"Precisely," said Barbican; "at a certain velocity it would take a parabolic curve; with a velocity considerably greater it should describe a hyperbolic curve."
"I always did like nice corpulent words," said Ardan, trying to laugh; "bloated and unwieldy, they express in a neat handy way exactly what you mean. Of course, I know all about the high—high—those high curves, and those low curves. No matter. Explain them to me all the same. Consider me most deplorably ignorant on the nature of these curves."
"Well," said the Captain, a little bumptiously, "a parabola is a curve of the second order, formed by the intersection of a cone by a plane parallel to one of its sides."
"You don't say so!" cried Ardan, with mouth agape. "Do tell!"
"It is pretty nearly the path taken by a shell shot from a mortar."
"Well now!" observed Ardan, apparently much surprised; "who'd have thought it? Now for the high—high—bully old curve!"
"The hyperbola," continued the Captain, not minding Ardan's antics, "the hyperbola is a curve of the second order, formed from the intersection of a cone by a plane parallel to its axis, or rather parallel to its two generatrices, constituting two separate branches, extending indefinitely in both directions."
"Oh, what an accomplished scientist I'm going to turn out, if only left long enough at your feet, illustrious maestro!" cried Ardan, with effusion. "Only figure it to yourselves, boys; before the Captain's lucid explanations, I fully expected to hear something about the high curves and the low curves in the back of an Ancient Thomas! Oh, Michael, Michael, why didn't you know the Captain earlier?"
But the Captain was now too deeply interested in a hot discussion with Barbican to notice that the Frenchman was only funning him. Which of the two curves had been the one most probably taken by the Projectile? Barbican maintained it was the parabolic; M'Nicholl insisted that it was the hyperbolic. Their tempers were not improved by the severe cold, and both became rather excited in the dispute. They drew so many lines on the table, and crossed them so often with others, that nothing was left at last but a great blot. They covered bits of paper with x's and y's, which they read out like so many classic passages, shouting them, declaiming them, drawing attention to the strong points by gesticulation so forcible and voice so loud that neither of the disputants could hear a word that the other said. Possibly the very great difference in temperature between the external air in contact with their skin and the blood coursing through their veins, had given rise to magnetic currents as potential in their effects as a superabundant supply of oxygen. At all events, the language they soon began to employ in the enforcement of their arguments fairly made the Frenchman's hair stand on end.
"You probably forget the important difference between a directrix and an axis," hotly observed Barbican.