A Chapter For The Cornell Girls
: All Around The MoonNo 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 c
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.
"Cock-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 cock," 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:--
1 2 2 r m' r r
--- (v' - v ) = gr {--- - 1 + --- (----- - -----) }
2 x m d - x d - r
"Which means?" asked Ardan.
"It means," said the Captain, now taking part in the discussion, "that
the half of v prime squared minus v squared equals gr multiplied
by r over x minus one plus m prime over m multiplied by r over
d minus x minus r over d minus r ... that is--"
"That is," interrupted Ardan, in a roar of laughter, "x stradlegs on
y, making for z and jumping over p! Do you mean to say you
understand the terrible jargon, Captain?"
"Nothing is clearer, Ardan."
"You too, Captain! Then of course I must give in gracefully, and declare
that the sun at noon-day is not more palpably evident than the sense of
Barbican's formula."
"You asked for Algebra, you know," observed Barbican.
"Rock crystal is nothing to it!"
"The fact is, Barbican," said the Captain, who had been looking over the
paper, "you have worked the thing out very well. You have the integral
equation of the living forces, and I have no doubt it will give us the
result sought for."
"Yes, but I should like to understand it, you know," cried Ardan: "I
would give ten years of the Captain's life to understand it!"
"Listen then," said Barbican. "Half of v prime squared less v
squared, is the formula giving us the half variation of the living
force."
"Mac pretends he understands all that!"
"You need not be a Solomon to do it," said the Captain. "All these
signs that you appear to consider so cabalistic form a language the
clearest, the shortest, and the most logical, for all those who can read
it."
"You pretend, Captain, that, by means of these hieroglyphics, far more
incomprehensible than the sacred Ibis of the Egyptians, you can
discover the velocity at which the Projectile should start?"
"Most undoubtedly," replied the Captain, "and, by the same formula I can
even tell you the rate of our velocity at any particular point of our
journey."
"You can?"
"I can."
"Then you're just as deep a one as our President."
"No, Ardan; not at all. The really difficult part of the question
Barbican has done. That is, to make out such an equation as takes into
account all the conditions of the problem. After that, it's a simple
affair of Arithmetic, requiring only a knowledge of the four rules to
work it out."
"Very simple," observed Ardan, who always got muddled at any kind of a
difficult sum in addition.
"Captain," said Barbican, "you could have found the formulas too, if
you tried."
"I don't know about that," was the Captain's reply, "but I do know that
this formula is wonderfully come at."
"Now, Ardan, listen a moment," said Barbican, "and you will see what
sense there is in all these letters."
"I listen," sighed Ardan with the resignation of a martyr.
"d is the distance from the centre of the Earth to the centre of the
Moon, for it is from the centres that we must calculate the
attractions."
"That I comprehend."
"r is the radius of the Earth."
"That I comprehend."
"m is the mass or volume of the Earth; m prime that of the Moon. We
must take the mass of the two attracting bodies into consideration,
since attraction is in direct proportion to their masses."
"That I comprehend."
"g is the gravity or the velocity acquired at the end of a second by a
body falling towards the centre of the Earth. Clear?"
"That I comprehend."
"Now I represent by x the varying distance that separates the
Projectile from the centre of the Earth, and by v prime its velocity
at that distance."
"That I comprehend."
"Finally, v is its velocity when quitting our atmosphere."
"Yes," chimed in the Captain, "it is for this point, you see, that the
velocity had to be calculated, because we know already that the initial
velocity is exactly the three halves of the velocity when the Projectile
quits the atmosphere."
"That I don't comprehend," cried the Frenchman, energetically.
"It's simple enough, however," said Barbican.
"Not so simple as a simpleton," replied the Frenchman.
"The Captain merely means," said Barbican, "that at the instant the
Projectile quitted the terrestrial atmosphere it had already lost a
third of its initial velocity."
"So much as a third?"
"Yes, by friction against the atmospheric layers: the quicker its
motion, the greater resistance it encountered."
"That of course I admit, but your v squared and your v prime squared
rattle in my head like nails in a box!"
"The usual effect of Algebra on one who is a stranger to it; to finish
you, our next step is to express numerically the value of these several
symbols. Now some of them are already known, and some are to be
calculated."
"Hand the latter over to me," said the Captain.
"First," continued Barbican: "r, the Earth's radius is, in the
latitude of Florida, about 3,921 miles. d, the distance from the
centre of the Earth to the centre of the Moon is 56 terrestrial radii,
which the Captain calculates to be...?"
"To be," cried M'Nicholl working rapidly with his pencil, "219,572
miles, the moment the Moon is in her perigee, or nearest point to the
Earth."
"Very well," continued Barbican. "Now m prime over m, that is the
ratio of the Moon's mass to that of the Earth is about the 1/81. g
gravity being at Florida about 32-1/4 feet, of course g x r must
be--how much, Captain?"
"38,465 miles," replied M'Nicholl.
"Now then?" asked Ardan.
"Now then," replied Barbican, "the expression having numerical values, I
am trying to find v, that is to say, the initial velocity which the
Projectile must possess in order to reach the point where the two
attractions neutralize each other. Here the velocity being null, v
prime becomes zero, and x the required distance of this neutral point
must be represented by the nine-tenths of d, the distance between the
two centres."
"I have a vague kind of idea that it must be so," said Ardan.
"I shall, therefore, have the following result;" continued Barbican,
figuring up; "x being nine-tenths of d, and v prime being zero, my
formula becomes:--
2 10 r 1 10 r r
v = gr {1 - ----- - ---- (----- - -----) }
d 81 d d - r "
The Captain read it off rapidly.
"Right! that's correct!" he cried.
"You think so?" asked Barbican.
"As true as Euclid!" exclaimed M'Nicholl.
"Wonderful fellows," murmured the Frenchman, smiling with admiration.
"You understand now, Ardan, don't you?" asked Barbican.
"Don't I though?" exclaimed Ardan, "why my head is splitting with it!"
"Therefore," continued Barbican,
" 2 10 r 1 10 r r
2v = 2gr {1 - ----- - ---- (----- - -----) }
d 81 d d - r "
"And now," exclaimed M'Nicholl, sharpening his pencil; "in order to
obtain the velocity of the Projectile when leaving the atmosphere, we
have only to make a slight calculation."
The Captain, who before clerking on a Mississippi steamboat had been
professor of Mathematics in an Indiana university, felt quite at home at
the work. He rained figures from his pencil with a velocity that would
have made Marston stare. Page after page was filled with his
multiplications and divisions, while Barbican looked quietly on, and
Ardan impatiently stroked his head and ears to keep down a rising
head-ache.
"Well?" at last asked Barbican, seeing the Captain stop and throw a
somewhat hasty glance over his work.
"Well," answered M'Nicholl slowly but confidently, "the calculation is
made, I think correctly; and v, that is, the velocity of the
Projectile when quitting the atmosphere, sufficient to carry it to the
neutral point, should be at least ..."
"How much?" asked Barbican, eagerly.
"Should be at least 11,972 yards the first second."
"What!" cried Barbican, jumping off his seat. "How much did you say?"
"11,972 yards the first second it quits the atmosphere."
"Oh, malediction!" cried Barbican, with a gesture of terrible despair.
"What's the matter?" asked Ardan, very much surprised.
"Enough is the matter!" answered Barbican excitedly. "This velocity
having been diminished by a third, our initial velocity should have been
at least ..."
"17,958 yards the first second!" cried M'Nicholl, rapidly flourishing
his pencil.
"But the Cambridge Observatory having declared that 12,000 yards the
first second were sufficient, our Projectile started with no greater
velocity!"
"Well?" asked M'Nicholl.
"Well, such a velocity will never do!"
"How??" }
"How!!" } cried the Captain and Ardan in one voice.
"We can never reach the neutral point!"
"Thunder and lightning"
"Fire and Fury!"
"We can't get even halfway!"
"Heaven and Earth!"
"Mille noms d'un boulet!" cried Ardan, wildly gesticulating.
"And we shall fall back to the Earth!"
"Oh!"
"Ah!"
They could say no more. This fearful revelation took them like a stroke
of apoplexy.
More
-
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After dinner Lennard excused himself, saying that he wanted to make a few more calculations; and then he got outside and lit his pipe, and walked up the winding path towards the observatory. "What am I to do?" he said between his teeth. "It's a ... A Glimpse Of The Peril
The morning was spent in a general overhaul of the observatory and the laboratory in which Lennard had discovered and perfected the explosive which had been used with such deadly effect in the guns of the Ithuriel. Lunch was an entirely delightful... A Glossary Of Names And Terms Used In The Martian Books
Aaanthor. A dead city of ancient Mars. Aisle of Hope. An aisle leading to the court-room in Helium. Apt. An Arctic monster. A huge, white-furred creature with six limbs, four of which, short and heavy, carry it over the snow and... A Green Man's Captive
When the light of day broke upon the little craft to whose deck the Princess of Ptarth had been snatched from her father's garden, Thuvia saw that the night had wrought a change in her abductors. No longer did their trappings gleam with the meta... A Guide Found To The Centre Of The Earth
In the evening I took a short walk on the beach and returned at night to my plank-bed, where I slept soundly all night. When I awoke I heard my uncle talking at a great rate in the next room. I immediately dressed and joined him. He was convers... A Gunpowder Tea-party
Nothing could be completer nor daintier than the cabin and its furnishings, divisions, and subdivisions. The rooms of necessity were small, but sufficiently large for convenience and comfort. A choice selection of best authors had been added by th... A Happy Breakfast
Mrs. Forbes was on the porch next morning when Mr. Evringham returned from his canter. "Fine morning, Mrs. Forbes," he said, as he gave Essex Maid into Zeke's hands. "Very fine. A regular weather breeder. It'll most probably rain to-morrow, an... A Hecatomb
The way of describing this unlooked-for scene, the history of the patriot ship, told at first so coldly, and the emotion with which this strange man pronounced the last words, the name of the Avenger, the significance of which could not escape me, a... A Hero In Kaol
It was daylight when I was awakened by the sound of stealthy movement near by. As I opened my eyes Woola, too, moved and, coming up to his haunches, stared through the intervening brush toward the road, each hair upon his neck stiffly erect. ... A High Old Time
A new phenomenon, therefore, strange but logical, startling but admitting of easy explanation, was now presented to their view, affording a fresh subject for lively discussion. Not that they disputed much about it. They soon agreed on a principle ... A Journey And A Disappointment
It was as the professor had said. From the day that Isaac Hakkabut had entered upon his mercantile career, his dealings had all been carried on by a system of false weight. That deceitful steelyard had been the mainspring of his fortune. But when ... A Journey To The Centre Of The Earth
... A Light On The Horizon
On the following day, without giving himself any further concern about the Jew's incredulity, the captain gave orders for the Hansa to be shifted round to the harbor of the Shelif. Hakkabut raised no objection, not only because he was aware that t... 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 did not change. Astronomically, it was daylight on the lower part, and night on the upper; so when dur... A Little Off The Track
Barbican's mind was now completely at rest at least on one subject. The original force of the discharge had been great enough to send the Projectile beyond the neutral line. Therefore, there was no longer any danger of its falling back to the Eart...