20 THE FOUNDATIONS OF SCIENCE 



the ground together, so long 'as the lighter body was 

 not sufficiently light to be retarded seriously by 

 the resistance of the air. Aristotle was shown to 

 be wrong, and a new era had begun. 



A falling body moves faster and faster as it travels 

 through space, and Galileo next set himself to examine 

 how this increase of velocity occurs. His first sup- 

 position was that the speed was proportional to the 

 distance travelled, but he soon convinced himself 

 that this idea was wrong. Then he tried the hypo- 

 thesis that the speed increased with the time of fall, 

 and cast about for a means of putting the relations 

 to the test of experiment. 



Bodies falling freely moved too fast to be dealt 

 with by the primitive apparatus then available, 

 and, to get a manageable velocity, Galileo assumed 

 that a ball rolling down an inclined plane would 

 follow the same kind of rule as a ball falling freely, 

 though it would fall with less speed. 



On the hypothesis that the speed of fall increased 

 with the time, he calculated the distance which the 

 ball should roll, and showed that it should be pro- 

 portional to the square of the time ; that is, if the 

 ball roll 1 foot in 1 second it will roll 4 feet in 2 

 seconds and 9 feet in 3 seconds. This result he 

 proceeded to test. 



His clocks were not sufficiently accurate or con- 

 venient, and so, to measure times, he took a large 

 vessel with a small hole in the bottom which he closed 



