502 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 



£2/ 1^21 7^22/ \jEo 



where the T's are given below 



(III-ll) 



Til = cosh riW cosh ^t + ~l sinh 7]W sinh ^t (III-12) 



Tn = - sinh vW cosh ^/ + ^ cosh riW sinh ^t (III-13) 



T21 = 4- cosh riW sinh ^^ + - sinh ryP^ cosh ^t (III-14) 



7^22 = A -sinh riW sinh ^t + cosh r/TF cosh ^t (III-15) 



It is easy to verify from the above that 



2^11^22 - TuT2i = 1 (III-16) 



If we now designate the lower surface of each conducting lamination suc- 

 cessively as points 0, 1, 2, 3,- • •, we can write down the following simul- 

 taneous difiference equations 



Hn+i = TnHn + TuEn (III-17) 



En+l =^ TnHn + r22£n (III-18) 



The solutions of these difference equations are 



Hn = ^r + 5^"" (III-19) 



En = A ^-:-Il' r + 5 ^^^ " ^'' ^~" (III-20) 



i 12 ^12 



where 



, = {':^^) + y/(?k±z.^y _ 1 (III-21) 



Let us now proceed to determine the skin depth to be associated with the 

 stack of laminae in Fig. 5. Since we have assumed the stack to be very 

 deep, A must be taken zero in equations (III- 19) and (III-20), and the 

 fields vary into the stack according to a factor /3~" , so that 



Hn = FoT" (111-22) 



If we now define 



yn^iW + t)n (III-23) 



