PLANE STATICS. 





-X 



. being the angle made by .Fwith the axis Ox. At the origin O 

 two equal and opposite forces X, X are applied along Ox, and 

 two equal and opposite 

 forces F, Y along Oy. 

 Thus, X at P is equivalent 

 to X at O in combination 

 with the couple formed by 

 X at P and -JTat <9 ; the 

 moment of this couple is 

 evidently yX. Similarly, 

 Fat P is replaced by Fat 

 O in combination with a 

 couple whose moment is xY. 



The force Fat P is therefore equivalent to the two forces X, Y 

 .at O in combination with a couple whose moment is xY yX. 



Proceeding in the same way with every given force, we obtain 

 a number of forces X along Ox which can be added algebrai- 

 cally into 2,X f and a number of forces Y along Oy which give 

 .2 Y. These two rectangular forces form the resultant 



whose direction is given by 

 tan = 



where a is the angle between Ox and R. 



In addition to this, we obtain a number of couples xYyX 

 ivhose algebraic sum forms the resulting couple 



143. The whole system is thus found equivalent to a 

 resultant force R in combination with a resultant couple H in 

 the same plane with R. The conditions of equilibrium R = o, 

 H=o (Art. 140) can therefore be expressed analytically by the 

 three equations 



