on the Form of a Susj)e)ided Wire or Tape. 169 



develop a t'ormuLa from which the correction can be calcu- 

 lated more readily than from (9), but before doing so some 

 other results will be obtained. 



It is no longer the case, as with the common catenary, that 

 T cos i/r = it7c and Tsini/r = it'5, for we have now to take 

 account of shear and bending moment as well as of tension. 

 All these quantities may be calculated with the aid of the 

 equations already obtained. 



Thus from (4) and (6) we get : — 



J Eldyjr Elcos^i/rr^ 2EI cos^^ -^ ,., . , ^,1 

 as c L ^(^c^ -I 



_EIcOs2'»/r 



c 



approximately. 



jj dL 2EI . , , d^Ir 



V = — . = sm -ur cos -v/r— ^ 



da c ^ ^ ds 



2EIsin-v/rcos'i/r r 2Er cos^ -i/r ,^ ,, ^1 



= ^ L^ ^0^^^^''-^-'^^! 



2E I sin -v/r cos^ -lir . , in • x- \ 



= 1 — -^(to the same order or approximation). 



, 1 d\] 

 i _ ^ w ds 



10 d-yjr 



ds 



X 



r c , 2EIcosiir o • 2 » \1 



TT-r + 3—^ (cos- Air — 2 sm2 ^^) 



LcOS- l/r ICC-^ ^ ^ ^ J 



= c sec sir H n- sin^ yjr cos^ ylr. 



To this order of approximation we have : — 



/TV o o 4EI . ^ 9 4EI 



I - I — s- = c" sec- i/r H ^sin^ ^lr cos -v/r — c- tan^ yjr sin^ yjr cos ylr 



= c^(sec^ ^/r — tan^ a/t) 



Hence to this order c is unaltered by the rigidity. 



For some purposes it is convenient to introduce the auxiliary 

 0, such that 



T 



— =6'cosh0; s = csinh^. 

 w 



