# Specific Gravity

Specific gravity is the ratio of density of a substance compared to the density of fresh water at 4°C (39° F). At this temperature the density of water is at its greatest value and equal 1 g/mL. Since specific gravity is a ratio, so it has no units. An object will float in water if its density is less than the density of water and sink if its density is greater that that of water. Similarly, an object with specific gravity less than 1 will float and those with a specific gravity greater than one will sink. Specific gravity values for a few common substances are: Au, 19.3; mercury, 13.6; alcohol, 0.7893; benzene, 0.8786. Note that since water has a density of 1 g/cm3, the specific gravity is the same as the density of the material measured in g/cm3.

## The Discovery of Specific Gravity

The discovery of specific gravity makes for an interesting story. Sometime around 250 B.C., the Greek mathematician Archimedes was given the task of determining whether a craftsman had defrauded King Heiro II of Syracuse. The king had provided a metal smith with gold to make a crown. The king suspected that the metal smith had added less valuable silver to crown and kept some of the gold for himself. The crown weighed the same as other crowns but due to its intricate designs it was impossible to measure the exact volume of the crown so its density could be determined. The king challenged Archimedes to determine if the crown was pure gold. Archimedes had no immediate answer and pondered this question for sometime.

One day while entering a bath, he noticed that water spilled over the sides of the pool, and realized that the amount of water that spilled out was equal in volume to the space that his body occupied. He realized that a given mass of silver would occupy more space than an equivalent mass of gold. Archimedes first weighed the crown and weighed out an equal mass of pure gold. Then he placed the crown in a full container of water and the pure gold in a container of water. He found that more water spilled over the sides of the tub when the craftsman’s crown was submerged. It turned out that the craftsman had been defrauding the King! Legend has it that Archimedes was so excited about his discovery that he ran naked through the streets of Sicily shouting Eureka! Eureka! (Which is Greek for “I have found it!”).