"Well, these stars, or rather corpuscules, only shine when they are heated by gliding over the atmospheric layers. Now, if they enter the atmosphere, they pass at least within forty miles of the earth, but they seldom fall upon it. The same with our projectile. It may approach very near to the moon, and yet not fall upon it." "But then," asked Michel, "I shall be curious to know how our erring vehicle will act in space?" "I see but two hypotheses," replied Barbicane, after some moments' reflection. "What are they?" "The projectile has the choice between two mathematical curves, and it will follow one or the other according to the speed with which it is animated, and which at this moment I cannot estimate." "Yes," said Nicholl, "it will follow either a parabola or a hyperbola." "Just so," replied Barbicane. "With a certain speed it will assume the parabola, and with a greater the hyperbola." "I like those grand words," exclaimed Michel Ardan; "one knows directly what they mean. And pray what is your parabola, if you please?" "My friend," answered the captain, "the parabola is a curve of the second order, the result of the section of a cone intersected by a plane parallel to one of its sides." "Ah! ah!" said Michel, in a satisfied tone. "It is very nearly," continued Nicholl, "the course described by a bomb launched from a mortar." "Perfect! And the hyperbola?" "The hyperbola, Michel, is a curve of the second order, produced by the intersection of a conic surface and a plane parallel to its axis, and constitutes two branches separated one from the other, both tending indefinitely in the two directions." "Is it possible!" exclaimed Michel Ardan in a serious tone, as if they had told him of some serious event. "What I particularly like in your definition of the hyperbola (I was going to say hyperblague) is that it is still more obscure than the word you pretend to define." Nicholl and Barbicane cared little for Michel Ardan's fun. They were deep in a scientific discussion. What curve would the projectile follow? was their hobby. One maintained the hyperbola, the other the parabola. They gave each other reasons bristling with _x_. Their arguments were couched in language which made Michel jump. The discussion was hot, and neither would give up his chosen curve to his adversary. This scientific dispute lasted so long that it made Michel very impatient. "Now, gentlemen cosines, will you cease to throw parabolas and hyperbolas at each other's heads? I want to understand the only interesting question in the whole affair. We shall follow one or other of these curves? Good. But where will they lead us to?" "Nowhere," replied Nicholl. "How, nowhere?" "Evidently," said Barbicane, "they are open curves, which may be prolonged indefinitely." "Ah, savants!" cried Michel; "and what are either the one or the other to us from the moment we know that they equally lead us into infinite space?"