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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

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