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

40 INTRODUCTION TO MATHEMATICS
Hence, by equation (A), W is known. But
w
W is the ratio of the weight of the crown to
w
the weight of an equal volume of water.
This ratio is the same for any lump of metal of
the same material: it is now called the specific
gravity of the material, and depends only on
the intrinsic nature of the substance and not
on its shape or quantity. Thus to test if the
crown were of gold, Archimedes had only to
take a lump of indisputably pure gold and
find its specific gravity by the same process.
If the two specific gravities agreed, the crown
was pure; if they disagreed, it was debased.
This argument has been given at length,
because not only is it the first precise example
of the application of mathematical ideas to
physics, but also because it is a perfect and
simple example of what must be the method
and spirit of the science for all time. The
discovery of the theory of specific gravity
marks a genius of the first rank.
The death of Archimedes by the hands of a
Roman soldier is symbolical of a world-change
of the first magnitude: the theoretical Greeks,
with their love of abstract science, were superseded in the leadership of the European world
by the practical Romans. Lord Beaconsfield, in one of his novels, has defined a practical man as a man who practises the errors of