Chapter 13: Is It a Matter of Figures?

IT WAS SEVEN o'clock in the evening. Judge Jarriquez had all the time been absorbed in working at the puzzle--and was no further advanced--and had forgotten the time of repast and the time of repose, when there came a knock at his study door.

It was time. An hour later, and all the cerebral substance of the vexed magistrate would certainly have evaporated under the intense heat into which he had worked his head.

At the order to enter--which was given in an impatient tone--the door opened and Manoel presented himself.

The young doctor had left his friends on board the jangada at work on the indecipherable document, and had come to see Judge Jarriquez. He was anxious to know if he had been fortunate in his researches. He had come to ask if he had at length discovered the system on which the cryptogram had been written.

The magistrate was not sorry to see Manoel come in. He was in that state of excitement that solitude was exasperating to him. He wanted some one to speak to, some one as anxious to penetrate the mystery as he was. Manoel was just the man.

"Sir," said Manoel as he entered, "one question! Have you succeeded better than we have?"

"Sit down first," exclaimed Judge Jarriquez, who got up and began to pace the room. "Sit down. If we are both of us standing, you will walk one way and I shall walk the other, and the room will be too narrow to hold us."

Manoel sat down and repeated his question.

"No! I have not had any success!" replied the magistrate; "I do not think I am any better off. I have got nothing to tell you; but I have found out a certainty."

"What is that, sir?"

"That the document is not based on conventional signs, but on what is known in cryptology as a cipher, that is to say, on a number."

"Well, sir," answered Manoel, "cannot a document of that kind always be read?"

"Yes," said Jarriquez, "if a letter is invariably represented by the same letter; if an _a, _ for example, is always a _p, _ and a _p_ is always an _x;_ if not, it cannot."

"And in this document?"

"In this document the value of the letter changes with the arbitrarily selected cipher which necessitates it. So a _b_ will in one place be represented by a _k_ will later on become a _z, _ later on an _u_ or an _n_ or an _f, _ or any other letter."

"And then?"

"And then, I am sorry to say, the cryptogram is indecipherable."

"Indecipherable!" exclaimed Manoel. "No, sir; we shall end by finding the key of the document on which the man's life depends."

Manoel had risen, a prey to the excitement he could not control; the reply he had received was too hopeless, and he refused to accept it for good.

At a gesture from the judge, however, he sat down again, and in a calmer voice asked:

"And in the first place, sir, what makes you think that the basis of this document is a number, or, as you call it, a cipher?"

"Listen to me, young man," replied the judge, "and you will be forced to give in to the evidence."

The magistrate took the document and put it before the eyes of Manoel and showed him what he had done.

"I began," he said, "by treating this document in the proper way, that is to say, logically, leaving nothing to chance. I applied to it an alphabet based on the proportion the letters bear to one another which is usual in our language, and I sought to obtain the meaning by following the precepts of our immortal analyst, Edgar Poe. Well, what succeeded with him collapsed with me."

"Collapsed!" exclaimed Manoel.

"Yes, my dear young man, and I at once saw that success sought in that fashion was impossible. In truth, a stronger man than I might have been deceived."

"But I should like to understand," said Manoel, "and I do not--"

"Take the document," continued Judge Jarriquez; "first look at the disposition of the letters, and read it through."

Manoel obeyed.

"Do you not see that the combination of several of the letters is very strange?" asked the magistrate.

"I do not see anything," said Manoel, after having for perhaps the hundredth time read through the document.

"Well! study the last paragraph! There you understand the sense of the whole is bound to be summed up. Do you see anything abnormal?"

"Nothing."

"There is, however, one thing which absolutely proves that the language is subject to the laws of number."

"And that is?"

"That is that you see three _h's_ coming together in two different places."

What Jarriquez said was correct, and it was of a nature to attract attention. The two hundred and fourth, two hundred and fifth, and two hundred and sixth letters of the paragraph, and the two hundred and fifty-eight, two hundred and fifty-ninth, and two hundred and sixtieth letters of the paragraph were consecutive _h's_. At first this peculiarity had not struck the magistrate.

"And that proves?" asked Manoel, without divining the deduction that could be drawn from the combination.

"That simply proves that the basis of the document is a number. It shows _à priori_ that each letter is modified in virtue of the ciphers of the number and according to the place which it occupies."

"And why?"

"Because in no language will you find words with three consecutive repetitions of the letter _h."_

Manoel was struck with the argument; he thought about it, and, in short, had no reply to make.

"And had I made the observation sooner," continued the magistrate, "I might have spared myself a good deal of trouble and a headache which extends from my occiput to my sinciput."

"But, sir," asked Manoel, who felt the little hope vanishing on which he had hitherto rested, "what do you mean by a cipher?"

"Tell me a number."

"Any number you like."

"Give me an example and you will understand the explanation better."

Judge Jarriquez sat down at the table, took up a sheet of paper and a pencil, and said:

"Now, Mr. Manoel, let us choose a sentence by chance, the first that comes; for instance:

_Judge Jarriquez has an ingenious mind._

I write this phrase so as to space the letters different and I get:

_Judgejarriquezhasaningeniousmind._

"That done," said the magistrate, to whom the phrase seemed to contain a proposition beyond dispute, looking Manoel straight in the face, "suppose I take a number by chance, so as to give a cryptographic form to this natural succession of words; suppose now this word is composed of three ciphers, and let these ciphers be 2, 3, and 4. Now on the line below I put the number 234, and repeat it as many times as are necessary to get to the end of the phrase, and so that every cipher comes underneath a letter. This is what we get:

_J u d g e j a r r I q u e z h a s a n I n g e n I o u s m I n d_ 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 And now, Mr. Manoel, replacing each letter by the letter in advance of it in alphabetical order according to the value of the cipher, we get: