382 ON SUSPENSION BRIDGES. 



Though the formula for z is complex, the 

 values of a?, y and 5, which would be much 

 more frequently needed by persons using them 

 for the purpose of building a bridge, may be 

 obtained without great difficulty ; as in the 

 following example to these last found. 



Suppose in a suspension bridge a = 600 tons, 

 b and c be 2 and 1 ton per yard respectively. 

 To find the values of y, s, x and z, when tv =. 

 300 tons. 



Here 7/i=z-^=:g^ = .5, n—\ + -^-\-\-\ =1.5, 

 y _- ^"^ X arc ("tan. = -^ ") = 244.9 X arc of 22°. 12^ 



But arc of 90 = 1.5708, and 22°.12' = 22.2, 

 /.90:22.2::1.5708:. 38746= arc of 22^.12, whence 

 y = 244.9 X .38746 = 94.89 yards = 284 feet 7 inches, 

 5 = . 5 X 600 - 1 X 94.89 = 205.11 tons, 



^= ^log. (\ 4- Yl)— ^^ X ^«ff' ^ • 16666=150 X 2 .3026 x 

 common log. 1.16666 = 23.124 yards, or 69 feet; since 

 hyp. log. = 2.3026 x common log., and 



