20 BELL SYSTEM TECHNICAL JOURNAL 



OX 



E, = 7($ - ^) - {F - 7^). 



Introducing new wave functions 



F' = F - 7^, 



$' = $ - ^, ^^^^ 



we have (dropping primes) 



E=-U ^22) 



where now $ and F are independent wave functions. 



If the foregoing analysis has been carefully followed, the important 

 advantage of equations (22) as compared with (8) will be appreciated. 

 The transformation of (8) into (22) is strictly dependent upon and 

 conditioned by the legitimacy of neglecting v"- — 7^ in the dielectric, 

 whereby the wave functions are essentially reduced to two-dimensional 

 potential functions. It is evident that the whole engineering theory 

 of transmission involves this approximation. 



V 



We are now prepared to sketch the general solution of the problem,^ 

 employing equations (13) in the conductors, and equations (22) in the 

 dielectric. The procedure is as follows: 



1. At the surfaces of the conductors the tangential component £, 

 in the x^-plane of E vanishes, as shown above. That is, 



Er= -A$= (23) 



OT 



• For detailed api^lications of this metiiod of solution to specific problems, the 

 published papers referred to in the introduction to this paper may be consulted. 



