so easy after all.⁠ ⁠… Hullo, here’s a three forty-six in the morning starting from Oxford. Nine-twelve⁠—that would be rather a one-horse sort of place; here you are, Hungerford. And Woodborough, wherever that is, leads off with an eight fifty-three.”

“Hungerford Oxford Woodborough. What a jolly message to get!” said Angela.

“Oh, why did they never teach you acrostics when you were young? Look at the initials⁠—‘How’; what’s wrong with that?”

“Miles, you are a pet sometimes. This is fearfully inciting. None for the seven thirty-three.”

“Moderately important, but not very important. I think we read straight down the page as far as possible. Seven thirty-three; that’s Devizes. An arrival, really, but he wouldn’t notice that. And two o’clock must be some terrific big junction⁠ ⁠… no, it isn’t.⁠ ⁠… Good God, think of arriving at Ilfracombe at two in the morning!”

“Di, then the next one will be another d,” suggested Angela. “Try Didcot.”

“Didcot it is; and Did it is. Now, eight-twelve is a more local sort of time; Aldermaston will do. What happens, I wonder, when there aren’t enough stations to go round? Oh, I suppose you take the second earliest train.”

“Miles, this is too exciting; I can’t stand it. Let’s just take down the names, and read the initials afterwards.”

“All right. Here goes.” And it went, until the last group was registered, and Angela, who had been keeping her hand over the page, revealed the following names in column formation:

“Hungerford Oxford Woodborough Devizes Ilfracombe Didcot Aldermaston Lavington Midgham Athelney Chippenham Upwey Thatcham Upwey Paddington Dorchester Edington Reading Evershot Kintbury.”

“Yes,” said Bredon. “Not a bad stunt. He missed out Theale, which ought to come before Thatcham, otherwise he seems to have made no mistakes.”

“Miles, don’t be so provoking! Don’t you see that this message is most frightfully important?”

“Oh,” said Bredon. “You think it is?”