the calculation yourself?" asked Michel Ardan.

"Certainly; Nicholl and I could have determined it if the notice from
the observatory had not saved us the trouble."

"Well, old fellow," answered Michel, "they might sooner cut off my head,
beginning with my feet, than have made me solve that problem!"

"Because you do not know algebra," replied Barbicane tranquilly.

"Ah, that's just like you dealers in _x_! You think you have explained
everything when you have said 'algebra.'"

"Michel," replied Barbicane, "do you think it possible to forge without
a hammer, or to plough without a ploughshare?"

"It would be difficult."

"Well, then, algebra is a tool like a plough or a hammer, and a good
tool for any one who knows how to use it."

"Seriously?"

"Quite."

"Could you use that tool before me?"

"If it would interest you."

"And could you show me how they calculated the initial speed of our
vehicle?"

"Yes, my worthy friend. By taking into account all the elements of the
problem, the distance from the centre of the earth to the centre of the
moon, of the radius of the earth, the volume of the earth and the volume
of the moon, I can determine exactly what the initial speed of the
projectile ought to be, and that by a very simple formula."

"Show me the formula."

"You shall see it. Only I will not give you the curve really traced by
the bullet between the earth and the moon, by taking into account their
movement of translation round the sun. No. I will consider both bodies
to be motionless, and that will be sufficient for us."

"Why?"

"Because that would be seeking to solve the problem called 'the problem
of the three bodies,' for which the integral calculus is not yet far
enough advanced."

"Indeed," said Michel Ardan in a bantering tone; "then mathematics have
not said their last word."

"Certainly not," answered Barbicane.

"Good! Perhaps the Selenites have pushed the integral calculus further
than you! By-the-bye, what is the integral calculus?"

"It is the inverse of the differential calculus," answered Barbicane
seriously.

"Much obliged."

"To speak otherwise, it is a calculus by which you seek finished
quantities of what you know the differential quantities."

"That is clear at least," answered Barbicane with a quite satisfied air.

"And now," continued Barbicane, "for a piece of paper and a pencil, and
in half-an-hour I will have found the required formula."

That said, Barbicane