ot 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."

"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 Alg