550 BELL SYSTEM TECHNICAL JOURNAL 



while for small values 



1 u u ^^^^ 



X,(«)=- + ^log|. 



The function Ii(u) becomes infinite and Ki(u) vanishes when u is 

 infinite. ^'^ When u is zero, Ii(u) vanishes and K\{u) becomes infinite. 

 The longitudinal electromotive intensity is calculated from the 

 third equation (12) with the aid of the following rules for differentiation 

 of modified Bessel functions of any order n: 



"3 v-"- J-n) ^ -'n— 1) 



d ^^^^ 



Thus, 

 where 



£, = vLAhiap) - BKoiapn (60) 



a 



(61) 



For reasons which will appear later, this quantity t] will be called the 

 intrinsic impedance of solid metal. 



The current density is merely the product of the intensity E^ and 

 the conductivity g. 



In a general way the behavior of the functions of zero order is 

 similar to that of the functions whose order is unity. Thus, for large 

 values of the argument, , 



Uiu) = -^ ( 1 + ^ 

 V27rM \ 8m 



(62) 



and for small values 



h{ii) = 1 - -4 ' 



(63) 

 Kq{u) = - log M + 0.116. 



" This statement is correct only as long as the real part of u is positive. This is 

 so in our case because out of two possible values of the square root representing a 

 we can always choose the one with the positive real part. 



