ON SUSPENSION BRIDGES. 371 



^>'>The co-efficient of dv being a rational fraction, 

 is therefore always integrable, and by known 

 rules. — Omitting then the process as tedious, 

 and afterwards substituting (or / g and v we 

 have, since w s^ o, when y = o, for the correct 

 integral 



;=^[iog.(v(««^-^i)4-^^)^;^^^ 



*^S- c + 6^/(u;»+l) J 



jj If c be less than b, or the weight of a given 

 length of the road-way with its load be less than 

 the weight of the same length of the chain, 

 s/(c* - b*) is imaginary, and the integral found 

 wholly by logarithms will fail ; it must therefore 

 in part be expressed by circular arcs as below : — 



y=yriog.(^(t.^+ !)+!.) 



Cor. If c = o, the chain only will be con- 

 sidered, and the equations become 



x = ^.(v(«,«+l)-l), 



3a2 



