r>0 A coin 



int D possesses tins remarkable property : lliat 

 vcr Pand Q are turned about their points of application 

 A and /?, their dir mainiiiL, r parallel, /> detennii; 



above reniaii ii point is in consequence, called 



Centre of the parallel forces /'and Q. 



It F=Q in the * A' = 



mid .r = oo, a result perfectly nugatory. I Wt us that the 

 incth>d fails by which we have attempted to compound two 

 equal and opposite parallel forces. In fact the addition of the 

 rces S still gives, in this case, two equal forces parallel 

 and opposite in their directions. 



Such a system of forces is called a Ct 



We shall investigate the laws of the composition and 

 resolution of couples, since to these we, shall reduce the com- 



n and resolution of forces of every description a 

 on a rigid body. 



40. From Art. 39 we might conjecture that two . 

 forces acting in parallel and opposite directions do not ad 

 a single resultant, which may be shewn as folio 



Suppose, if possible, that the single force 7? will maintain 

 equilibrium with two forces, each denoted by /'. "ing in 

 parallel and opposite directions. 



Draw a straight line mcrtin.ir at A and Jl the directions of 

 the forces P, and that of// Ifakc M> //A', and apply 



at D two forces T and S each=7' and parallel to // but 

 in opposi; ns; this will not disturb the equilibrium. 



>'. '/'are in equilibrium. l>ut 

 since J', r and Ji form a system in equilibrium, so by sym- 



