﻿108 Mr. A. E. Young on the Form of a Suspended 



whence 



•\2r=Asinhas + B cosh as + -,- , where a 2 = ^, 



J-o & l 



= A sinh as -f r -rr , since B = with 5 = for a|t = 0. 

 J-o 



And since 



x 



^fcos^=T(i--^+..:)^ ? 



we have the sag correction 



i 



= | nry + :: V~ sinh as -f A 2 sinh 2 as] ds, 

 J L J-o i J 



( 7 1 oil . -, at \ 

 ZC0S}1 2 _ Smh l>) /rinhaZ ZA 



2a a 2 7 + I 4a 4/ # 



In the case of constrained ends we have yjr = when 



3= - ; hence 



a/ 

 2T smh 



ond s:j<>- correction 



J^ril 3Z 2 / Z 3 n 



-T 2 24 Q , u al + a 2 . 2 a/ ' 



8a tan h -^ 16 smh -^- _J 



the same as already found by the Cartesian method. 

 If in equation (i9) we put as a first approximation 



E1^=0 



we find tan yfr = tt 



% 



ws 



or -vjr = tan ~ ] rTr = tan - ; 



G 1 



hence 



o 7 -^ _ co> 2 \^ (i 2 ^ _ 2 sm ijr cos 3 -^ 



a 7 * c ' aV c 2 



T sin ^ cos 3 yfr T . 



— 2EI — - T = — ws cos -v/r + 1 sin yfr. 



