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Roughly, specific gravity compares the volume of an item and its weight to an equal volume and weight of water. Archimedes first used it as a way to determine if a king's crown was made of pure gold. If the crown was put in a bucket and the water level rose to the same level as an equal level as it did with an equal weight of pure gold, then the crown was made of pure gold. If it did not, then the king's crown was made of something else.

Hardness is totally different. A hardness scale was developed based on what materials would scratch other materials. On that scale, an emerald is 8, a ruby is 9, and a diamond is 10. A ruby and a diamond will scratch an emerald. But only a diamond will scratch a ruby. The original scale had a total of 10 items. Scientists started with it but have modified it. They have gone over to a pressure based scale. South African diamonds are twice as hard as Australian diamonds. Australian diamonds are still extremely hard. Scientists have created a compound that does not exist in nature with a hardness of 11. They have also gone over to a more scientific scale which uses units of force for hardness.

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