364 ON SUSPENSION BRIDGES. 



The equation (11) then becomes -^-^ = 6*, 



or -J-* J- = 2 ; which is the differential equation 

 of the common catenary, whose tension at 

 the vertex B in lengths of the chain is -^. 



Prob. 2nd. Suppose the road-way with its 

 load (if any) to be so heavy that the weight 

 of the chain and suspension rods may be neg- 

 lected. What is the nature of the curve? 



Here b and e are each equal nothing, and 

 Equation (11) becomes —-r— = cy, /. — dx := ydy, 



ay c 



integrating fx—o when y — oj gives —x = v^ 



C "^ ' 



The curve is therefore a parabola, whose para- 

 meter is — —, the vertex being at B. 



This Problem is a case which might often 

 occur, particularly where the span or width of 

 the river is very small, and the height of the 

 attachments great. A drove of oxen or a loaded 

 waggon passing over the bridge, (Jig, 3,) is an 

 example of it. 



