148 ON THE ORIGIN OF THE PLANETARY SYSTEM. 



further it is removed from the attracting body, and 

 this is the reason that an ellipse is described, one of 

 whose foci lies in the centre of attraction. The two 

 foci, a and 6, are two points which lie symmetrically 

 towards the ends of the ellipse, and are characterised 

 by the property that the sum of their distances, 

 am+bm, is the same from any given points. 



Kepler had found that the paths of the planets are 

 ellipses of this kind ; and since, as the above example 

 shows, the form and position of the orbit depend on 

 the law according to which the magnitude of the 

 attracting force alters, Newton could deduce from the 

 form of the planetary orbits the well-known law of the 

 force of gravitation, which attracts the planets to the 

 sun, according to which this force decreases with 

 increase of distance as the square of that distance. 

 Terrestrial gravity must obey this law, and Newton 

 had the wonderful self-denial to refrain from publish- 

 ing his important discovery until it had acquired a 

 direct confirmation; this followed from the observa- 

 tions, that the force which attracts the moon towards 

 the earth, bears towards the gravity of a terrestrial 

 body the ratio required by the above law. 



In the course of the eighteenth century the power 

 of mathematical analysis, and the methods of astrono- 

 mical observation, increased so far that all the compli- 

 cated actions, which take place between all the planets, 



