Lest the tenor of our observations on Cryptography should be misunderstood, and especially lest the nature of our challenge should be misconceived, we take occasion to refer to our Review of Mr. Walsh’s “Sketches of Conspicuous Living Characters of France,” published in the April number of the Magazine. M. Berryer, the French Minister, is there said to have displayed the highest ingenuity in the solution of a cipher addressed by the Duchess of Berri to the legitimists of Paris, but of which she had neglected to furnish the key. Berryer discovered this to be the phrase “Le gouvernement provisoire.” Beneath this sentence the alphabet had been placed, letter for letter; and thus when _a_ was intended _l_ was written, when _b_ was meant _e_ was substituted, and so on throughout. This species of cryptograph is justly considered very difficult. We remarked, however, that we would engage to read any one _of the kind_; and to this limit our correspondents must confine themselves. To be sure, we said, in our last number, that “human ingenuity could not construct a cipher which human ingenuity could not resolve”—but then we do not propose, just now, to make ourselves individually the test of “human ingenuity” in general. We do not propose to solve _all_ ciphers. Whether we can or cannot do this is a question for another day—a day when we have more leisure than at present we have any hope of enjoying. The most simple cryptograph requires, in its solution, labor, patience, and much time. We therefore abide by the limits of our cartel. It is true that in attempting the perusal of Dr. Frailey’s we have exceeded these limits by very much; but we were seduced into the endeavor to read it by the decided manner in which an opinion was expressed that we could not. E. St. J. will observe that his cipher includes _every_ letter of the natural alphabet. Then (admitting it to be a cipher of the kind proposed) his key-phrase must contain every letter of the natural alphabet. In such case no letter of the phrase can stand _for more than one_ of the alphabet, and the whole would be nothing more than a simple cipher, where the natural characters are represented, invariably and respectively, by arbitrary ones. But in this supposition there could be no such words as _ll_, &c.—words seen in the cryptograph. _Therefore_, his cipher is _not_ within the limits prescribed—Q. E. D. We do not say that we _cannot_ solve it, but that we will not make the attempt. This for the obvious reasons above assigned. P. S. We have just received the annexed letter from Mr. Thomas, enclosing one from Dr. Frailey: Washington, July 6th, 1841. My Dear Sir, This morning I received yours of yesterday, deciphering the “cryptograph” which I sent you last week, from my friend, Doctor Frailey. You request that I would obtain the Doctor’s acknowledgment of your solution. I have just received the enclosed from him.