Unstiffened Roadway in a Suspension Bridge. 451 



nates to the vertex, 



N b c~ 



and -^r = 



ftfi-iV 



C C 



By precisely similar reasoning it may be shown that, if Y is 

 measured from the other end of the roadway and towards the 

 left, the equation to the curve corresponding to the part on which 

 the train is not situated is also a parabola, the equation being 



_k'C 



(»-?»' 



lx '"7 V i (% y—>7) \ 



and the vertex is at the highest point of the curve, and its coor- 

 dioates given by 



N' _ b d E _ V b d) 



T~~3C" andjj-— - g . 



1 c' L ~7 



These two parabolas have a common point corresponding to 

 the place where the end of the train is, and they touch each 

 other at that point. For at this point Y=t in the first, and 

 =26 — t in the second parabola, and 



X 

 H 



-(f- 1 )'- 1 -^*-^- V( x - i) 2 )> by (21) 



=(i- i y- i -^-^-c 3 - i )( i -i)' 2 } 



tj- in the second parabola, when Y=26 — /. 



2H2 



