ON SUSPENSION BRIDGES. 



365 



Fio. 3. 



i 



Scholium. The weight of the chain and 

 suspension rods in this instance being considered 

 so small, comparatively with the load, that they 

 might be neglected, it is evident that a small 

 increase of strength, and consequently weight 

 in the higher parts of the chain would not 

 materially alter the form of the curve. Hence 

 if we wished to adapt its strength to the strain 

 upon it, we have from what was said (Art. 2nd.) 

 in the commencement of this essay, only to 

 increase the strength of the different parts of 

 the curve, according to the secant of their 

 angles of inclination to the horizon. To perform 



which — since -n — is the tangent of the curve's 



inclination, taking from the equation of the curve, 



the value of this ratio, or -^, in numbers, we 



may by a table of natural tangents find the 



