It may be interesting, before leaving for the present this branch of the subject, to advert more particularly to one of the philosophical systems of the Greeks, which, when compared with the discoveries of modern astronomy, illustrates the great addition that has been made to our means of sound speculation upon the origin of the material universe. I refer to the system of the Pythagoreans--one of the most remarkable instances of the invention of facts to fit and carry out a theory that can be found in the history of philosophy, although we are not without striking examples of this practice in modern speculations. It has already been seen that, during the whole period of Greek philosophy before the time of Plato, the problem was to find a primordial and universal agent by which the sensible universe was built up and produced; supplying, that is to say, the matter and force required for the generation of successive products.[6] It has been seen that the Thalesian philosophers undertook to solve this problem by the employment of some primordial physical substance, such as water, fire, air, etc. Pythagoras and his school held that the essence of things consisted in number; by which they did not mean simply that all things could be numbered, but they meant that numbers were substance, endowed with an active force, by which things were constituted as we know them. In the Pythagorean doctrine number was the self-existing reality; not, as in Plato's system of ideas, separate from things, but as the essence or determining principles of things, and having, moreover, magnitude and active force.[7] This remarkably subtle conception of an agent in the production of material things evinces the effort that was making, in a direction opposite to that of Thales and his immediate successors, to find a First Cause. It was carried out by the Pythagoreans in the movements of the heavenly bodies, in the works of human art, and in musical harmony; in all of which departments, according to Mr. Grote, they considered measure and number as the producing and directing agencies. We are here concerned only with their application of this theory to the celestial bodies. One of their writers is quoted by Mr. Grote as a representative of the school which was founded by Pythagoras (about 530 B. C.), and which extended into the Græco-Italian cities, where, as a brotherhood, they had political ascendency until they were put down and dispersed about 509 B. C.; but they continued for several generations as a social, religious, and philosophical sect. According to this writer (Philolaus), "the Dekad, the full and perfect number, was of supreme and universal efficacy as the guide and principle of life, both to the Kosmos and to man. The nature of number was imperative and law-giving, affording the only solution of all that was perplexing or unknown; without number all would be indeterminate and unknowable."