In tracing the history of ideas concerning the structure of the heavens among the Greek philosophers, we meet with other modifications which it will be interesting to recount. Thus Eudoxus, who paid greater attention than others to the variations of the motions of the planets, gave more than one sphere to each of them to represent these observed changes. Each planet, according to him, has a separate part of the heaven to itself, which is composed of several concentric spheres, whose movements, modifying each other, produce that of the planet. He gave three spheres to the sun: one which turned from east to west in twenty-four hours, to represent the diurnal rotation; a second, which turned about the pole of the ecliptic in 365-1/4 days, and produced its annual movement; and a third was added to account for a certain supposed motion, by which the sun was drawn out of the ecliptic, and turned about an axis, making such an angle with that of the ecliptic, as represented the supposed aberration. The moon also had three spheres to produce its motions in longitude and latitude, and its diurnal motion. Each of the other planets had four, the extra one being added to account for their stations and retrogressions. It should be added that these concentric spheres were supposed to fit each other, so that the different planets were only separated by the thicknesses of these crystal zones. Polemarch, the disciple of Eudoxus, who went to Athens with his pupil Calippus for the express purpose of consulting Aristotle on these subjects, was not satisfied with the exactness with which these spheres represented the planetary motions, and made changes in the direction of still greater complication. Instead of the twenty-six spheres which represented Eudoxus' system, Calippus established thirty-three, and by adding also intermediary spheres to prevent the motion of one planet interfering with that of the adjacent ones, the number was increased to fifty-six. There is extant a small work, ascribed to Aristotle, entitled "Letter of Aristotle to Alexander on the system of the world," which gives so clear an account of the ideas entertained in his epoch that we shall venture to give a somewhat long extract from it. The work, it should be said, is not by all considered genuine, but is ascribed by some to Nicolas of Damas, by others to Anaximenas of Lampsacus, a contemporary of Alexander's, and by others to the Stoic Posidonius. It is certain, however, that Aristotle paid some attention to astronomy, for he records the rare phenomena of an eclipse of Mars by the moon, and the occultation of one of the Gemini by the planet Jupiter, and the work may well be genuine. It contains the following:--