INDUCTIVE EPOCH OF NEWTON. 399 



CHAPTER H. 



The Inductive Epoch op Newton. — Discovert of the Univer- 

 sal Gravitation of Matter, according to the Law of the 

 Inverse Square of the Distance. 



IN order that we may the more clearly consider the bearing of this, 

 the greatest scientific discovery ever made, we shall resolve it into 

 the partial propositions of which it consists. Of these we may enumer- 

 ate five. The doctrine of universal gravitation asserts, 



1. That the force by which the different planets are attracted to the 

 sun is in the inverse proportion of the squares of their distances ; 



2. That the force by which the same planet is attracted to the sun, 

 in different parts of its orbit, is also in the inverse proportion of the 

 squares of the distances ; 



3. That the earth also exerts such a force on the moon, and that this 

 force is identical with the force of gravity ; 



4. That bodies thus act on other bodies, besides those which revolve 

 round them ; thus, that the sun exerts such a force on the moon and 

 satellites, and that the planets exert such forces on one another ; 



5. That this force, thus exerted by the general masses of the sun, 

 e/irth, and planets, arises from the attraction of each particle of these 

 massejs ; which attraction follows the above law, and belongs to all 

 matter alike. 



The history of the establishment of these five truths will be given in 

 order. 



1. Sun's Force on Different Planets. — With regard to the first of 

 the above five propositions, that the different planets are attracted to 

 the sun by a force which is inversely as the square of the distance, 

 Newton had so far been anticipated, that several persons had discover- 

 ed it to be true, or nearly true ; that is, they had discovered that if the 

 orbits of the planets were circles, the proportions of the central force to 

 the inverse square of the distance would follow from Kepler's third 

 law, of the sesquiplicate proportion of the periodic times. As we have 

 seen, Huyghens' theorems would have proved this, if they had been so 

 applied ; Wren knew it ; Hooke not only knew it, but claimed a prior 

 knowledge to Newton ; and Halley had satisfied himself that it was at 



