40 



FORCE AND MOTION. 



88. Composition of More than Two 

 Forces. If more than two forces act upon the point of 

 application, the resultant of any two may be combined 

 with a third, their resultant with a fourth, and so on. 

 The last diagonal will represent the resultant of all the 

 given forces. Suppose that four 

 forces act upon the point A, as 

 represented in the diagram. By 

 compounding the two forces AB 

 and AC, we get the partial re- 

 sultant, Ar; by compounding 

 this with AD, we get the second 

 partial resultant, Ar'; by com- 

 pounding this with AE, we get 

 the resultant, AR . 



FIG. 12. 



89. Polygon of Forces. This resultant may be 

 more easily obtained by the polygon of forces. If a num- 

 ber of forces be in equilibrium, 

 they may be graphically repre- 

 sented by the sides of a closed 

 polygon taken in order. If the 

 forces are not in equilibrium, the 

 lines representing them in magni- 

 tude and direction will form a 

 figure which does not close. The line that completes the 

 figure and closes the polygon will, when taken in the same 

 order, indicated by the arrow-head at x, represent the 

 equilibrant ; when taken in the opposite order, indicated 

 by the arrow-head at z, it will represent the resultant. 

 This will be evident from a comparison of the diagram with 

 the one preceding, the forces compounded being the same. 



FIG. 13. 



