366 ON SUSPENSION BRIDGES. 



angle at any point, and thence its secant for 

 the strength. 



The same observation will apply to the two 

 following problems. — 



Prob. 3rd. Suppose h and c Equation (11) 

 are each = o, the suspension rods only being 

 considered. 



We have then -^ = c/icty. Differentiating, 

 making dy constant and dividing by dy 



we have — —- zz e x. 



Multiplying by 2 die gives a ^ ^ — 2exdx. 



(dx \* _ 

 _J - ex^ + C. But 



when a; = o, the curve being perpendicular to 

 the axis of the abscissae, dx is infinitely small 



dx 



comparatively with dy :. -^ = o, and Const. 

 = 0. Hence dy = / -^ 



y = \/^~r ^yp- ^^^- ^ "^ Const. 



Cor. When a; = o, y = — oo , when a; = 1, 

 y r= Const., the curve has therefore a horizontal 



