“In the first place,” answered Barbicane, “all aerolites do not fall upon the surface of the earth; only a small proportion do so.  Therefore, if we are aerolites it does not necessarily follow that we shall fall upon the moon.”

“Still,” answered Michel, “if we get near enough—­”

“Error,” replied Barbicane.  “Have you not seen shooting stars by thousands in the sky at certain epochs?”

“Yes.”

“Well, those stars, or rather corpuscles, only shine by rubbing against the atmospheric strata.  Now, if they pass through the atmosphere, they pass at less than 16 miles from our globe, and yet they rarely fall.  It is the same with our projectile.  It may approach very near the moon, and yet not fall upon it.”

“But then,” asked Michel, “I am curious to know how our vehicle would behave in space.”

“I only see two hypotheses,” answered Barbicane, after some minutes’ reflection.

“What are they?”

“The projectile has the choice between two mathematical curves, and it will follow the one or the other according to the velocity with which it is animated, and which I cannot now estimate.”

“Yes, it will either describe a parabola or an hyperbola.”

“Yes,” answered Barbicane, “with some speed it will describe a parabola, and with greater speed an hyperbola.”

“I like those grand words!” exclaimed Michel Ardan.  “I know at once what you mean.  And what is your parabola, if you please?”

“My friend,” answered the captain, “a parabola is a conic section arising from cutting a cone by a plane parallel to one of its sides.”

“Oh!” said Michel in a satisfied tone.

“It is about the same trajectory that the bomb of a howitzer describes.”

“Just so.  And an hyperbola?” asked Michel.

“It is a curve formed by a section of a cone when the cutting plane makes a greater angle with the base than the side of the cone makes.”

“Is it possible?” exclaimed Michel Ardan in the most serious tone, as if he had been informed of a grave event.  “Then remember this, Captain Nicholl, what I like in your definition of the hyperbola—­I was going to say of the hyperhumbug—­is that it is still less easy to understand than the word you pretend to define.”

Nicholl and Barbicane paid no attention to Michel Ardan’s jokes.  They had launched into a scientific discussion.  They were eager about what curve the projectile would take.  One was for the hyperbola, the other for the parabola.  They gave each other reasons bristling with x’s.  Their arguments were presented in a language which made Michel Ardan jump.  The discussion was lively, and neither of the adversaries would sacrifice his curve of predilection.

This scientific dispute was prolonged until Michel Ardan became impatient, and said—­

“I say, Messrs. Cosine, do leave off throwing your hyperbolas and parabolas at one’s head.  I want to know the only interesting thing about the business.  We shall follow one or other of your curves.  Very well.  But where will they take us to?”