The Moon-Voyage, Jules Verne [e book reader pdf txt] 📗

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 9-1/81 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—

     2 10r 1 10r r
    v = 2 gr { 1 - —- —- ( —- - —-) }
     0 9d 81 d 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 the atmosphere I have only to calculate."

The captain, like a man used to overcome all difficulties, began to calculate with frightful rapidity. Divisions and multiplications grew under his fingers. Figures dotted the page. Barbicane followed him with his eyes, whilst Michel Ardan compressed a coming headache with his two hands.

"Well, what do you make it?" asked Barbicane after several minutes' silence.

"I make it 11,051 metres in the first second."

"What do you say?" said Barbicane, starting.

"Eleven thousand and fifty-one metres."

"Malediction!" cried the president with a gesture of despair.

"What's the matter with you?" asked Michel Ardan, much surprised.

"The matter! why if at this moment the velocity was already diminished one-third by friction, the initial speed ought to have been—"

"Sixteen thousand five hundred and seventy-six metres!" answered
Nicholl.

"But the Cambridge Observatory declared that 11,000 metres were enough at departure, and our bullet started with that velocity only!"

"Well?" asked Nicholl.

"Why it was not enough!"

"No."

"We shall not reach the neutral point."

"The devil!"

"We shall not even go half way!"

"Nom d'un boulet!" exclaimed Michel Ardan, jumping up as if the projectile were on the point of striking against the terrestrial globe.

"And we shall fall back upon the earth!"

CHAPTER V. THE TEMPERATURE OF SPACE.

This revelation acted like a thunderbolt. Who could have expected such an error in calculation? Barbicane would not believe it. Nicholl went over the figures again. They were correct. The formula which had established them could not be mistrusted, and, when verified, the initial velocity of 16,576 metres, necessary for attaining the neutral point, was found quite right.

The three friends looked at one another in silence. No one thought about breakfast after that. Barbicane, with set teeth, contracted brow, and fists convulsively closed, looked through the port-light. Nicholl folded his arms and examined his calculations. Michel Ardan murmured—

"That's just like savants! That's the way they always do! I would give twenty pistoles to fall upon the Cambridge Observatory and crush it, with all its stupid staff inside!"

All at once the captain made a reflection which struck Barbicane at once.

"Why," said he, "it is seven o'clock in the morning, so we have been thirty-two hours on the road. We have come more than half way, and we are not falling yet that I know of!"

Barbicane did not answer, but after a rapid glance at the captain he took a compass, which he used to measure the angular distance of the terrestrial globe. Then through the lower port-light he made a very exact observation from the apparent immobility of the projectile. Then rising and wiping the perspiration from his brow, he put down some figures upon paper. Nicholl saw that the president wished to find out from the length of the terrestrial diameter the distance of the bullet from the earth. He looked at him anxiously.

"No!" cried Barbicane in a few minutes' time, "we are not falling! We are already more than 50,000 leagues from the earth! We have passed the point the projectile ought to have stopped at if its speed had been only 11,000 metres at our departure! We are still ascending!"

"That is evident," answered Nicholl; "so we must conclude that our initial velocity, under the propulsion of the 400,000 lbs. of gun-cotton, was greater than the 11,000 metres. I can now explain to myself why we met with the second satellite, that gravitates at more than 2,000 leagues from the earth, in less than thirteen minutes."

"That explanation is so much the more probable," added Barbicane, "because by throwing out the water in our movable partitions the projectile was made considerably lighter all at once."

"That is true," said Nicholl.

"Ah, my brave Nicholl," cried Barbicane, "we are saved!"

"Very well then," answered Michel Ardan tranquilly, "as we are saved, let us have breakfast."

Nicholl was not mistaken. The initial speed had happily been greater than that indicated by the Cambridge Observatory, but the Cambridge Observatory had no less been mistaken.

The travellers, recovered from their false alarm, sat down to table and breakfasted merrily. Though they ate much they talked more. Their confidence was greater after the "algebra incident."

"Why should we not succeed?" repeated Michel Ardan. "Why should we not arrive? We are on the road; there are no obstacles before us, and no stones on our route. It is free—freer than that of a ship that has to struggle with the sea, or a balloon with the wind against it! Now if a ship can go where it pleases, or a balloon ascend where it pleases, why should not our projectile reach the goal it was aimed at?"

"It will reach it," said Barbicane.

"If only to honour the American nation," added Michel Ardan, "the only nation capable of making such an enterprise succeed—the only one that could have produced a President Barbicane! Ah! now I think of it, now that all our anxieties are over, what will become of us? We shall be as dull as stagnant water."

Barbicane and Nicholl made gestures of repudiation.

"But I foresaw this, my friends," resumed Michel Ardan. "You have only to say the word. I have chess, backgammon, cards, and dominoes at your disposition. We only want a billiard-table!"

"What?" asked Barbicane, "did you bring such trifles as those?"

"Certainly," answered Michel; "not only for our amusement, but also in the praiseworthy intention of bestowing them upon Selenite inns."

"My friend," said Barbicane, "if the moon is inhabited its inhabitants appeared some thousands of years before those of the earth, for it cannot be doubted that the moon is older than the earth. If, therefore, the Selenites have existed for thousands of centuries—if their brains are organised like that of human beings—they have invented all that we have invented, already, and even what we shall only invent in the lapse of centuries. They will have nothing to learn from us, and we shall have everything to learn from them."

"What!" answered Michel, "do you think they have had artists like
Phidias, Michael Angelo, or Raphael?"

"Yes."

"Poets like Homer, Virgil, Milton, Lamartine, and Hugo?"

"I am sure of it."

"Philosophers like Plato, Aristotle, Descartes, and Kant?"

"I have no doubt of it."

"Savants like Archimedes, Euclid, Pascal, and Newton?"

"I could swear it."

"Clowns like Arnal, and photographers like—Nadar?"

"I am certain of it."

"Then, friend Barbicane, if these Selenites are as learned as we, and even more so,