THE SECOND LAW 29 



to alter the natural state, we next inquire as to what is the law 

 which governs the effect produced by force. Given a force, by 

 how much will this alter the natural state of uniform motion in a 

 straight line ? An answer to this is provided by the second law : 



LAW II. The rate of change of momentum is proportional to the 

 impressed force, and takes place in the direction of the straight line 

 in which the force acts. 



The force, then, produces change in a certain quantity, the 

 momentum of the body on which the force acts, and the force 

 is proportional to the rate of change of this momentum. 



By momentum is meant the product of the velocity of the body 

 by a quantity known as the mass of the body. The mass meas- 

 ures simply the quantity of matter of which a body is composed, 

 and so does not depend on the motion of the body. Thus 



rate of change of momentum = mass X rate of change of velocity 



= mass X acceleration, 



by the definition of acceleration. We therefore see that the force 

 is proportional to the product of two quantities, the mass of the 

 body and its acceleration. 



21. Measurement of mass. If we drop a body from our hand, 

 it will, in general, be acted on by two forces, the resistance of the 

 air and its weight. If we suspend the body in a vacuum, with an 

 arrangement for letting it drop at any instant we please, we get 

 rid of the resistance of the air, and the only force acting on the 

 body will be its weight. Now if any two bodies are suspended 

 side by side in a vacuum, and are let fall at precisely the same 

 instant, it will be found that they remain side by side during the 

 whole time they are falling towards the earth. Thus at any 

 instant their accelerations are the same. 



It follows from the second law of motion that the forces acting 

 are proportional to their masses. These forces, as we have seen, are 

 simply the weights of the bodies, so that, as the experimental 

 result is true whatever the two bodies may be, we have the gen- 

 eral law : The masses of bodies are proportional to their weights. 



