40 



Pascal, and Wallis had glimpses of a new method of calculating. 

 Galileo had made discoveries in applied mathematics far more 

 important than his astronomical discoveries, which anyone with 

 a telescope could see. He had formulated two laws of motion, 

 the principle of virtual velocities, the law of acceleration of 

 falling bodies, the parabolic path of a projectile, and the 

 isochronism of pendular vibrations. Soon after Galileo's death, 

 England, stimulated by Bacon's works, took the lead in experi- 

 mental philosophy. 



As yet no connected ideas upon the constitution of the 

 universe had been evolved by the new Science. The old 

 Ptolemaic system, now overthrown, was at least complete. 

 Ptolemy has placed the earth in the centre of the universe ; 

 eight crystalline spheres surround it like the balls of a Chinese 

 puzzle, containing successively the Moon, Mercury, Venus, the 

 Sun, Mars, Jupiter, Saturn, and the fixed stars. All these 

 spheres continually revolved with incredible swiftness round the 

 earth ; and since they were all perfect, their motions took place 

 in the most perfect figure, a circle. 



This system, however, found a severe stumbling-block in 

 the apparent irregularities that could be observed, owing to the 

 complex and looped paths of the planets among the fixed stars ; 

 and additions of cycles, epicycles, and deferents were brought in 

 explanation. This caused King Alphonso to say that if he had 

 been consulted at the creation of the world he would have 

 suggested several great improvements. Kepler supposed that 

 the solar system was shaped like a wheel, each planet being on 

 one of the spokes, and having an angel to push it. 



So, when Newton began his career, a new mathematics was 

 required for calculation, and a new system of the world was 

 required to take the place of the Ptolemaic, which was at least con- 

 sistent and complete, however false and clumsy. Newton pro- 

 duced both the new tools and the new I'esults. After mastering 

 all that was known of mathematics in his time, Newton, in 1665, 

 produced that extraordinary weapon of Science, the infinitesimal 

 calculus. But he did not publish it, and thus got into a very 

 unpleasant controversy thirty years later. The advantages of 

 this discovery were discussed at length. 



The familiar story of the fall of the apple that led to the 

 working out on such a tremendous scale of the principle of 

 gravitation then came under the Lecturer's attention. Gravita- 

 tion was known to exist on the tops of mountains, and at the 

 bottoms of mines, and at every spot on the surface of the earth. 

 Newton thought within himself, " Does it extend beyond the 

 earth?" The ancient idea was that the centre of the earth 

 attracted all heavy substances to it. This idea we find enunciated 

 in Shakespeare's Tmilus awl Cirssiila, and in detail at the end of 



