No, I shall consider these two orbs as perfectly motionless, which will answer all our purpose."

"And why?"

"Because it will be trying to solve the problem called `the problem of the three bodies,' for which the integral calculus is not yet far enough advanced."

"Then," said Michel Ardan, in his sly tone, "mathematics have not said their last word?"

"Certainly not," replied Barbicane.

"Well, perhaps the Selenites have carried the integral calculus farther than you have; and, by the bye, what is this `integral calculus?'"

"It is a calculation the converse of the differential," replied Barbicane seriously.

"Much obliged; it is all very clear, no doubt."

"And now," continued Barbicane, "a slip of paper and a bit of pencil, and before a half-hour is over I will have found the required formula."

Half an hour had not elapsed before Barbicane, raising his head, showed Michel Ardan a page covered with algebraical signs, in which the general formula for the solution was contained.

"Well, and does Nicholl understand what that means?"

"Of course, Michel," replied the captain. "All these signs, which seem cabalistic to you, form the plainest, the clearest, and the most logical language to those who know how to read it."

"And you pretend, Nicholl," asked Michel, "that by means of these hieroglyphics, more incomprehensible than the Egyptian Ibis, you can find what initiatory speed it was necessary to give the projectile?"

"Incontestably," replied Nicholl; "and even by this same formula I can always tell you its speed at any point of its transit."

"On your word?"

"On my word."

"Then you are as cunning as our president."

"No, Michel; the difficult part is what Barbicane has done; that is, to get an equation which shall satisfy all the conditions of the problem. The remainder is only a question of arithmetic, requiring merely the knowledge of the four rules."

"That is something!" replied Michel Ardan, who for his life could not do addition right, and who defined the rule as a Chinese puzzle, which allowed one to obtain all sorts of totals.

"The expression v zero, which you see in that equation, is the speed which the projectile will have on leaving the atmosphere."

"Just so," said Nicholl; "it is from that point that we must calculate the velocity, since we know already that the velocity at departure was exactly one and a half times more than on leaving the atmosphere."

"I understand no more," said Michel.

"It is a very simple calculation," said Barbicane.

"Not as simple as I am," retorted Michel.

"That means, that when our projectile reached the limits of the terrestrial atmosphere it had already lost one-third of its initiatory speed."

"As much as that?"

"Yes, my friend; merely by friction against the atmospheric strata. You understand that the faster it goes the more resistance it meets with from the air."

"That I admit," answered Michel; "and I understand it, although your x's and zero's, and algebraic formula, are rattling in my head like nails in a bag."

"First effects of algebra," replied Barbicane; "and now, to finish, we are going to prove the given number of these different expressions, that is, work out their value."

"Finish me!" replied Michel.

Barbicane took the paper, and began to make his calculations with great rapidity. Nicholl looked over and greedily read the work as it proceeded.

"That's it! that's it!" at last he cried.

"Is it clear?" asked Barbicane.

"It is written in letters of fire," said Nicholl.

"Wonderful fellows!" muttered Ardan.

"Do you understand it at last?" asked Barbicane.

"Do I understand it?" cried Ardan; "my head is splitting with it."

"And now," said Nicholl, "to find out the speed of the projectile when it leaves the atmosphere, we have only to calculate that."

The captain, as a practical man equal to all difficulties, began to write with frightful rapidity. Divisions and multiplications grew under his fingers; the figures were like hail on the white page. Barbicane watched him, while Michel Ardan nursed a growing headache with both hands.