DISCOVERY OF THE LAWS OF MOTION. 35 



that this cannot be known without knowing what 

 Weight is, which comes to the same thing; as to 

 your example, I grant that it proves that every 

 degree of velocity is infinitely divisible, but not 

 that a falling body actually passes through all these 

 divisions." 



The Principles of the Motion of Falling Bodies 

 being thus established by Galileo, the Deduction of 

 the principal mathematical consequences was, as is 

 usual, effected with great rapidity, and is to be 

 found in his works, and in those of his scholars and 

 successors. The motion of bodies falling freely 

 was, however, in such treatises, generally combined 

 with the motion of bodies Falling along Inclined 

 Planes ; a part of the theory of which we have still 

 to speak. 



The Notion of Accelerating Force and of its 

 operation, once formed, was naturally applied in 

 other cases than that of bodies falling freely. The 

 different velocities with which heavy and light 

 bodies fall were explained by the different resist- 

 ance of the air, which diminishes the accelerating 

 force 9 ; and it was boldly asserted, that in a vacuum 

 a lock of wool and a piece of lead would fall equally 

 quickly. It was also maintained 10 that any falling 

 body, however large and heavy, would always have 

 its velocity in some degree diminished by the air in 

 which it falls, and would at last be reduced to a 

 state of uniform motion, as soon as the resistance 



9 Galileo, iii. 43. 10 iii. 54. 



D2 



