“Nothing is easier,” said Barbicane.

“And could you have made 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 became absorbed in his work, whilst Nicholl looked into space, leaving the care of preparing breakfast to his companion.

Half-an-hour had not elapsed before Barbicane, raising his head, showed Michel Ardan a page covered with algebraical signs, amidst which the following general formula was discernible:—­