378 ON SUSPENSION BRIDGES. 



Mr. Davies Gilbert has given, in his excellent 

 memoir on suspension bridges, (Philosophical 

 Transactions, 1826,) a solution of this Problem, 

 with tables deduced from it ; assuming that the 

 road-way and suspending rods might both be 

 considered as collected in the chain. But it 

 appears to me that, in many cases, the road- 

 way being much shorter than the curve, a near 

 approximation to the form of the curve could 

 only be obtained by considering the road-way 

 as a separate part. The solution of the follow- 

 ing problem will therefore include this latter 

 case. , 



Prob. 9. To find the curve of equilibrium, 

 and the law of variation in the thickness of the 

 chain in a suspension bridge, when the weight 

 of the chain and road-way are considered. 



If in the formula of the variable catenary 

 (Equation 3, Art. 4,) where adz — dy s/(a ^ w)^ 



we substitute for dz^ its value — 



derived from equation (1) above, we obtain, 



'^ds = dy(a'^^w'') (6). 



Now, from the supposition of this problem, 

 It) =1 5 + cy, .*. dw = cf5 4- cdy. Eliminating ds, 

 between equation (6) and this, gives. 



