Round the Moon Jules Verne (english readers TXT) 📖

“I would rather be hung!”

“That appears a good solution, Barbicane,” said Nicholl, who was examining the formula like a connaisseur. “It is the integral of the equation of ‘vis viva,’ and I do not doubt that it will give us the desired result.”

“But I should like to understand!” exclaimed Michel. “I would give ten years of Nicholl’s life to understand!”

“Then listen,” resumed Barbicane. “The half of v minus v zero square is the formula that gives us the demi-variation of the ‘vis viva.’ ”

“Good; and does Nicholl understand what that means?”

“Certainly, Michel,” answered the captain. “All those signs that look so cabalistic to you form the clearest and most logical language for those who know how to read it.”

“And do you pretend, Nicholl,” asked Michel, “that by means of these hieroglyphics, more incomprehensible than the Egyptian ibis, you can find the initial speed necessary to give to the projectile?”

“Incontestably,” answered Nicholl; “and even by that formula I could always tell you what speed it is going at on any point of the journey.”

“Upon your word of honour?”

“Yes.”

“Then you are as clever as our president.”

“No, Michel, all the difficulty consists in what Barbicane has done. It is to establish an equation which takes into account all the conditions of the problem. The rest is only a question of arithmetic, and requires nothing but a knowledge of the four rules.”

“That’s something,” answered Michel Ardan, who had never been able to make a correct addition in his life, and who thus defined the rule: “A Chinese puzzle, by which you can obtain infinitely various results.”

Still Barbicane answered that Nicholl would certainly have found the formula had he thought about it.

“I do not know if I should,” said Nicholl, “for the more I study it the more marvellously correct I find it.”

“Now listen,” said Barbicane to his ignorant comrade, “and you will see that all these letters have a signification.”

“I am listening,” said Michel, looking resigned.

“d,” said Barbicane, “is the distance from the centre of the earth to the centre of the moon, for we must take the centres to calculate the attraction.”

“That I understand.”

“r is the radius of the earth.”

“r, radius; admitted.”

“m is the volume of the earth; m prime that of the moon. We are obliged to take into account the volume of the two attracting bodies, as the attraction is in proportion to the volume.”

“I understand that.”

“g represents gravity, the speed acquired at the end of a second by a body falling on the surface of the earth. Is that clear?”

“A mountain stream!” answered Michel.

“Now I represent by x the variable distance that separates the projectile from the centre of the earth, and by v the velocity the projectile has at that distance.”

“Good.”

“Lastly, the expression v zero which figures in the equation is the speed the bullet possesses when it emerges from the atmosphere.”

“Yes,” said Nicholl, “you were obliged to calculate the velocity from that point, because we knew before that the velocity at departure is exactly equal to ³⁄₂ of the velocity upon emerging from the atmosphere.”

“Don’t understand any more!” said Michel.

“Yet it is very simple,” said Barbicane.

“I do not find it very simple,” replied Michel.

“It means that when our projectile reached the limit of the terrestrial atmosphere it had already lost one-third of its initial velocity.”

“As much as that?”

“Yes, my friend, simply by friction against the atmosphere. You will easily understand that the greater its speed the more resistance it would meet with from the air.”

“That I admit,” answered Michel, “and I understand it, although your v zero two and your v zero square shake about in my head like nails in a sack.”

“First effect of algebra,” continued Barbicane. “And now to finish we are going to find the numerical known quantity of these different expressions⁠—that is to say, find out their value.”

“You will finish me first!” answered Michel.

“Some of these expressions,” said Barbicane, “are known; the others have to be calculated.”

“I will calculate those,” said Nicholl.

“And r,” resumed Barbicane, “r is the radius of the earth under the latitude of Florida, our point of departure, d⁠—that is to say, the distance from the centre of the earth to the centre of the moon equals fifty-six terrestrial radii⁠—”

Nicholl rapidly calculated.

“That makes 356,720,000 metres when the moon is at her perigee⁠—that is to say, when she is nearest to the earth.”

“Very well,” said Barbicane, “now m prime upon m⁠—that is to say, the proportion of the moon’s volume to that of the earth equals ¹⁄₈₁.”

“Perfect,” said Michel.

“And g, the gravity, is to Florida 9¹⁄₈₁ metres. From whence it results that gr equals⁠—”

“Sixty-two million four hundred and twenty-six thousand square metres,” answered Nicholl.

“What next?” asked Michel Ardan.

“Now that the expressions are reduced to figures, I am going to find the velocity v zero⁠—that is to say, the velocity that the projectile ought to have on leaving the atmosphere to reach the point of equal attraction with no velocity. The velocity at that point I make equal zero, and x, the distance where the neutral point is, will be represented by the nine-tenths of d⁠—that is to say, the distance that separates the two centres.”

“I have some vague idea that it ought to be so,” said Michel.

“I shall then have, x equals nine-tenths of d, and v equals zero, and my formula will become⁠—”

Barbicane wrote rapidly on the paper⁠—

v 0 2 = 2 g r { 1 − 10r 9d − 1 81 ( 10r d − r d − r ) }

Nicholl read it quickly.

“That’s it! that is it!” he cried.

“Is it clear?” asked Barbicane.

“It is written in letters of fire!” answered Nicholl.

“Clever fellows!” murmured Michel.

“Do you understand now?” asked Barbicane.

“If I understand!” cried Michel Ardan. “My head is bursting with it.”

“Thus,” resumed Barbicane, “v zero square equals 2 gr multiplied by 1 minus 10 r upon 9 d minus ¹⁄₈₁ multiplied by 10 r upon d minus r upon d minus r.”

“And now,” said Nicholl, “in order to obtain the velocity of the bullet as it emerges from