FORCE, A SPACE RATE OF ENERGY 141 



potential energy is in turn converted into kinetic 

 energy. 



During the centuries, however, which followed New- 

 ton and before the modern ideas of energy were ac- 

 cepted, the word "force" in the Newtonian sense be- 

 came firmly fixed in scientific language. Thus scien- 

 tists to-day speak of frictional forces as if these were 

 the causes of the slowing down of a moving body even 

 though they realize that changes in the form and loca- 

 tion of its energy are the real causes. 



In the case of the gravitation of bodies toward the 

 earth we still speak of the "force" of gravitation in- 

 stead of saying that the earth and any other body form 

 a system, the potential energy of which decreases as 

 they approach one another. The reader will find 

 this phenomenon almost always described in terms of 

 force as a cause. In part this is due to the form in 

 which Newton expressed his so-called Law of Universal 

 Gravitation. This states that any two bodies (or 

 strictly "particles") attract each other with a force 

 which is proportional to the product of their masses 

 and inversely as the square of the distance between 

 their centers. 1 If Newton had lived after the Prin- 

 ciple of the Conservation of Energy had been accepted 

 it is quite probable that he would have expressed his 

 law of gravitation in terms of energy instead of force. 

 Later we shall see how nearly he came to recognizing 



1 If the masses are mi and ra 2 and the distance between centers 

 is r, then the force, /, is 



or/ = (1) 



