by Lieutenant
Parker Hitt; and "Cryptography,"
by Andre Langie,
translated from the French by J. C. H. Macbeth.
N view of the certain similarity that exists between transposition ciphers and anagrams, skill at anagramming is a necessary qualification of the cryptographer.
In the transposition cipher, the letters are transposed in a predetermined order, forming an unintelligible sequence of letters in the transposed series, or cryptogram. In the anagram, however, the letters are transposed in any manner whatsoever that will result in an intelligible sequence of letters in the transposed series, or anagram.
In solving either the anagram or the transposition cipher, therefore, the problem is to discover the original text by rearranging the letters.
It is, of course, obvious in this connection, that methods of solution peculiar to transposition ciphers cannot be used to effect a solution of the anagram. But it is equally clear that anagramming may afford a method of solving the transposition cipher; and a consideration of this will form the substance of this article.
The word anagram comes from the Greek ana, backward, and graphein, to write. And it was fonnerly applied only to words or sentences that read exactly the same both forward or backward. The term palindrome, however, came to be used for this yariety of anagram, LEVEL, NOON, and DEED being instances of it in the word, and NAME NO ONE MAN an example in the sentence.
The anagram is a very ancient form of amusement, its invention being somewhat; doubtfully attributed to the Jews. But anagrams were also well known to the ancient Greeks and Romans. And during the Middle Ages they became popular throughout Europe, and especially in France, where, during the reign of Louis XIII, a certain Thomas Billon held the curious office of anagramatist to the king.
An interesting anagram of this period, to cite one from many, and incidentally to illustrate this kind of device, is A JUST MASTER, made upon JAMES STUART by the courtiers of James 1.
Anagrams were put to a practical use by medieval and early modern savants, who seem to have employed them as a means of concealing scientific discoveries during their periods of verification. Thus it was in the anagram, " Haec immatura a me jam frustra leguntur—oy," made upon " Cynthiæ figuras æmulatur Mater Amorum," that Galileo hid his discovery that Venus had phases like the moon.
The procedure of anagramming is very simple. Letters that spell a word are selected from the text being anagrammed. Other words capable of being used with the first are similarly formed from any remaining letters. In the pure anagram this process is continued until every letter of the original text has been used up in the formation of the anagram. In the impure anagram there is a remainder of unused letters.
In making or solving an anagram, a convenient method is to write each letter upon a slip of paper, as this permits of the rapid formation and breaking up of letter combinations.
The cryptographer can also call into play his tables of digraphs, trigraphs, and so on, as these suggest probable sequences of letters that can be developed into longer sequences, or used en bloc with other combinations.
Often it is possible to form more than one anagram from the same letters. Take the word RAPIERS, for example, which can be anagrammed into PARRIES, ASPIRER, PRAISER, and REPAIRS.
More than a single solution to some anagrams and transposition cryptograms thus looms as a possibility. In the case of ciphers, this contingency is rendered even more probable by the fact that many cryptograms necessarily contain null letters, which are unknown to the decipherer, and which, of course, should not be used in anagramming.
Consequently, in solving a transposition cipher by anagramming, every advantage should be taken of any information that might suggest the nature of the message, or afford a clew as to the identity of any of its words. For not only will this simplify the problem in any case, but it will also tend to insure the correct decipherment when more than one legitimate interpretation is possible.
Ordinarily anagramming can be used to advantage with almost any transposition cryptogram, either in its entirety, or with some of its letters in the discovery of one or more words. But to better demonstrate the possibilities of anagramming as a cryptographic method, it should preferably be illustrated with a cipher that cannot be readily solved in any other way.
Such a cipher is the following, in which the order of transposition is determined by a numerical key obtained from a key word, phrase, or sentence, of any length; the key — HONOR AND COUNTRY— having been used in this instance.
Message: AMMUNITION WILL BE SHIPPED TONIGHT. WATCH OUT FOR SPECIAL SERVICE SQUAD.
H O N O R A N D C O U N T R Y 4 8 5 9 11 1 6 3 2 10 14 7 13 12 15 A M M U N I T I O N W I L L B E S H I P P E D T O N I G H T W A T C H O U T F O R S P E C I A L S E R V I C E S Q U A D 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 I O I A M T I M U N N L L W B P T D E H E I S I O P H G N T O F T W T U S A C O H E P R C R C I I L V Q A S E E A U S D Cryptogram: IOIAM TIMUN NLLWB PTDEH EISIO PHGNT OFTWT USACO HEPRC RCIIL VQASE EAUSD.
In transforming the literal key of this cipher into a numerical key, as shown above, its letters are numbered serially in alphabetical order, repeated letters being taken from left to right.
Thus, there being an A in the present key, it is assigned the number 1. B is not used, and consequently C and D, which occur once each, are numbered 2 and 3 respectively. Similarly H, next in alphabetical order, is numbered 4. N, occurring three times, is next after H alphabetically, and is therefore numbered 5, 6, 7, from left to right. The remaining letters are treated in the same manner; the whole of the numerical key being shown in the accompanying illustration.
This key contains fifteen numbers. Accordingly the message is written beneath it in lines of fifteen letters each, forming fifteen columns, each headed by a key number. Should there not be enough letters in a given message to completely fill the last line, nonsignificant or null letters must be supplied, so that it will equal each of the other lines in length.
The letters in each row are now transposed in the order indicated by the numerical key. When a message forms more than one such row of letters, as in this instance, this can be more rapidly done by transposing the columns, than by a separate manipulation for each line.
Finally, to complete the process, the letters are transcribed in this transposed order, grouped as desired, but usually by fives as herewith.
A cryptogram enciphered in this system actually consists of one or more cycles of transposed letters, the length of the cycle being entirely dependent upon the length of the key. Such a cipher can be deciphered with the
key, of course, by a mere reversal of the process just described. But to decipher a cryptogram in any system of this kind by the method here proposed, it is first required to find the length of the transposition cycle, and then the order of transposition in the cycle.
In ciphers of this kind the number of letters in a cryptogram is always a multiple of the length of the transposition cycle. And, in illustrating the method, the cryptogram already given can be used as a representative example of such transposition ciphers.
The present cryptogram consists of 6o letters. Hence it might have been enciphered in 1 cycle of 60 letters; in 2 cycles of 30 letters each; in 3 cycles of 20 letters; in 4 cycles of 15; and so on.
When several cycles are thus possible by factoring, some of them can ordinarily be eliminated by testing for the usual proportions of 40% for the vowels AEIOU, 30% for the consonants LNRST, and 2% for the consonants JKQXZ.
For all letters in any cycle of the length actually used form a consecutive series in the original text, and cannot therefore vary much from the above averages. On the other hand, if the cryptogram is divided into cycles of any other length, the letters of such cycles do not form consecutive series in the text, and will often vary considerably from these normal proportions.
This is because the rather uniform intermixture of vowels and consonants in ordinary English is often so disarranged by transposition that the vowels or consonants collect in bunches, thus sometimes altering from normal the proportions of these letters in cycles other than that actually used.
The following figure illustrates this by showing how nine consonants from the first two real 15-letter cycles of the present cryptogram would accumulate in this way in the second 10-letter cycle, when the cryptogram is divided into cycles of this supposed length.
(6 vowels=40%) (5 vowels=33%)
┌───────────────────────────┐ ┌──────────────────
I O I A M T I M U N N L L W B P T D E H E I S . . .
└─────────────────┘ └─────────────────┘└──────
(6 vowels=6o%) (1 vowel=1o%)
The following tabulation shows the vowel counts for the different cycles possible in case of the present cryptogram. Tests for the consonant groups may also be made, but those for vowels are usually sufficient. Counts can be made, of course, either directly from the cryptogram, or by writing the latter in lines of the various lengths and counting the vowels per line.
Length Number Vowels of cycle of cycles per cycle 60 1 23 30 2 11-12 20 3 7-8-8 15 4 6-5-5-7 12 5 6-4-3-4-6 10 6 6-1-4-4-3-5 6 10 4-2-0-4-1-2-3-1-2-4 et cetera.
These figures' show that the d-letter cycle is impossible, for the third cycle of six letters contains no vowels whatever, and five other cycles contain but one or two vowels. The /o-letter cycle can also be rejected, for the second cycle of ten letters contains but one vowel. And in the 72-letter cycle, the third cycle contains but three vowels, or only twenty-five per cent of the number of letters in the cycle.
Vowel tests for cycles of 15, 20, and 30 letters—and, of course, 60 letters—are all normal. However, a little thought will show that the use of any given cycle must result in normal tests also in all cycles which are multiples of it in length.
The normal test here for the 30-letter cycle thus probably results from the use of a 15-letter cycle, which should accordingly be tried first as more probable than one of 30 or 60, or even of 20 letters.
Accordingly the cryptogram is now transcribed in lines of fifteen letters each, whereupon, by numbering the columns so formed from 1 up to 75 in regular order, the same arrangement as was reached above in enciphering will be restored.
In some cases these tests will indicate a cycle of the same length as the cryptogram itself. In this event the cipher must be solved by straight anagramming, as briefly outlined above. In general, the difficulty of solving such a cipher increases with the length of the message.
In the present instance, however, the cryptogram has been found to comprise several cycles, each of which, to our purpose, constitutes an anagram whose letters have been arbitrarily transposed. Since an identical order of transposition very probably exists in all of these cycles, this will now permit their solution simultaneously by a method that might well be called multiple anagramming.
This method is most easily applied by transcribing the columns of letters just obtained upon as many slips of paper, of which there would here be fifteen, each bearing four letters, and a key number at the top.
These slips may now be anagrammed, or tried in various combinations, to secure probable sequences of letters in all lines. It is sometimes practical to try for some certain word whose presence is suspected in the message. Or any frequently used digraph, such as TH, HE, ER, IN, et cetera, may be taken as the nucleus about which to build up the solution. A complete table of digraphs, with frequencies per ten thousand, was printed in FLYNN'S WEEKLY for January 23, 1926.
The present cryptogram, however, contains Q. And a peculiarity of this letter in the English language is that it is always followed by U, and then by another vowel, A, E, I , or O. Of course this Q might be a null; and in this connection it is important that allowance always be made for improbable sequences that might be caused by null letters, these being most commonly used at the beginnings or ends of messages, but possible anywhere.
In this case the combination of slips 7-13, forming QU in line four, also gives good sequences—IL, IG, and SP—in the first three lines.
There are now six different slips having a vowel in the last line to be tried after the 7-13 combination, all of which form more or less probable sequences throughout. Of several such sequences, that which is mathematically the most probable can be determined at any stage of the decipherment by comparing the total frequencies of the digraphs formed by each pair of slips, as in the subjoined tabulation.
13—3 13—4 13—8 13—10 13—11 13—12
L I 52 L A 30 L M 4 L N 0 L N 0 L L 42
G D 2 G E 25 G S 7 G O 22 G P 3 G H 25
P T 10 P W 2 P A 30 P O 33 P H 4 P E 31
U I 3 U I 3 U A 6 U E 8 U E 8 U A 6
——— ——— ——— ——— ——— ———
67 60 47 63 15 104
The numbers following each digraph are taken from the table of digraphs just mentioned. The total 104 for slips 13-12 is far in excess of any of the others, and therefore this combination, giving the series 7-13-12, is the most probable.
ILL in the first line of this combination is probably WILL, since there is a W in the first line of slip 14. And the combination 14-7-13-12, so formed, gives SQUA in line four, probably SQUAD, as slip 15 has D in line four, thus expanding series to 14-7-13-12-15.
Next, WILLB in line one looks like WILL BE, and -SPEC in line three suggests SPECIAL. But there is no E in the first line of any slip, nor an I in the third. However, these letters are found in the second ahd fourth lines respectively of slip 4. And this seems to indicate that SQUAD ends the message, slip 15 being the last of the series, and slip 4 the first.
In further developing the word SPECIAL, both slips 8 and 12 have an A in the fourth line, and form very probable combinations throughout with what has already been worked out. By the digraph test, however, 4-8 wins out over 4-12 by a heavy margin. The frequency for 1A is here omitted, since it would only equally increase both totals.
4—8 4—12
A M 32 A L 63
E S 115 E H 28
W A 55 W E 31
I A .. I A ..
——— ———
202 122
Adding slip 5, to complete SPECIAL, the message and numerical key are now developed to the point shown in the following illustration:
| 8 | 4 | 5 | |||||
| 14 | 7 | 13 | 12 | 15 | |||
| A | M | M | |||||
| W | I | L | L | B | B | S | E |
| N | I | G | H | T | W | A | T |
| R | S | P | E | C | I | A | L |
| S | Q | U | A | D |
The key thus far discovered is 4-8-5. . . 14-7-13-12-15. By a continuation of the process, which is here unnecessary, the whole of this key can be found. This method should demonstrate that a transposition cipher is of maximum value when the transposition cycle is as long as the cryptogram itself, and when it is possible to prevent the accumulation of cryptograms of the same length and in the same key. It can be used to solve any transposition cipher using a fixed transposition cycle, such as the cipher here used, the Fleissner grille, or the Nihilist transposition method. Or by its means more than one cryptogram of the same length and key can be solved at one operation.
Further, having solved a cipher by this method, a consideration of the numerical key so obtained will often aid in identifying the system when this is unknown, or in the discovery of additional facts about it. Thus, here it would be possible to recover the literal key by an analysis of this series of numbers, although how to do this is somewhat beyond the scope of this article.
To try the skill of the decipherer at the present method, two ciphers of the key phrase type are here offered for solution. These ciphers, which purport to be intercepted messages written by members of a band of counterfeiters, are, as a matter of fact, purely fictitious.
But, for our purpose, they might just as well be genuine messages written by desperate criminals. Any police department, with the translations of these ciphers, would probably make short work of capturing this band of counterfeiters.
What if their arrest depended upon your deciphering these messages?
Would you be there at the round-up?
CIPHER No. 1.
ANAQY URRRA ESDWR EEET
CIPHER No. 2.
OCVEI WRREE NEIDE UDYSO ERTSA EEBSN DFYID ERTIO EEFYE HADSL EAYWD OCEFY SAARR DNULF ENAAE YLDRO VAURL QPTPS SH.
ANOTHE R FRE E SUBSCRIPTIO N To FLYNN'S WEEKL Y
In cipher No. 3, submitted by Charles P. Winsor, Boston, Massachusetts, the fans again have an opportunity to win a year's subscription to this magazine.
The first correct solution submitted will be awarded the subscription, postmarks determining the priority of entry. In case of more than one solution submitted on the same date, the one accompanied by the clearest explanation of the cipher system will be winner.
All solutions to receive consideration must be mailed within one month from the date of this issue. A complete explanation of the cipher will be printed in an early issue of FLYNN'S WEEKLY.
CIPHER No. 3 (Charles P. Winsor).
GENERAL J. E. B. STUART:
171143 149045 228420 146531 487688
153040 387262 041543 603680 582030
338032 157641 069261 034139 559636
541210 251040 122266 236490 622266
236236 545404 140555 143531 569533
413345 220383 555433 151487 425137
418265 203410 558629 487247 236387
686582 035058 545155 639549 116045
563251 532117 410546 143418 399047
387425 418504 636257 223648
R. E. LEE, General.
Mrs. Charles J. Mundy, Thibodaux, Louisiana, is the propounder of the next problem, which presents an interesting study of the simple substitution cipher. If you solve it, see what you can hnd out about the structure of the alphabet.
CIPHER No. 4 (Mrs. Charles J. Mundy).
PAOQ OQUI GXAE VJOP AUXU PVOY POIM EGJA DIAL PORO BEQP AEDO VQPA URDY DPAE URXA UNEP PAER UPPE VAUR DNEO ZSQO CXRG VEKE VQET
Mr. Bellamy, of Boston, the author of No. 5, says his cipher " looks like a REBUS." (Note the third from last group). But really it is a transposition cipher that can be solved by the method given in this article. After you solve this, try to identify the cipher system.
CIPHER No. 5 (Arthur Bellamy).
AEGTS RATIE OSSLA CVIRI MPONH AOARF RNDDI TIERS DIENA CRGLR RTSAO YINAO NFEET BPITO ELHSI LDLUE TWTHI REBUS ENFOT OININ
About No. 6 there is an unmistakable ring of challenge. Read this correspondent's letter, and let us know if you agree with him:
DEAR SIR:
I am sending you a cipher which I think is a "sockdolager," if there ever was one, the objection to it being that one has to be too dog-gone careful in writing a message or he will make mistakes that will throw the whole thing out of gear.
So sure am I that this cipher is almost impossible to solve that I am writing the solution right here—"EASY IF YOU KNOW HOW, BUT ALMOST IMPOSSIBLE IF YOU DON'T ''—and you can print both the cipher and the sentence itself, if you wish, as a defy to anybody interested in such.
W. E. MCCRACKEN.
San Antonio, Texas.
CIPHER No. 6 (W. E. McCracken).
25,23,19,7—11,24—20,17,7—17,4,2,9— 12,8,9—631—5,12,2,3,5,2—16,5,4,26, 5,27,17,20,11,20—5,24—20,17,7— 10,12,26,7.
Whether your school days are present day realities, or only memories of the past, you will enjoy the ensuing letter, and the cipher that came with it.
DEAR SIR:
You will probably remember in your own school days as in the days of Huckleberry Finn and Tom Sawyer, one of the chief amusements after school was the organizing and operating of a "Secret Society" with the usual caves, dens, and so forth.
I know we used to have one, and the following is a sample of the "secret writing " which we invented.
I am inclosing it, not so much for the purpose of puzzling any one, as to show the ingenuity of the schoolboy's mind at the age of about twelve or thirteen.
A, S. BINNIE.
Waterton Lakes Park, Alberta, Canada.
CIPHER No. 7 (A. S. Binnie).
THE SCHOOLBOY'S MESSAGE
21 33 21 73 42 32 34 63 12
73 32 73 22 23 62 32 61 23
2 53 2 61 22 62 62 41 23
63 21 73 20 13 73 62 23 51
32 73 22 14 19 53 32 13 10
44 61 61 13 31 61 21 51 63
79 63 18 51 53 21 72 17 22
73 98 51 23 23 73 20 72 32
22 34 61 32 34 72 42 21 33
32 32 13 13 13 61 23 73 80
53 62 82 12 88 13 22 61 21
73 62 73 30 71 73 13 76 53
54 3 23 23 23 85 63 23 12
9 72 89 71 53 23 23 71 23
73 61 33 —— 78 71 13 40 26
22 61 62 22 —— —— 73 ——
61 73 21 32 22
—— —— 13 63 61
—— —— ——
Try your skill at these ciphers, fans, and send in your solutions. Or submit a cipher of your own devising, if you wish, to puzzle your fellow decipherers.
The solutions to all the ciphers in this issue, excepting No. 3, will be published in the next Solving Cipher Secrets.
How many of you correctly deduced from the given data the identity of the key volume used with the No. 1 book cipher in the May 22 issue of FLYNN'S WEEKLY?
They who reasoned this out after the manner of Sherlock Holmes must have reached the conclusion that, since the key volume was necessarily a book in the possession of every reader of the magazine, it could hardly be anything else than the May 22 issue of FLYNN'S WEEKLY itself!
In fact, the first number of each group of two in this cipher referred to a paragraph of the May 22 Solving Cipher Secrets; and the second, to a word in that paragraph.
Thus, the first pair of numbers, 41-26, indicates the 26th word—WARN—of the 41st paragraph of that article. The entire message, similarly deciphered, follows:
WARN LUSITANIA PASSENGERS 41—26; 43—10; 42—2; THROUGH THE PRESS AGAINST 42—7; 40—21; 42—12; 41—28; THE ATLANTIC VOYAGE. 43—19; 41—35; 41—32.
Did you get it?
To decipher No. 2 (Jos. J. Morello) it was only necessary to read the first letter after each numeral. All other letters, and all of the figures, were nonsignificants. Here is a small sample of this cryptogram, with the significants italicized:
B C O 1 1 3 T U V W 2 H H P Q W N 2 9 I R S 6 2 3 S 9 2—etc.
The whole of it, similarly treated, reads: " THIS CIPHER IS THE RESULT OF MY IMPRISONMENT. " This cipher, as you may remember, was quickly improvised under stress of emergency, and, although simple in structure, it proved adequate for its intended purpose.
The simple numerical alphabet—A=1; B=2; C= 3 . . . Z—26—formed the basis of cipher No. 3 (A. Krieger). Normal word divisions were observed, the number for any letter being modified according to its location in the word; 1 being added to the number representing the first letter of a word, 2 to that for the second, 3 to the third, and so on.
Mr. Krieger's message is: " UNLOAD AT MIDNIGHT AT FOOT OF PORTER STREET. WATCH OUT FOR THE COAST GUARD. " The first two words, deciphered herewith, are sufficient to explain the principle of this cipher.
Cipher: 22—16—15—19—6—10 2—22
Key: 1 2 3 4 5 6 1 2
———————————————— ————
Subtracting: 21 14 12 15 1 4 1 20
Message: U N L O A D A T
The key to No. 4 (M. Walker), a Gronsfeld cipher, is 31416, familiar to every public schoolboy under the guise of pi—3.1416.
Cipher: BFGBR ONIDN LFJBT... Key: 31416 31416 31416... Message: YECAL LMECH IEFAN...
Mr. Walker's message: "Ye call me chief, and ye do well to call him chief, who for ten long years has met on the arena every shape of man or beast."
And now for No. 5 (J. G. Meerdink), the Nihilist transposition cipher, which was enciphered in a 6x6 square with 4-2-6-1-3-5, as a key.
4 2 6 1 3 5
4 O R N O R W
2 O D L N C O
6 E A Y S F L
I L I A W L L
3 T E M I S O
5 T G T I H A
The grouping in this cryptogram was arbitrary, having no relation to the words of the message: "WILL LAN D COOLIES TO-MORROW NIGHT SAFELY."
Cipher No. 6 (Dr. G. A. Ferrell) is of the autokey variety, a type that has not yet been discussed in the department. A message is enciphered in such a system by means of itself as a key. An auxiliary key, sometimes employed at the beginnings of such ciphers, here consists of doubling the first number.
To illustrate the present system with the first words of Dr. Ferrell's message, each letter, at (a), is first replaced by its equivalent in the simple numerical alphabet—A=i . . . Z =2 6—as shown at (b).
Each number thus obtained—with the exception of the first, which is keyed with itself—is placed under the number next following it, as at (c). The final cipher is now formed at (d) by adding the numbers in lines (b) and (c).
(a) T H E R E I S ...
(b) 20 8 5 18 5 9 19 ...
(c) 20 20 8 5 18 5 9 ...
—— —— —— —— —— —— ——
(d) 40 28 13 23 23————14 28—
In deciphering, divide the first number by two, obtaining the numerical equivalent of the first letter. Subtract this number from the second number of the cryptogram to get the second letter of the message; and so on. Here is the complete translation of Dr. Ferrell's message:
There is no royal road to knowledge; neither is there a short cut to cryptography. To master this noble science takes patience, thought, and perseverance. FLYNN'S WEEKLY is doing a wonderful work keeping this flame burning.
An explanation of No. 3 (J. R. Midford), the free subscription cipher in FLYNN' S WEEKLY for April 24, will complete the Jot for this time.
(a) C C J J T C C E G C ... (b) 3×3 10+10 20+3 3×5 7×3 ... (c) 9 20 23 15 21 ... (d) I T W O U ...
In deciphering this cryptogram each of the letters at (a) is replaced at (b) by its numerical equivalent in the popular A=1 . . . Z=26 alphabet. The numbers in line (c) represent either the products of two numbers—or the sums of two, three, and sometimes four numbers—in line (b). Substituting at (d) the alphabetical equivalents for the numbers at (c) will now give the message:
It would please me immensely to be able to exchange some of my ciphers with you. I am always ready and willing to exchange with a real fan like yourself. Can I hope to hear from you soon? From one fan to another.
The fact that either multiplication or addition can be used at (b) sometimes makes more than one interpretation possible at (d). For example, CC could be either F (3+3) or I (3×3). To further complicate the cipher, sometimes a letter is represented by itself; and again the numerical values of three or even four letters are added together to form the substitute. Thus, in the present cryptogram, T is variously represented by T itself, DE (4×5), ED (5×4), JJ (10+10), NF (14+6), and JFD (10+6+4). And many other substitutes for this letter are possible.
The following correct solutions to the March 20 ciphers have been received. Solvers with equal numbers of solutions are listed in the order submitted.
A list of solvers of the April 24 ciphers, including Mr. Midford's prize cipher, will be printed in next Solving Cipher Secrets.
A number of our correspondents have taken exception to the following paragraph printed in this department for April 24, 1926.
A canvass of publishers reveals the startling fact that there is not a single work on cryptography in print in the English language. Any new books on the subject or new editions of older works, will be announced here when published.
These correspondents submit titles of the following two books:
"Manual for the Solution of Military Ciphers,"
by Lieutenant
Parker Hitt; and "Cryptography,"
by Andre Langie,
translated from the French by J. C. H. Macbeth.
However, it appears that neither of these two books is at present available. The publishers of the "Manual" say that their edition of this work is entirely exhausted, and that it will not be reprinted.
And the publishers of "Cryptography" have informed us that this book is at present out of print, and that they did not know exactly when a new edition would be ready.
Both of these books are excellent. We hope to announce the new edition of Langie-Macbeth soon in these columns; or our readers, if they prefer, can write directly to the publishers, F. P. Dutton & Co., 681 Fifth Avenue, New York, N. Y. , for information.
''Solving Cipher Secrets" will appear again soon