ON SUSPENSION BRIDGES. 367 



asymptote. When y is positive, x and y 

 increase together. 



An analogous problem to this with some 

 inquiries of the same nature, is met with among 

 the excellent investigations on the catenary in 

 Whevveirs Mechanics. 



Prob. 4th. Suppose the weights of the road- 

 way and suspension rods are considered, 



Here by only, = o, in the formula (H), 



and -^ = ^y + «yirfy. 



Differentiating making dy constant and divid- 

 ing by €/y gives _i-=:c + «x. 



Multiplying by 2dx we have 



f fl \2 



Integrating o(^-^j = 2« + «.» + C. 



But when x=<,, -^ =o. .-. Const = o. 

 Whence Jy =^(~^)= ^-f • v(.^?n7) 



