the tension of overhead wires supported by equidistant poles. 20S 



If T be represented by unity we shall have 



G 

 Ti represented by the ordinate at a; = j^, 



T — — - 



the general form of the curve being that shown in the figure. 

 It may be proved that 



4 [ ^J<y 



2 



Vr 



7 iVl - 7 + 1 

 where 



■^<G<\, 



7 = 



^T^ + s^^w^E' 



As a limiting form of the above inequality we have 



or -54134... < (7 <1. 



For the safety of the system of poles it is requisite that the 

 maximum deflecting force should lie within a certain limit. This 

 maximum deflecting force is clearly equal to T^. 



Section II. Investigation of Convergency. 



In order to complete our investigation we must examine into 

 the question of the convergency of the series which we have 

 obtained. In order to do so we write 



26 



cosh ft) — 1 

 _ s^^w'E 

 ~ 3T3 + s^w'^E' 



The equations connecting the successive coefficients then 

 become 



_ cosh &) — 1 7 2 

 ^ cosh 2a) — cosh to 2 ^ ' 



cosh ft) — 1 7 / , ., n \ 



' cosh 3ft) - cosh ft) 2 ^ ^' 



