Martin (in his Études sur le Timée de Platon, vol. ii. p. 107) and Gruppe (Die Kosmischen Systeme der Griechen, ch. iv.) maintain that the original system proposed by Pythagoras was a geocentric system, afterwards transformed by Philolaus and other Pythagoreans into that which stands in the text. But I agree with Boeckh (Ueber das Kosmische System des Platon, p. 89 seqq.), and with Zeller (Phil. d. Griech., vol. i. p. 308, ed. 2), that this point is not made out. That which Martin and Gruppe (on the authority of Alexander Polyhistor, Diog. viii. 25, and others) consider to be a description of the original Pythagorean system as it stood before Philolaus, is more probably a subsequent transformation of it; introduced after the time of Aristotle, in order to suit later astronomical views.] [Side-note: Music of the Spheres.] The revolutions of such grand bodies could not take place, in the opinion of the' Pythagoreans, without producing a loud and powerful sound; and as their distances from the central fire were supposed to be arranged in musical ratios,[40] so the result of all these separate sounds was full and perfect harmony. To the objection--Why were not these sounds heard by us?--they replied, that we had heard them constantly and without intermission from the hour of our birth; hence they had become imperceptible by habit.[41] [Footnote 40: Playfair observes (in his dissertation on the Progress of Natural Philosophy, p. 87) respecting Kepler--"Kepler was perhaps the first person who conceived that there must be always a law capable of being expressed by arithmetic or geometry, which connects such phenomena as have a physical dependence on each other". But this seems to be exactly the fundamental conception of the Pythagoreans: or rather a part of their fundamental conception, for they also considered their numbers as active forces bringing such law into reality. To illustrate the determination of the Pythagoreans to make up the number of Ten celestial bodies, I transcribe another passage from Playfair (p. 98). Huygens, having discovered one satellite of Saturn, "believed that there were no more, and that the number of the planets was now complete. The planets, primary and secondary, thus made up twelve--the double of six, the first of the perfect numbers."] [Footnote 41: Aristot. De Coelo, ii. 9; Pliny, H.N. ii. 20. See the Pythagorean system fully set forth by Zeller, Die Philosophie der Griechen, vol. i. p. 302-310, ed. 2nd.] [Side-note: Pythagorean list of fundamental Contraries--Ten opposing pairs.]