CHAPTER V 



MATTER IN RELATION TO MOTION 



Equality of Masses. We have hitherto considered motion 

 and mass separately, but in this chapter their relations to one 

 another will be described. It has been shown that equality of 

 mass can be tested by weighing. The balance thus furnishes us 

 with a convenient practical method of comparing masses, but it 

 does not give a fundamental conception of what mass means. 

 To obtain a clear idea of the subject, consider first of all that 

 we are dealing with two variable quantities, namely, mass, or 

 quantity of matter, and motion. Suppose two bodies moving in 

 opposite directions with equal velocities to collide with one another 

 and stick together. If the two bodies stopped dead after the 

 impact we could conclude that their masses were equal, and that 

 each exactly destroyed the motion of the other ; but if the com- 

 bined bodies moved after the collision, the masses could evidently 

 not have been equal. With this in mind, it will readily be con- 

 ceded that the following definition of equality of mass holds 

 good : 



Two masses are equal, if when they are made to impinge on 

 one another in opposite directions with equal speeds and stick 

 together, they come to rest. 1 



The effect of the impact of two moving bodies thus depends 

 upon the masses of the bodies and the velocities before the 

 collision. If both the velocities and masses are equal, the bodies 

 come to rest ; if the velocities are equal, but the masses are un- 

 equal, the greater mass predominates after collision, and if the 

 masses are equal while the velocities are unequal the greater 

 velocity will predominate. 



1 This definition and one or two others in this chapter are given by Prof. \V. M. 

 llicks in his inspiring \vork on Elementary Dynamics of Particles and Solids. 



