202 Mr Rohh, Discussion of a difference equation relating to 



This equation may be best solved by tracing the curve 

 36? 



y = l-x 



cosh 2ft) — cosh ft) 

 6 



4 + 



186> 



cosh 3ft) — cosh ft) \ cosh 2ft) — cosh g) 



a? 



and noting where it cuts the axis of x. 



This series changes sigu if we substitute first x = Q and then 

 x=\,BO that there must be a root between and 1 if it be con- 

 vergent. Further, since the terms involving x are all of one sign, 

 there cannot be more than one positive root which must be the 

 quantity we require. 



Having in this way found the value of C, we may find the 



G 

 tension in the rith section by substituting -y^ for x. 



The corresponding ordinate will then bear to unity the same 

 ratio that Tn bears to T. 



It may be readily shown that the curve meets the axis of y, so 

 as to form an angle of 45°, and has an asymptote parallel to that 

 axis and at a distance from it equal to CK. 



