"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:-- 1 2 2 r m' r r - (v - v ) = gr { --- - 1 + --- ( --- - ---) } 2 0 x m d-x d-r "And what does that mean?" asked Michel. "That means," answered Nicholl, "that the half of _v_ minus _v_ zero square equals _gr_ multiplied by _r_ upon _x_ minus 1 plus _m_ prime upon _m_ multiplied by _r_ upon _d_ minus _x_, minus _r_ upon _d_ minus _x_ minus _r_--" "_X_ upon _y_ galloping upon _z_ and rearing upon _p_" cried Michel Ardan, bursting out laughing. "Do you mean to say you understand that, captain?" "Nothing is clearer." "Then," said Michel Ardan, "it is as plain as a pikestaff, and I want nothing more." "Everlasting laugher," said Barbicane, "you wanted algebra, and now you shall have it over head and ears." "I would rather be hung!" "That appears a good solution, Barbicane," said Nicholl, who was examining the formula like a _connaisseur_. "It is the integral of the equation of 'vis viva,' and I do not doubt that it will give us the desired result." "But I should like to understand!" exclaimed Michel. "I would give ten years of Nicholl's life to understand!" "Then listen," resumed Barbicane. "The half of _v_ minus _v_ zero square is the formula that gives us the demi-variation of the 'vis viva.'" "Good; and does Nicholl understand what that means?" "Certainly, Michel," answered the captain. "All those signs that look so cabalistic to you form the clearest and most logical language for those who know how to read it." "And do you pretend, Nicholl," asked Michel, "that by means of these hieroglyphics, more incomprehensible than the Egyptian ibis, you can find the initial speed necessary to give to the projectile?"