All Around the Moon

Chapter 4

A CHAPTER FOR THE CORNELL GIRLS.

No incident worth recording occurred during the night, if night indeed

it could be called. In reality there was now no night or even day in the

Projectile, or rather, strictly speaking, it was always _night_ on the

upper end of the bullet, and always _day_ on the lower. Whenever,

therefore, the words _night_ and _day_ occur in our story, the reader

will readily understand them as referring to those spaces of time that

are so called in our Earthly almanacs, and were so measured by the

travellers' chronometers.

The repose of our friends must indeed have been undisturbed, if absolute

freedom from sound or jar of any kind could secure tranquillity. In

spite of its immense velocity, the Projectile still seemed to be

perfectly motionless. Not the slightest sign of movement could be

detected. Change of locality, though ever so rapid, can never reveal

itself to our senses when it takes place in a vacuum, or when the

enveloping atmosphere travels at the same rate as the moving body.

Though we are incessantly whirled around the Sun at the rate of about

seventy thousand miles an hour, which of us is conscious of the

slightest motion? In such a case, as far as sensation is concerned,

motion and repose are absolutely identical. Neither has any effect one

way or another on a material body. Is such a body in motion? It remains

in motion until some obstacle stops it. Is it at rest? It remains at

rest until some superior force compels it to change its position. This

indifference of bodies to motion or rest is what physicists call

_inertia_.

Barbican and his companions, therefore, shut up in the Projectile, could

readily imagine themselves to be completely motionless. Had they been

outside, the effect would have been precisely the same. No rush of air,

no jarring sensation would betray the slightest movement. But for the

sight of the Moon gradually growing larger above them, and of the Earth

gradually growing smaller beneath them, they could safely swear that

they were fast anchored in an ocean of deathlike immobility.

Towards the morning of next day (December 3), they were awakened by a

joyful, but quite unexpected sound.

"c**k-a-doodle! doo!" accompanied by a decided flapping of wings.

The Frenchman, on his feet in one instant and on the top of the ladder

in another, attempted to shut the lid of a half open box, speaking in an

angry but suppressed voice:

"Stop this hullabaloo, won't you? Do you want me to fail in my great

combination!"

"Hello?" cried Barbican and M'Nicholl, starting up and rubbing their

eyes.

"What noise was that?" asked Barbican.

"Seems to me I heard the crowing of a c**k," observed the Captain.

"I never thought your ears could be so easily deceived, Captain," cried

Ardan, quickly, "Let us try it again," and, flapping his ribs with his

arms, he gave vent to a crow so loud and natural that the lustiest

chanticleer that ever saluted the orb of day might be proud of it.

The Captain roared right out, and even Barbican snickered, but as they

saw that their companion evidently wanted to conceal something, they

immediately assumed straight faces and pretended to think no more about

the matter.

"Barbican," said Ardan, coming down the ladder and evidently anxious to

change the conversation, "have you any idea of what I was thinking about

all night?"

"Not the slightest."

"I was thinking of the promptness of the reply you received last year

from the authorities of Cambridge University, when you asked them about

the feasibility of sending a bullet to the Moon. You know very well by

this time what a perfect ignoramus I am in Mathematics. I own I have

been often puzzled when thinking on what grounds they could form such a

positive opinion, in a case where I am certain that the calculation must

be an exceedingly delicate matter."

"The feasibility, you mean to say," replied Barbican, "not exactly of

sending a bullet to the Moon, but of sending it to the neutral point

between the Earth and the Moon, which lies at about nine-tenths of the

journey, where the two attractions counteract each other. Because that

point once passed, the Projectile would reach the Moon's surface by

virtue of its own weight."

"Well, reaching that neutral point be it;" replied Ardan, "but, once

more, I should like to know how they have been able to come at the

necessary initial velocity of 12,000 yards a second?"

"Nothing simpler," answered Barbican.

"Could you have done it yourself?" asked the Frenchman.

"Without the slightest difficulty. The Captain and myself could have

readily solved the problem, only the reply from the University saved us

the trouble."

"Well, Barbican, dear boy," observed Ardan, "all I've got to say is, you

might chop the head off my body, beginning with my feet, before you

could make me go through such a calculation."

"Simply because you don't understand Algebra," replied Barbican,

quietly.

"Oh! that's all very well!" cried Ardan, with an ironical smile. "You

great _x+y_ men think you settle everything by uttering the word

_Algebra_!"

"Ardan," asked Barbican, "do you think people could beat iron without a

hammer, or turn up furrows without a plough?"

"Hardly."

"Well, Algebra is an instrument or utensil just as much as a hammer or a

plough, and a very good instrument too if you know how to make use of

it."

"You're in earnest?"

"Quite so."

"And you can handle the instrument right before my eyes?"

"Certainly, if it interests you so much."

"You can show me how they got at the initial velocity of our

Projectile?"

"With the greatest pleasure. By taking into proper consideration all the

elements of the problem, viz.: (1) the distance between the centres of

the Earth and the Moon, (2) the Earth's radius, (3) its volume, and (4)

the Moon's volume, I can easily calculate what must be the initial

velocity, and that too by a very simple formula."

"Let us have the formula."

"In one moment; only I can't give you the curve really described by the

Projectile as it moves between the Earth and the Moon; this is to be

obtained by allowing for their combined movement around the Sun. I will

consider the Earth and the Sun to be motionless, that being sufficient

for our present purpose."

"Why so?"

"Because to give you that exact curve would be to solve a point in the

'Problem of the Three Bodies,' which Integral Calculus has not yet

reached."

"What!" cried Ardan, in a mocking tone, "is there really anything that

Mathematics can't do?"

"Yes," said Barbican, "there is still a great deal that Mathematics

can't even attempt."

"So far, so good;" resumed Ardan. "Now then what is this Integral

Calculus of yours?"

"It is a branch of Mathematics that has for its object the summation of

a certain infinite series of indefinitely small terms: but for the

solution of which, we must generally know the function of which a given

function is the differential coefficient. In other words," continued

Barbican, "in it we return from the differential coefficient, to the

function from which it was deduced."

"Clear as mud!" cried Ardan, with a hearty laugh.

"Now then, let me have a bit of paper and a pencil," added Barbican,

"and in half an hour you shall have your formula; meantime you can

easily find something interesting to do."

In a few seconds Barbican was profoundly absorbed in his problem, while

M'Nicholl was watching out of the window, and Ardan was busily employed

in preparing breakfast.

The morning meal was not quite ready, when Barbican, raising his head,

showed Ardan a page covered with algebraic signs at the end of which

stood the following formula:--