more palpably evident than the sense of Barbican's formula."
"You asked for Algebra, you know," observed Barbican.
"Rock crystal is nothing to it!"
"The fact is, Barbican," said the Captain, who had been looking over the paper, "you have worked the thing out very well. You have the integral equation of the living forces, and I have no doubt it will give us the result sought for."
"Yes, but I should like to understand it, you know," cried Ardan: "I would give ten years of the Captain's life to understand it!"
"Listen then," said Barbican. "Half of v prime squared less v squared, is the formula giving us the half variation of the living force."
"Mac pretends he understands all that!"
"You need not be a Solomon to do it," said the Captain. "All these signs that you appear to consider so cabalistic form a language the clearest, the shortest, and the most logical, for all those who can read it."
"You pretend, Captain, that, by means of these hieroglyphics, far more incomprehensible than the sacred Ibis of the Egyptians, you can discover the velocity at which the Projectile should start?"
"Most undoubtedly," replied the Captain, "and, by the same formula I can even tell you the rate of our velocity at any particular point of our journey."
"You can?"
"I can."
"Then you're just as deep a one as our President."
"No, Ardan; not 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 Algebra on one who is a stranger to it; to finish you, our next step is to express numerically the value of these several symbols. Now some of them are already known, and some are to be calculated."
"Hand the latter over to me," said the Captain.
"First," continued Barbican: "r, the Earth's radius is, in the 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.
"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:—
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,
