ARCHIMEDES
AND THE CROWN
We remember the man, who runs out of the
bathhouse naked and shouts : “Eureka!”. He directly
goes to palace and says that he could actually find
out if the crown was only made up of gold or not,
without damaging the crown. We all know the rest
of the story, he puts the golden crown, as said, in
a beaker with water and observes the amount of
water that spills over. Then he does the same with
a golden bullion with the same weight, and sees
that there is less water spilling over. Therefore the
crown was not completely made up of gold, there
was something else in the crown. This was silver, as
stated in the story. In fact, is this a real story ? If it
really is, is that the whole process ?
The hero of this story is, as known, Archimedes
who died BC 227 in Sicily. The very first book for
the King’s Crown was published after 200 years,
by a roman architect Vitruvius. Of couse, Vitruvius
wrote all the second-hand information in his book
because there was no written documents about this
story , or even eye wittnesses. The first scientist that
got suspicious by this story was Galileo. In one of
his books, that he wrote in the age of 22, he says
that it is impossible to see the difference in the
overflowing water by eye, because they were in the
same weight. He says though, that Archimedes did
actually use a different method to find out if the
crown was actually made up of gold. Galileo talks
about this method in his book, clearly explaining
this mechanism of Archimedes.
Let’s first see if Galileo was right by getting
suspicious about this great story of Archimedes.
The crown that is being tested in this case, has a
radius of 18 cm and weighs 700g. If we want to put
this crown in a beaker, the beaker should have such
radius that is greater than 18 cm, which means a
really big beaker. We can observe how much water
overflows if we put the crown and a golden bullion
in this beaker. If there is a little amount of silver in
the crown, the water that overflows will be more.
However, the amount of water that overflows when
we put the crown and a golden bullion in a beaker
can not be observable, because with this size of
crown the difference would be less than 1mm.
Galileo says that this can not be observable by eye.
In a way, Galileo was right because it is hard to say
that the difference was only because of the silver
in the crown, not because of the air bubbles in the
crown. Overall, it is impossible to understand if
the crown was actually gold by using Archimedes’
technique.
We are now facing that the hypothesis of this great
story of Archimedes is meaningless in real life.
However, Galileo thought that this story should be
clarified, that is what he does. Knowing that it is hard
to observe the difference in the level of the water
because of the silver in the crown, Galileo thought
that the difference in the masses of a golden and a
fake crown can be observed with a balance.
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THE CLAPPER 2015 - 2016