The ancients attribute to Archimedes more than forty mechanical inventions —among which are the endless screw; the combination of pulleys; an hydraulic organ, according to Tertullian; a machine called the HELIX, or screw, for launching ships; and a machine called loculus, which appears to have consisted of forty pieces, by the putting together of which various objects could be framed, and which were used by boys as a sort of artificial memory.

Archimedes is said to have obtained the friendship and confidence of Hiero by the following incident. The king had delivered a certain weight of gold to a workman, to be made into a crown. When the crown was made and sent to the king, a suspicion arose in the royal mind that the gold had been adulterated by the alloy of a baser metal, and he applied to Archimedes for his assistance in detecting the imposture; the difficulty was to measure the bulk of the crown without melting it into a regular figure; for silver being, weight for weight, of greater bulk than gold, any alloy of the former in place of an equal weight of the latter would necessarily increase the bulk of the crown; and at that time there was no known means of testing the purity of metal. Archimedes, after many unsuccessful attempts, was about to abandon the subject altogether, when the following circumstance suggested to his discerning and prepared mind a train of thought which led to the solution of the difficulty. Stepping into his bath one day, as was his custom, his mind doubtless fixed on the object of his research, he chanced to observe that, the bath being full, a quantity of water of the same bulk as his body must flow over before he could immerse himself. He probably perceived that any other body of the same bulk would have raised the water equally; but that another body of the same weight, but less bulky, would not have produced so great an effect. In the words of Vitruvius, "as soon as he had hit upon this method of detection, he did not wait a moment, but jumped. joyfully out of the bath, and running forthwith toward his own house, called out with a loud voice that he had found what he sought. For as he ran he called out, in Greek, "Eureka! Eureka!—I have found it! I have found it!" When his emotion had sobered down, he proceeded to investigate the subject calmly. He procured two masses of metal, each of equal weight with the crown—one of gold and the other of silver—and having filled a vessel very accurately with water, he plunged into it the silver, and marked the exact quantity of water that over-flowed. He then treated the gold in the same manner, and observed that a less quantity of water overflowed than before. He next plunged the crown into the same vessel full of water, and observed that it displaced more of the fluid than the gold had done, and less than the silver; by which he inferred that the crown was neither pure gold nor pure silver, but a mixture of both. Hiero was so gratified with this result as to declare that from that moment he could never refuse to believe anything Archimedes told him.

Travelling in Egypt, and observing the necessity of raising the water of the Nile to points which the river did not reach, as well as the difficulty of clearing the land from the periodical overflowings of the Nile, Archimedes invented for this purpose the screw which bears his name. It was likewise used as a pump to clear water from the holds of vessels; and the name of Archimedes was held in great veneration by seamen on this account. The screw may be briefly described as a long spiral with its lower extremity immersed in the water, which, rising along the channels by the revolution of the machine on its axis, is discharged at the upper extremity. When applied to the propulsion of steam-vessels the screw is horizontal; and being put in motion by a steam-engine, drives the water backward, when its reaction, or return, propels the vessel.

The mechanical ingenuity of Archimedes was next displayed in the various machines which he constructed for the defence of Syracuse during a three years' siege by the Romans. Among these inventions were catapults for throwing arrows, and ballistæ for throwing masses of stone; and iron hands or hooks attached to chains, thrown to catch the prows of the enemy's vessels, and then overturn them. He is likewise stated to have set their vessels on fire by burning-glasses; this, however, rests upon modern authority, and Archimedes is rather believed to have set the ships on fire by machines for throwing lighted materials.

After the storming of Syracuse, Archimedes was killed by a Roman soldier, who did not know who he was. The soldier inquired, but the philosopher, being intent upon a problem, begged that his diagram might not be disturbed; upon which the soldier put him to death. At his own request, expressed during his life, a sphere inscribed in a cylinder was sculptured on his tomb, in memory of his discovery that the solid contents of a sphere is exactly two-thirds of that of the circumscribing cylinder; and by this means the memorial was afterward identified. One hundred and fifty years after the death of Archimedes, when Cicero was residing in Sicily, he paid homage to his forgotten tomb. "During my quæstorship," says this illustrious Roman, "I diligently sought to discover the sepulchre of Archimedes, which the Syracusans had totally neglected, and suffered to be grown over with thorns and briars. Recollecting some verses, said to be inscribed on the tomb, which mentioned that on the top was placed a sphere with a cylinder, I looked round me upon every object at the Agragentine Gate, the common receptacle of the dead. At last I observed a little column which just rose above the thorns, upon which was placed the figure of a sphere and cylinder. This, said I to the Syracusan nobles who were with me, this must, I think, be what I am seeking. Several persons were immediately employed to clear away the weeds and lay open the spot. As soon as a passage was opened, we drew near, and found on the opposite base the inscription, with nearly half the latter part of the verses worn away. Thus would this most famous, and formerly most learned, city of Greece have remained a stranger to the tomb of one of its most ingenious citizens, had it not been discovered by a man of Arpinum."

To Archimedes is attributed the apophthegm: "Give me a lever long enough, and a prop strong enough, and with my own weight I will move the world." This arose from his knowledge of the possible effects of machinery; but however it might astonish a Greek of his day, it would now be admitted to be as theoretically possible as it is practically impossible. Archimedes would have required to move with the velocity of a cannon-ball for millions of ages to alter the position of the earth by the smallest part of an inch. In mathematical truth, however, the feat is performed by every man who leaps from the ground; for he kicks the world away when he rises, and attracts it again when he falls back.

Under the superintendence of Archimedes was also built the renowned galley for Hiero. It was constructed to half its height, by three hundred master workmen and their servants, in six months. Hiero then directed that the vessel should be perfected afloat; but how to get the vast pile into the water the builders knew not, till Archimedes invented his engine called the helix, by which, with the assistance of very few hands he drew the ship into the sea, where it was completed in six months. The ship consumed wood enough to build sixty large galleys; it had twenty tiers of bars and three decks; the middle deck had on each side fifteen dining apartments besides other chambers, luxuriously furnished, and floors paved with mosaics of the story of the "Iliad." On the upper deck were gardens with arbors of ivy and vines; and here was a temple of Venus, paved with agates, and roofed with Cyprus-wood; it was richly adorned with pictures and statues, and furnished with couches and drinking-vessels. Adjoining was an apartment of box-wood, with a clock in the ceiling, in imitation of the great dial of Syracuse; and here was a huge bath set with gems called Tauromenites. There were also on each side of this deck, cabins for the marine soldiers, and twenty stables for horses; in the forecastle was a fresh-water cistern which held 253 hogsheads; and near it was a large' tank of sea-water, in which fish were kept. From the ship's sides projected ovens, kitchens, mills, and other offices, built upon beams, each supported by a carved image nine feet high. Around the deck were eight wooden towers, from each of which was raised a breastwork full of loopholes, whence an enemy might be annoyed with stones, each tower being guarded by four armed soldiers and two archers. On this upper deck was also placed the machine invented by Archimedes to fling stones of 300 pounds weight and darts eighteen feet long, to the distance of 120 paces; while each of the three masts had two engines for throwing stones. The ship was furnished with four anchors of wood and eight of iron; and "the water-screw" of Archimedes, already mentioned, was used instead of a pump for the vast ship; "by the help of which one man might easily and speedily drain out the water, though it were very deep." The whole ship's company consisted of an immense multitude, there being in the forecastle alone 600 seamen. There were placed on board her 60,000 bushels of corn, 10,000 barrels of salt fish, and 20,000 barrels of flesh, besides the provisions for her company. She was first called the Syracuse, but afterward the Alexandria. The builder was Archias, the Corinthian shipwright. The vessel appears to have been armed for war, and sumptuously fitted for a pleasure-yacht, yet was ultimately used to carry corn. The timber for the main mast, after being in vain sought for in Italy, was brought from England. The dimensions are not recorded, but they must have exceeded those of any ship of the present day; indeed, Hiero, finding that none of the surrounding harbors sufficed to receive his vast ship, loaded it with corn and presented the vessel with its cargo to Ptolemy, King of Egypt, and on arriving at Alexandria it was hauled ashore, and nothing more is recorded respecting it. A most elaborate description of this vast ship has been preserved to us by Athenæus, and translated into English by Burchett, in his "Naval Transactions."

Archimedes has been styled the Homer of geometry; yet it must not be concealed that he fell into the prevailing error of the ancient philosophers—that geometry was degraded by being employed to produce anything useful. "It was with difficulty," says Lord Macaulay, "that he was induced to stoop from speculation to practice. He was half ashamed of those inventions which were the wonder of hostile nations, and always spoke of them slightingly, as mere amusements, as trifles in which a mathematician might be suffered to relax his mind after intense application to the higher parts of his science."