ON SUSPENSION BRIDGES. 



367 



parts were so disposed as to make it assume 

 the same curve. Hence, when the form of the 

 polygon or curve is one of the data, it is easy 

 to find the rest. — But if instead of the curve 

 we have the weights and the tension of some 

 part of the curve given to find the form of the 

 curve the problem is frequently much more 

 difficult. We will now proceed to the general 

 consideration of this latter case. 



4. Let then in the catenarian curve A B C D, 

 Fig. 2. 



suspended from A and D, B I be vertical 

 = ax, I C horizontal = y, B C the curve = z, 

 the weight of z with any other weight attached 

 to it (as that of the road-way EF, &c.) = ir, 

 the tension at B = a. 



Now the chain B C, whether it have any 

 other weight hanging from it or not, is kept 

 at rest by three forces ; by the tension at B in 

 the direction y\ by the tension at C in the 

 direction of r', and \>y gravity in the direction 



