PARALLEL FORCES. 



73 



Hence, if the height of a suspension bridge be h, its span 2 /, 

 its total weight 2 W, we have for the horizontal tension //, and 

 the tension T at the point of support 



H T W 



125. The form of equilibrium assumed by a homogeneous cord 

 is an ordinary catenary. 



To find its equation, we again consider the equilibrium of a 



portion OP=s (Fig. 29) of the cord, beginning at the lowest 

 point O. 



The weight of this portion is now W=ws, and if a be the 

 angle made by the tangent at P with a horizontal line, we have 

 the conditions of equilibrium 





 ds 



ds 



Dividing and putting H/w=c, we have the differential equation 



of the curve in the form 



dx _c 

 *dy s 



Substituting this value of dx]dy in the relation 



we obtain 



( ' ds^ , c 2 j sds 



]=i+ or dy = 



^dy) s 2 





