224 MOTION OF SYSTEMS OF PARTICLES 



regarded as a vector, is constant. This is known as the principle 

 of the conservation of momentum. Stated in words it is as follows : 



When any system of particles moves without being acted on by 

 external forces, the total momentum of the system remains constant 

 in magnitude and direction. 



MOTION OF CENTER OF GRAVITY OF SYSTEM 



180. Let us now return to the consideration of the general 

 equations (71), 



' - (75) 



Let x, y, z denote the coordinates of the center of gravity of the 

 particles of the system at any instant, and let the components of 

 the velocity of this point be denoted by u, v } w. Then we have 



* = f,etc. . ' (76) 



The value of x is, by equation (8), 



so that if M is the total mass, > of all the particles, we have 



