the tension of overhead vjires .mpported by equidistant poles. 201 



Then ^ (k + -j^j = cosh co, 



and since K must be greater than unity if T^ is to be finite, 

 we have 



Further H f^"" + frm) = ^'^^^ ^^<"' 



so that the value of these expressions may be at once obtained by 

 the use of the tables and considerable calculation thereby avoided. 

 We then have 



^ cosh 2q) — cosh ft) ^ ' 

 n 



cosh S(o — cosh ft) 



Since cosh moi — cosh co is alwa} s positive, these coefficients will 

 all be positive if aj is so. The value of aj is arbitrary, but the 

 presence of the constant C enables us to make it unity without 

 loss of generality. We have therefore 



«i = 1, 



se 



cosh 2ft) — cosh ft) ' 



f, 186' 



4 + 



cosh 3ft) — cosh ft) 1 cosh 2ft) — cosh &)[ ' 



Thus 



iT'^ cosh 2ft) - cosh ft) K^'' 



ft I iM ^j^l 



cosh 3ft) — cosh ft) V cosh 2ft) — cosh ft)/ ^^^'^ 

 Now since To = we get 



cosh 2ft) — cosh ft) 



18^ 



4 + 



cosh 3ft) — cosh ft) \ cosh 2a> — cosh (o 

 an equation which determines C. 



)c^-- = o, 



14—2 



