became absorbed in his work, whilst Nicholl looked
into space, leaving the care of preparing breakfast to his companion.

Half-an-hour had not elapsed before Barbicane, raising his head, showed
Michel Ardan a page covered with algebraical signs, amidst which the
following general formula was discernible:--

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