ON SUSPENSION BRIDGES. 378 







And since, (1) Art. 4, adxzzw(fy, 



cfa = 1 ^ (2) 



If we substitute in the equation dz = ^ -^ 



o b 



above, the value of dy obtained from eqnation 

 (1) we have 



dw ac dw 



dz= . — — 





Of these differentials that in equation (2) may 

 be immediately integrated if we put »*for a* + w^ 

 and substitute accordingly. — To integrate equa- 

 tion (1) and the latter part of equation (S) make 

 >/(a'^-fio*)=a-hW'v, and by ordering as in the 

 second differential of the preceding Problem 

 we obtain , 



^^ - 26(1+ v^)dv 



^ + V(a* H-tr*) (6+C+ (b-^c) ti^ (I -r«)' 



a rational function which may therefore be in- 

 tegrated by the rules for such quantities; and, 

 that done, the integrals of equations (\) and 

 (3) are easily obtained. 



