ACTION AND REACTION. 



197 



ACTION AND REACTION. 



The effects of inertia or inactivity are such as may be manifested by a sin- 

 gle insulated body, without reference to, or connexion with, any other body 

 whatever ; they might all be recognised, if there were but one body existing 

 in the universe. There are, however, other important results of this universal 

 property of matter, to the development of which two bodies at least are neces- 

 sary. If a mass of matter, moving in any direction, encounter another equal 

 mass which is quiescent, the two masses will .move together after the impact ; 

 but it will be observed, that their speed after the impact will be only half that 

 of the former mass. Thus the body which was moving before the impact loses 

 half its velocity, and that which was quiescent receives exactly the same amount 

 of motion ; the one, therefore, receives just so much motion as the other loses, 

 and therefore the actual quantity of motion after the impact is the same as be- 

 fore it. 



Again, let A and B be two masses, B being twice that of A. If, as before, 

 A strikes B with a certain velocity, B being previously quiescent, it will be 

 found that the velocity of the combined masses of A and B after the impact 

 will be just one third of the velocity of A before it. Thus, after the impact A 

 loses two thirds of its velocity, and B consisting of two masses, each equal 

 to A, each of these receives one third of A's motion, so that the whole 

 motion received by B is two thirds of the motion of A before impact. 

 By the impact, therefore, as much motion exactly is received by B as is lost 

 by A. 



A similar result will be obtained, whatever proportion may subsist between 

 the masses A and B. Suppose B to be ten times A, then the whole motion of 

 A must, after the impact, be distributed among the parts of the united masses 

 A and B ; but these united masses are in this case eleven times the mass of A. 

 Now, as they all move with a common motion, it follows that A's former mo- 

 tion must be equally distributed among them, so that each part shall have an 

 eleventh part of it j therefore the velocity after impact will be the eleventh 



