in one year; the planets Mars, Jupiter, and Saturn in longer periods respectively, according to their distances from the center; lastly, the outermost circle of the fixed stars (the Olympus, or the Asslanes), in some unknown period of very long duration. "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, so the result of all these separate sounds was full and perfect harmony. To the objection, Why were not the 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." Beautiful as was this theory--the origin of the phrase, "the music of the spheres"--it owed its perfection as a theory to a pure invention, resorted to in order to carry out the hypothesis of the sacred number Ten, of which all the greater numbers were only compounds and derivatives. This perfect and normal Ten, as a basis on which to rest a bold astronomical hypothesis, required the imagination of the Antichthon, or counter-earth, in order, with the other bodies, to make up the primordial number to whose generative force the whole of these bodies owed their origin. The resort to this conception of number, as a formative and active agent, was doubtless due to the fact that the Pythagoreans were the earliest cultivators of mathematical science. We are told, in fact, that they paved the way for Euclid and Archimedes, notwithstanding their symbolical and mystical fancies, and from their mathematical studies they were led to give exclusive supremacy to arithmetical and geometrical views of Nature. But what is curious about this whole speculation is, that in the invention or substitution of certain facts in order to make a perfect theory, it resembles some modern hypotheses, in which facts have been assumed, or argued as existing from analogies, when there is no evidence which establishes them. Modern instances of this will appear hereafter.