524 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 



with kn given by (V-8) and w = 1, 3, 5, • • • . At oc = 0, 



B+Zc.cos'^=M cos ^i+HN. cos '^ (Vn-20) 



-B - ;, 2^Cm[-^] cos"^ 



or 



Thus, we have for the transmitted power 



and for the incident power 



j/f"' 



The ratio of transmitted power to incident power is therefore 



(VII-21) 



Let us again let ei = e. By adding and subtracting we find 



_ 1 V C„ ^ cos ^ = 2 E iV« cos ^ (VII-22) 



tk m a a n 2d 



2B + i Z C„ ^ cos t?^ = 2M cos ^ (VII-23) 



tk m a a 2d 



From (VII-23) it is clear that 



2B = I- f 2M cos ^ dy (VII-24) 



2<i J— d 2a 



B = -M (VII-25) 





(VlI-27) 



just as in equation (VII- 14). There is thus the same power loss in crossing 

 the boundary in either direction. It is interesting to note, however, that in 

 the second case the non-propagating modes in the unlaminated line are 

 excited. 



