96 



STATICS OF KIGLD BODIES 



instead of at B. Then we have the body acted on by two forces 

 P, Q which act on the same particle C. These may be compounded, 

 according to the rules explained in Chapter III, into a single force 



n acting at C. Thus we can 

 compound forces of which 

 the lines of action intersect, 

 even though they do not act 

 on the same particle. 



Having compounded two 

 forces into a single force, we 

 may compound this resultant 

 with any third force which 

 lies in the same plane as the 

 two original forces, and in 

 this way obtain a resultant 

 FIG. so of three forces, and so on. 



Thus any number of forces which all lie in one plane may be 

 compounded into a single force. This force is called the resultant of 

 the original force. 



72. An exception arises when we attempt 

 to compound two parallel forces, for their 

 lines of action do not meet. This difficulty, 

 however, is easily surmounted. Let P, Q 

 be the two forces to be compounded, and 

 let AB be any line cutting their lines of 

 action in A, B. Let us add to the system 



P, Q two forces : , 



A 



(a) a force E acting along BA ; 



(b) a force R acting along AB. 



R 



FIG. 51 



These two forces being equal and opposite 

 can be introduced without producing any 

 effect. On compounding the first with P 

 we obtain a resultant P' acting at A y and on compounding the 

 second with Q we obtain a resultant Q' acting at B. Thus the 



