with reference to Bridges, 233 



whence, by approximations, it will be found, that 

 xr= 0.81 very nearly 

 a and x being now given, z will be found from Equation A, 



and y from Equation B. 

 The four quantities and b will therefore stand 



X =: 0.81 Log 9.9084850 



a=: 1 



y = 1.1995 Log 0.0790003 



z = 1.5087 Log 0.1786029 



6=1.81 Log 0.2576786 



Angle of suspension 56°.28', as deduced through the 

 incremental triangle from a z and h. 



By applying these deductions to a span of 560 feet, equal to 

 that of the proposed bridge across the Menai Strait, 



a =z 233.4 Feet ^ Where all the quantities must be con- 

 «=r 189.1 Feet I sidered as feet of the suspending chains, 

 y = 280 Feet / augmented proportionally in weight by 

 z = 352.2 Feet the horizontal bridge, and by the media 

 b = 422.5 Feet J of suspension 



It is obvious, from these values of x and y, that the curva- 

 ture is never likely in any practical instance to meet the theo- 

 retical maximum. 



When X is small in comparison of z, a much easier method 



may be used than that by approximation, and sufficiently near 



to the truth. 



z-\-x , 



y has been found equal Xjo ay,h L, but when 



Z—'X 



z-\-x 

 X is small in comparison of z, the k L. of will 



2x 

 not differ much from — then 



z 



y =: 2a — but a == -^ — Equ. A N° 3 



*^ z 2x ^ 



Z* '- X* X T?— X' 



.V = 2 X —27- X 7" *•* 3^ = — — '''^^ = 2»- ^ ^ 



a^ — yzrz x"* By completing the square, S^c. 

 Vol. X. R 



