crewe went to the table and picked up the plan.
“my first impression was that the circle of figures represented some form of letters of the alphabet arranged on what is called the cardboard or trellis cipher, in which a message is concealed by altering the places of the letters without changing their powers. such messages are generally written after the chinese fashion—upwards and downwards—but there is no reason why a circle should not be used to conceal the message. in this case i did not expect to find a message hidden in the circle, but rather, the key to the solution of the letters above the circle, which, i was convinced, formed the real cryptogram.
“the recurring t’s and m’s in the top line seemed to indicate that it was some form of changed letter cipher, complicated by having to be read in connection with the figures in the circle, which represented other letters of the alphabet. the numbers, representing an ascending series from 6 to 89, with one recurring 6, suggested the possibility of this form of cryptogram having been used. the numbers in the centre suggested a sum, which, when done, would throw some light on the 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 ultimately came to the conclusion that the solution did not lie within them. i am not an arithmetician, but my calculations told me enough to make me realize that i was on the wrong track.
“i next attempted to ascertain if the two mysterious messages—the lines on the top and the circle of figures—were two separate messages read independently of one another. i did not think they were, but i determined to put it to the test. obviously, if they were, the top line was merely a changed letter cipher, and nothing more. these are usually easy to decipher because of the frequency with which certain letters 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 down to 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 these as a basis to give me the key, i tried all likely combinations on the changed letter basis, but without success.
“i came back to my original idea that the figures in the circle were the solvent of the line of letters above, and concentrated my efforts in attempting to discover their meaning. i finally came to the conclusion that the figures represented the pages or lines of some book.”
“like the cryptograms i used to solve when i was at school,” suggested marsland, with a smile.
“rather more difficult than that. in that form of cryptogram rows of figures are turned into words once you hit on the right book. this cryptogram is much more ingenious, for it consists of three parts—a line of meaningless letters and a circle of equally meaningless figures, with other figures within it, and some plain english verses of scripture, the whole probably interdependent. if the circle of figures represented some book necessary to the solution of the whole cryptogram, the first thing to find out was the book from which the figures had been taken. i had not much difficulty in arriving at the conclusion that this book was a large brass-bound family bible i saw at cliff farm.”
“i suppose the texts on the bottom of the sheet suggested that idea to you?” said marsland.
crewe shook his head.
“i’ve learnt to mistrust guesswork,” he said. “it would be a jump at random to come to the conclusion that the cryptogram had been drawn on the fly-leaf of a bible because it contained some scripture texts. there is no connection between the facts. in fact, it seemed unlikely to me at first that a religious man like the old farmer would have mutilated his family bible for such a purpose. i was inclined to the view that he had taken a fly-leaf from one of his leisure hour bound volumes, which at the farm range from 1860 to the early seventies—a period of years when this kind of glossy thick paper was much used for fly-leaves by english printers. but while i was examining the sheet through the magnifying glass i detected this mark on the edge, which proved conclusively to me that the cryptogram had been drawn on the fly-leaf of the family bible. have a look at it through the glass—you cannot detect it with the naked eye.”
crewe held the sheet edgeways as he spoke, and pointed to one of the outer corners. marsland gazed intently through the glass, and was able to 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 understand what it means.”
“it is dutch metal or gold-leaf. the book from which this sheet was cut was gilt-edged. that disposes of the volumes of leisure hour and other bound periodicals, none of which is gilt-edged. when i was looking at the books at the farm i noticed only two with gilt-edged leaves. one was the big family bible, and the other was a large, old fashioned language of flowers. but this sheet could not have been cut from the language of flowers.”
“why not?”
“because it has two rounded corners. as a rule, only sacred books and poetry are bound with rounded corners. in any case, i remember that the language of flowers at the farm is square-edged. therefore the sheet 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 arrangement of the contents. the pages are numbered, the chapters are divided into verses which are numbered, and there is a numbered table of contents at the beginning of each chapter. obviously, the bible is an excellent book from which to devise a cryptogram of numbers owing to the multiplicity of figures used in it and the variety of ways in which they are arranged. i found both a bible and prayer book in the bookshelves, here, and set to work to study the numerical arrangement of the chapters, the divisions of the verses, and the arrangement of figures at the head of the chapters.”
“it was while i was thus engaged that i remembered that at the beginning of the authorised version of the bible is inserted a table of the books of the old and new testaments, the pages on which they begin, and the number of chapters in each. here was the possibility of a starting-point, sufficiently unusual to make a good concealment, yet not too remote. i turned to the table, and, on running my eye down it, 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 was really fortunate in starting off with this discovery, because otherwise i might have been led off the track by the doubling and trebling of the 3 in the second line of central figures, and have wasted time trying to fathom some mystic interpretation of the 9—a numeral which has always had a special significance for humanity: the nine muses, the nine worthies, ‘dressed up to the nines,’ and so on. but with 150 as the indication that the cryptogram had been composed from the book of psalms, it was obvious that the next line of numerals in the centre directed attention to some particular portion of them. as there are not 396 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 i turned to the thirty-ninth psalm. verse six of that psalm reads:
“‘surely every man walketh in a vain shew: surely they are disquieted in 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, before i was able to start on the table which had been used to build up the cryptogram. the fact that the figures in the outside circle start at 6 indicated that there was some connection between it and the inner 6. 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 he thought the figure 1 was too clear an indication of the commencement of his cryptogram, or else he made his start from the sixth letter of the text. i thought the former the likelier solution, but i tried them both, to make sure. the first five figures on the latter solution gave me a recurring y, which indicated that i was on the wrong track because it was essential there should be no recurring letters. there are no recurring 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 with the 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 circle is correct—that the old man started from six because he thought the use of the figure one gave away too much—we will substitute for these figures the letters which appear underneath them in the table. the substitution 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 to reconstruct the old man’s cryptogram. we can, i think, go forward with the assurance that they are the actual letters represented by the 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. the u has been taken from the second ‘surely’ instead of the first, to mislead the solver. otherwise you would have surely for the first five numbers, which would be too clear an indication. the same reason exists for making a the tenth letter instead of the eighth; which would reveal the word ‘man.’ the final letter—the ‘g’ in ‘gather’—has been excluded, for a reason which i will presently explain.”
“what about the second s—the final letter? do you not call that a recurring letter?” asked marsland, who was closely examining the table the detective had prepared.
“not in the cryptographic sense. it is the first letter of the text repeated after the line had been completed without recurring letters. there is a special reason for its use. the old man has worked on what is called the keyword cipher, which is the most difficult of all ciphers to discover. this system consists of various arrangements, more or less elaborate, of tables of letters, set down in the form of the multiplication table, and from the table agreed upon messages are constructed whose solution depends on the use of some preconcerted keyword. the most scientific adaptation of this principle was constructed by admiral sir francis beaufort. in his system the letters of the alphabet are set down one under another from a to z, then a is added to the line. the next line starts with b and runs to another b at the bottom. you continue till you have the whole alphabet set down in this fashion. from this table and an agreed keyword, which may consist of a proper name or a sentence of several words, you construct a cipher message.”
“how?” asked marsland, in a tone of keen interest.
“that is what i now propose to demonstrate to you, if, as i think, the old man constructed his cryptogram in accordance with this principle. i have come to the conclusion that he modified and adapted this system to his own ends, using the letters of the text from the bible to conceal it better, and then made it more difficult still by turning the letters into figures after the manner i have described. he has also made a slight but not uncommon variation from the beaufort principle by striking out the ‘g’ in ‘gather,’ which would follow the ‘o’ if every 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 my mind that he had worked on this principle are the two figures 6 coming together at the top of the circle. in the substituted letters they form two s’s. now, why does he have two s’s when he carefully avoids recurring letters in the rest of the table? and why did he insert the first s again, as represented by the figure 6, instead of taking the next s in this table?
“in pondering over these points i discovered, as i believe, the system of cryptogram he used to construct his secret. he wanted to make the cryptogram difficult of solution, but at the same time he wanted to give some indication of the form of cryptogram he was using when his heirs came to search for the money. the recurring s indicates that he was working on a modification of the system i have explained, in which you add the first letter of your first column to the bottom, and continue 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 man worked 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 he constructed 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 it upside-down. he returned it to crewe with a disappointed shake of his head.
“i can make nothing of it,” he said.
“it is necessary for us to discover the keyword he worked on before we can make use of it,” said crewe. “once we get the keyword, we will have no trouble in deciphering the mysterious message. the keyword is the real difficulty in ciphers of this kind. it is like the keyword of a combination lock. without it, you cannot unlock the cipher. it is absolutely insoluble. suppose, for example, he had picked a word at random out of the dictionary, and died without divulging it to anybody, 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 keyword cipher is practically insoluble without knowledge of the keyword. it is not even necessary to have a word. a prearranged code of letters will do, known only to the composer of the cryptogram. if he wanted anybody else to decipher his cryptogram, he would have to divulge to him not only the form of table he worked on but the code of letters forming the keyword.”
“well, i do not see we are much further forward,” said marsland despondently. “of course, it’s very clever of you to have found out what you have, but we are helpless without the keyword. the old man is not 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 be insoluble; he wanted his heirs to have his money, but he did not want it found very easily. you have forgotten the texts at the bottom of the paper. they have not been placed there for nothing. the keyword is hidden in them.”
“i forgot all about the texts—i was so interested in your reconstruction of the cryptogram,” said marsland. “as you say, he didn’t put the texts there for nothing, so it seems likely that he has hidden the keyword in them. but even now we may have some difficulty in finding it. do you propose to take the texts word for word, testing each with the table, till you find the right one?”
“that would take a long while,” said crewe. “i hope to simplify the process considerably. in fact, i think i have already discovered the keyword.”
“you have!” exclaimed marsland, in astonishment. “how have you managed that?”
“by deduction from the facts in front of us—or perhaps i should say by reflecting on the hints placed in the texts. isn’t there something about 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 notice anything peculiar about them. i should say they were from the old testament, but i couldn’t tell you what part of it.”
“the texts are from the old testament, from jeremiah xxv and isaiah vii. they are remarkable for the fact that they represent two passages—the only two instances in the whole bible—where the writers used cryptograms to hide their actual meaning. in the first instance the prophet, jeremiah, living in dangerous times, veils his attack on the king of babylon by writing sheshak for babel—babylon; that is, instead of using b b l, the second and twelfth letters of the hebrew alphabet, from the beginning, he wrote sh sh k from the end—a simple form of cryptogram which is frequently used, even now. in the second instance the prophet isaiah, working on a very similar form of cryptogram, writes ‘tabeal’ for ‘remaliah.’
“now, we are faced by two facts concerning the presence of these two texts on the paper containing the cryptogram. in the first place, the cryptogram was complete without the texts; for what purpose, then, could they have been at the bottom of the sheet except to give a clue to the discovery of that keyword without which no recovery of the hidden treasure was possible, unless it was found by a lucky chance? in the second place, the selection by the old man of the only two cryptographic texts in the bible was certainly not chance, but part of a deliberate harmonious design to guide the intelligent searcher to the right keyword. he was evidently versed in cryptography, constructed this one as carefully as a mechanic putting together a piece of mechanism, fitting all the parts carefully into one another. the figures in the centre of the circle give the key to the outside figures: the outside figures are the key to the cryptographic table of letters from which the cryptogram is to be solved; there remains the key to be found. it is not likely that the composer of such an ingenious 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 from the bible. why? such an act might be deemed irreverent in a deeply religious man like the old man was, but when we piece the thing together we find that he was actuated by a religious spirit throughout. not the least skilful part of his cryptogram is his concealment of the keyword in the text at the bottom. the text would convey nothing to most people, for very few people know anything about cryptograms, still fewer people would know that these texts contain the only two cryptograms in the bible. therefore, in accordance with his harmonious design, it seems to me that the keyword should be found in the five alternatives of the cryptic texts: babel, babylon, sheshak, remaliah, or tabeal.
“babel and babylon may be discarded because there is no letter b in the cryptographic table, and it is essential that the keyword shall contain no letter which doesn’t also appear in the table. ‘sheshak’ may also be discarded for the present as unlikely because of the awkwardness of the recurring ‘sh’ in a keyword. there remain tabeal and remaliah. the tendency of the composer would be to use the longer word, because a long keyword is the better for the purpose. i think, therefore, we should 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 this keyword to the table?”
“easily enough. on this sheet of paper we will write down the cryptogram; 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 column of the table for it, and then run your eye across the table for the first letter of the keyword. when you have found it, look at the top of the column and tell me the letter.”
“k,” said marsland.
“very well, then. we put down ‘k’ as the first word of the solution and proceed in like manner through the whole of the cipher. the second letter is y—find it in the table, then look across for the second letter of the key e, and then to the top of the column. what letter have you?”
“c,” said marsland.
“kc, then, are the first two letters of our solution, and we go on to the third, always repeating the same process. n in the first column, m across, and the top gives you?”
“o,” said marsland.
“the next letter is m in the cryptogram and a in the keyword. what does the top of the column give you?”
“l,” replied marsland. “but i say, crewe, do you think we are on the right track? k, c, o, l, is a queer start for a word isn’t it? i know of no word commencing like that.”
“i may be mistaken, but i do not think so,” replied crewe firmly. “let us 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 wrong word, crewe. these letters mean nothing; you’ll have to try again.”
but crewe did not reply. he was examining the result of his night’s labours closely. suddenly he put down the paper with an unusual light in his eye.
“no,” he said. “i am right, the old man was thorough to the last detail. he has given another clue to his heirs in the circle and the two lines. they represent a clock face. but the figures round them run the reverse way to clock figures. the cryptogram reads backwards. hold it 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.
