"A c.o.c.k!" said Nicholl.

"Why no, my friends," Michel answered quickly; "it was I who wished to awake you by this rural sound." So saying, he gave vent to a splendid c.o.c.k-a-doodledoo, which would have done honor to the proudest of poultry-yards.

The two Americans could not help laughing.

"Fine talent that," said Nicholl, looking suspiciously at his companion.

"Yes," said Michel; "a joke in my country. It is very Gallic; they play the c.o.c.k so in the best society."

Then turning the conversation:

"Barbicane, do you know what I have been thinking of all night?"

"No," answered the president.

"Of our Cambridge friends. You have already remarked that I am an ignoramus in mathematical subjects; and it is impossible for me to find out how the savants of the observatory were able to calculate what initiatory speed the projectile ought to have on leaving the Columbiad in order to attain the moon."

"You mean to say," replied Barbicane, "to attain that neutral point where the terrestrial and lunar attractions are equal; for, starting from that point, situated about nine-tenths of the distance traveled over, the projectile would simply fall upon the moon, on account of its weight."

"So be it," said Michel; "but, once more; how could they calculate the initiatory speed?"

"Nothing can be easier," replied Barbicane.

"And you knew how to make that calculation?" asked Michel Ardan.

"Perfectly. Nicholl and I would have made it, if the observatory had not saved us the trouble."

"Very well, old Barbicane," replied Michel; "they might have cut off my head, beginning at my feet, before they could have made me solve that problem."

"Because you do not know algebra," answered Barbicane quietly.

"Ah, there you are, you eaters of _x_^1; you think you have said all when you have said `Algebra.'"

"Michel," said Barbicane, "can you use a forge without a hammer, or a plow without a plowshare?"

"Hardly."

"Well, algebra is a tool, like the plow or the hammer, and a good tool to those who know how to use it."

"Seriously?"

"Quite seriously."

"And can you use that tool in my presence?"

"If it will interest you."

"And show me how they calculated the initiatory speed of our car?"

"Yes, my worthy friend; taking into consideration all the elements of the problem, the distance from the center of the earth to the center of the moon, of the radius of the earth, of its bulk, and of the bulk of the moon, I can tell exactly what ought to be the initiatory speed of the projectile, and that by a simple formula."

"Let us see."

"You shall see it; only I shall not give you the real course drawn by the projectile between the moon and the earth in considering their motion round the sun. 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.