An introduction to mathematics, by A. N. Whitehead.

METHODS OF APPLICATION 29
wish to reckon in terms of forces such as the
weight of a mass of 1 lb., the number which
k represents must be extremely small; for
when m and M and d are each put equal to
1, mM- becomes the gravitational attraction
of two equal masses of 1 lb. at the distance of
one mile, and this is quite inappreciable.
However, we have now got our formula for
the force of attraction. If we call this force
mM.
F, it is F=k -, giving the correlation between the variables F, m, 3M, and d. We all
know the story of how it was found out.
Newton, it states, was sitting in an orchard
and watched the fall of an apple, and then
the law of universal gravitation burst upon
his mind. It may be that the final formulation of the law occurred to him in an
orchard, as well as elsewhere-and he must
have been somewhere. But for our purposes
it is more instructive to dwell upon the vast
amount of preparatory thought, the product
of many minds and many centuries, which
was necessary before this exact law could be
formulated. In the first place, the mathematical habit of mind and the mathematical
procedure explained in the previous two
chapters had to be generated; otherwise
Newton could never have thought of a formula representing the force between any two