510 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 



The constants are also determined to be 



cosh ^h 

 B = r (IV-11) 



cosh r^ + - - sinh ^s 



A = B 



C = --Ib (IV-12) 



Just as before, it is obvious from equation (IV-6) that k must be nearly- 

 equal to o)^hq€ if the fields are to penetrate deeply into the laminations. Let 

 us guess on physical grounds that this can be accomplished by setting 

 €i = c. Under these conditions from equation (IV-9) and (IV-6) 



tO)€ 



^ = /|/~r (IV-13) 



and 



iCO€ / h 



t'.-A/fV-,)M 



0' 



Thus, if (^s) is not to be very large and ( - ) is not greater than 100, ^h will 



be a very small number. We can therefore set tanh ^h = ^h and rewrite 

 equation (IV-10) as 



its) tanh (fs) + ^ ^"^ = (IV-14) 



1 + 0,. 



From equation (IV-3), rjh = (1 -{- i)- . We shall imagine that h is many 







times greater than the skin depth in the outer shield and may therefore 

 reduce equation (IV-14) to 



1 — i /5\ /(t\ 2 , -y 



<»tanh.+ — gy(»^ + - = (IV-15) 



where (^s) has been set equal to $. Now, if s is also many times the skin 

 depth in the outer conductor, the second term in equation (IV-15) may be 



