WAVE PROPAGATION OVER CONTINUOUSLY LOADED WIRES 199 



(y) 



where 



^'' ^ .V: L^' .vi /o'(.ri) 



(Note that Zoo' = Zoo" - Zoi"), 



t^y = - 3'y[/o(xy)i^o'(>'y) - /o'Cv/)A'o(xy)], 



V, = - ylMyi)K,{xj) - Mxj)Ko(yn, 



U/ = - ylJo'{xj)Ko'(yi) - Jo'{y^)Ko'(xjn 



V/ = - ylMyi)Ko'(xj) - Jo'(.r,)i^o(v/)]. 



(10) 



Jo and Ko are Bessel functions of zero order of the first and second 

 kind, respectively, and Jo' and Ko' are their derivatives with respect 

 to the arguments, which are given by 



X: = ad-^A:Tri(j)iXjKj, 



(11) 



3'; = hji->^AiriwiXj\j, 



where w = It times the frequency, i — V— 1, a; and bj are the outer 

 and inner radii respectively of conductor j, and ixj and Xy are its 

 permeability and conductivity. Quantities wath the subscript 1 refer 

 to the wire and those with the subscript 2 refer to the sheath. All 

 quantities are expressed in the electromagnetic c.g.s. system of units. 



Writing Maxwell's Law, curl E = — -7- , around the contours indi- 

 cated by the dotted rectangles in Fig. 1 gives 



where I'l, V2 are the potential differences between the surfaces of 



