358 ON SUSPENSION BRIDGES. 



x' . Therefore by the principles of statics these 

 forces are as the sides of the incremental triangle 

 formed by their directions. 



Whence dy \dx\\a \ w 



and ^ = ^ 0) 



In every curve d^=^^(dy^-\-diA=dx^f^<i + lY 

 Hence substituting for -j- its value derived 



cue 



from equation (1). 



< 



dz = dx ^^[ ~^ "*" 7' which trans- 

 posed gives dx = ;^J^ (2) 



If in equation (2) vfe substitute for dx its 

 value derived from equation ( 1 ) we have 



wdy ^ w dz 





dx^ 

 dy 



, XV. dx w - . 



Tlie formula (1) gives -^ = —5 and smce 



