rofoundly absorbed in his problem, while
M'Nicholl was watching out of the window, and Ardan was busily employed
in preparing breakfast.

The morning meal was not quite ready, when Barbican, raising his head,
showed Ardan a page covered with algebraic signs at the end of which
stood the following formula:--

1 2 2 r m' r r
--- (v' - v ) = gr {--- - 1 + --- (----- - -----) }
2 x m d - x d - r

"Which means?" asked Ardan.

"It means," said the Captain, now taking part in the discussion, "that
the half of _v_ prime squared minus _v_ squared equals _gr_ multiplied
by _r_ over _x_ minus one plus _m_ prime over _m_ multiplied by _r_ over
_d_ minus _x_ minus _r_ over _d_ minus _r_ ... that is--"

"That is," interrupted Ardan, in a roar of laughter, "_x_ stradlegs on
_y_, making for _z_ and jumping over _p_! Do _you_ mean to say you
understand the terrible jargon, Captain?"

"Nothing is clearer, Ardan."

"You too, Captain! Then of course I must give in gracefully, and declare
that the sun at noon-day is not 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; n