It was during the reign of Hiero II. that Archimedes, a native of Syracuse, and a supposed distant relation of the king, made the scientific discoveries and inventions that have secured for him the honor of being the most celebrated mathematician of antiquity. He was equally skilled in astronomy, geometry, mechanics, hydrostatics, and optics. His discovery of the principle of specific gravity is related in the following well-known story: Hiero, suspecting that his golden crown had been fraudulently alloyed with silver, put it into the hands of Archimedes for examination. The latter, entering a bath-tub one day, and noticing that he displaced a quantity of water equal in bulk to that of his body, saw that this discovery would give him a mode of determining the bulk and specific gravity of King Hiero's crown. Leaping out of the tub in his delight, he ran home, crying, "Eure'ka! eureka!" I have found it! I have found it! To show Hiero the wonderful effects of mechanical power, Archimedes is said to have drawn some distance toward him, by the use of ropes and pulleys, a large galley that lay on the shore; and during the siege of his native city by the Romans, his great mechanical skill was displayed in the invention and manufacture of stupendous engines of defence. Later historians than Polybius, Livy, and Plutarch say that on this occasion, also, he burnt many Roman ships by concentrating upon them the sun's rays from numerous mirrors. SCHILLER gives the following poetic account of a visit, to Archimedes, by a young scholar who asked to be taught the art that had won the great master's fame: To Archimedes once a scholar came: "Teach me;" he said, "the Art that won thy fame; The godlike Art which gives such boons to toil, And showers such fruit upon thy native soil; The godlike Art that girt the town when all Rome's vengeance burst in thunder on the wall!" "Thou call'st Art godlike--it is so, in truth, And was," replied the master to the youth, "Ere yet its secrets were applied to use-- Ere yet it served beleaguered Syracuse. Ask'st thou from Art but what the Art is worth? The fruit? For fruit go cultivate the Earth. He who the goddess would aspire unto Must not the goddess as the woman woo!" --Trans. by BULWER. Among the discoveries of Archimedes was that of the ratio between the cylinder and the inscribed sphere, and he requested his friends to place the figures of a sphere and cylinder on his tomb. This was done, and, one hundred and thirty-six years after, it enabled Cicero, the Roman orator, to find the resting-place of the illustrious inventor. The story of his visit to Syracuse, and his search for the tomb of Archimedes, is told by the HON. R C. WINTHROP in a lecture entitled Archimedes and Franklin, from which we quote as follows: Visit of Cicero to the Grave of Archimedes.