Read Online All Around the Moon by Jules Verne - Free Book Online Page A
Authors: Jules Verne
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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:—
TeX source:
"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:—
TeX source: