222 MOTION OF SYSTEMS OF PARTICLES 



Substituting these expressions for the components of accelera- 

 tion into the equations of motion (66), we obtain these equations in 

 the new form 







Z = m 



* < 68) 



178. Suppose we have a system of particles, m l at x lt y^ z^ 

 m 2 at x 2 , y 2 , z 2 ; etc., and let the components of force acting on 

 them be X lt Y lf Z^ X 2 , F 2 , ^ 2 ; etc. 



Then, from the equation just obtained, 



so that, by addition, 





 2==m *~d/' ' 



where denotes summation over all the particles of the system. 

 The left-hand member 2jX is the sum of the components along 

 Ox of all the forces acting on all the particles of the system. As 

 in 50, these forces may be divided into two classes : 



(a) external forces forces applied to the particles from outside 

 the system ; 



(b) internal forces forces of interaction between pairs of par- 

 ticles of the system. 



As in 50, we find that the contribution to 5}-3T from the 

 second class of forces is nil. For all these forces fall into pairs, 

 each pair consisting of an action and reaction, of which the com- 

 ponents are equal and opposite. 



Thus hi calculating ^X we need only take account of exter- 

 nal forces. 



