Free All Around the Moon by Jules Verne

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.
    MY HEAD IS SPLITTING WITH IT.
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:—
    TeX source: v^2=gr\left\{1-\frac{10r}{d}-\frac{1}{81}\left(\frac{10r}{d}-\frac{r}{d-r}\right)\right\}
    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.
    "Don't I though?" exclaimed Ardan, "why my head is splitting with it!"
    "Therefore," continued Barbican,
    TeX source: 2v^2=2gr\left\{1-\frac{10r}{d}-\frac{1}{81}\left(\frac{10r}{d}-\frac{r}{d-r}\right)\right\}
    "And now," exclaimed M'Nicholl, sharpening his pencil; "in order to obtain the velocity of the Projectile when leaving the atmosphere, we have only to make a slight calculation."
    The Captain, who before clerking on a Mississippi steamboat had been professor of Mathematics in an Indiana university, felt quite at home at the work. He rained figures from his pencil with a velocity that would have made Marston stare. Page after page was filled with his multiplications and divisions, while Barbican looked quietly on, and Ardan impatiently stroked his head and ears to keep down a rising head-ache.
    "Well?" at last asked Barbican, seeing the Captain stop and throw a somewhat hasty glance over his work.
    "Well," answered M'Nicholl slowly but confidently, "the calculation is made, I think correctly; and v , that is, the velocity of the Projectile when quitting the atmosphere, sufficient to carry it to the neutral point, should be at least ..."
    "How much?" asked Barbican, eagerly.
    "Should be at least 11,972 yards the first second."
    "What!" cried Barbican, jumping off his seat. "How much did you say?"
    "11,972 yards the first second it quits the atmosphere."
    "Oh, malediction!" cried Barbican, with a gesture of terrible despair.
    "What's the matter?" asked Ardan, very much surprised.
    "Enough is