200 



ACTION AND REACTION. 



Before impact. 

 Mass of A 8 

 Velocity of A 17 



Quantity of motion of A 8 X 17* or 136 



Mass of B 6 



Velocity of B 10 



Quantity of motion of B 6 X 10 or 60 



After impact. 

 Mass of A 8 



Common velocity 14 



Quantity of motion of A 



Mass of B 6 



Common velocity 14 

 Quantity of motion of B 



8 X 14 or 112 



6 X 14 or 84 



By this calculation it appears that in the impact A has lost a quantity of mo- 

 tion expressed by 24, and that B has received exactly that amount. The'efTect, 

 therefore, of the impact is a transfer of motion from A to B ; but no new mo- 

 tion is produced in the direction A C which did not exist before. This is ob- 

 viously consistent with the property of inertia, and, indeed, an inevitable re- 

 sult of it. 



This phenomenon is an example of a law deduced from the property of iner- 

 tia, and generally expressed thus : " Action and reaction are equal, and in con- 

 trary directions." The student must, however, be cautious not to receive these 

 terms in their ordinary acceptation. After the full explanation of inertia, in the 

 lecture on matter and its physical properties, it is, perhaps, scarcely necessary 

 here to repeat that, in the phenomena manifested by the motion of two bodies, 

 there can be neither " action" nor " reaction," properly so called. The bodies 

 are absolutely incapable either of action or resistance. The sense in which 

 these words must be received, as used in the law, is merely an expression of 

 the transfer of a certain quantity of motion from one body to another, which is 

 called an action in the body which loses the motion, and a reaction in the body 

 which receives it. The accession of motion to the latter is said to proceed 

 from the action of the former ; and the loss of the same motion in the former is 

 ascribed to the reaction of the latter. The whole phraseology is, however, most 

 objectionable and unphilosophical, and is calculated to create wrong notions. 



The bodies impinging were, in the last case, supposed to move in the same 

 direction. We shall now consider the case in which they move in opposite 

 directions. 



First, let the masses A and B be supposed to be equal, and moving in oppo- 

 site directions with the same velocity. Let C, fig. 1, be the point at which 



Fig. 1. 

 c 



m 



they meet. The equal motions *in opposite directions will, in this case, destroy 

 each other, and both masses will be reduced to a state of rest. Thus the mass 

 A loses all its motion in the direction A C, which it may be supposed to trans- 

 fer to B at the moment of impact. But B, having previously had an equal 

 quantity of motion in the direction B C, will now have two equal motions im- 

 pressed upon it, in directions immediately opposite ; and, these motions neu- 

 tralizing each other, the mass becomes quiescent. In this case, therefore, as 

 in all the former examples, each body transfers to the other all the motion which 

 it loses, consistently with the principle of " action and reaction." 



The masses A and B being still supposed equal, let them move toward C 

 with different velocities. Let A move with the velocity 10, and B with the 

 velocity 6. Of the 10 parts of motion with which A is endued, 6 being trans- 

 ferred to B, will destroy the equal velocity 6, which B has in the direction B 

 C. The bodies will then move together in the direction C B, the four remain- 



The sign X when placed between two numbers means that they are to be multiplied together. 



