THE ASTRONOMICAL VIEW OF NATURE. 317 



natural, and allow us to make them subservient to our 

 purposes. 



Whoever grasps the significance of the change which 10. 



When first 



the exact or mathematical treatment of knowledge has introduced 



into science 



worked in our life and thought, will readily place that 

 name at the entrance of a history of modern thought, 

 which is identified with a few simple mathematical for- 

 mulse t by which ever since his time the progress of science 

 has been guided. Though belonging to an earlier period, 

 the full meaning of Newton's work has only been recog- 

 nised in the course of our century. In fact the New- 

 tonian philosophy can be said to have governed at least 

 one entire section of the scientific research of the first 

 half of this period : only in the second half of the period 

 have we succeeded in defining more clearly the direction 

 in which Newton's views require to be extended or modi- 

 fied. Newton's greatest achievement was to combine the 

 purely mechanical laws which Galileo and Huygens had 

 established with the purely physical relations which 

 Kepler following Copernicus and Tycho had discovered 

 in the planetary motions, and to abstract in so doing 

 the general formula of universal attraction or gravitation. 

 Newton looked upon the motion of the moon round the 

 earth, or the planets round the sun, as examples on a 

 large scale of the motion of falling bodies studied by 

 Galileo on the surface of the earth. Delayed in the 

 publication of this simple rule of planetary motion 

 through the absence of correct measurements, and through 

 the necessity of inventing a new calculus by which the 

 .mathematical results of the formula could be ascertained, 

 Newton did not publish his 'Principia' till 1687. The 



