362 ON SUSPENSION BRIDGES. 



The weight of a unity of lengtfi in the curve = b 



The weight of a unity of length in the. 

 road-way, which is supposed to be divided 

 transversely into separate parts, and may 

 include any weight uniformly distributed 

 over it, with that of the suspension rods 

 below the horizontal line G B H. (Jlf^* 2 J. 



= c 



The weight of a unity of vertical surface J 

 in the suspending rods, (the rods being f 

 here supposed to be uniformly distributed, \ z=l e 

 and indefinitely near to one another, and i 

 therefore reckoned as a uniform surface.) J 



6. In the small triangle formed by x' y' z\ (fig\ 

 2,) the weight therefore of the part z' of the 

 chain = b z' , and the contemporary increment 

 of the road-way being y' ^ its weight '=■ c y\ 

 and the increment of the suspending rods above 

 G H, being = the area (Cg)xy^=:xy\ its 

 weight = exy' . 



Hence increment of w? or lo' = 6 z' + c/ + e x /. 



Ultimately dw—hdz + c dy + ex dy. 



Integrating w zz bz +cy+ e/xdy. Which 



