28 THE FOUNDATIONS OF SCIENCE 



of working out the consequences of this theory, by 

 mathematical methods often invented by him in the 

 process. At the end of that time he had placed the 

 theory of the heavens on a mechanical basis, and the 

 publication of Newton's Principia in 1687 marks the 

 greatest step ever made in the advance of knowledge. 

 Besides the creation of gravitational astronomy, 

 Newton placed the science of mechanics firm on the 

 base prepared by Galileo. He first formulated 

 clearly the distinction between the mass of a body, 

 invariable and unalterable in all conditions of 

 mechanical experiment, and its weight, which de- 

 pends on the attraction of the earth, and would 

 vanish altogether at some point between the earth 

 and the moon where their pulls were equal as well 

 as opposite. He collected the principles of mechanics, 

 which had now become clear as the result of inductive 

 reasoning from experience, and expressed them in 

 three laws. These laws, the summit of the inductive 

 process, collect and state in short-hand form the 

 experimental knowledge of mechanical phenomena. 

 In turn, the laws are the starting-point of the de- 

 ductive science of mechanics, in which, by mathe- 

 matical reasoning, ideal cases of motion may be 

 investigated. These ideal cases may be suggested 

 by actual physical phenomena to which they may be 

 made to approach more or less nearly. The nearer 

 be the concordance between an actual case we wish 

 to investigate and the ideal and usually simplified 



