I'h'OI'.ICIIlOX Orih' I'.tR.lt.l! I. (<)XI>C(T(^RS .U5 



Whfn thf coiuluotors an- \ery thin IuIh's, i.e.. iliin as compared to 

 the radius, ((j— u) ii is lU'Cfssarily small and. in ni-nt-ral. .v— v is 

 small. Of course, wlii-n iht- frc<|ut'ncy is liiuli (.'nouKJi. .v— v becomes 

 large in any case. When this is true with respect to thin tubes, how- 

 ever, .V and V will usnaliy be lar^e enoui;li to ni.ike the asymptotic for- 

 mulae applicai)le: but, if x—y is small, tiie approximations 



y»(n=A(j)-(j-nA'({) + --^f-'-^/'a), 



reduce the correction factor lo 





, .a — a 



where p= , 



a 



(1+^/2)' ^ cj 

 ^ X+ff+ff-- do' 



X* 



.■=i+(„+.)>.+ '"+'y"+^v . 



and the resistance with concentric return to 



" 2xXa(a-a) H-/3/2 " ^ ^ 



I 2)rXn(a — a) is. of course, the direct current resistance of a \ery thin 

 conductor. 



If (a — a) a is very small and negligible compared w'ith 2n 'x-, where 

 n is the number of terms in which the series of (\') converge to a 

 re(|uired order of apprf>xiniati(»n. 



j (i-— ")j y*-^+2*=.iog(i-*=.)i 



2 \ / I a - a I k*s'' ) 



