STATICS. 



[123. 



instance, the case approximately in a suspension bridge with 

 uniformly loaded roadbed, the proper weight of the chains being 

 neglected. 



123. This result can easily be derived independently of 

 Art. 121, by considering the equilibrium of any portion OP of 

 the chain beginning at the lowest point O (Fig. 28). The forces 

 acting on this portion are the horizontal tension H at O. the 

 tension T along the tangent at P, and the proper weight W si 

 the chain. As this weight is assumed to be uniformly distribu- 

 ted over the horizontal projection OP' =x of OP, the weight 

 is Wwx, and bisects OP 1 . 



Resolving the forces in the horizontal and vertical directions, 

 we find, as conditions of equilibrium, 



ds 



ds 



whence, eliminating ds, 



dy _ w 

 dx~ H 



x. 



Integrating and considering that x=o when j=o, we find the 

 equation of the parabola as above, 



y =^-x* 

 y 2H 



124. The three forces H, T, W are in equilibrium ; they must 

 intersect in a point Q which bisects OP', and the force polygon 

 must be similar to the triangle QPP'. 



