380 ON SUSPENSION BRIDGES. 



But w [—s-\-cy) and 07 vanish together, .*. Const. 



To obtain z. If in adz = dy s/(d^-^w^), 

 (equation 3, Art. 4^ , we substitute for dy its 

 value derived from equation (l) above, we obtain, 



dz — — • 2 12 - - - - (10). 



where a'^n -t- 1? = a^l +-f.) +w^* = «'+ -x + ^'- 



Dividing the numerator of equation (10) by 

 its denominator transposed gives, 



^J {(]^ ^vp-]dw _ dw a^ dw 



2 



a 



u C 



If a\ + w^ be put for a* + mj^ + ^, as in equa- 

 tion (10), we have, 



J a ^ dw d^c dw ^ .^ . 



The first of these differentials is of the same 

 form as the first in Prob. 8, and presents no 

 difficulty. The second may be made rational, 

 and therefore integrable, by putting N/(a*H-M;') 

 = a-\-wv, and finding the value in terms of v, 



