THE THIED LAW . 31 



which is the mathematical expression of Newton's second law. 

 Here the force P must be measured in absolute units. 



23. LAW III. To every action there corresponds an equal and 

 opposite reaction. 



It is a matter of common observation that a body A cannot 

 exert force on a second body B without B at the same time exert- 

 ing force on A. Thus an athlete trying to throw the hammer has 

 to be oh his guard that the hammer does not throw him ; the force 

 he exerts on the hammer is accompanied by the hammer exerting 

 force on him, and he must steady himself against the effects of 

 this force. So also when a gun fires a shot by exerting force on it, 

 the shot exerts force on the gun, which is shown in the recoil of 

 the gun. Thus all forces Qj2llLJiL-Daiis, which may conveniently 

 be spoken of as action and reaction. The third law of motion tells 

 us thai; the two forces which constitute such a pair are equal in 

 magnitude and opposite in direction. 



The meaning of the third law will be seen on examining the reaction 

 corresponding to the forces which we have already used for illustrative 

 purposes. The first illustration employed was that of a collision between 

 two railway trucks. Truck A runs into truck B, exerting force on it and 

 setting it in motion. The third law tells us that at the instant of collision 

 B must exert force on A , this force being equal in amount to that exerted 

 by A on B, and opposite in direction. The force of reaction will result in 

 a change of velocity of A , lasting during the instant of collision only, and 

 this may either merely check the motion of A , so that after the collision 

 A proceeds with diminished velocity, or it may reverse the motion of A, 

 so that truck A is seen to rebound from B and return in the direction in 

 which it came. 



After B has been set in motion we have imagined it to be acted on by 

 three forces : 



(a) the resistance of the air ; 



(6) the friction of the rails ; 



(c) the pressure of the rails on the flanges, turning the truck round a 

 curve. 



The reaction corresponding to the first force is a force exerted by the 

 truck on the air in front of it and near it, tending to set the air in motion 

 in the direction in which the car is moving ; it is, in fact, this force which 

 clears the air away from the space occupied at any instant by the truck. 



