How Did Archimedes Determine the Crown's Purity?

[hanson]

Hi all, I am so confused by the famous Archimedes's story of telling if the crown is made of pure gold.

As far as I understand from information posted in the internet, such as http://hyperphysics.phy-astr.gsu.edu/hbase/pbuoy.html

Archimedes first determines the volume of the crown by measuring the apparent mass when the crown is immersed into water by a mass spring for example.
Then the difference between the actual mass and the apparent mass will be the buoyant force, which is given by the volume of the crown * density of water.
From this, we know the volume of the crown.

And we can divide the actual mas of the crown by the density of water to get the density of the crown.

But can't one just measure the volume of the water displaced when the crown is immersed into the water, and that should be equal to the volume of the crown?
Can we get the volume of the crown that way?

 

[mushinskull]

Yeah, I can see your confusion.

Wikipedia's article on the word Eureka: http://en.wikipedia.org/wiki/Eureka states

'he reportedly proclaimed "Eureka!" when he stepped into a bath and noticed that the water level rose—he suddenly understood that the volume of water displaced must be equal to the volume of the part of his body he had submerged. This meant that the volume of irregular objects could be measured with precision, a previously intractable problem.'​

And that is how he originally determined the density of the crown.


I think that later on he continued researching it and came up with the whole buoyancy force is the difference between the actual weight and apparent weight, which is the weight of the displaced water deal. And that is known as the Archimedes' principle (described in http://en.wikipedia.org/wiki/Archimedes'_principle)


Hope that clarifies things a bit.