24 THE FOUNDATIONS OF SCIENCE 



then made a guess at a possible law : that the speed 

 of fall was proportional to the distance fallen through. 

 He reasoned out the consequences of this hypothesis, 

 and found that they were self-contradictory. His 

 guess was clearly wrong. 



He tried again. He tried the supposition that the 

 final speed varied as the time of fall. Here the con- 

 sequences deduced were consistent ; the hypothesis 

 was worth testing by experiment. 



But the hypothesis itself was not fitted for direct 

 experiment at all events, by means of Galileo's 

 apparatus. Therefore he took one of its conse- 

 quences, which he had obtained by deductive mathe- 

 matical reasoning the consequence that the distance 

 fallen should be proportional to the square of the 

 time. 



He had now formulated his experimental problem, 

 and had to face the practical mechanical difficulties. 

 First, he improved the conditions of the process from 

 the experimental point of view, reducing the velocity 

 by making the falling body run down an inclined 

 plane instead of fall freely through space. Secondly, 

 having no apparatus delicate enough to measure the 

 small intervals of time involved, he invented a new 

 form of water-clock for this special purpose. Thus, 

 the conditions being made favourable, and his appa- 

 ratus being made adequate, he measured the times 

 taken by the falling body to run over marked 

 distances on the inclined plane. Small divergences 



