AECHES AND ARCHED KIBS 



163 



is the resultant of P' and P lt OCis the resultant of OB and P 2 , etc., and 

 finally OE, or P'", represents the resultant of P', P lf P 2 , P 3 , P 4 . If 

 then P'" is combined with P", the resultant R is obtained as before. 



Xo\v to find the line of action of R, suppose that P' and P l are 

 combined into a resultant R^ acting in the direction A'B' (Fig. 119 ( C)) 

 parallel to the ray OB of the force polygon (Fig. 119 (B)). Prolong 

 A'B' until it intersects P 2 , and then combine R l and P 2 into a result- 

 ant J? 2 acting in the direction B' C' parallel to the ray OC of the force 

 ^>n. Continue in this manner until P"' is obtained. Theli the 

 resultant of P' and P" f will give both the magnitude and line of 



120 



action of the resultant of the original system P lt P 2 , P 8 , P 4 . The 

 !. .s.-d figure A'B'C'&E'F' obtained in tliis way is called an equilibrium 

 polygon. 



F<>r a system of parallel forces the equilibrium polygon is con- 

 structed in the same manner as above, the only difference being that 

 in this case tin- IMP-.- pol yu'ou becomes a straight line, as shown in 

 120. 



Si net- /'' and P" are entirely arbitrary both in magnitude and 

 direction, the point O, called the pole, may be chosen anywhere in the 

 plane. Therefore, in constructing an equilibrium polygon correspond- 

 ing to any Lfiven system of forces, the force polygon ABODE (Fig. 119) 

 is first dra\vn, then any convenient point O is chosen and joined to 

 the vertices A, B, C, D, E of the force polygon, and finally the equi- 

 librium polygon is construi-ted by drawing its sides parallel to the 

 rays OA, OB, OC, etc., of the force diagram. 



