32 FOKCE AND THE LAWS OF MOTION 



The reaction corresponding to the second force is a force tending to 

 drag the rails along with the truck. The rails are, of course, fastened 

 down, so that this force cannot actually produce motion. 



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

 flanges of the truck wheels on the outer rail of the curve. The rails press on 

 the flanges in a direction towards the center of the curve, so that the flanges 

 press the rails outwards and away from the center of the curve. If the rails 

 are not securely fixed, this pressure will cause them to move in the direction 

 just mentioned ; the rails will " spread" and the truck will run off the track. 



In the illustration of the bullet we again had three forces operating on 

 the bullet : 



(a) the pressure of the powder before the shot leaves the barrel ; 



(6) the resistance of the air during the flight of the bullet ; 



(c) the weight of the bullet, dragging it downwards to the earth. 



The reaction corresponding to the first force is the pressure of the shot 

 driving the powder back. This in turn is transmitted to the gun, producing 

 the " recoil " of the gun. 



The reaction corresponding to the second force, just as with the truck, 

 sets the air in motion, carving out a path for the bullet and producing 

 the wind which accompanies its flight. 



The reaction corresponding to the third force, the weight of the bullet, 

 is more interesting, because we can obtain no direct evidence as to its 

 existence. We merely infer from the principle of the uniformity of nature 

 that as, in every case which has ever been tested, an action is accompanied 

 by an equal and opposite reaction, therefore in this case, which is similar 

 except in that it cannot be tested, we may suppose the action to be accom- 

 panied by its equal and opposite reaction. 



The force which we can observe is the weight of the bullet, dragging 

 it earthwards. This, we believe, represents a force exerted by the earth 

 itself on the bullet, the force of gravitation. This force must be accom- 

 panied by its reaction, so that the bullet must act on the earth with 

 a force equal to the weight of the bullet, this force dragging the earth 

 upwards to meet the bullet. The force exerted by the bullet on the 

 earth is, by the third law, just as great as that exerted by the earth on the 

 bullet. The upward acceleration produced in the earth by the bullet is, 

 however, very much less than the downward acceleration produced in the 

 bullet by the earth ; for the force is jointly proportional to the mass and 

 acceleration of the body acted on, and as the mass of the earth is very 

 great compared with that of the bullet, its acceleration will be very small 

 in comparison with that of the bullet. 



Although for these reasons the acceleration produced in the earth by 

 a bullet flying above it cannot be observed directly, yet in a very similar 

 case the acceleration can be observed directly. 



