368 ON SUSPENSION BRIDGES. 



When y = 0, X = o .-. C = _ ^^hyp. log. — • 

 .-. y= ^—-hypAos. ^— T7 '-< 



e 



This equation may be put under a different 

 ^d rather more famiUar form thus: multiply 



both sides by — and divide by ^ ~ and 



we obtain 



__ hyp. log.* ^ ^—J, 



e 



an equation of the common catenary, whose 



c y 



abscissa is = Xy ordinate = , ; and tension 



V a e 



at the vertex in lengths of its curve = — . 



Prob. 5th. Suppose the weights of the chain 

 and road-way are considered, the suspension 

 rods only being neglected ; to find the nature of 

 the curve. 



• All the logarithms In this paper are those called hyper- 

 l>olic, whether mentioned so or not. 



