CHAPTER V. 



GENERAL PRINCIPLES OF THE MOTION OF 

 A SYSTEM OF BODIES. 



§ 18. General equation of the motion of a system, P. 50. 



317. Theorem. If we have any number 

 of bodies, w, m\ w^ . . . , the places of which 

 are denoted by the coordinates x^ y^ z^ a\ y\ z\ 

 : . . 5 and which are subject to the forces P, Q, 

 R, P', Q', P', . . . , respectively, we shall have, 



supposing d^ constant, O-xlmlxi^-^ — P) + 



^^^ini — Q)+^^^{'^ — ^)\ > ^^^ characte- 

 ristic 2 implying the sum of all the quantities 

 of the same form, belonging to each of the 

 bodies respectively. 



The laws of the motion of a point have been compared 

 with those of its equilibrium, by [conceiving' the motion 

 created or destroyed in each instant to form an equilibrium 

 with the force or forces producing the change, or, in other 

 words, by] decomposing its momentary motion into two 

 parts, one of which it retains in the next instant, while the 

 other is destroyed by the effect of the forces to which it is 

 subjected. The same method may be employed in order 

 to determine the motion of a system of bodies, m, m\ m'^, 



