62 



STATICS. 



[108. 



the supports, construct the force polygon by laying off in succession on a 

 vertical line 12 = W l9 23 = W 2 , 34 = W^ 45 = /^; select any point O 

 as pole and join it to the points i, 2, 3, 4, 5. 



Now we may regard i O and 02 as components into which W^ has 

 been resolved; similarly 2 6? and (9 3 as components of W. 2 , 3 O and 

 (9 4 as components of lV Zt and 4 (9 and 6*5 as components of W. 

 This resolution of the weights into components is transferred into the 



Fig. 24. 



main figure by constructing the funicular polygon as follows : through 

 any point A' on the direction of the reaction A draw a parallel to O i 

 and let it meet W l in I ; through I draw I II parallel to 6>2 ; through 



II draw II III parallel to #3; through III draw III IV parallel to 

 6>4 ; and through IV draw IV B 1 parallel to O$ ; the point J3 1 being on 

 the direction of the reaction B. 



If now each weight be regarded as resolved along the sides adjacent 

 to it in the funicular polygon, since the two components falling into 

 I II are equal and opposite, and also those falling into II III and 



III IV, the system of weights is reduced to the two componepts along 





