ON SUSPENSION BRIDGES. 377 



Prob. 8. To determine the curve of equilibrium^ 

 and the strength of the chain in every part, 

 when the chain only is considered. 



In this case s zz w, in equation (1) Art. 10. 



Hence, dz= ^ . ^( ^^^^^ (2). 



Integrating {s = o, when z zz o), 



.= -llog.i±:^)----(3). 



an equation of a uniform catenary between a 

 curve s, and ordinate bz. 



If in equations (2) and (3^ article 4, we 

 substitute for dz, its value derived from equation 

 (i) art. 10, and change w into s we have 



, a sds 



6 a*+s» ' 



a* ds 



Integrating these equations, we have 



a2 + «2 



X 





and iy = a circular arc, whose radius is a, 

 and tangent s. Or reducmg the quantities to 

 radius 1, we have 



y = y- arc (tan. =^)- - - - - - (5). 



3 B 



