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

38 INTRODUCTION TO MATHEMATICS
physical research. Luckily, it is simple
enough to be explained here in detail. It is
one of the best easy examples of the method of
application of mathematical ideas to physics.
Hiero, King of Syracuse, had sent a quantity of gold to some goldsmith to form the
material of a crown. He suspected that the
craftsmen had abstracted some of the gold
and had supplied its place by alloying the
remainder with some baser metal. Hiero
sent the crown to Archimedes and asked him
to test it. In these days an indefinite number of chemical tests would be available.
But then Archimedes had to think out the
matter afresh. The solution flashed upon
him as he lay in his bath. He jumped
up and ran through the streets to the
palace, shouting Eureka! Eureka! (I have
found it, I have found it). This day, if we
knew which it was, ought to be celebrated as
the birthday of mathematical physics; the
science came of age when Newton sat in his
orchard. Archimedes had in truth made a
great discovery. He saw that a body when
immersed in water is pressed upwards by the
surrounding water with a resultant force
equal to the weight of the water it displaces.
This law can be proved theoretically from the
mathematical principles of hydrostatics and
can also be verified experimentally. Hence,
if W lb. be the weight of the crown, as weighed