372 ON SUSPENSION BRIDGES. 



The values of x and y above are obtained 

 in terms of iv (the tangent of the curve's incU- 

 nation at any point to the horizon) which is 

 nothing when x and y are each equal to nothing. 

 Assuming therefore different values for w, and 

 substituting them in the expressions for x and 

 y, we shall have so many points in the curve. 



8. When the strengths of the chain and 

 road-way continue unchanged, b and c being 

 then constant, the ratio of a; to y at any point 

 depends alone on the tangent w of the curve's 

 inclination there. This curious property it 

 appears then is not confined to the common 

 catenary in which (Cor. 2. Art. 4) it was shewn 

 to exist. 



Prob. 6. We might find the values of x 

 and y in terms of the sums of the weights of the 

 chain and road-way, and thence deduce the 

 values of z : — For since by equation (3) article 4, 



adz - dy a/ (a' + iv^\ 

 and in the supposition of this Problem w = bz + cy^ 



dw c 



(Art. 6,) .\dz=: — y % • Substituting 



this for dz in the preceding equation gives 



^dte^ ^dy=dysy{a^^^,^) 



