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meet with nothing but a negation of it. He would see the character in situations where it could not possibly represent e. He might, for instance, be puzzled by four i's forming of themselves a single word, without the intervention of any other character; in which case, of course, they could not be all e's. It will be seen that the word wise might be thus constructed. We say this may be seen now, by us, in possession of the key-phrase; but the question will, no doubt, occur, how, without the key-phrase, and without cognizance of any single letter in the cipher, it would be possible for the interceptor of such a cryptograph to make any thing of such a word as iiii?

But again. A key-phrase might easily be constructed, in which one character would represent seven, eight, or ten letters. Let us then imagine the word iiiiiiiiii presenting itself in a cryptograph to an individual without the proper key-phrase; or, if this be a supposition somewhat too perplexing, let us suppose it occurring to the person for whom the cipher is designed, and who has the key-phrase. What is he to do with such a word as iiiiiiiiii? In any of the ordinary books upon Algebra will be found a very concise formula (we have not the necessary type for its insertion here) for ascertaining the number of arrangements in which m letters may be placed, taken n at a time. But no doubt there are none of our readers ignorant of the innumerable combinations which may be made from these ten i's. Yet, unless it occur otherwise bv accident, the correspondent receiving the cipher would have to write down all these combinations before attaining the word intended; and even when he had written them, he would be inexpressibly perplexed in selecting the word designed from the vast number of other words arising in the course of the permutation.

To obviate, therefore, the exceeding difficulty of deciphering this species of cryptograph, on the part of the possessors of the key-phrase, and to confine the deep intricacy of the puzzle to those for whom the cipher was not designed, it becomes necessary that some order should be agreed upon by the parties corresponding--some order in reference to which those characters are to be read which represent more than one letter--and this order must be held in view by the writer of the cryptograph. It may be agreed, for example, that the f rat time an i occurs in the cipher, it is to be understood as representing that character which stands against the first i in the key-phrase; that the second time an i occurs it must be supposed to represent that letter which stands opposed to the second i in the key-phrase, &c. &c. Thus the location of each cipherical letter must be considered in connexion with the character itself, in order to determine its exact signification.

We say that some pre-concerted order of this kind is necessary, lest the cipher prove too intricate a lock to yield even to its true key. But it will be evident, upon inspection, that our correspondent at Stonington has inflicted upon us a cryptograph in which no order has been preserved; in which many characters, respectively, stand, at absolute random, for many others. If, therefore, in regard to the gauntlet we threw down in April, he should be half inclined to accuse us of braggadocio, he will yet admit that we have more than acted up to our boast. If what we then said was not said suaviter in modo, what we now do is at least done fortiter in re.

In these cursory observations we have by no means attempted to exhaust the subject of Cryptography. With such object in view, a folio might be required. We have indeed mentioned only a few of the ordinary modes of cipher. Even two thousand years ago, Æneas Tacticus detailed twenty distinct methods; and modern ingenuity has added much to the science. Our design has been chiefly suggestive; and perhaps we have already bored the readers of the Magazine. To those who desire farther information upon this topic, we may say that there are extant treatises by Trithemius, Cap. Porta, Vignere, and P. Niceron. The works of the two latter