For the various systems, see Boeckh, _Kleine Schriften_, vol. iii. pp. 169 sqq., and Carl v. Jan, “Die Harmonie der Sphären” (_Philol._ 1893, pp. 13 sqq.). They vary with the astronomy of their authors, but they bear witness to the fact stated in the text. Many give the highest note to Saturn and the lowest to the Moon, while others reverse this. The system which corresponds best, however, with the Pythagorean planetary system must include the heaven of the fixed stars and the earth. It is that upon which the verses of Alexander of Ephesos quoted by Theon of Smyrna, p. 140, 4, are based: γαῖα μὲν οὖν ὑπάτη τε βαρεῖά τε μέσσοθι ναίει· ἀπλανέων δὲ σφαῖρα συνημμένη ἔπλετο νήτη, κ.τ.λ. The “base of Heaven’s deep Organ” in Milton’s “ninefold harmony” (_Hymn on the Nativity_, xiii.) implies the reverse of this. The theory that the proper motion of the sun, moon, and planets is from west to east, and that they also share in the motion from east to west of the heaven of the fixed stars, makes its first appearance in the Myth of Er in Plato’s _Republic_, and is fully worked out in the _Timaeus_. In the _Republic_ it is still associated with the “harmony of the spheres,” though we are not told how it is reconciled with that theory in detail.[838] In the _Timaeus_ we read that the slowest of the heavenly bodies appear the fastest and _vice versa_; and, as this statement is put into the mouth of a Pythagorean, we might suppose the theory of a composite movement to have been anticipated by some members at least of that school.[839] That is, of course, possible; for the Pythagoreans were singularly open to new ideas. At the same time, we must note that the theory is even more emphatically expressed by the Athenian Stranger in the _Laws_, who is in a special sense Plato himself. If we were to praise the runners who come in last in the race, we should not do what is pleasing to the competitors; and in the same way it cannot be pleasing to the gods when we suppose the slowest of the heavenly bodies to be the fastest. The passage undoubtedly conveys the impression that Plato is expounding a novel theory.[840] Footnote 838: