120.] 



PARALLEL FORCES. 



6 9 



side in common with the nexj one. Thus the complete force 

 polygon of the whole cord is formed, as shown on the right in 

 Fig. 26. Its vertical line represents the successive weights 

 W l =i2, ^ = 23, F 3 = 34, F 4 = 45, ^=56, while the lines 



Fig. 26. 



radiating from the point O, or pole, represent on the same 

 scale the tensions in Al t I II, II III, III IV, IV V, V B. 



119. The polygon AI II III IV VB is called the funicular poly- 

 gon. It will be noticed that if we have given the fixed points 

 A, B, the magnitudes of the weights, their horizontal distances, 

 say from A, and the directions of the first and last sides AI, 

 VB (whatever may be the number of the forces), the remaining 

 sides of the funicular polygon can be found by laying off on a verti- 

 cal line the weights f / F 1 = 12, ^ = 23, etc., in succession, drawing 

 through i a parallel to the first side, through the end of the last 

 weight (6 in Fig. 26) a parallel to the last side, and joining the 

 intersection O of these parallels to the points 2, 3, etc. The 

 sides of the funicular polygon must be parallel to the lines 

 radiating from O ; at the same time these lines represent the 

 tensions in these sides. 



120. For the analytical investigation, let P t be that vertex of a 

 funicular polygon of any number of sides at which the z'th and 



