ON SUSPENSION BRIDGES. 363 



needs no correction, since ar, y and z vanish 

 together. 



Substituting this value for «;, in the equation 

 (1) where — - = w we have 



-^ -^^'^^V'\' ^fxdy (11), 



which is the general differential equation of 

 the curve when the weights of the chain, 

 road-way, and suspension roads are consi- 

 dered. The road- way being here supposed to 

 be divided by transverse cuts into indefinitely 

 small separate parts, capable of sliding past one 

 another, each part forming a separate weight: 

 which is admissible since the curve must always 

 adjust itself so as to leave the road- way a 

 straight line. 



7. The equation (11) being comphcated, and 

 therefore not so useful in practice, we will first 

 consider the cases where one or other of the 

 weights are neglected. 



Prob. 1st. To find the form of the curve when 

 c and e are each equal to nothing, or the weights 

 of the road-way and suspension rods are omitted. 

 2 z 2 



