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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.
"Don't I though?" exclaimed Ardan, "why my head is splitting with it!"
"Therefore," continued Barbican,
" 2 10 r 1 10 r r
2v = 2gr {1 - ----- - ---- (----- - -----) }
d 81 d d - r "
"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 .
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