CHAPTER I. Archimedes

ARCHIMEDES

THE land of Italy is shaped like a boot, and at the toe of the boot lies a three-cornered island called Sicily. It was famous in ancient times for its cities, temples, and palaces; for its fruit-gardens and cornfields; and for its great volcano called Etna, from the top of which a cloud of steam and dust ascends, and sometimes a fiery stream of molten rock flows down.

Sicily has often been shaken by earthquakes, but the worst of all was the earthquake which destroyed the town of Messina at Christmas 1908.

The greatest city of Sicily was called Syracuse. It is now a town of 25,000 inhabitants, built on an island joined to the mainland by a bridge. But in ancient times it had ten times as many people, and its buildings covered the heights and cliffs opposite, and extended along the banks of the river, up to where the papyrus plants grow, which the ancients made into paper.

In that great city dwelt a man called Archimedes. He was a rich and wise man, a friend and relative of the king, and had he chosen, he could have spent all his days in the pursuit of pleasure, going to the races and matches and theatres, and dining every day at the king’s table. But his mind was given to the pursuit of science and of truth. His great delight lay in studying the laws of Nature, and finding out the secrets of her working. He believed that everything happens according to some law or principle, and that if once he could discover the law he could rule the world.

Archimedes was born 300 years before Christ. When he was young, war was raging in Sicily between the Greeks and Romans and the people of the city of Carthage in Africa, each wishing to possess the beautiful and fertile island. The king of Syracuse joined the Romans, and as they proved the strongest, he was able to reign in peace for fifty years. During that time the trade and commerce of the city flourished. The king built many ships, some of them larger than any seen before, and these ships sailed to Egypt and Greece, Africa and Spain, and along the coasts of France and Italy, exchanging grain and fruit for purple and gems, Arabian horses, and amber from the shores of the Baltic.

Archimedes spent much of his time in the harbour and in the shipbuilding yards, watching the sailors and shipwrights at their work, and helping them with his new inventions. He saw them lift heavy weights, and taught them how to do it without great exertion. They already knew how to use a lever, or crowbar, for lifting heavy stones. They pushed the end of the lever under the stone, and rested the lever or bar on another stone close to it.

In that way they could exert a great force. Archimedes measured the force they could exert in this way, and found it was increased when the bar was made longer and the distance between the stone and the support was made less. When the distance between the support and the hand was five times the distance between the support and the stone, Archimedes found that the force of the hand was multiplied by five, and one man could lift a stone which it would take five men to lift without a lever. “Now,” he said, “if you make the lever long enough there is no weight too heavy for us to lift.” He told the king about this discovery, and said to him, “If you gave me some place on which to stand, I could move the whole earth.”

Archimedes knew, of course, that the matter was not quite so simple as that. He knew that the lever required to move the earth would have to be exceedingly stout and strong, as thick, indeed, as the earth itself. For, otherwise, it would not stand the strain. Besides, he knew he would also require a fixed support against which to rest the lever. And the place on which he was to stand would have also to be firmly fixed, so as to allow him to exert the force required. We know now that the earth floats freely in space, and that there is no fixed place anywhere. Therefore we cannot, after all these 2200 years, try the great experiment suggested by Archimedes.

But many other things which Archimedes proposed are now used every day. One of these is the Endless Screw, by means of which Archimedes is said to have drawn a ship, with cargo and crew, along the sand as easily as if it were floating in water, to the great delight of his friend the king.

Not long after this the king showed Archimedes a great mark of favour and confidence. This is how it came about.

The king had given one of his goldsmiths a certain weight of gold, and instructed him to make it into a golden crown which he wanted to present to one of the temples. After a few weeks the goldsmith came to the palace and brought the crown to the king. The king weighed the crown, and found it was the same weight as the gold he had given out. But somebody told him that the goldsmith had mixed a quantity of silver with the gold, and kept the remaining gold for himself.

The king was a just man, and did not want to accuse the goldsmith of the crime without having a proof of his guilt. He therefore sent for Archimedes and gave him the crown, asking him to find out whether any silver had been mixed with the gold, or whether it was made of pure gold.

Archimedes was long puzzled over this problem. He weighed the crown, and found the weight was correct. It also looked like pure gold, so that the amount of silver could not be very much. Archimedes made two blocks, one of silver and the other of gold, of exactly the same size, and found that the block of gold weighed nearly twice as much as the block of silver. “Now,” he said to himself, “if I could melt up the crown and make it into a square block, and make another block of exactly the same size of pure gold, both should weigh the same if the crown is pure gold, but if it is not, the block made from the crown should be lighter.” He wished for a moment to melt up the crown, but it was beautifully made, and he thought it a pity to throw away the fine work. If he could only find out the exact bulk of the crown, he thought he could determine easily if it was the proper weight which it should be if made of pure gold. The problem then was how to find out the total bulk of the crown without melting it up into a block.

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.

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.

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.

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.