94 BELL SYSTEM TECHNICAL JOURNAL 



to the elementary contour shown in Fig 1 we get 



- IP + £i+i - E'/ = f^ip^j, (10) 



or 



TVj-\- E'j+i - E'j' = nip^ (11 



where ^j is the magnetic flux threading the contour and is given by 



$, = 2 (7i + /2 + ... + /,) log ^\ 



From the law 



div kE = 47r(2, 



Er = ^((2i + <22 + . . . + (2.) 



where Qj is the charge on the f^ conductor and kj is the dielectric 

 constant of the medium, whence, 



^•'■ = l^°g¥'('3i + <22... + <2i)- (12) 



Furthermore, the rate of gain of charge is 



I ((2i + <32 + . . . + <2i) = - 1^ (/i + /2 + . . . + /.•) 



- 47r((2i + (22 + . . . + G) gj/kj, (13 



where the last term represents the leakage current, gj being the 

 specific conductivity of the dielectric. 

 From (13) we have 



^ (47r&+ ipkj) ((2i + (22 + . . . + <2,) = r (/i + /2 + . . . + Ij,) 

 kj 



and substituting this value of (Qi -\- Q2 + ■ ■ ■ -\- Qj) in (12) gives 



F, = 2 (/. + A + . . . + /,) j^^^^ log '-^ (14) 



and from this and (11) 



- [gTtW. ~ '^^0 (^' + ^' + ■••+« = £/+■ - £" (15) 



where 



2 log ''J+i 2 log ^' "' 



aj Uj 



