"First effect of algebra," continued Barbicane. "And now to finish we
are going to find the numerical known quantity of these different
expressions--that is to say, find out their value."

"You will finish me first!" answered Michel.

"Some of these expressions," said Barbicane, "are known; the others have
to be calculated."

"I will calculate those," said Nicholl.

"And _r_," resumed Barbicane, "_r_ is the radius of the earth under the
latitude of Florida, our point of departure, _d_--that is to say, the
distance from the centre of the earth to the centre of the moon equals
fifty-six terrestrial radii--"

Nicholl rapidly calculated.

"That makes 356,720,000 metres when the moon is at her perigee--that is
to say, when she is nearest to the earth."

"Very well," said Barbicane, "now _m_ prime upon _m_--that is to say,
the proportion of the moon's volume to that of the earth equals 1/81."

"Perfect," said Michel.

"And _g_, the gravity, is to Florida 9-1/81 metres. From whence it
results that _gr_ equals--"

"Sixty-two million four hundred and twenty-six thousand square metres,"
answered Nicholl.

"What next?" asked Michel Ardan.

"Now that the expressions are reduced to figures, I am going to find the
velocity _v zero_--that is to say, the velocity that the projectile
ought to have on leaving the atmosphere to reach the point of equal
attraction with no velocity. The velocity at that point I make equal
_zero_, and _x_, the distance where the neutral point is, will be
represented by the nine-tenths of _d_--that is to say, the distance that
separates the two centres."

"I have some vague idea that it ought to be so," said Michel.

"I shall then have, _x_ equals nine-tenths of _d_, and _v_ equals
_zero_, and my formula will become--"

Barbicane wrote rapidly on the paper--

2 10r 1 10r r
v = 2 gr { 1 - --- --- ( --- - ---) }
0 9d 81 d d-r

Nicholl read it quickly.

"That's it! that is it!" he cried.

"Is it clear?" asked Barbicane.

"It is written in letters of fire!" answered Nicholl.

"Clever fellows!" murmured Michel.

"Do you understand now?" asked Barbicane.

"If I understand!" cried Michel Ardan. "My head is bursting with it."

"Thus," resumed Barbicane, "_v zero_ square equals 2 _gr_ multiplied by
1 minus 10 _r_ upon 9 _d_ minus 1/81 multiplied by 10 _r_ upon _d_ minus
_r_ upon _d_ minus _r_."

"And now," said Nicholl, "in o