“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.”

“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.”