A letter thus written being intercepted, and the key-phrase unknown, the individual who should attempt to decipher it may be imagined _guessing_, or otherwise attempting to convince himself, that a certain character (_i_, for example,) represented the letter _e_. Looking throughout the cryptograph for confirmation of this idea, he would 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 by 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.