(414) 



1156 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1952 



s 

 Ey^^^Ho sin P-I^tS^ e-^^\ 



gs s 



for |6 ^ I 2/ I = 2«, and again the upper signs refer to the upper 

 stack and the lower signs to the lower stack. 



In a complete Clogston 2 the expressions for the fields simplify a 

 good deal. For the modes with odd subscripts 2p -{- 1 the fields are, 

 for -^a ^ ij ^ ^a, 



i/,;^^,C0S^-?^-+il^6-— , 



a 



Ey^-ji/l i/o COS (?^±i)iL^ e-^-- (415) 



ye a 



ga a 



while for the modes with even subscripts 2p, 



H, ^ Ho sin ?^^ 6-^^"^ 

 a 



Ey^ - \/\ Fo sin ?^ e-^^-^ (416) 



€ a 



^.;^-?^i/ocos?^.-^^^ 

 ga a 



The fields of the higher modes in a plane Clogston 2 are simply related 

 to the fields of the principal mode shown in Fig. 13(d). The fields of 

 the pth mode may be obtained conceptually by stacking up p "layers", 

 each of thickness a/p, the fields in each layer being identical with the 

 fields of the principal mode except for the scale reduction and a phase 

 difference of 180° between adjacent layers. Equation (407) shows that 

 the attenuation constant of the pth mode in a plane Clogston 2 with 

 infinitesimally thin laminae and high-impedance walls is just p times 

 the attenuation constant of the principal mode. 



It may be observed that if we are considering a partially filled plane 

 Clogston line with 6 > 0, then the propagation constants of the 2pth 



