"You too, Captain! Then of course I must give in gracefully, and declare that the sun at noon-day is not more palpably evident than the sense of Barbican's formula." "You asked for Algebra, you know," observed Barbican. "Rock crystal is nothing to it!" "The fact is, Barbican," said the Captain, who had been looking over the paper, "you have worked the thing out very well. You have the integral equation of the living forces, and I have no doubt it will give us the result sought for." "Yes, but I should like to understand it, you know," cried Ardan: "I would give ten years of the Captain's life to understand it!" "Listen then," said Barbican. "Half of _v_ prime squared less _v_ squared, is the formula giving us the half variation of the living force." "Mac pretends he understands all that!" "You need not be a _Solomon_ to do it," said the Captain. "All these signs that you appear to consider so cabalistic form a language the clearest, the shortest, and the most logical, for all those who can read it." "You pretend, Captain, that, by means of these hieroglyphics, far more incomprehensible than the sacred Ibis of the Egyptians, you can discover the velocity at which the Projectile should start?" "Most undoubtedly," replied the Captain, "and, by the same formula I can even tell you the rate of our velocity at any particular point of our journey." "You can?" "I can." "Then you're just as deep a one as our President." "No, Ardan; not at all. The really difficult part of the question Barbican has done. That is, to make out such an equation as takes into account all the conditions of the problem. After that, it's a simple affair of Arithmetic, requiring only a knowledge of the four rules to work it out." "Very simple," observed Ardan, who always got muddled at any kind of a difficult sum in addition. "Captain," said Barbican, "_you_ could have found the formulas too, if you tried." "I don't know about that," was the Captain's reply, "but I do know that this formula is wonderfully come at." "Now, Ardan, listen a moment," said Barbican, "and you will see what sense there is in all these letters." "I listen," sighed Ardan with the resignation of a martyr. "_d_ is the distance from the centre of the Earth to the centre of the Moon, for it is from the centres that we must calculate the attractions." "That I comprehend." "_r_ is the radius of the Earth." "That I comprehend." "_m_ is the mass or volume of the Earth; _m_ prime that of the Moon. We must take the mass of the two attracting bodies into consideration, since attraction is in direct proportion to their masses." "That I comprehend." "_g_ is the gravity or the velocity acquired at the end of a second by a body falling towards the centre of the Earth. Clear?" "That I comprehend." "Now I represent by _x_ the varying distance that separates the Projectile from the centre of the Earth, and by _v_ prime its velocity at that distance." "That I comprehend."