The Mystery of the Downs
Page 23
CHAPTER XXIII
CREWE went to the table and picked up the plan.
"My first impression was that the circle of figures representedsome form of letters of the alphabet arranged on what is called thecardboard or trellis cipher, in which a message is concealed byaltering the places of the letters without changing their powers. Suchmessages are generally written after the Chinese fashion--upwards anddownwards--but there is no reason why a circle should not be used toconceal the message. In this case I did not expect to find a messagehidden in the circle, but rather, the key to the solution of theletters above the circle, which, I was convinced, formed the realcryptogram.
"The recurring T's and M's in the top line seemed to indicate that itwas some form of changed letter cipher, complicated by having to beread in connection with the figures in the circle, which representedother letters of the alphabet. The numbers, representing an ascendingseries from 6 to 89, with one recurring 6, suggested the possibilityof this form of cryptogram having been used. The numbers in thecentre suggested a sum, which, when done, would throw some light onthe arithmetical puzzle in the centre of the circle by division,subtraction, or multiplication.
"I worked for a solution on these lines for some time, but ultimatelycame to the conclusion that the solution did not lie within them. I amnot an arithmetician, but my calculations told me enough to make merealize that I was on the wrong track.
"I next attempted to ascertain if the two mysterious messages--thelines on the top and the circle of figures--were two separate messagesread independently of one another. I did not think they were, but Idetermined to put it to the test. Obviously, if they were, the topline was merely a changed letter cipher, and nothing more. These areusually easy to decipher because of the frequency with which certainletters recur. In English the letter that occurs oftenest is E, then T,then A, O, N, I, then R, S, H; the others in lessening frequency downto J and Z, which are the least used letters in the English alphabet.The recurring letters in our cryptogram are T's and M's. Using theseas a basis to give me the key, I tried all likely combinations on thechanged letter basis, but without success.
"I came back to my original idea that the figures in the circlewere the solvent of the line of letters above, and concentrated myefforts in attempting to discover their meaning. I finally came to theconclusion that the figures represented the pages or lines of somebook."
"Like the cryptograms I used to solve when I was at school," suggestedMarsland, with a smile.
"Rather more difficult than that. In that form of cryptogram rows offigures are turned into words once you hit on the right book. Thiscryptogram is much more ingenious, for it consists of three parts--aline of meaningless letters and a circle of equally meaninglessfigures, with other figures within it, and some plain English versesof Scripture, the whole probably interdependent. If the circle offigures represented some book necessary to the solution of the wholecryptogram, the first thing to find out was the book from which thefigures had been taken. I had not much difficulty in arriving at theconclusion that this book was a large brass-bound family Bible I saw atCliff Farm."
"I suppose the texts on the bottom of the sheet suggested that idea toyou?" said Marsland.
Crewe shook his head.
"I've learnt to mistrust guesswork," he said. "It would be a jump atrandom to come to the conclusion that the cryptogram had been drawnon the fly-leaf of a Bible because it contained some Scripture texts.There is no connection between the facts. In fact, it seemed unlikelyto me at first that a religious man like the old farmer would havemutilated his family Bible for such a purpose. I was inclined to theview that he had taken a fly-leaf from one of his _Leisure Hour_ boundvolumes, which at the farm range from 1860 to the early seventies--aperiod of years when this kind of glossy thick paper was much used forfly-leaves by English printers. But while I was examining the sheetthrough the magnifying glass I detected this mark on the edge, whichproved conclusively to me that the cryptogram had been drawn on thefly-leaf of the family Bible. Have a look at it through the glass--youcannot detect it with the naked eye."
Crewe held the sheet edgeways as he spoke, and pointed to one of theouter corners. Marsland gazed intently through the glass, and was ableto detect a minute glittering spot not much larger than a pin's point.
"I see it," he said, relinquishing the glass. "But I do not understandwhat it means."
"It is Dutch metal or gold-leaf. The book from which this sheet wascut was gilt-edged. That disposes of the volumes of _Leisure Hour_and other bound periodicals, none of which is gilt-edged. When I waslooking at the books at the farm I noticed only two with gilt-edgedleaves. One was the big family Bible, and the other was a large, oldfashioned _Language of Flowers_. But this sheet could not have been cutfrom _The Language of Flowers_."
"Why not?"
"Because it has two rounded corners. As a rule, only sacred books andpoetry are bound with rounded corners. In any case, I remember that_The Language of Flowers_ at the farm is square-edged. Therefore thesheet on which the cryptogram has been drawn was cut from the Bible.
"The next question that faced me was how the numbers had been used:they did not represent the numbers of the pages, I was sure of that.The Bible is a book in which figures are used freely in the arrangementof the contents. The pages are numbered, the chapters are dividedinto verses which are numbered, and there is a numbered table ofcontents at the beginning of each chapter. Obviously, the Bible isan excellent book from which to devise a cryptogram of numbers owingto the multiplicity of figures used in it and the variety of ways inwhich they are arranged. I found both a Bible and Prayer Book in thebookshelves, here, and set to work to study the numerical arrangementof the chapters, the divisions of the verses, and the arrangement offigures at the head of the chapters."
"It was while I was thus engaged that I remembered that at thebeginning of the authorised version of the Bible is inserted a tableof the books of the Old and New Testaments, the pages on which theybegin, and the number of chapters in each. Here was the possibilityof a starting-point, sufficiently unusual to make a good concealment,yet not too remote. I turned to the table, and, on running my eye downit, I saw that the Psalms, and the Psalms alone, contain 150 chapters.Now, the first line of central figures in the cryptogram is 150. I wasreally fortunate in starting off with this discovery, because otherwiseI might have been led off the track by the doubling and trebling of the3 in the second line of central figures, and have wasted time tryingto fathom some mystic interpretation of the 9--a numeral which hasalways had a special significance for humanity: the Nine Muses, theNine Worthies, 'dressed up to the nines,' and so on. But with 150 asthe indication that the cryptogram had been composed from the Book ofPsalms, it was obvious that the next line of numerals in the centredirected attention to some particular portion of them. As there are not396 verses in any chapter of the Psalms----"
"Just what I was going to point out," broke in Marsland.
"Quite so. But it was possible that 396 meant Psalm 39, 6. Therefore Iturned to the thirty-ninth Psalm. Verse six of that Psalm reads:
"'Surely every man walketh in a vain shew: surely they are disquietedin vain: he heapeth up riches, and knoweth not who shall gather.'"
"Appropriate enough," commented Marsland.
"There remained the final 6, under the 396, to be explained, beforeI was able to start on the table which had been used to build up thecryptogram. The fact that the figures in the outside circle start at6 indicated that there was some connection between it and the inner6. I came to the conclusion that the inner 6 meant one of two things:either the designer preferred to start from the number 6 because hethought the figure 1 was too clear an indication of the commencementof his cryptogram, or else he made his start from the sixth letter ofthe text. I thought the former the likelier solution, but I tried themboth, to make sure. The first five figures on the latter solution gaveme a recurring Y, which indicated that I was on the wrong track becauseit was essential there should be no recurring le
tters. There are norecurring letters in the other key, as the table shows:
6 7 8 9 10 11 12 13 14 15 16 17 18 19 S u r e l y e v e r y m a n 1 2 3 4 5 6 7 8 9 10 11 12 13 14
20 21 22 23 24 25 26 27 28 29 30 31 32 33 w a l k e t h i n a v a i n 15 16 17 18 19 20 21 22 23 24 25 26 27 28
34 35 36 37 38 39 40 41 42 43 44 45 46 47 s h e w: s u r e l y t h e y 29 30 31 32 33 34 35 36 37 38 39 40 41 42
48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 a r e d i s q u i e t e d i n 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57
63 64 65 66 67 68 69 70 71 72 73 74 75 v a i n: h e h e a p e t h 58 59 60 61 62 63 64 65 66 67 68 69 70
76 77 78 79 80 81 82 83 84 85 86 u p r i c h e s a n d 71 72 73 74 75 76 77 78 79 80 81
87 88 89 90 91 92 93 94 95 96 97 98 99 k n o w e t h n o t w h o 82 83 84 85 86 87 88 89 90 91 92 93 94
100 101 102 103 104 105 106 107 108 109 110 s h a l l g a t h e r 95 96 97 98 99 100 101 102 103 104 105
"The circle of figures taken in their ascending order and starting withthe second six, run thus:
6, 8, 9, 10, 11, 13, 17, 19, 20, 21, 23, 25, 26, 27, 39, 51, 54, 72, 80, 89.
Now, assuming that my interpretation of the solitary six in the circleis correct--that the old man started from six because he thought theuse of the figure one gave away too much--we will substitute for thesefigures the letters which appear underneath them in the table. Thesubstitution gives us the following row of letters:
S R E L Y V M N W A K T H I U D Q P C O S
"This is the line of letters from which we will endeavour toreconstruct the old man's cryptogram. We can, I think, go forwardwith the assurance that they are the actual letters represented bythe cryptogram, for several reasons. There are no recurring letters,and they represent every letter in the text in consecutive order,with three exceptions which are capable of a simple explanation. TheU has been taken from the second 'surely' instead of the first, tomislead the solver. Otherwise you would have surely for the firstfive numbers, which would be too clear an indication. The same reasonexists for making A the tenth letter instead of the eighth; which wouldreveal the word 'man.' The final letter--the 'G' in 'gather'--has beenexcluded, for a reason which I will presently explain."
"What about the second S--the final letter? Do you not call that arecurring letter?" asked Marsland, who was closely examining the tablethe detective had prepared.
"Not in the cryptographic sense. It is the first letter of the textrepeated after the line had been completed without recurring letters.There is a special reason for its use. The old man has worked on whatis called the keyword cipher, which is the most difficult of allciphers to discover. This system consists of various arrangements,more or less elaborate, of tables of letters, set down in the form ofthe multiplication table, and from the table agreed upon messages areconstructed whose solution depends on the use of some preconcertedkeyword. The most scientific adaptation of this principle wasconstructed by Admiral Sir Francis Beaufort. In his system the lettersof the alphabet are set down one under another from A to Z, then A isadded to the line. The next line starts with B and runs to another B atthe bottom. You continue till you have the whole alphabet set down inthis fashion. From this table and an agreed keyword, which may consistof a proper name or a sentence of several words, you construct a ciphermessage."
"How?" asked Marsland, in a tone of keen interest.
"That is what I now propose to demonstrate to you, if, as I think, theold man constructed his cryptogram in accordance with this principle.I have come to the conclusion that he modified and adapted this systemto his own ends, using the letters of the text from the Bible toconceal it better, and then made it more difficult still by turning theletters into figures after the manner I have described. He has alsomade a slight but not uncommon variation from the Beaufort principleby striking out the 'G' in 'gather,' which would follow the 'O' ifevery letter in the text was used once, and substituting the final S,instead of placing the 'S' after 'G.' But the clue that suggested to mymind that he had worked on this principle are the two figures 6 comingtogether at the top of the circle. In the substituted letters theyform two S's. Now, why does he have two S's when he carefully avoidsrecurring letters in the rest of the table? And why did he insert thefirst S again, as represented by the figure 6, instead of taking thenext S in this table?
"In pondering over these points I discovered, as I believe, the systemof cryptogram he used to construct his secret. He wanted to make thecryptogram difficult of solution, but at the same time he wanted togive some indication of the form of cryptogram he was using when hisheirs came to search for the money. The recurring S indicates thathe was working on a modification of the system I have explained, inwhich you add the first letter of your first column to the bottom, andcontinue on that system throughout the table. It is not much of a hint,because we have got to find the keyword before we can use the table,but by its help we will start with the assumption that the old manworked on the following table:
S R E L Y V M N W A K T H I U D Q P C O S R E L Y V M N W A K T H I U D Q P C O S R E L Y V M N W A K T H I U D Q P C O S R E L Y V M N W A K T H I U D Q P C O S R E L Y V M N W A K T H I U D Q P C O S R E L Y V M N W A K T H I U D Q P C O S R E L Y V M N W A K T H I U D Q P C O S R E L Y V M N W A K T H I U D Q P C O S R E L Y V M N W A K T H I U D Q P C O S R E L Y V M N W A K T H I U D Q P C O S R E L Y V M N W A K T H I U D Q P C O S R E L Y V M N W A K T H I U D Q P C O S R E L Y V M N W A K T H I U D Q P C O S R E L Y V M N W A K T H I U D Q P C O S R E L Y V M N W A K T H I U D Q P C O S R E L Y V M N W A K T H I U D Q P C O S R E L Y V M N W A K T H I U D Q P C O S R E L Y V M N W A K T H I U D Q P C O S R E L Y V M N W A K T H I U D Q P C O S R E L Y V M N W A K T H I U D Q P C O S R E L Y V M N W A K T H I U D Q P C O S R E L Y V M N W A K T H I U D Q P C O S
"It is from this table, unless I am very much mistaken, that heconstructed the cipher at the top of the sheet," said Crewe.
Marsland examined the curious table of letters, with close scrutiny,from various points of view, finally reversing it and examining itupside-down. He returned it to Crewe with a disappointed shake of hishead.
"I can make nothing of it," he said.
"It is necessary for us to discover the keyword he worked on beforewe can make use of it," said Crewe. "Once we get the keyword, we willhave no trouble in deciphering the mysterious message. The keyword isthe real difficulty in ciphers of this kind. It is like the keywordof a combination lock. Without it, you cannot unlock the cipher. Itis absolutely insoluble. Suppose, for example, he had picked a wordat random out of the dictionary, and died without divulging it toanybody, we should have to go through the dictionary word for word,working the table on each word, till we came to the right one."
"But that would take years," exclaimed Marsland blankly.
"Unless we hit on it by a lucky accident. That is why the keywordcipher is practically insoluble without knowledge of the keyword. It isnot even necessary to have a word. A prearranged code of letters willdo, known only to the composer of the cryptogram. If he wanted anybodyelse to decipher his cryptogram, he would have to divulge to him notonly the form of table he worked on but the code of letters forming thekeyword."
"Well, I do not see we are much further forward," said Marslanddespondently. "Of course, it's very clever of you to have found outwhat you have, but we are helpless without the keyword. The old man isnot likely to have divulged it to anybody."
"You are wrong," said Crewe. "He has divulged it."
"To whom?"
"To this paper. As I said before, he did not want his cryptogram to beinsoluble; he wanted his heirs to have his money,
but he did not wantit found very easily. You have forgotten the texts at the bottom ofthe paper. They have not been placed there for nothing. The keyword ishidden in them."
"I forgot all about the texts--I was so interested in yourreconstruction of the cryptogram," said Marsland. "As you say, hedidn't put the texts there for nothing, so it seems likely that he hashidden the keyword in them. But even now we may have some difficultyin finding it. Do you propose to take the texts word for word, testingeach with the table, till you find the right one?"
"That would take a long while," said Crewe. "I hope to simplify theprocess considerably. In fact, I think I have already discovered thekeyword."
"You have!" exclaimed Marsland, in astonishment. "How have you managedthat?"
"By deduction from the facts in front of us--or perhaps I should sayby reflecting on the hints placed in the texts. Isn't there somethingabout those texts that strikes you as peculiar?"
Marsland examined them attentively for some time, and shook his head.
"I'm afraid I'm not sufficiently well up in the Scriptures to noticeanything peculiar about them. I should say they were from the OldTestament, but I couldn't tell you what part of it."
"The texts are from the Old Testament, from Jeremiah XXV and IsaiahVII. They are remarkable for the fact that they represent twopassages--the only two instances in the whole Bible--where the writersused cryptograms to hide their actual meaning. In the first instancethe prophet, Jeremiah, living in dangerous times, veils his attackon the King of Babylon by writing Sheshak for Babel--Babylon; thatis, instead of using B B L, the second and twelfth letters of theHebrew alphabet, from the beginning, he wrote Sh Sh K from the end--asimple form of cryptogram which is frequently used, even now. In thesecond instance the prophet Isaiah, working on a very similar form ofcryptogram, writes 'Tabeal' for 'Remaliah.'
"Now, we are faced by two facts concerning the presence of these twotexts on the paper containing the cryptogram. In the first place, thecryptogram was complete without the texts; for what purpose, then,could they have been at the bottom of the sheet except to give a clueto the discovery of that keyword without which no recovery of thehidden treasure was possible, unless it was found by a lucky chance?In the second place, the selection by the old man of the only twocryptographic texts in the Bible was certainly not chance, but partof a deliberate harmonious design to guide the intelligent searcherto the right keyword. He was evidently versed in cryptography,constructed this one as carefully as a mechanic putting together apiece of mechanism, fitting all the parts carefully into one another.The figures in the centre of the circle give the key to the outsidefigures: the outside figures are the key to the cryptographic tableof letters from which the cryptogram is to be solved; there remainsthe key to be found. It is not likely that the composer of such aningenious cryptogram would leave the keyword to guesswork.
"The whole thing is a Bible cryptogram from first to last: figures,letters, words, and texts. It is even drawn on a sheet cut fromthe Bible. Why? Such an act might be deemed irreverent in a deeplyreligious man like the old man was, but when we piece the thingtogether we find that he was actuated by a religious spirit throughout.Not the least skilful part of his cryptogram is his concealment ofthe keyword in the text at the bottom. The text would convey nothingto most people, for very few people know anything about cryptograms,still fewer people would know that these texts contain the only twocryptograms in the Bible. Therefore, in accordance with his harmoniousdesign, it seems to me that the keyword should be found in the fivealternatives of the cryptic texts: Babel, Babylon, Sheshak, Remaliah,or Tabeal.
"Babel and Babylon may be discarded because there is no letter B in thecryptographic table, and it is essential that the keyword shall containno letter which doesn't also appear in the table. 'Sheshak' may alsobe discarded for the present as unlikely because of the awkwardnessof the recurring 'Sh' in a keyword. There remain Tabeal and Remaliah.The tendency of the composer would be to use the longer word, becausea long keyword is the better for the purpose. I think, therefore, weshould first try whether Remaliah is the keyword we are in search of."
"By Jove, Crewe, that is cleverly reasoned out!" exclaimed Marsland,in some excitement. "Let's put it to the test. How do we apply thiskeyword to the table?"
"Easily enough. On this sheet of paper we will write down thecryptogram; and the keyword underneath it, letter for letter, thus:
T Y N M V R T T H S M R E M A L I A H R E M
"Now, the first word of the cryptogram is T. Look in the first columnof the table for it, and then run your eye across the table for thefirst letter of the keyword. When you have found it, look at the top ofthe column and tell me the letter."
"K," said Marsland.
"Very well, then. We put down 'K' as the first word of the solutionand proceed in like manner through the whole of the cipher. The secondletter is Y--find it in the table, then look across for the secondletter of the key E, and then to the top of the column. What letterhave you?"
"C," said Marsland.
"KC, then, are the first two letters of our solution, and we go on tothe third, always repeating the same process. N in the first column, Macross, and the top gives you?"
"O," said Marsland.
"The next letter is M in the cryptogram and A in the keyword. What doesthe top of the column give you?"
"L," replied Marsland. "But I say, Crewe, do you think we are on theright track? K, C, O, L, is a queer start for a word isn't it? I knowof no word commencing like that."
"I may be mistaken, but I do not think so," replied Crewe firmly. "Letus keep on till we've finished it, at all events."
They resumed their task, and ultimately brought out the letters: K, C,O, L, C, H, C, R, A, E, S. Marsland gazed at the result in dismay.
"By Jove, we're on the wrong track," he said ruefully. "It is the wrongword, Crewe. These letters mean nothing; you'll have to try again."
But Crewe did not reply. He was examining the result of his night'slabours closely. Suddenly he put down the paper with an unusual lightin his eye.
"No," he said. "I am right, the old man was thorough to the lastdetail. He has given another clue to his heirs in the circle and thetwo lines. They represent a clock face. But the figures round them runthe reverse way to clock figures. The cryptogram reads backwards. Holdit up to that mirror, and see."
Marsland did so, and laid down the paper with a look of bewilderment.
"Search clock! The old grandfather clock at Cliff Farm!" he said.