Whence it appears that in the uniform catenary 

 the values of x and y do not depend on the 



length of the curve alone, but on the ratio -^ = wi, 

 the tangent of the inclination of the curve at 

 that point to the horizon. And where the 

 inclination of the curve is the same, the ratio 

 of a; to y is a constant quantity, whatever the 

 values z and a, and consequently the form of 

 the common catenary may be. And at the point 

 where a =i z^ m being then = 1 , the angle is 



1 ..« , , -a; 4142 



always 45°, and the ratio — = qq,^ • 



We will now proceed to the application of the 

 general formulae above in suspension bridges. 



6. In the chain bridge the strain proceeds 

 from three distinct causes, — the weight of the 

 catenarian chain, — the weight of the road- way, — 

 and that of the suspension rods which connect by 

 vertical lines the two former together ; the last of 

 these weights being very small comparatively with 

 the others, may probably without much error 

 be neglected, we shall however introduce it. 



To find the value of w in the preceding 

 formulae call: — 



2 z 



