Eight Hundred Leagues on the Amazon by Jules Verne

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"What did Edgar Poe do?" he repeated. "First of all he began by
finding out the sign--here there are only letters, let us say the
letter--which was reproduced the oftenest. I see that that is _h,_
for it is met with twenty-three times. This enormous proportion
shows, to begin with, that _h_ does not stand for _h,_ but, on the
contrary, that it represents the letter which recurs most frequently
in our language, for I suppose the document is written in Portuguese.
In English or French it would certainly be _e,_ in Italian it would
be _i_ or _a,_ in Portuguese it will be _a_ or _o_. Now let us say
that it signifies _a_ or _o."_

After this was done, the judge found out the letter which recurred
most frequently after _h,_ and so on, and he formed the following
table:

    _h_ = 23 times
    _y_ = 19  --
    _u_ = 17  --
  _d p q_ = 16  --
   _g v_ = 13  --
_o r x z_ = 12  --
   _f s_ = 10  --
_e k l m n_ =  9  --
   _j t_ =  8  --
   _b i_ =  8  --
   _a c_ =  8  --

"Now the letter _a_ only occurs thrice!" exclaimed the judge, "and it
ought to occur the oftenest. Ah! that clearly proves that the meaning
had been changed. And now, after _a_ or _o,_ what are the letters
which figure oftenest in our language? Let us see," and Judge
Jarriquez, with truly remarkable sagacity, which denoted a very
observant mind, started on this new quest. In this he was only
imitating the American romancer, who, great analyst as he was, had,
by simple induction, been able to construct an alphabet corresponding
to the signs of the cryptogram and by means of it to eventually read
the pirate's parchment note with ease.

The magistrate set to work in the same way, and we may affirm that he
was no whit inferior to his illustrious master. Thanks to his
previous work at logogryphs and squares, rectangular arrangements and
other enigmas, which depend only on an arbitrary disposition of the
letters, he was already pretty strong in such mental pastimes. On
this occasion he sought to establish the order in which the letters
were reproduced--vowels first, consonants afterward.

Three hours had elapsed since he began. He had before his eyes an
alphabet which, if his procedure were right, would give him the right
meaning of the letters in the document. He had only to successively
apply the letters of his alphabet to those of his paragraph. But
before making this application some slight emotion seized upon the
judge. He fully experienced the intellectual gratification--much
greater than, perhaps, would be thought--of the man who, after hours
of obstinate endeavor, saw the impatiently sought-for sense of the
logogryph coming into view.

"Now let us try," he said; "and I shall be very much surprised if I
have not got the solution of the enigma!"

Judge Jarriquez took off his spectacles and wiped the glasses; then
he put them back again and bent over the table. His special alphabet
was in one hand, the cryptogram in the other. He commenced to write
under the first line of the paragraph the true letters, which,
according to him, ought to correspond exactly with each of the
cryptographic letters. As with the first line so did he with the
second, and the third, and the fourth, until he reached the end of
the paragraph.

Oddity as he was, he did not stop to see as he wrote if the
assemblage of letters made intelligible words. No; during the first
stage his mind refused all verification of that sort. What he desired
was to give himself the ecstasy of reading it all straight off at
once.

And now he had done.

"Let us read!" he exclaimed.

And he read. Good heavens! what cacophony! The lines he had formed
with the letters of his alphabet had no more sense in them that those
of the document! It was another series of letters, and that was all.
They formed no word; they had no value. In short, they were just as
hieroglyphic.

"Confound the thing!" exclaimed Judge Jarriquez.

CHAPTER XIII

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:

                              _j_ + 2 = _l_
                              _u_ + 3 = _x_
                              _d_ + 4 = _h_
                              _g_ + 2 = _i_
                              _e_ + 3 = _h_
                              _j_ + 4 = _n_
                              _a_ + 2 = _c_
                              _r_ + 3 = _u_
                              _r_ + 4 = _v_
                              _i_ + 2 = _k_
                              _q_ + 3 = _t_
                              _u_ + 4 = _y_
                              _e_ + 2 = _g_
                              _a_ + 3 = _c_
                              _h_ + 4 = _t_
                              _a_ + 2 = _c_
                              _s_ + 3 = _v_
                              _a_ + 4 = _e_
                              _n_ + 2 = _p_
                              _i_ + 3 = _l_
                              _n_ + 4 = _r_
                              _g_ + 2 = _i_
                              _e_ + 3 = _h_
                              _n_ + 4 = _r_
                              _i_ + 2 = _k_
                              _o_ + 3 = _r_
                              _u_ + 4 = _y_
                              _s_ + 2 = _u_
and so on.

"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
replaced 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.

"And so we must trust to chance alone," continued Jarriquez, who
shook his head, "and chance does not often do much in things of this
sort."

"But still," said Manoel, "chance might give us this number."

"This number," exclaimed the magistrate--"this number? But how many
ciphers is it composed of? Of two, or three, or four, or nine, or
ten? Is it made of different ciphers only or of ciphers in different
order many times repeated? Do you not know, young man, that with the
ordinary ten ciphers, using all at a time, but without any
repetition, you can make three million two hundred and sixty-eight
thousand and eight hundred different numbers, and that if you use the
same cipher more than once in the number, these millions of
combinations will be enormously increased! And do you not know that
if we employ every one of the five hundred and twenty-five thousand
and six hundred minutes of which the year is composed to try at each
of these numbers, it would take you six years, and that you would
want three centuries if each operation took you an hour? No! You ask
the impossible!"

"Impossible, sir?" answered Manoel. "An innocent man has been branded
as guilty, and Joam Dacosta is to lose his life and his honor while
you hold in your hands the material proof of his innocence! That is
what is impossible!"

"Ah! young man!" exclaimed Jarriquez, "who told you, after all, that
Torres did not tell a lie? Who told you that he really did have in
his hands a document written by the author of the crime? that this
paper was the document, and that this document refers to Joam
Dacosta?"

"Who told me so?" repeated Manoel, and his face was hidden in his
hands.

In fact, nothing could prove for certain that the document had
anything to do with the affair in the diamond province. There was, in
fact, nothing to show that it was not utterly devoid of meaning, and
that it had been imagined by Torres himself, who was as capable of
selling a false thing as a true one!

"It does not matter, Manoel," continued the judge, rising; "it does
not matter! Whatever it may be to which the document refers, I have
not yet given up discovering the cipher. After all, it is worth more
than a logogryph or a rebus!"

At these words Manoel rose, shook hands with the magistrate, and
returned to the jangada, feeling more hopeless when he went back than
when he set out.

CHAPTER XIV

CHANCE!

A COMPLETE change took place in public opinion on the subject of Joam
Dacosta. To anger succeeded pity. The population no longer thronged
to the prison of Manaos to roar out cries of death to the prisoner.
On the contrary, the most forward of them in accusing him of being
the principal author of the crime of Tijuco now averred that he was
not guilty, and demanded his immediate restoration to liberty. Thus
it always is with the mob--from one extreme they run to the other.
But the change was intelligible.

The events which had happened during the last few days--the struggle
between Benito and Torres; the search for the corpse, which had
reappeared under such extraordinary circumstances; the finding of the
"indecipherable" document, if we can so call it; the information it
concealed, the assurance that it contained, or rather the wish that
it contained, the material proof of the guiltlessness of Joam
Dacosta; and the hope that it was written by the real culprit--all
these things had contributed to work the change in public opinion.
What the people had desired and impatiently demanded forty-eight
hours before, they now feared, and that was the arrival of the
instructions due from Rio de Janeiro.

These, however, were not likely to be delayed.

Joam Dacosta had been arrested on the 24th of August, and examined
next day. The judge's report was sent off on the 26th. It was now the
28th. In three or four days more the minister would have come to a
decision regarding the convict, and it was only too certain that
justice would take its course.

There was no doubt that such would be the case. On the other hand,
that the assurance of Dacosta's innocence would appear from the
document, was not doubted by anybody, neither by his family nor by
the fickle population of Manaos, who excitedly followed the phases of
this dramatic affair.

But, on the other hand, in the eyes of disinterested or indifferent
persons who were not affected by the event, what value could be
assigned to this document? and how could they even declare that it
referred to the crime in the diamond arrayal? It existed, that was
undeniable; it had been found on the corpse of Torres, nothing could
be more certain. It could even be seen, by comparing it with the
letter in which Torres gave the information about Joam Dacosta, that
the document was not in the handwriting of the adventurer. But, as
had been suggested by Judge Jarriquez, why should not the scoundrel
have invented it for the sake of his bargain? And this was less
unlikely to be the case, considering that Torres had declined to part
with it until after his marriage with Dacosta's daughter--that is to
say, when it would have been impossible to undo an accomplished fact.

All these views were held by some people in some form, and we can
quite understand what interest the affair created. In any case, the
situation of Joam Dacosta was most hazardous. If the document were
not deciphered, it would be just the same as if it did not exist; and
if the secret of the cryptogram were not miraculously divined or
revealed before the end of the three days, the supreme sentence would
inevitably be suffered by the doomed man of Tijuco. And this miracle
a man attempted to perform! The man was Jarriquez, and he now really
set to work more in the interest of Joam Dacosta than for the
satisfaction of his analytical faculties. A complete change had also
taken place in his opinion. Was not this man, who had voluntarily
abandoned his retreat at Iquitos, who had come at the risk of his
life to demand his rehabilitation at the hands of Brazilian justice,
a moral enigma worth all the others put together? And so the judge
had resolved never to leave the document until he had discovered the
cipher. He set to work at it in a fury. He ate no more; he slept no
more! All his time was passed in inventing combinations of numbers,
in forging a key to force this lock!

This idea had taken possession of Judge Jarriquez's brain at the end
of the first day. Suppressed frenzy consumed him, and kept him in a
perpetual heat. His whole house trembled; his servants, black or
white, dared not come near him. Fortunately he was a bachelor; had
there been a Madame Jarriquez she would have had a very uncomfortable
time of it. Never had a problem so taken possession of this oddity,
and he had thoroughly made up his mind to get at the solution, even
if his head exploded like an overheated boiler under the tension of
its vapor.

It was perfectly clear to the mind of the worthy magistrate that the
key to the document was a number, composed of two or more ciphers,
but what this number was all investigation seemed powerless to
discover.

This was the enterprise on which Jarriquez, in quite a fury, was
engaged, and during this 28th of August he brought all his faculties
to bear on it, and worked away almost superhumanly.

To arrive at the number by chance, he said, was to lose himself in
millions of combinations, which would absorb the life of a first-rate
calculator. But if he could in no respect reckon on chance, was it
impossible to proceed by reasoning? Decidedly not! And so it was "to
reason till he became unreasoning" that Judge Jarriquez gave himself
up after vainly seeking repose in a few hours of sleep. He who
ventured in upon him at this moment, after braving the formal
defenses which protected his solitude, would have found him, as on
the day before, in his study, before his desk, with the document
under his eyes, the thousands of letters of which seemed all jumbled
together and flying about his head.

"Ah!" he explaimed, "why did not the scoundrel who wrote this
separate the words in this paragraph? We might--we will try--but no!
However, if there is anything here about the murder and the robbery,
two or three words there must be in it--'arrayal,' 'diamond,'
'Tijuco,' 'Dacosta,' and others; and in putting down their
cryptological equivalents the number could be arrived at. But there
is nothing--not a single break!--not one word by itself! One word of
two hundred and seventy-six letters! I hope the wretch may be blessed
two hundred and seventy-six times for complicating his system in this
way! He ought to be hanged two hundred and seventy-six times!"

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