142 THE REALITIES OF MODERN SCIENCE 



in his third law of motion the idea of the conserva- 

 tion of energy. 



The Law of Universal Gravitation may be stated as 

 follows : Any two bodies form a system the potential 

 energy of which tends to decrease and is always less 

 than it would be if the bodies were infinitely far apart 

 by an amount proportional to the product of the masses 

 and inversely as the distance between centers. Thus 

 let P x represent the potential energy when the bodies 

 are at an infinite distance from each other, and P r the 

 potential energy when they are separated by some 

 finite distance, r. Let mi and m^ be the masses of the 



two bodies, then 



(2) 



where k is a factor which reduces m * m2 to the same units 



r 



as are used in expressing P r and P^. 



As a special case consider a body of mass m resting 

 on the surface of the earth. Represent the mass and 

 radius of the earth by M and R respectively. Then 

 the potential energy of the system is 



(3) 



If the mass m is raised a distance x above the surface 

 the distance r of equation (2) is no longer R but is 

 R+x, and hence 



P -p -k Mm (4\ 



^R+x 



The increase in potential energy occasioned by raising 

 the body is found by subtracting (3) from (4) thus 



