The Works of Archimedes

water-screw (also called kochlias), which was apparently invented by him in Egypt for the purpose of irrigating fields. It was also used for pumping water out of mines or from the hold of ships.

Another invention was that of a sphere constructed to imitate the motions of the sun, the moon, and the five planets in the heavens. Cicero actually saw this contrivance and 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 eclipses of the sun and moon. Hultsch conjectures that it was moved by water. We know from Pappus that Archimedes wrote a book on the construction of such a sphere, and 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 "a unique spectator of the heavens and the stars." 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 the observation and in the deduction therefrom." It appears therefore that Archimedes had considered the question of the length of the year, as Ammianus also states. Macrobius says that he discovered the distances of the planets. Archimedes himself describes in the Sand-reckoner the apparatus by which he measured the apparent diameter of the sun, or the angle subtended by it at the eye.

The story that he set the Roman ships on fire by an arrangement of burning-glasses or concave mirrors is not found in any