It was in connexion with his discovery of the solution of the problem _To move a given weight by a given force_ that Archimedes uttered the famous saying, "Give me a place to stand on, and I can move the earth" ([Greek: dos moi pou sto kai kino ten gen], or in his broad Doric, as one version has it, [Greek: pa bo kai kino tan gan]). Plutarch represents him as declaring to Hieron that any given weight could be moved by a given force, and boasting, in reliance on the cogency of his demonstration, that, if he were given another earth, he would cross over to it and move this one. "And when Hieron was struck with amazement and asked him to reduce the problem to practice and to show him some great weight moved by a small force, he fixed on a ship of burden with three masts from the king's arsenal which had only been drawn up by the great labour of many men; and loading her with many passengers and a full freight, sitting himself the while afar off, with no great effort but quietly setting in motion with his hand a compound pulley, he drew the ship towards him smoothly and safely as if she were moving through the sea." Hieron, we are told elsewhere, was so much astonished that he declared that, from that day forth, Archimedes's word was to be accepted on every subject! Another version of the story describes the machine used as a _helix_; this term must be supposed to refer to a screw in the shape of a cylindrical helix turned by a handle and acting on a cog-wheel with oblique teeth fitting on the screw. Another invention was that of a sphere constructed so as to imitate the motions of the sun, the moon, and the five planets in the heavens. Cicero actually saw this contrivance, and he gives a description of it, stating that it represented the periods of the moon and the apparent motion of the sun with such accuracy that it would even (over a short period) show the eclipses of the sun and moon. It may have been moved by water, for Pappus speaks in one place of "those who understand the making of spheres and produce a model of the heavens by means of the regular circular motion of water". In any case it is certain that Archimedes was much occupied with astronomy. Livy calls him "unicus spectator caeli siderumque". Hipparchus says, "From these observations it is clear that the differences in the years are altogether small, but, as to the solstices, I almost think that both I and Archimedes have erred to the extent of a quarter of a day both in observation and in the deduction therefrom." It appears, therefore, that Archimedes had considered the question of the length of the year. Macrobius says that he discovered the distances of the planets. Archimedes himself describes in the _Sandreckoner_ the apparatus by which he measured the apparent diameter of the sun, i.e. the angle subtended by it at the eye.