Archimedes was in the habit of following up a problem steadily until he had solved it. He allowed nothing to come in the way. Sometimes he was found tracing lines and circles in the ashes of the grate, working out some problem. Sometimes, even, when he had had his bath, and his slaves had rubbed him with oil to make his skin smooth, he traced diagrams with his fingers on the layer of oil on his skin. He could think of nothing but the problem he was trying to solve. The problem of the crown puzzled him greatly; but one day the solution flashed upon him just as he was having his bath. He was taking a bath in a kind of large cup of his own size, as the Greeks used to do. The cup stood on a pedestal, with a sink round it to let the water flow off. When he got in, the cup was full of water to the brim, therefore it overflowed as he was getting in. He dipped himself entirely under water, head and all, and when he got out again the water was no longer up to the brim, but considerably below it. _The amount of water which had flowed out was exactly the bulk of his own body_. The truth came upon Archimedes like a flash. He had found a way of determining the bulk of his own body without melting himself down into a block, and why should he not find the bulk of the crown in the same manner? He was so excited that he forgot to dry and clothe himself, but ran home just as he was, calling out, “I have found it! I have found it!” He took a big jug full of water to the brim, and carefully let down the crown into it, holding it by a thread. A quantity of water overflowed, and when the crown was taken out the water was on a lower level. He took a measuring glass, and carefully measured how much water was required to bring the water up to the brim again. That quantity of water had the same bulk as the crown. He then measured out a quantity of gold and a quantity of silver, both quantities weighing exactly the same as the crown. These quantities he melted up into blocks. In this manner he got three things weighing exactly the same: a block of gold, a block of silver, and the crown which the goldsmith had made. He then dipped the gold block into the jug filled to the brim. It displaced a certain amount of water. Again, he dipped the silver block into the jug. It displaced nearly twice as much water. Finally, he dipped the crown into the full jug. It displaced more water than the gold block, but less water than the silver block. And so it was proved that _the crown contained a quantity of silver_. Archimedes next made some other blocks, containing gold mixed with various proportions of silver, but always of the same weight as the crown. In the end he obtained a block of silver and gold which displaced exactly as much water as the crown. He went to the king and told him exactly how much silver was in the crown, and how much gold the goldsmith had stolen.