376 ON SUSPENSION BRIDGES. 



An equation of the common parabola, whose 

 vertex is at B (jig- 2,J and parameter 



_ a— a' . ^* 



— 2 ^ — « From which it appears that by a 



near approximation, in the case of Prob. 5, 

 where the weight of the chain and road-way 

 are considered, the curve is a parabola ; as in 

 Prob. 2nd, but with a different parameter. 



9. In the preceding problems the thickness of 

 the catenarian chain, forming the main support 

 of the bridge, was uniform — in those which 

 follow the nature of the curve of equiUbrium is 

 sought when the strength of the chain is as the 

 strain upon it. 



10. Referring then to the general properties 

 of the catenary in Art. 4, and making s to re- 

 present the weight of any length z of the 

 variable chain alone, (w representing that of the 

 chain and any other bodies attached to it ;) and 

 supposing moreover the weight of any very 

 small length dz at the bottom B to be hdz 

 (Art. 6:) we shall have, when the strength of 

 the chain is as the strain upon it, by equation 

 (5) Art. 4, 



a : v/ (a« + MJ* ) : : hdz : rf*. 



a 



ds 



'''''= T ' N/(a'' + u;2) ^'-^ 



