MOTION OF CENTER OF GRAVITY 225 



Equation (75) now becomes 



***.*** dt 9 



and similarly we have the equations 



m 



:. (79) 



^Y=M% (78) 



Remembering that 



du dv dw 

 dt dt dt 



are the components of acceleration of the center of gravity, we see 

 that the motion of the center of gravity is the same as it would 

 be if it were replaced by a particle of mass M, acted upon by a 

 force of components 2/X, 2/F, ^Z. This force again is simply 

 the force which would be the resultant of all the external forces, 

 if they were all applied to the imaginary particle which we are 

 supposing to move with the center of gravity. 



181. In the particular case in which there are no external forces, 

 the center of gravity moves as if it were a particle acted on by no 

 forces, so that its motion will be a motion of uniform velocity in a 

 straight line. 



182. The motion of the center of gravity in this particular case, 

 and in the more general case in which external forces act, may 

 accordingly be supposed to be governed by the two following laws : 



LAW I. The center of gravity of every system of particles con- 

 tinues in a state of rest, or of uniform motion in a straight line, 

 except in so far as the action of external forces on the system com- 

 pels 'it to change that state. 



LAW II. When external forces act on the system, the motion of 

 the center of gravity is the same as it would le if all the masses of 

 the particles were concentrated in a single particle which moved 

 with the center of gravity, and all the external forces were applied 

 to this particle. 



