Round the Moon

motionless. No movement indicated its journey through space. However rapidly change of place may be effected, it cannot produce any sensible effect upon the organism when it takes place in the void, or when the mass of air circulates along with the travelling body. What inhabitant of the earth perceives the speed which carries him along at the rate of 68,000 miles an hour? Movement under such circumstances is not felt more than repose. Every object is indifferent to it. When a body is in repose it remains so until some foreign force puts it in movement. When in movement it would never stop if some obstacle were not in its road. This indifference to movement or repose is inertia.
Barbicane and his companions could, therefore, imagine themselves absolutely motionless, shut up in the interior of the projectile. The effect would have been the same if they had placed themselves on the outside. Without the moon, which grew larger above them, and the earth that grew smaller below, they would have sworn they were suspended in a complete stagnation.
That morning, the 3rd of December, they were awakened by a joyful but unexpected noise. It was the crowing of a cock in the interior of their vehicle.
Michel Ardan was the first to get up; he climbed to the top of the projectile and closed a partly-open case.
“Be quiet,” said he in a whisper. “That animal will spoil my plan!”
In the meantime Nicholl and Barbicane awoke.
“Was that a cock?” said Nicholl.
“No, my friends,” answered Michel quickly. “I wished to awake you with that rural sound.”
So saying he gave vent to a cock-a-doodle-do which would have done honour to the proudest of gallinaceans.
The two Americans could not help laughing.
“A fine accomplishment that,” said Nicholl, looking suspiciously at his companion.
“Yes,” answered Michel, “a joke common in my country. It is very Gallic.

We perpetrate it in the best society.”
Then turning the conversation⁠—
“Barbicane, do you know what I have been thinking about all night?”
“No,” answered the president.
“About our friends at Cambridge. You have already remarked how admirably ignorant I am of mathematics. I find it, therefore, impossible to guess how our savants of the observatory could calculate what initial velocity the projectile ought to be endowed with on leaving the Columbiad in order to reach the moon.”
“You mean,” replied Barbicane, “in order to reach that neutral point where the terrestrial and lunar attractions are equal; for beyond this point, situated at about 0.9 of the distance, the projectile will fall upon the moon by virtue of its own weight merely.”
“Very well,” answered Michel; “but once more; how did they calculate the initial velocity?”
“Nothing is easier,” said Barbicane.
“And could you have made the calculation yourself?” asked Michel Ardan.
“Certainly; Nicholl and I could have determined it if the notice from the observatory had not saved us the trouble.”
“Well, old fellow,” answered Michel, “they might sooner cut off my head, beginning with my feet, than have made me solve that problem!”
“Because you do not know algebra,” replied Barbicane tranquilly.
“Ah, that’s just like you dealers in x! You think you have explained everything when you have said ‘algebra.’ ”
“Michel,” replied Barbicane, “do you think it possible to forge without a hammer, or to plough without a ploughshare?”
“It would be difficult.”
“Well, then, algebra is a tool like a plough or a hammer, and a good tool for any one who knows how to use it.”
“Seriously?”
“Quite.”
“Could you use that tool before me?”
“If it would interest you.”
“And could you show me how they calculated the initial speed of our vehicle?”
“Yes, my worthy friend. By taking into account all the elements of the problem, the distance from the centre of the earth to the centre of the moon, of the radius of the earth, the volume of the earth and the volume of the moon, I can determine exactly what the initial speed of the projectile ought to be, and that by a very simple formula.”
“Show me the formula.”
“You shall see it. Only I will not give you the curve really traced by the bullet between the earth and the moon, by taking into account their movement of translation round the sun. No. I will consider both bodies to be motionless, and that will be sufficient for us.”
“Why?”
“Because that would be seeking to solve the problem called ‘the problem of the three bodies,’ for which the integral calculus is not yet far enough advanced.”
“Indeed,” said Michel Ardan in a bantering tone; “then mathematics have not said their last word.”
“Certainly not,” answered Barbicane.
“Good! Perhaps the Selenites have pushed the integral calculus further than you! By the by, what is the integral calculus?”
“It is the inverse of the differential calculus,” answered Barbicane seriously.
“Much obliged.”
“To speak otherwise, it is a calculus by which you seek finished quantities of what you know the differential quantities.”
“That is clear at least,” answered Barbicane with a quite satisfied air.
“And now,” continued Barbicane, “for a piece of paper and a pencil, and in half-an-hour I will have found the required formula.”
That said, Barbicane became absorbed in his work, whilst Nicholl looked into space, leaving the care of preparing breakfast to his companion.
Half-an-hour had not elapsed before Barbicane, raising his head, showed Michel Ardan a page covered with algebraical signs, amidst which the following general formula was discernible:⁠—

1 2 ( v 2 − v 0 2 ) = g r { r x - 1 + m’ m ( r d − x − r d − r ) }

“And what does that mean?” asked Michel.
“That means,” answered Nicholl, “that the half of v minus v zero square equals gr multiplied by r upon x minus 1 plus m prime upon m multiplied by r upon d minus x, minus r upon d minus x minus r⁠—”
“x upon y galloping upon z and rearing upon p” cried Michel Ardan, bursting out laughing. “Do you mean to say you understand that, captain?”
“Nothing is clearer.”
“Then,” said Michel Ardan, “it is as plain as a pikestaff, and I want nothing more.”
“Everlasting laugher,” said Barbicane, “you wanted algebra, and now you shall have it over