SOLUTION FOUND IN BATHTUB!
Archimedes, son of an astronomer, was one of the ancient world's main men of science. Just about the most famous story about him is that of his running, wet and naked, through the streets of Syracuse yelling, "Eureka!" ("I have found it!"). What had he found that was so astounding that he forgot his bathrobe? We will never know the true details of the story, but it might go like this
The king of the time had commissioned a new crown, supplying the gold for it himself. But His Majesty had the suspicion that the new crown was not all it seemed, he suspected that the goldsmith had kept some of the expensive gold and mixed cheaper silver in with the rest to make the weight of metal the same.
The king asked Archimedes to prove this one way or another - without damaging the crown, just in case. "OK", thought Archimedes, "I can easily weigh the crown, and then make a lump of pure gold of the same weight. But I need to know the volume of both of them as well, if the crown contains some, lighter, silver it will take up more space for the same weight. The lump of pure gold is easy to measure, but the crown is a difficult shape, I can't measure all these fiddly bits accurately!"
Archimedes puzzled over this until he felt tired and decided to have a nice soak at the bath house. As Archimedes lowered himself slowly in he noticed that the water level rose. Later he got out of the bath and the water level went back down. Then the realisation hit him, the difference in height of the bath water had to be exactly the same volume as his own, submerged body (complete with all his fiddly bits)! If he were to place the crown in a full tub of water, the displaced water must be the same volume as the crown!
So happy was Archimedes that he forgot his naked state and rushed of to tell the king of his idea He had a wide "jug", with a long spout, made and filled this until the water overflowed from the spout. When this flow stopped he lowered the crown into the jug, but this time carefully collected the displaced water from the spout. Making a mark where the water level was on the collecting vessel he emptied that and dried it, then refilled the jug and repeated the process, this time dunking the lump of pure gold and collecting the new overflow in the same measuring vessel.
The displaced water from the gold did not quite reach the first mark. This meant that the gold lump had a smaller volume than the crown even though it weighed the same, it was more dense than the crown. Therefore the crown was a mixture of gold and silver!
Archimedes had temporarily lost his head in his joy at finding his solution; we can assume the goldsmith lost his head in a more permanent way!
OK, even if this is a bit fictional history has recorded the fact that Archimedes obviously felt a real emotional lift in finding a simple solution to what he thought was a very difficult problem. That is one of the rewards of working in science and technology - that sense of discovery, of creating new ideas or inventions. It doesn't happen that often, and it can take a lot of time and work, but when it does happen it's a real buzz!
Archimedes' method has remained just as important for every single moment of the two thousand two hundred odd years since he found it. It is still used today for many purposes, including being still the most accurate way to measure the volume of the human body. From this and the person's weight the density of his or her body can be found which is a good indicator of the amount of fat someone has, a very important factor in medical research and treatment.