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Archemides' priciple and the relative density of different materials.
You need a something to find your item's volume (a graduated syringe would do) and then accurate (perhaps chemist or school lab) scales to measure its weight.
Now you now its volume and weight. 24 Carat or pure Gold has a density of 19.31 grammes per millilitre. Devide its weight by the volume and you will have its density.
The impurities used in gold to harden or colour it are usually silver or copper. These have a density of around half that of gold so it easy to tell the difference.
For further details on this goto: http://www.iun.edu/~cpanhd/C101webnotes/matter-and-energ y/density.html
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