The history of the changes leading up to our modern astronomical conception makes a vivid chapter. How Copernicus contributed the idea of placing the sun at the centre of things, Kepler the idea of the orbits of the planets as ellipses, Bruno the idea of the boundlessness of space and time, and how Galileo, corroborating these theories by empirical investigations, was put under the ban of the church――all this shows what heroism must have been required to tear down a time-honored and firmly intrenched traditional conception. Probably the speculative astronomers were not conscious that they were undermining the whole astronomical structure, and probably their sole motive was to simplify the Ptolemaic conception, not to destroy it. For Copernicus accepted the Ptolemaic system, except that he put the sun instead of the earth at the centre, and thereby simplified it by making many of the epicycles unnecessary; and Kepler simplified it further by supplanting the epicycles with ellipses. However, the result was inevitably an entirely new conception of the universe, and with it a new conception of the relation among particular material things. It was in this way that new scientific methods arose. The universe now comes to be regarded as a mechanism, and what was formerly looked upon as the influence of spirits or as Providential guidance becomes an impersonal law of causal necessity. In the heavens above and the earth beneath there are no longer vital forces and supernatural influences. _The universe becomes a homogeneous whole throughout_, in which there is no difference between the fall of an apple and the revolution of the planets, no distinction between terrestrial and celestial spheres. The Christian heaven is nowhere in it; the Mediæval spirits are banished from it. The Greek gods have been pushed out, and the Christian God has been made to stand aside. The demand that the new conception of the universe be verified in concrete experiments, if it were to replace the old Ptolemaic system, the revival of the study of Archimedes, the rivalry in trade and inventions among the Italian towns, were three causes for the demand for greater exactness. Investigation, experiment, and invention came into vogue. Magic, alchemy, astrology, and conjurations were no longer accepted as serious methods. In the Middle Ages deduction had been purely the logical employment of the syllogism in theological discussions, while induction, so far as it was used at all, had been the reference of nature phenomena to spiritual forces. Now deduction and induction[6] come to be used for other purposes, and mathematics is necessarily conjoined with both. The new Natural Science period is essentially a “strife of methods”; it is the period when the true plan of scientific procedure is being determined. It is here that the importance and influence of Galileo is seen upon modern science and philosophy.