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

28 INTRODUCTION TO MATHEMATICS
nature must start from some assumed law of
nature, such, for instance, as the assumed
law of the cost of building stated above.
Accordingly, however accurately we have
calculated that some event must occur, the
doubt always remains-Is the law true? If
the law states a precise result, almost certainly it is not precisely accurate; and thus
even at the best the result, precisely as calculated, is not likely to occur. But then we
have no faculty capable of observation with
ideal precision, so, after all, our inaccurate
laws may be good enough.
We will now turn to an actual case, that
of Newton and the Law of Gravity. This law
states that any two bodies attract one another with a force proportional to the product
of their masses, and inversely proportional to
the square of the distance between them.
Thus if m and M are the masses of the two
bodies, reckoned in lbs. say, and d miles is
the distance between them, the force on either
body, due to the attraction of the other and
directed towards it, is proportional to mm
thus this force can be written as equal to
kmM
d, where k is a definite number depending
on the absolute magnitude of this attraction
and also on the scale by which we choose to
measure forces. It is easy to see that, if we