1 2 2 r m’ r r
    — (v — v ) = gr { —–­ — 1 + —–­ ( —–­ — —–­) }
    2 0 x m d-x d-r

“And what does that mean?” asked Michel.

“That means,” answered Nicholl, “that the half of v minus v zero square equals gr multiplied by r upon x minus 1 plus m prime upon m multiplied by r upon d minus x, minus r upon d minus x minus r—­”

“X upon y galloping upon z and rearing upon p” cried Michel Ardan, bursting out laughing.  “Do you mean to say you understand that, captain?”

“Nothing is clearer.”

“Then,” said Michel Ardan, “it is as plain as a pikestaff, and I want nothing more.”

“Everlasting laugher,” said Barbicane, “you wanted algebra, and now you shall have it over head and ears.”

“I would rather be hung!”

“That appears a good solution, Barbicane,” said Nicholl, who was examining the formula like a connaisseur.  “It is the integral of the equation of ‘vis viva,’ and I do not doubt that it will give us the desired result.”

“But I should like to understand!” exclaimed Michel.  “I would give ten years of Nicholl’s life to understand!”

“Then listen,” resumed Barbicane.  “The half of v minus v zero square is the formula that gives us the demi-variation of the ‘vis viva.’”

“Good; and does Nicholl understand what that means?”

“Certainly, Michel,” answered the captain.  “All those signs that look so cabalistic to you form the clearest and most logical language for those who know how to read it.”

“And do you pretend, Nicholl,” asked Michel, “that by means of these hieroglyphics, more incomprehensible than the Egyptian ibis, you can find the initial speed necessary to give to the projectile?”

“Incontestably,” answered Nicholl; “and even by that formula I could always tell you what speed it is going at on any point of the journey.”

“Upon your word of honour?”

“Yes.”

“Then you are as clever as our president.”

“No, Michel, all the difficulty consists in what Barbicane has done.  It is to establish an equation which takes into account all the conditions of the problem.  The rest is only a question of arithmetic, and requires nothing but a knowledge of the four rules.”

“That’s something,” answered Michel Ardan, who had never been able to make a correct addition in his life, and who thus defined the rule:  “A Chinese puzzle, by which you can obtain infinitely various results.”

Still Barbicane answered that Nicholl would certainly have found the formula had he thought about it.

“I do not know if I should,” said Nicholl, “for the more I study it the more marvellously correct I find it.”

“Now listen,” said Barbicane to his ignorant comrade, “and you will see that all these letters have a signification.”