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In the cryptographs, on the other hand, which have been sent us by our correspondent at Stonington, and which are identical in conformation with the cipher resolved by Berryer, no such permanent advantage is to be obtained.

Let us refer to the second of these puzzles. Its key-phrase runs thus:

Surfeiter ire mono, fortiter in ret

Let us now place the alphabet beneath this phrase, letter beneath letter —

S|u|a|v|i|t|e|r|i|n|m|o|d|o|f|o|r|t|i|t|e|r|i|n|r|e

A|b|c|d|e|f|g|h|i|j|k|l|m|n|o|p|q|r|s|t|u|v|w|x|y|z

We here see that

a stands for — — — — — — — — — — — c

d " " — — — — — — — — — — — m

e " " — — — — — — — — — — — z

f " " g, u and o

i " " — — — — — — — — — — — w

m " " e, i, s and k

n " " j and x

o " " — — — — — — — — — — — p

r " " h, q, v and y

s " " — — — — — — — — — — — a

t " " — — — — — — — — — — — t

u " " f, r, and b

v " " — — — — — — — — — — — d

In this manner n stands for two letters, and e, o, and t for three each, while i and r represent each as many as four. Thirteen characters are made to perform the operations of the whole alphabet. The result of such a key-phrase upon the cipher, is to give it the appearance of a mere medley of the letters e, o, t, r and i — the latter character greatly predominating, through the accident of being employed for letters which, themselves, are inordinately prevalent in most languages — we mean e and i. [column 2:]

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 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