Swinburne University of Technology Sarawak Campus

Vulgarity, beauty and the father of non-destructive testing

October 13, 2010

By Dr Manas Kumar Haldar

(Published in’Campus & Beyond’, a weekly column written by Swinburne academics in the Borneo Post newspaper)

Dumpy, our know-all senior in school, was holding his court. “You guys are stupid”, he said, “You have not read any physics yet. Have you read about Archimedes? He jumped out of his tub and ran naked around the town shouting Eureka, Eureka. Ha, Ha, Ha, what a sight it would have been!”

I went off to the library and read the story from a kid’s physics book. Indeed Dumpy was right. The story goes like this. King Hiero II of Syracuse had a crown made of gold, but he suspected that the goldsmith had cheated him and substituted some silver for gold. Now different materials have different density which is mass per unit volume. Therefore if the density of the crown could be found to be the same as that of gold, it would be pure, otherwise it had impurities. The problem was that the volume of the crown could not be measured unless it was melted into a proper shape such as a bar, but the king would have none of this. Could Archimedes, the famous scientist, find it out without destroying the crown? The story continues that when Archimedes was having a bath, he noticed that his body had changed the level of the water. As water is considered to be an incompressible fluid, the volume of water displaced is equal to the volume of his body. So the volume of the crown could be determined by determining the volume of water displaced when it is immersed in water. Then by determining its weight, its density could be determined. So excited was Archimedes that he took to the streets naked, crying “Eureka (I have found it)”.

The story has no historical basis. But coming back to the problem, if the amount of impurity is small, one would have to measure the volume to a great accuracy to give a verdict. Think of making the measurement yourself with the equipment around you and you will appreciate the difficulty they would have in Archimedes’ days (more than 200BC). Instead it is said that Archimedes must have used the principle going by his name. Archimedes principle states that a body immersed in an incompressible fluid loses a part of its weight equal to the weight of displaced fluid. The latter is called the force of buoyancy. It is equal to the weight of the displaced fluid and acts in a direction opposite to that of gravity. Now if we put the crown and its equal weight of gold on the opposite arms of a balance and immerse them in water, the balance will tilt if the crown has impurities. This is because the impure crown has greater volume than the volume of pure gold of the same weight causing a greater upward buoyancy force on the crown. The crown immersed in water will weigh less. Physicists consider this to be great science, which indeed it is. The force of buoyancy and a body’s weight determine whether a body will float or sink. It is of great importance to ships. But do you realise that this experiment was probably the first use of non-destructive testing in science? Considerable research goes on various methods of non-destructive testing even today.

The story may not be true but the word Eureka has caught on. When one suddenly gets a brilliant idea, we call it his Eureka moment. Perhaps you know about the story of Newton getting the idea of gravity when an apple fell on his head. That was his Eureka moment.

It all depends on how we look at things. If you read like Dumpy, you might find this story vulgar. But if you read like me, I hope that you will find it beautiful.

Dr Manas Kumar Haldar is an Associate Professor with the School of Engineering, Computing and Science, at Swinburne University of Technology Sarawak Campus. He can be contacted at mhaldar@swinburne.edu.my