arithmetic, and requires
nothing but a knowledge of the four rules."

"That's something," answered Michel Ardan, who had never been able to
make a correct addition in his life, and who thus defined the rule: "A
Chinese puzzle, by which you can obtain infinitely various results."

Still Barbicane answered that Nicholl would certainly have found the
formula had he thought about it.

"I do not know if I should," said Nicholl, "for the more I study it the
more marvellously correct I find it."

"Now listen," said Barbicane to his ignorant comrade, "and you will see
that all these letters have a signification."

"I am listening," said Michel, looking resigned.

"_d_," said Barbicane, "is the distance from the centre of the earth to
the centre of the moon, for we must take the centres to calculate the
attraction."

"That I understand."

"_r_ is the radius of the earth."

"_r_, radius; admitted."

"_m_ is the volume of the earth; _m prime_ that of the moon. We are
obliged to take into account the volume of the two attracting bodies, as
the attraction is in proportion to the volume."

"I understand that."

"_g_ represents gravity, the speed acquired at the end of a second by a
body falling on the surface of the earth. Is that clear?"

"A mountain stream!" answered Michel.

"Now I represent by _x_ the variable distance that separates the
projectile from the centre of the earth, and by _v_ the velocity the
projectile has at that distance."

"Good."

"Lastly, the expression _v_ zero which figures in the equation is the
speed the bullet possesses when it emerges from the atmosphere."

"Yes," said Nicholl, "you were obliged to calculate the velocity from
that point, because we knew before that the velocity at departure is
exactly equal to 3/2 of the velocity upon emerging from the atmosphere."

"Don't understand any more!" said Michel.

"Yet it is very simple," said Barbicane.

"I do not find it very simple," replied Michel.

"It means that when our projectile reached the limit of the terrestrial
atmosphere it had already lost one-third of its initial velocity."

"As much as that?"

"Yes, my friend, simply by friction against the atmosphere. You will
easily understand that the greater its speed the more resistance it
would meet with from the air."

"That I admit," answered Michel, "and I understand it, although your _v_
zero two and your _v_ zero square shake about in my head like nails in a
sack."