The annexed letter from a gentleman whose abilities we very highly respect, was received, unfortunately, at too late a period to appear in our November number:

    DEAR SIR:

        I should perhaps apologise for again intruding a subject upon which you have so ably commented, and which may be supposed by this time to have been almost exhausted; but as I have been greatly interested in the articles upon "Cryptography," which have appeared in your Magazine, I think that you will excuse the present intrusion of a few remarks. With secret writing I have been practically conversant for several years, and I have found, both in correspondence and in the preservation of private memoranda, the frequent benefit of its peculiar virtues. I have thus a record of thoughts, feelings and occurrences, — a history of my mental existence, to which I may turn, and in imagination, retrace former pleasures, and again live through bygone scenes, — secure in the conviction that the magic scroll has a tale for my eye alone. Who has not longed for such a confidante?

    Cryptography is, indeed, not only a topic of mere curiosity, but is of general interest, as furnished an excellent exercise for mental discipline, and of high practical importance on various occasions; — to the statesman and the general — to the scholar and the traveller, — and, may I not add "last though not least," to the lover? What can be so delightful amid the trials of absent lovers, as a secret intercourse between them of their hopes and fears, — safe from the prying eyes of some old aunt, or it may be, of a perverse and cruel guardian? — a billet doux that will not betray its mission, even if intercepted, and that can "tell no tales" if lost, or, (which sometimes occurs,) if stolen from its violated depository.

    In the solution of the various ciphers which have been submitted to your examination, you have exhibited a power of analytical and synthetical reasoning I have never seen equalled; and the astonishing skill you have displayed — particularly in deciphering the cryptograph of Dr. Charles J. Frailey, will, I think, crown you the king of "secret-readers." But notwithstanding this, I think your opinion that [page 307:] the construction of a real cryptograph is impossible, not sufficiently supported. Those examples which you have published have indeed not been of that character, as you have fully proved. They have, moreover, not been sufficiently accurate, for where the key was a phrase, (and consequently the same character was employed for several letters,) different words would be formed with the same ciphers. The sense could then only be ascertained from the context, and this would amount to a probability — generally of a high degree, I admit — but still not to a positive certainty. Nay, a case might readily be imagined, where the most important word of the communication, and one on which the sense of the whole depended, should have so equivocal a nature, that the person for whose benefit it was intended, would be unable, even with the aid of his key, to discover which of two very different interpretations should be the correct one. If necessary, this can easily be shown; thus, for example, suppose a lady should receive from her affianced, a letter written in ciphers, containing this sentence, "4 5663 967 268 26 3633," and that a and n were represented by the figure 2, — e, m, and r by 3, — i by 4, — l by 5, — o, s, and v by 6, — u by 7, — w by 8, — and y by 9; a moment's inspection will show that the sentence might either be "I love you now as ever," or "I love you now no more." How "positively shocking," to say the least of it; and yet several of the ciphers that you have published have required a greater number of letters to be represented by one character, than any to be found in the example before us. It is evident, then, that this is not a very desirable system, as it would scarcely be more useful than a lock without its key, or with one that did not fit its wards.

    I think, however, that there are various methods by which a hieroglyphic might be formed, whose meaning would be perfectly "hidden; " and I shall give one or two examples of what I consider such. A method which I have adopted for my own private use, is one which I am satisfied is of this nature, as it cannot possibly be solved without the assistance of its key, and that key, by which alone it can be unlocked, exists only in my mind; at the same time it is so simple, that with the practice in it which I have had, I now read it, and write it, with as much facility as I can the English character. As I prefer not giving it here, I shall be compelled to have recourse to some other plan that is more complicated. By a CRYPTOGRAPH, I understand — a communication which, though clearly ascertained by means of its proper key, cannot possibly be without it. To most persons, who have not thought much upon the subject, an article written in simple cipher, (by which I mean with each letter uniformly represented by a single distinct character,) would appear to be an impenetrable mystery; and they would doubtless imagine that the more complicated the method of constructing such a cipher, the more insoluble — to use a chemical expression — would be the puzzle, since so much less would be the chance of discovering its key. This very natural conclusion is, however, erroneous, as it is founded on the supposition that possession must first be obtained of the key, in order to unravel the difficulty, — which is not the case. The process of reasoning employed in resolving " secret writing " has not the slightest relation to the form or description of the characters used, but refers simply to their succession, and to a comparison of words in which the same letters occur. By these means any cipher of this nature can be unriddled as experience has fully shown. A very successful method of avoiding detection, would be to apply the simple cipher to words written backwards and continuously. This, I conceive, might be called a perfect cryptograph, since from the want of spaces, and consequently the impossibility of comparing words, it would utterly perplex the person attempting to discover its hidden import, and yet with the help of the key, each letter being known, the words could easily be separated and inverted. I give a short specimen of this style, and would feel much gratified with your opinion of the possibility of reading it.

, † § : ‡ ] [ , ? ‡ ) , [ ¡ ¶ ? , † , ) ¡ , § [ ¶  , : ¶ ! [ .§ ( , † § ¡ || ( ?  ? , _{* *} (  ¡ ( [ , ¶ * .  [ § ¡ ¶ § ¡ .¶ ] ¿ , † § [
? ( § [ : : ( † [ .  ( * ; ( || ( , † § ¡ ‡ [ * .: , ] ! ¶ † || ] ? _* ! ¶  † § ¶ || , _* ( † ¡ ( , ? ‡ § ( ¡  ¡ ¶ [ ¡ ¶ [ ? ( ,
; § ‡  ‡ ] † § § : ( † [ † [ ¶ ? ‡ ] : .* ¡ ¶ : ( § ? ] ! ¶ † § ‡ ] ; § ? ‡  † ¡  ‡  ¶ ! ( , † § ? ( || * ] [ § ¡ ‘ ¡ , : , , †
§  ) , ? || * ] ? , § § ( !  ¡ ( , .† § † [ ‡ ! ) * ] [  : ? ] ||

    Agreeably to a part of my foregoing definition, that cannot be a proper cryptograph, in which a single character is made [column 2:] to represent more than one letter. Let us for a moment see what would be the result if this was reversed, — that is, if more than one cipher were used for a single letter. In case each letter were represented by two different characters, (used alternately or at random, ) it is evident that while the certainty of reading such a composition correctly, by help of the key, would not be at all diminished, the difficulty of its solution without that help, would be vastly increased. This then is an approach to the formation of a secret cipher. If, now, the number of the characters were extended to three or four for each letter, it might be pronounced with tolerable certainty that such a writing would be " secret." Or, to take an extreme case, a communication might be made, in which no two characters would be alike ! Here all reasoning would be entirely baffled, as there would evidently be no objects of comparison; and even if half a dozen words were known, they would furnish no clue to the rest. Here, then, is a complete non plus to investigation, and we have arrived at a perfect cryptograph. For, since any given cipher would stand for but one letter in the key, there could be but a single and definite solution; and thus both conditions of my definition are fully satisfied. In the following specimen of this method, I have employed the Roman-capital, small letter, and small capital, with their several inversions, giving me the command of 130 characters, or an average of five to each letter. This is to " make assurance doubly sure," for I am satisfied that were an average of three characters used for each letter, such a writing would be emphatically secret. If you will be so kind as to give my cipher a place in your interesting Magazine, I will immediately forward you its key. Hoping that you will not be displeased with my tedious letter,

    The difficulty attending the cipher by key-phrase, viz: that the same characters may convey various meanings — is a difficulty upon which we commented in our first article upon this topic, and more lately at greater length in a private letter to our friend, F. W. Thomas.

    The key-phrase cryptograph is, in fact, altogether inadmissible. The labor requisite for its elucidation, even with the key, would, alone, render it so. Lord Bacon very properly defines three essentials in secret correspondence. It is required, first, that the cipher be such as to elude suspicion of being a cipher; secondly, that its alphabet be so simple of formation as to demand but little time in the construction of an epistle; thirdly, that it shall be absolutely insoluble without the key — we may add, fourthly, that, with the key, it be promptly and certainly decipherable.

    Admitting, now, that the ingenious cryptograph proposed by our correspondent be absolutely what he supposes it, impenetrable, it would still, we think, be inadmissible on the first point above stated and more so on the second. But of its impenetrability we are by no means sure, notwithstanding what, at a cursory glance, appears to be the demonstration of the writer. In the key-phrase cipher an arbitrary character is sometimes made to represent five, six, seven, or even more letters. Our correspondent proposes merely to reverse the operation: — and this simple statement of the case will do more towards convincing him of his error than an elaborate argument, for which he would neither have time, nor our readers patience. In a key-phrase cryptograph, equally as in his own, each discovery is independent, not [page 308:] necessarily affording any clue to farther discovery. Neither is the idea of our friend, although highly ingenious, philosophical, and unquestionably original with him, (since he so assures us,) original in itself. It is one of the many systems tried by Dr. Wallis and found wanting. Perhaps no good cipher was ever invented which its originator did not conceive insoluble; yet, so far, no impenetrable cryptograph has been discovered. Our correspondent will be the less startled at this, our assertion, when he bears in mind that he who has been termed the '` wisest of mankind " — we mean Lord Verulam — was as confident of the absolute insolubility of his own mode as our present cryptographist is of his. What he said upon the subject in his De Augmentis was, at the day of its publication, considered unanswerable. Yet his cipher has been repeatedly unriddled. We may say, in addition, that the nearest approach to perfection in this matter, is the chiffre quarre of the French Academy. This consists of a table somewhat in the form of our ordinary multiplication tables, from which the secret to be conveyed is so written that no letter is ever represented twice by the same character. Out of a thousand individuals nine hundred and ninety-nine would at once pronounce this mode inscrutable. It is yet susceptible, under peculiar circumstances, of prompt and certain solution.

    Mr. T. will have still less confidence in his hastily adopted opinions on this topic when we assure him, from personal experience, that what he says in regard to writing backwards and continuously without intervals between the words — is all wrong. So far from "utterly perplexing the decipherer," it gives him no difficulty, legitimately so called — merely taxing to some extent his patience. We refer him to the files of "Alexander's Weekly Messenger," for 1839 — where he will see that we read numerous ciphers of the class described, even when very ingenious additional difficulties were interposed. We say, in brief, that we should have little trouble in reading the one now proposed.

    "Here," says our friend, referring to another point, "all reasoning would be entirely baffled, as there would evidently be no objects of comparison." This sentence assures us that he is laboring under much error in his conception of cipher solutions. Comparison is a vast aid unquestionably; but not an absolute essential in the elucidation of these mysteries.

    We need not say, however, that this object is an excessively wide one. Our friend will forgive us for not entering into details which would lead us — God knows whither. The ratiocination actually passing through the mind in the solution of even a single cryptograph, if detailed step by step, would fill a large volume. Our time is much occupied, and notwithstanding the limits originally placed to our cartel, we have found ourselves overwhelmed with communications on this subject, and must close it, perforce — deeply interesting as we find it. To this resolution we had arrived last month; but the calm and truly ingenious reasoning of our correspondent has induced us to say these few words more. We print his cipher — with no promise to attempt its solution ourselves — much as we feel inclined to make the promise — and to keep it. Some of our hundred thousand readers will, no doubt, take up the gauntlet thrown down; and our pages shall be open for any communication on the subject, which shall not tax our own abilities or time.

    In speaking of our hundred thousand readers (and we can scarcely suppose the number to be less), we are reminded that of this vast number one, and only one has succeeded in solving the cryptograph of Dr. Frailey. The honor of the solution, is however, due to Mr. RICHARDBOLTON, of Pontotoc, Mississippi. His letter did not reach us until three weeks after the completion of our November number, in which we should, otherwise, have acknowledged it.