54 STATICS. [96. 



II. Concurrent Forces. 



96. Let there be given any number n of forces F v F 2 , F B , . . ., 

 F n , whose directions all pass through the same point. By Art. 

 85, we can find the resultant R 1 of F l and F 2 , next the resultant 

 R% of R l and F& then the resultant R% of R 2 and F^ and so on. 

 The resultant R of R n _ 2 and F n is evidently equivalent to the 

 whole system F v F v F s , . . ., F M and is called its resultant. We 

 thus have the proposition that a system consisting of any num- 

 ber of concurrent forces is equivalent to a single resultant. 



97. It may of course happen that this resultant is zero. In 

 this case, the system is said to be in equilibrium. The condition 

 of equilibrium of a system of concurrent forces is therefore R = o. 



98. In practice, the process of finding the resultant indicated 

 in Art. 96 is inconvenient when the number of forces is large. 



Fig. 19. 



If the forces are given graphically, by their vectors, we have 

 only to add these vectors geometrically (see Kinematics, Art. 46), 

 and this can best be done in a separate diagram, called the force 

 polygon, or stress diagram. Thus, in Fig. 19, 12 is drawn equal 

 and parallel to F v 2 3 equal and parallel to F v 3 4 to F 9 , 4 5 to 

 F, 5 6 to F & . The closing line of the force polygon, viz,, i 6 in 



