"Finally, _v_ is its velocity when quitting our atmosphere." "Yes," chimed in the Captain, "it is for this point, you see, that the velocity had to be calculated, because we know already that the initial velocity is exactly the three halves of the velocity when the Projectile quits the atmosphere." "That I don't comprehend," cried the Frenchman, energetically. "It's simple enough, however," said Barbican. "Not so simple as a simpleton," replied the Frenchman. "The Captain merely means," said Barbican, "that at the instant the Projectile quitted the terrestrial atmosphere it had already lost a third of its initial velocity." "So much as a third?" "Yes, by friction against the atmospheric layers: the quicker its motion, the greater resistance it encountered." "That of course I admit, but your _v_ squared and your _v_ prime squared rattle in my head like nails in a box!" "The usual effect of Algebra on one who is a stranger to it; to finish you, our next step is to express numerically the value of these several symbols. Now some of them are already known, and some are to be calculated." "Hand the latter over to me," said the Captain. "First," continued Barbican: "_r_, the Earth's radius is, in the latitude of Florida, about 3,921 miles. _d_, the distance from the centre of the Earth to the centre of the Moon is 56 terrestrial radii, which the Captain calculates to be...?" "To be," cried M'Nicholl working rapidly with his pencil, "219,572 miles, the moment the Moon is in her _perigee_, or nearest point to the Earth." "Very well," continued Barbican. "Now _m_ prime over _m_, that is the ratio of the Moon's mass to that of the Earth is about the 1/81. _g_ gravity being at Florida about 32-1/4 feet, of course _g_ x _r_ must be--how much, Captain?" "38,465 miles," replied M'Nicholl. "Now then?" asked Ardan. [Illustration: MY HEAD IS SPLITTING WITH IT.] "Now then," replied Barbican, "the expression having numerical values, I am trying to find _v_, that is to say, the initial velocity which the Projectile must possess in order to reach the point where the two attractions neutralize each other. Here the velocity being null, _v_ prime becomes zero, and _x_ the required distance of this neutral point must be represented by the nine-tenths of _d_, the distance between the two centres." "I have a vague kind of idea that it must be so," said Ardan. "I shall, therefore, have the following result;" continued Barbican, figuring up; "_x_ being nine-tenths of _d_, and _v_ prime being zero, my formula becomes:-- 2 10 r 1 10 r r v = gr {1 - ----- - ---- (----- - -----) } d 81 d d - r " The Captain read it off rapidly. "Right! that's correct!" he cried. "You think so?" asked Barbican. "As true as Euclid!" exclaimed M'Nicholl. "Wonderful fellows," murmured the Frenchman, smiling with admiration. "You understand now, Ardan, don't you?" asked Barbican.