Dadourian — Progressive Development of Mechanics. 169 



ther let F 12 denote the force on m 1 due to m 2 and F 21 the force 

 on m„ due to m v Then if the two particles are considered as 

 one system the only external actions are their kinetic reactions, 

 therefore the action jji-inciple gives 



m 1 w 1 + m 2 v a = 0, (1) 



h=- m \ (2) 



V 2 n\ v ' 



which states that the mutual acceleration of two particles are 

 oppositely directed and are inversely proportional to their 

 masses. When the particles are regarded as separate systems, 

 then the action principle gives 



F 12 + m 1 v 2 =0 (3) 



and F 21 + W 2 V 2 = 0. (4) 



From the last two equations and equation (1) we obtain 



F ]2 = - F„ , (5) 



which is Newton's third law of motion. 



Sloane Physical Laboratory, 



Yale University, New Haven, Conn. 



