by Jules Verne
CHAPTER IV
A LITTLE ALGEBRA
The night passed without incident. The word "night," however,is scarcely applicable.
The position of the projectile with regard to the sun didnot change. Astronomically, it was daylight on the lower part,and night on the upper; so when during this narrative thesewords are used, they represent the lapse of time between risingand setting of the sun upon the earth.
The travelers' sleep was rendered more peaceful by theprojectile's excessive speed, for it seemed absolutely motionless.Not a motion betrayed its onward course through space. The rateof progress, however rapid it might be, cannot produce anysensible effect on the human frame when it takes place in avacuum, or when the mass of air circulates with the body whichis carried with it. What inhabitant of the earth perceives itsspeed, which, however, is at the rate of 68,000 miles per hour?Motion under such conditions is "felt" no more than repose; andwhen a body is in repose it will remain so as long as no strangeforce displaces it; if moving, it will not stop unless anobstacle comes in its way. This indifference to motion orrepose is called inertia.
Barbicane and his companions might have believed themselvesperfectly stationary, being shut up in the projectile; indeed,the effect would have been the same if they had been on theoutside of it. Had it not been for the moon, which wasincreasing above them, they might have sworn that they werefloating in complete stagnation.
That morning, the 3rd of December, the travelers were awakened bya joyous but unexpected noise; it was the crowing of a cockwhich sounded through the car. Michel Ardan, who was the firston his feet, climbed to the top of the projectile, and shuttinga box, the lid of which was partly open, said in a low voice,"Will you hold your tongue? That creature will spoil my design!"
But Nicholl and Barbicane were awake.
"A cock!" said Nicholl.
"Why no, my friends," Michel answered quickly; "it was I whowished to awake you by this rural sound." So saying, he gavevent to a splendid cock-a-doodledoo, which would have done honorto the proudest of poultry-yards.
The two Americans could not help laughing.
"Fine talent that," said Nicholl, looking suspiciously at his companion.
"Yes," said Michel; "a joke in my country. It is very Gallic;they play the cock so in the best society."
Then turning the conversation:
"Barbicane, do you know what I have been thinking of all night?"
"No," answered the president.
"Of our Cambridge friends. You have already remarked that I aman ignoramus in mathematical subjects; and it is impossible forme to find out how the savants of the observatory were able tocalculate what initiatory speed the projectile ought to have onleaving the Columbiad in order to attain the moon."
"You mean to say," replied Barbicane, "to attain that neutralpoint where the terrestrial and lunar attractions are equal;for, starting from that point, situated about nine-tenths of thedistance traveled over, the projectile would simply fall uponthe moon, on account of its weight."
"So be it," said Michel; "but, once more; how could theycalculate the initiatory speed?"
"Nothing can be easier," replied Barbicane.
"And you knew how to make that calculation?" asked Michel Ardan.
"Perfectly. Nicholl and I would have made it, if theobservatory had not saved us the trouble."
"Very well, old Barbicane," replied Michel; "they might have cutoff my head, beginning at my feet, before they could have mademe solve that problem."
"Because you do not know algebra," answered Barbicane quietly.
"Ah, there you are, you eaters of _x_^1; you think you have saidall when you have said `Algebra.'"
"Michel," said Barbicane, "can you use a forge without a hammer,or a plow without a plowshare?"
"Hardly."
"Well, algebra is a tool, like the plow or the hammer, and agood tool to those who know how to use it."
"Seriously?"
"Quite seriously."
"And can you use that tool in my presence?"
"If it will interest you."
"And show me how they calculated the initiatory speed of our car?"
"Yes, my worthy friend; taking into consideration all theelements of the problem, the distance from the center of theearth to the center of the moon, of the radius of the earth, ofits bulk, and of the bulk of the moon, I can tell exactly whatought to be the initiatory speed of the projectile, and that bya simple formula."
"Let us see."
"You shall see it; only I shall not give you the real coursedrawn by the projectile between the moon and the earth inconsidering their motion round the sun. No, I shall considerthese two orbs as perfectly motionless, which will answer allour purpose."
"And why?"
"Because it will be trying to solve the problem called `theproblem of the three bodies,' for which the integral calculus isnot yet far enough advanced."
"Then," said Michel Ardan, in his sly tone, "mathematics havenot said their last word?"
"Certainly not," replied Barbicane.
"Well, perhaps the Selenites have carried the integral calculusfarther than you have; and, by the bye, what is this`integral calculus?'"
"It is a calculation the converse of the differential," repliedBarbicane seriously.
"Much obliged; it is all very clear, no doubt."
"And now," continued Barbicane, "a slip of paper and a bit ofpencil, and before a half-hour is over I will have found therequired formula."
Half an hour had not elapsed before Barbicane, raising his head,showed Michel Ardan a page covered with algebraical signs, inwhich the general formula for the solution was contained.
"Well, and does Nicholl understand what that means?"
"Of course, Michel," replied the captain. "All these signs,which seem cabalistic to you, form the plainest, the clearest,and the most logical language to those who know how to read it."
"And you pretend, Nicholl," asked Michel, "that by means ofthese hieroglyphics, more incomprehensible than the EgyptianIbis, you can find what initiatory speed it was necessary togive the projectile?"
"Incontestably," replied Nicholl; "and even by this same formulaI can always tell you its speed at any point of its transit."
"On your word?"
"On my word."
"Then you are as cunning as our president."
"No, Michel; the difficult part is what Barbicane has done; thatis, to get an equation which shall satisfy all the conditions ofthe problem. The remainder is only a question of arithmetic,requiring merely the knowledge of the four rules."
"That is something!" replied Michel Ardan, who for his lifecould not do addition right, and who defined the rule as aChinese puzzle, which allowed one to obtain all sorts of totals.
"The expression _v_ zero, which you see in that equation, is thespeed which the projectile will have on leaving the atmosphere."
"Just so," said Nicholl; "it is from that point that we mustcalculate the velocity, since we know already that the velocityat departure was exactly one and a half times more than onleaving the atmosphere."
"I understand no more," said Michel.
"It is a very simple calculation," said Barbicane.
"Not as simple as I am," retorted Michel.
"That means, that when our projectile reached the limits of theterrestrial atmosphere it had already lost one-third of itsinitiatory speed."
"As much as that?"
"Yes, my friend; merely by friction against the atmospheric strata.You understand that the faster it goes the more resistance it meetswith from the air."
"That I admit," answered Michel; "and I understand it,although your x's and zero's, and algebraic formula, arerattling in my head like nails in a bag."
"First effects of algebra," replied Barbicane; "and now, tofinish, we are going to prove the given number of thesedifferent expressions, that is, work out their value."
"Finish me!" replied Michel.
Barbicane took the paper,
and began to make his calculationswith great rapidity. Nicholl looked over and greedily read thework as it proceeded.
"That's it! that's it!" at last he cried.
"Is it clear?" asked Barbicane.
"It is written in letters of fire," said Nicholl.
"Wonderful fellows!" muttered Ardan.
"Do you understand it at last?" asked Barbicane.
"Do I understand it?" cried Ardan; "my head is splitting with it."
"And now," said Nicholl, "to find out the speed of theprojectile when it leaves the atmosphere, we have only tocalculate that."
The captain, as a practical man equal to all difficulties, beganto write with frightful rapidity. Divisions and multiplicationsgrew under his fingers; the figures were like hail on the white page.Barbicane watched him, while Michel Ardan nursed a growing headachewith both hands.
"Very well?" asked Barbicane, after some minutes' silence.
"Well!" replied Nicholl; every calculation made, _v_ zero, thatis to say, the speed necessary for the projectile on leaving theatmosphere, to enable it to reach the equal point of attraction,ought to be----"
"Yes?" said Barbicane.
"Twelve thousand yards."
"What!" exclaimed Barbicane, starting; "you say----"
"Twelve thousand yards."
"The devil!" cried the president, making a gesture of despair.
"What is the matter?" asked Michel Ardan, much surprised.
"What is the matter! why, if at this moment our speed hadalready diminished one-third by friction, the initiatory speedought to have been----"
"Seventeen thousand yards."
"And the Cambridge Observatory declared that twelve thousandyards was enough at starting; and our projectile, which onlystarted with that speed----"
"Well?" asked Nicholl.
"Well, it will not be enough."
"Good."
"We shall not be able to reach the neutral point."
"The deuce!"
"We shall not even get halfway."
"In the name of the projectile!" exclaimed Michel Ardan, jumpingas if it was already on the point of striking the terrestrial globe.
"And we shall fall back upon the earth!"
