another as bodies whose sound requires for its production, contact, friction, or shock, in response to which, and as the negation of its particularity its own momentary individuality resounds in elasticity; for heavenly bodies are independent of one another, and have only a general, non-individual, free motion. We may thus set aside sound; the music of the spheres is indeed a wonderful conception, but it is devoid of any real interest for us. If we retain the conception that motion, as measure, is a necessarily connected system of numbers, as the only rational part of the theory, we must maintain that nothing further has transpired to the present day. In a certain way, indeed, we have made an advance upon Pythagoras. We have learned from Kepler about laws, about eccentricity, and the relation of distances to the times of revolution, but no amount of mathematics has as yet been able to give us the laws of progression in the harmony through which the distances are determined. We know empirical numbers well enough, but everything has the semblance of accident and not of necessity. We are acquainted with an approximate rule of distances, and thus have correctly foretold the existence of planets where Ceres, Vesta, Pallas, &c., were afterwards discovered—that is, between Mars and Jupiter. But astronomy has not as yet found in it a consistent sequence in which there is rationality; on the other hand, it even looks with disdain on the appearance of regularity presented by this sequence, which is, however, on its own account, a most important matter, and one which should not be forgotten. d. The Pythagoreans also applied their principle to the Soul, and thus determined what is spiritual as number. Aristotle (De anim. I. 2) goes on to tell that they thought that solar corpuscles are soul, others, that it is what moves them; they adopted this idea because the corpuscles are ever moving, even in perfect stillness, and hence they must have motion of their own. This does not signify much, but it is evident from it that the determination of self-movement was sought for in the soul. The Pythagoreans made a further application of number-conceptions to the soul after another form, which Aristotle describes in the same place as follows:—“Thought is the one, knowledge or science is the two, for it comes alone out of the one. The number of the plane is popular idea, opinion; the number of the corporeal is sensuous feeling. Everything is judged of either by thought, or science, or opinion, or feeling.” In these ideas, which we must, however, ascribe to later Pythagoreans, we may undoubtedly find some adequacy, for while thought is pure universality, knowledge deals with something “other,” since it gives itself a determination and a content; but feeling is the most developed in its determinateness. “Now because the soul moves itself, it is the self-moving number,” yet we never find it said that it is connected with the monad.