FORCE, A SPACE RATE OF ENERGY 149 



as compared to that of the man this velocity may well 

 be both imperceptible and negligible. 



That actions occur in pairs, equal and opposite, we 

 recognize in our daily acts. Thus if one wishes to exert 

 a force he braces himself against some firm backing, 

 that is, something of such mass that the momentum he 

 imparts to it will produce but a negligible velocity. 

 The firmest backing is, of course, the earth. Its mass 

 is so large that any motion which we can impart to it, 

 as for example by shooting a shell from a howitzer, is 

 so small that we frequently overlook the fact that the 

 action is similar to that of the man jumping from the 

 boat. 



Consider the stresses in the case of a man lifting a 

 mass from the earth. As he pushes up he also pushes 

 down on the earth. There are then 

 two pairs of mutual actions, namely 

 those between the man and the mass 

 and those between the man and the 

 earth. The man pushes up on the 

 body, its reaction is down on him. He 

 pushes down on the earth, which reacts 

 on him, pushing up. These actions 

 and reactions are represented in Fig. 

 12 by the arrows. 



We may consider either force of a pair as the action 

 and the other as the reaction. Thus in the present 

 figure we consider AI to be the action of the man on 

 the body and Ri to be its reaction on him. We are 

 thus viewing the action from the standpoint of the man. 

 On the other hand, consider the crushing effect of the 

 weight which the man is trying to support. We now 



