ON SUSPENSION BRIDGES. 381 



as in Prob. 6. — Neglecting the process, we have, 

 when w is restored and the integrals corrected, 



Cor. If c z= o, or there be no horizontal 

 road-way, s zzw, and the formulae for y, a;, 

 and Zy above will become. 



y = -T-arc (tan. =— )> 



= ^log.l+^^I^l±-L), 



deductions in accordance with those in 

 Problem 8. 



We should express the formulae of this 

 Problem somewhat more simply if we assumed 

 the variable quantity w to be some multiple, wi, 

 of the tension at the apex : thus, supposing 

 w = ma, and consequently — = wi, gives, 



y = -T— arc ( tan. = — =: j 9 



»= »«« ~ cy» (by supposition of this prob J 



=i? iog.(.*^<H-.)-(iy,.g.:^=<i^^±^j. 



