THE SAG IN A TELEGRAPH WIRE 271 



Hence s = 4a | cosh 2 dO 



J 



+ cosh20)d0 

 - 2a[0 + ^ sinh 201 



, r . . x xVx 2 + 4a 2 ~ 

 2a sinh- 1 r + - 5 - 

 2a 4a 2 



L 



'[lg.- 



2a 



+ 



4a 2 



!]< 



-lo 



2a|~log e . 



2a 



2a 



4a 2 



where 



["log, {a -f Va 2 + 1 } + a Va 2 

 Z 



a = 



2a 



Now 



Hence s = 2alog e l + a + + al + 



and since d is very small compared with I, a is very small com- 



pared with 1, and (1 + a 2 )? = 1 + -a 2 approximately. 



2 



a 8 



2a 2a + ^a 3 neglecting the higher powers of a 



} 



12a 2 

 - 2 ' + f 



Then 

 and 



3 Z 



-6Z 2 



