"
"What!" cried Ardan, in a mocking tone, "is there really anything that
Mathematics can't do?"
"Yes," said Barbican, "there is still a great deal that Mathematics
can't even attempt."
"So far, so good;" resumed Ardan. "Now then what is this Integral
Calculus of yours?"
"It is a branch of Mathematics that has for its object the summation of
a certain infinite series of indefinitely small terms: but for the
solution of which, we must generally know the function of which a given
function is the differential coefficient. In other words," continued
Barbican, "in it we return from the differential coefficient, to the
function from which it was deduced."
"Clear as mud!" cried Ardan, with a hearty laugh.
"Now then, let me have a bit of paper and a pencil," added Barbican,
"and in half an hour you shall have your formula; meantime you can
easily find something interesting to do."
In a few seconds Barbican was profoundly 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.
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