io8.] 



PARALLEL FORCES. 



6l 



107. The resultant of two parallel forces can also be found by 

 the following simple process. Intersect the two parallel forces 

 P y Q by any transversal in/ and q (Fig. 23) and apply at these 

 points along pq two equal and opposite forces F, F; find the 

 resultant P' of F and P and the resultant P ff of -F and Q ; 

 these resultants P 1 and P" will intersect (unless P and Q be 

 equal and opposite) and their resultant R can be found. 



Fig. 23. 



It will be noticed that this construction reduces to that given 

 in Art. 104 if for /^we select the force 2 O in the force polygon, 

 Fig. 22, p. 59. 



108. Resultant of Any Number of Parallel Forces. The graphi- 

 cal method of Art. 104 is readily extended to the general case of 

 any number of parallel forces lying in the same plane. What- 

 ever the number of the forces, the force polygon gives magni- 

 tude, direction, and sense of the resultant, which is simply the 

 algebraic sum of the given forces ; while the funicular polygon 

 (formed by the lines I, II, III, etc.) gives the position of the 

 resultant by furnishing one of its points, viz. the intersection of 

 the first and last sides of the funicular polygon. 



The process will best be understood from the following 

 example. 



The horizontal beam AB (Fig. 24). resting freely on the fixed sup- 

 ports A, B carries four weights W^ W^ W 3 , W. 



To determine the position of the resultant and the reactions A, B of 



