by Jules Verne
CHAPTER IV.
A LITTLE ALGEBRA.
The night passed without incident. The word "night," however, is scarcelyapplicable.
The position of the projectile with regard to the sun did not change.Astronomically, it was daylight on the lower part, and night on the upper;so when during this narrative these words are used, they represent thelapse of time between the rising and setting of the sun upon the earth.
The travellers' sleep was rendered more peaceful by the projectile'sexcessive speed, for it seemed absolutely motionless. Not a motionbetrayed its onward course through space. The rate of progress, howeverrapid it might be, cannot produce any sensible effect on the human framewhen it takes place in a vacuum, or when the mass of air circulateswith the body which is carried with it. What inhabitant of the earthperceives its speed, which, however, is at the rate of 68,000 miles perhour? Motion under such conditions is "felt" no more than repose; andwhen a body is in repose it will remain so as long as no strange forcedisplaces it; if moving, it will not stop unless an obstacle comes inits way. This indifference to motion or repose is called inertia.
Barbicane and his companions might have believed themselves perfectlystationary, being shut up in the projectile; indeed, the effect wouldhave been the same if they had been on the outside of it. Had it not beenfor the moon, which was increasing above them, they might have sworn thatthey were floating in complete stagnation.
That morning, the 3rd of December, the travellers were awakened by ajoyous but unexpected noise; it was the crowing of a cock which soundedthrough the car. Michel Ardan, who was the first on his feet, climbedto the top of the projectile, and shutting a box, the lid of whichwas partly open, said in a low voice, "Will you hold your tongue? Thatcreature will spoil my design!"
But Nicholl and Barbicane were awake.
"A cock!" said Nicholl.
"Why no, my friends," Michel answered quickly; "it was I who wished toawake you by this rural sound." So saying, he gave vent to a splendidcock-a-doodledoo, which would have done honour to the proudest ofpoultry-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 playthe 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 am anignoramus in mathematical subjects; and it is impossible for me tofind out how the savants of the Observatory were able to calculate whatinitiatory speed the projectile ought to have on leaving the Columbiadin order to attain the moon."
"You mean to say," replied Barbicane, "to attain that neutral point wherethe terrestrial and lunar attractions are equal; for, starting from thatpoint, situated about nine-tenths of the distance travelled over, theprojectile would simply fall upon the moon, on account of its weight."
"So be it," said Michel; "but, once more; how could they calculate theinitiatory 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 the Observatory had notsaved us the trouble."
"Very well, old Barbicane," replied Michel; "they might have cut off myhead, beginning at my feet, before they could have made me solve thatproblem."
"Because you do not know algebra," answered Barbicane quietly.
"Ah, there you are, you eaters of _x_^1; you think you have said allwhen you have said 'Algebra.'"
"Michel," said Barbicane, "can you use a forge without a hammer, orplough without a ploughshare?"
"Hardly."
"Well, algebra is a tool, like the plough or the hammer, and a good toolto 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 the elements ofthe problem, the distance from the centre of the earth to the centre ofthe moon, of the radius of the earth, of its bulk, and of the bulk ofthe moon, I can tell exactly what ought to be the initiatory speed ofthe projectile, and that by a simple formula."
"Let us see."
"You shall see it; only I shall not give you the real course drawnby the projectile between the moon and the earth in considering theirmotion round the sun. No, I shall consider these two orbs as perfectlymotionless, which will answer all our purpose."
"And why?"
"Because it will be trying to solve the problem called 'the problem ofthe three bodies,' for which the integral calculus is not yet far enoughadvanced."
"Then," said Michel Ardan, in his sly tone, "mathematics have not saidtheir last word?"
"Certainly not," replied Barbicane.
"Well, perhaps the Selenites have carried the integral calculus fartherthan you have; and, by the bye, what is 'integral calculus?'"
"It is a calculation the converse of the differential," replied Barbicaneseriously.
"Much obliged; it is all very clear, no doubt."
"And now," continued Barbicane, "a slip of paper and a bit of pencil,and before a half-hour is over I will have found the required formula."
Half an hour had not elapsed before Barbicane, raising his head, showedMichel Ardan a page covered with algebraical signs, in which the generalformula for the solution was contained.
"Well, and does Nicholl understand what that means?"
"Of course, Michel," replied the captain. "All these signs, which seemcabalistic to you, form the plainest, the clearest, and the most logicallanguage to those who know how to read it."
"And you pretend, Nicholl," asked Michel, "that by means of thesehieroglyphics, more incomprehensible than the Egyptian Ibis, you can findwhat initiatory speed it was necessary to give to the projectile?"
"Incontestably," replied Nicholl; "and even by this same formula I canalways 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; that is, toget an equation which shall satisfy all the conditions of the problem.The remainder is only a question of arithmetic, requiring merely theknowledge of the four rules."
"That is something!" replied Michel Ardan, who for his life could notdo addition right, and who defined the rule as a Chinese puzzle, whichallowed one to obtain all sorts of totals.
"The expression _v_ zero, which you see in that equation, is the speedwhich the projectile will have on leaving the atmosphere."
"Just so," said Nicholl; "it is from that point that we must calculatethe velocity, since we know already that the velocity at departure wasexactly one and a half times more than on leaving 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 the terrestrialatmosphere it had already lost one-third of its initiatory speed."
"As much as that?"
"Yes, my friend; merely by friction against the atmospheric strata. Youunderstand that the faster it goes the more resistance it meets with fromthe air."
"That I admit," answered Michel; "and I understand it, although your x'sand zero's, and algebraic formulae, are rattling in my head like nailsin a bag."
"First effects of algebra," replied Barbicane; "and now, to finish, weare going to prove the given number of these different expressions, thatis, work out their value."
"Finish me!" replied Michel.
Barbica
ne took the paper, and began again to make his calculations withgreat rapidity. Nicholl looked over and greedily read the work as itproceeded.
"That's it! that's it!" at last he cried.
"Is it clear?" asked Barbicane.
Illustration: "DO I UNDERSTAND IT?" CRIED ARDAN; "MY HEAD IS SPLITTING WITH IT."
"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 the projectile whenit left the atmosphere, we have only to calculate that."
The captain, as a practical man equal to all difficulties, began to writewith frightful rapidity. Divisions and multiplications grew under hisfingers; the figures were like hail on the white page. Barbicane watchedhim, whilst Michel Ardan nursed a growing headache with both hands.
"Very well?" asked Barbicane, after some minutes' silence.
"Well!" replied Nicholl; "every calculation made, _v_ zero, that is tosay, the speed necessary for the projectile on leaving the atmosphere,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 had alreadydiminished one-third by friction, the initiatory speed ought to havebeen--"
"Seventeen thousand yards."
"And the Cambridge Observatory declared that 12,000 yards was enough atstarting; and our projectile, which only started 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 half way."
"In the name of the projectile!" exclaimed Michel Ardan, jumping as ifit was already on the point of striking the terrestrial globe.
"And we shall fall back upon the earth!"