"If, on account of the value of the ciphers which compose the number I come to the end of the alphabet without having enough complementary letters to deduct, I begin again at the beginning. That is what happens at the end of my name when the _z_ is replaced by the 3. As after _z_ the alphabet has no more letters, I commence to count from _a,_ and so get the _c_. That done, when I get to the end of this cryptographic system, made up of the 234--which was arbitrarily selected, do not forget!--the phrase which you recognize above is replace by

_lxhihncuvktygclveplrihrkryupmpg._

"And now, young man, just look at it, and do you not think it is very much like what is in the document? Well, what is the consequence? Why, that the signification of the letters depends on a cipher which chance puts beneath them, and the cryptographic letter which answers to a true one is not always the same. So in this phrase the first _j_ is represented by an _l,_ the second by an _n;_ the first _e_ by an _h,_ the second b a _g,_ the third by an _h;_ the first _d_ is represented by an _h,_ the last by a _g;_ the first _u_ by an _x,_ the last by a _y;_ the first and second _a's_ by a _c,_ the last by an _e;_ and in my own name one _r_ is represented by a _u,_ the other by a _v._ and so on. Now do you see that if you do not know the cipher 234 you will never be able to read the lines, and consequently if we do not know the number of the document it remains undecipherable."

On hearing the magistrate reason with such careful logic, Manoel was at first overwhelmed, but, raising his head, he exclaimed:

"No, sir, I will not renounce the hope of finding the number!"

"We might have done so," answered Judge Jarriquez, "if the lines of the document had been divided into words."

"And why?"

"For this reason, young man. I think we can assume that in the last paragraph all that is written in these earlier paragraphs is summed up. Now I am convinced that in it will be found the name of Joam Dacosta. Well, if the lines had been divided into words, in trying the words one after the other--I mean the words composed of seven letters, as the name of Dacosta is--it would not have been impossible to evolve the number which is the key of the document."

"Will you explain to me how you ought to proceed to do that, sir?" asked Manoel, who probably caught a glimpse of one more hope.

"Nothing can be more simple," answered the judge. "Let us take, for example, one of the words in the sentence we have just written--my name, if you like. It is represented in the cryptogram by this queer succession of letters, _ncuvktygc_. Well, arranging these letters in a column, one under the other, and then placing against them the letters of my name and deducting one from the other the numbers of their places in alphabetical order, I see the following result:

                            Between _n_ and _j_ we have 4 letters                               --    _c_ -- _a_    --    2    --                               --    _u_ -- _r_    --    3    --                               --    _v_ -- _r_    --    4    --                               --    _k_ -- _i_    --    2    --                               --    _t_ -- _q_    --    3    --                               --    _y_ -- _u_    --    4    --                               --    _g_ -- _e_    --    2    --                               --    _c_ -- _z_    --    3    --

"Now what is the column of ciphers made up of that we have got by this simple operation? Look here! 423 423 423, that is to say, of repetitions of the numbers 423, or 234, or 342."

"Yes, that is it!" answered Manoel.

"You understand, then, by this means, that in calculating the true letter from the false, instead of the false from the true, I have been able to discover the number with ease; and the number I was in search of is really the 234 which I took as the key of my cryptogram."

"Well, sir!" exclaimed Manoel, "if that is so, the name of Dacosta is in the last paragraph; and taking successively each letter of those lines for the first of the seven letters which compose his name, we ought to get----"

"That would be impossible," interrupted the judge, "except on one condition."

"What is that?"

"That the first cipher of the number should happen to be the first letter of the word Dacosta, and I think you will agree with me that that is not probable."

"Quite so!" sighed Manoel, who, with this improbability, saw the last chance vanish.