The king thanked his clever friend. He sent for the goldsmith and told him he had found him out. The goldsmith confessed his guilt, and the king made him restore the gold and kept him in prison until he had been justly punished for his crime. Archimedes continued his experiments with all sorts of bodies and substances. [Illustration: Fig. 4.--An Archimedes Cup.] He weighed things in air and in water, and found that when they were suspended in water by a thread, and the thread was attached to one arm of a balance, the weight necessary to counterbalance it was less than when the body hangs in air. The difference in the counterbalancing weight is equal to the weight of the water which the body displaces. This may be proved by a simple experiment. A glass beaker with a spout, like that in Fig. 4, has water poured into it until the water just runs out of the spout. The beaker with the water in it is placed in one pan of a balance, and weights are put in the other pan until the balance is even. A block of wood is then weighed and floated on the water in the cup. Some of the water flows out of the spout and may be caught in another beaker. But when the cup is weighed with the floating block it is found that the weight is exactly the same as before. The wood exerts no additional weight, since its weight is equal to that of the water which flowed over, as may be proved by weighing the water caught in the small beaker. Archimedes put this rule into a few words as follows: “Every body loses as much weight in water as the displaced water weighs.” This is called the Principle of Archimedes. [Illustration: Fig. 5.--Ancient. War-Engine for throwing Rocks.] When, after fifty years’ peace, the Romans made war on Syracuse, Archimedes took charge of the defence of the city. He made great war-engines which threw rocks upon the attacking army, and sank the enemy’s ships in the harbour. Marcellus, the Roman general, could not help admiring the genius of the great Syracusan engineer, and when he captured the city at last he ordered his soldiers to spare Archimedes. One of them came upon the great inventor just as he was working out a problem with a stick in the sand on the floor. When the soldier asked his name, he told him to wait till he had solved the problem, and not to tread upon his circles. Thereupon the soldier killed him. Marcellus was greatly grieved, and tried to atone for this by showing great kindness to the relatives. Archimedes was buried near the city. On his grave was put a monument in the shape of a cylinder enclosing a ball or sphere. It was one of his proudest achievements to find that a ball enclosed in a cylinder of the same height fills up just two-thirds of its bulk. No more suitable device could have been placed on the grave of one of the greatest men of science that ever lived. CHAPTER II THE WISE MEN OF ALEXANDRIA