Aristotle, Ptolemy, and Hipparchus. [#] _Paradise Lost_, iii. 481. "They pass the planets seven, and pass the fixed, And that crystalline sphere whose balance weighs The trepidation talked, and that first moved." So far, the doctrine of the fifty-five "spheres" might be no more than a legitimate mathematical fiction, a convenient device for analysing the complicated apparent movements of the heavenly bodies into circular components. This was originally the part played by "spheres" in ancient astronomical theory, and it is worth while to be quite clear about the fact, as there is a mistaken impression widely current to-day that Aristotle’s astronomy is typical of Greek views in general. The truth is that it is peculiar to himself. The origin of the theory was Academic. Plato proposed to the Academy as a subject of inquiry, to devise such a mathematical analysis of astronomical motions as will best "save the appearances," _i.e._ will most simply account for the apparent paths of the planets. The analysis of these paths into resultants of several rotations was offered as a solution by the astronomer Eudoxus of Cnidus. So far, the "spheres," then, were a mere mathematical hypothesis. What Aristotle did, and it is perhaps the most retrograde step ever taken in the history of a science, was to convert the mathematical hypothesis into physical fact. The "spheres" become with him real bodies, and as none of the bodies we are familiar with exhibit any tendency to rotate in circles when left to themselves, Aristotle was forced to introduce into Physics the disastrous theory, which it was a great part of Galileo’s life-work to destroy, that the stuff of which the spheres are made is a "fifth body," different from the "elements" of which the bodies among which we live are made. Hence he makes an absolute distinction between two kinds of matter, "celestial matter," the "fifth body," and "terrestrial" or "elementary" matter. The fundamental difference is that "terrestrial" or "elementary" matter, left to itself, follows a rectilinear path, "celestial" matter rotates, but it is further inferred from the supposed absolute uniformity of the celestial movements that "celestial matter" is simple, uncompounded, incapable of change, and consequently that no new state of things can ever arise in the heavens. The spheres and planets have always been and will always be exactly as they are at the present moment. Mutability is confined to the region of "terrestrial" or "elementary" matter, which only extends as far as the orbit of the moon, the "lowest of the celestial bodies," because it is only "terrestrial" things which are, as we should say, chemical compounds. This is the doctrine which Galileo has in mind when he dwells on such newly-discovered astronomical facts as the existence of sun-spots and variable stars, and the signs of irregularity presented by the moon’s surface. The distinction is peculiar to Aristotle.