ON SUSPENSION BRIDGES. 375 



This is of the same form as the second equation 

 obtained in Problem 4 ; ordering then as in that 

 Problem we have 



a—a^^ , X + 





-r+v(»' + v') , 



Or multiplying by — and dividing by ^ ( \ we obtain 



e 



Which is the equation of the ordinary, or 

 uniform, catenary whose abscissa is Xj ordinate 



,, ^ / . 9 and tension at the vertex in lengtlis 

 of its curve = — • 



c 



The ordinate y is therefore equal to that of the 

 common catenary, above, divided by — ~ — ,~. 



Cor. If 6 = 0, or the weight of the suspending 

 rods is neglected, the preceding equation, 



(a — o! ) dx = cydy -f edylxdy , becomes 



(a^a') dx = cydy. 



Integrating, (x = o, when y = o,) gives 



a -a' 

 2 -— » = y\ 



