i8 SCIENTIFIC METHOD 



(2) When the squares of the times are as the cubes of 

 the radii, i. e. the distances, the centripetal forces of 

 the bodies will be inversely as the squares of the radii, 

 i.e. the distances (Principia, Book I, Prop. 4, Cor. 6). 



The squares of the periodic times of the planets are 

 as the cubes of their mean distances from the sun l 

 (Ibid., Book III, Phen. 4 : Kepler's Third Law). 



Therefore, the centripetal forces of the planets tending 

 to the sun are inversely as the squares of their distances 

 from the sun (Ibid., Book III, Prop. 2). 



Thus one of the greatest discoveries of all time, the 

 application of mechanics to astronomy, the identification 

 of the laws of motion and gravitation in the sublunary 

 and stellar worlds, the revelation of the real cause 

 which makes the planets revolve, not round the earth, 

 but round the sun, the final confirmation of the Copernican 

 system and Kepler's Laws by explaining them, was found 

 from experience and after induction, but beyond both 

 these narrower operations by the comprehensive power 

 of analytic deduction from the facts of planetary motion to 

 their cause, centripetal force tending to the sun. More- 

 over, this deduction was essentially syllogistic, from a 

 mechanical major and an astronomical minor to an astro- 

 nomical conclusion, by a method fundamentally Aristo- 

 telian. It was a 'syllogism of fact', as Aristotle would 

 call it ; that is, not from cause to effect, but from fact to 

 cause. It was an analytic syllogism, in which the fact is 

 in astronomy, the cause in mathematical mechanics ; and 

 Aristotle, who had already 2 made this distinction, saw 

 that the fact may be in physics and the cause in mathe- 

 matics, many centuries before Newton entitled his book 



1 For example, as compared with the earth, Jupiter's time squared, 

 12*, is nearly equal to his distance cubed, 5^ 3 , from the sun. 



2 Aristotle, Posterior Analytics, i. 13. 



