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Hence, by equation ${\displaystyle (A)}$, ${\displaystyle {\tfrac {W}{w}}}$ is known. But ${\displaystyle {\tfrac {W}{w}}}$ is the ratio of the weight of the crown to the weight of an equal volume of water. This ratio is the same for any lump of metal of the same material: it is now called the specific gravity of the material, and depends only on the intrinsic nature of the substance and not on its shape or quantity. Thus to test if the crown were of gold, Archimedes had only to take a lump of indisputably pure gold and find its specific gravity by the same process. If the two specific gravities agreed, the crown was pure; if they disagreed, it was debased.

This argument has been given at length, because not only is it the first precise example of the application of mathematical ideas to physics, but also because it is a perfect and simple example of what must be the method and spirit of the science for all time. The discovery of the theory of specific gravity marks a genius of the first rank.

The death of Archimedes by the hands of a Roman soldier is symbolical of a world-change of the first magnitude: the theoretical Greeks, with their love of abstract science, were superseded in the leadership of the European world by the practical Romans. Lord Beaconsfield, in one of his novels, has defined a practical man as a man who practises the errors of