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.
The story that he set the Roman ships on fire by an arrangement of burning-glasses or concave mirrors is not found in any authority earlier than Lucian (second century A.D.); but there is no improbability in the idea that he discovered