"
"Well, Algebra is an instrument or utensil just as much as a hammer or a
plough, and a very good instrument too if you know how to make use of
it."
"You're in earnest?"
"Quite so."
"And you can handle the instrument right before my eyes?"
"Certainly, if it interests you so much."
"You can show me how they got at the initial velocity of our
Projectile?"
"With the greatest pleasure. By taking into proper consideration all the
elements of the problem, viz.: (1) the distance between the centres of
the Earth and the Moon, (2) the Earth's radius, (3) its volume, and (4)
the Moon's volume, I can easily calculate what must be the initial
velocity, and that too by a very simple formula."
"Let us have the formula."
"In one moment; only I can't give you the curve really described by the
Projectile as it moves between the Earth and the Moon; this is to be
obtained by allowing for their combined movement around the Sun. I will
consider the Earth and the Sun to be motionless, that being sufficient
for our present purpose."
"Why so?"
"Because to give you that exact curve would be to solve a point in the
'Problem of the Three Bodies,' which Integral Calculus has not yet
reached.
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