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:—
"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
