158 THE WORLD-ENERGY 



But the motion produced in these cases, according to 

 the second law, must be proportional to the impressed 

 force, and must take place in the direction of the line 

 in which the force acts ; that is, in the direction of the 

 line joining the mutually attracting groups of force- 

 centers. And not only so, but in tracing the develop- 

 ment of the conditions of the action of force, we have 

 seen that, as indicated in the formulation of the universal 

 law of gravity, the force impressed upon each other by 

 the approaching groups must increase with the decrease 

 of the distance between them must ever be inversely 

 proportional to the square of that distance. 



But, again, the motion is proportional to the im- 

 pressed force. And we have now to inquire whether 

 this impressed force, and consequent motion, is the same, 

 or different, for the two bodies. 



To this the answer must be that either can act upon 

 the other only so far as it is acted upon by the other. 

 The action is necessarily mutual ; or, the action and reac- 

 tion between them must be equal, as well as in opposite 

 directions. Hence, the quantity of force impressed by 

 the greater mass upon the less is precisely the same as 

 that impressed by the less upon the greater. And when 

 we recall the fact that the distance separating them is at 

 any moment but one and the same distance, it is evident 

 that the force of gravity which the one body exerts or 

 "impresses" upon any other body must necessarily be 

 precisely the same as that exerted or impressed by the 

 second upon the first. Indeed, the gravitative strain 

 exerted by the two bodies upon each other consti- 

 tutes but one indivisible relation between the attracting 

 bodies. 



