rwards a charge was made that gold had been abstracted and
an equivalent weight of silver had been added in the manufacture of the
crown. Hiero, thinking it an outrage that he had been tricked, and yet
not knowing how to detect the theft, requested Archimedes to consider
the matter. The latter, while the case was still on his mind, happened
to go to the bath, and on getting into a tub observed that the more his
body sank into it the more water ran out over the tub. As this pointed
out the way to explain the case in question, without a moment's delay,
and transported with joy, he jumped out of the tub and rushed home
naked, crying with a loud voice that he had found what he was seeking;
for as he ran he shouted repeatedly in Greek, "[Greek: Eureka, eureka]."

11. Taking this as the beginning of his discovery, it is said that he
made two masses of the same weight as the crown, one of gold and the
other of silver. After making them, he filled a large vessel with water
to the very brim, and dropped the mass of silver into it. As much water
ran out as was equal in bulk to that of the silver sunk in the vessel.
Then, taking out the mass, he poured back the lost quantity of water,
using a pint measure, until it was level with the brim as it had been
before. Thus he found the weight of silver corresponding to a definite
quantity of water.

12. After this experiment, he likewise dropped the mass of gold into the
full vessel and, on taking it out and measuring as before, found that
not so much water was lost, but a smaller quantity: namely, as much less
as a mass of gold lacks in bulk compared to a mass of silver of the same
weight. Finally, filling the vessel again and dropping the crown itself
into the same quantity of water, he found that more water ran over for
the crown than for the mass of gold of the same weight. Hence, reasoning
from the fact that more water was lost in the case of the crown than in
that of the mass, he detected the mixing of silver with the gold, and
made the theft of the contractor perfectly clear.

13. Now let us turn our thoughts to the researches of Archytas of
Tarentum and Eratosthenes of Cyrene. They made many discoveries from
mathematics which are welcome to men, and so, though they deserve our
thanks for other discoveries, they are particularly worthy of admiration
for their ideas in that field. For example, each in a different way
solved the problem enjoined upon Delos by Apollo in an oracle, t